From 761883a622a103d28c67442fd2e7e2b72aa6ccce Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 25 Oct 2025 19:05:52 +0200
Subject: [PATCH 01/87] add nbstripout pre-commit rule

---
 .pre-commit-config.yaml | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index f331c47..8a753d5 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -65,3 +65,9 @@ repos:
 #   rev: v2.2.5
 #   hooks:
 #   - id: codespell
+
+- repo: https://github.com/kynan/nbstripout
+  rev: 0.8.1
+  hooks:
+    - id: nbstripout
+      args: [--extra-keys=metadata.kernelspec metadata.language_info]

From f01c4951860642933a63d8458708cee6557b8f09 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 25 Oct 2025 22:34:01 +0200
Subject: [PATCH 02/87] Add ChainableArray class, 28 new mapping functions and
 numpy ufunc registration

---
 LICENSE.txt                |    2 +-
 pyproject.toml             |    7 +
 src/pyamapping/__init__.py |   78 ++-
 src/pyamapping/mappings.py | 1052 +++++++++++++++++++++++++++++++++++-
 4 files changed, 1114 insertions(+), 25 deletions(-)

diff --git a/LICENSE.txt b/LICENSE.txt
index a1a87e4..f31a526 100644
--- a/LICENSE.txt
+++ b/LICENSE.txt
@@ -1,6 +1,6 @@
 The MIT License (MIT)
 
-Copyright (c) 2023 Dennis Reinsch
+Copyright (c) 2023-2025 Thomas Hermann and Dennis Reinsch
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
diff --git a/pyproject.toml b/pyproject.toml
index 89a5bed..19cf8da 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -7,3 +7,10 @@ build-backend = "setuptools.build_meta"
 # For smarter version schemes and other configuration options,
 # check out https://github.com/pypa/setuptools_scm
 version_scheme = "no-guess-dev"
+
+[tool.ruff]
+line-length = 88
+lint.select = ["D"]
+
+[tool.ruff.lint.pydocstyle]
+convention = "numpy"
diff --git a/src/pyamapping/__init__.py b/src/pyamapping/__init__.py
index 0ae280d..e696760 100644
--- a/src/pyamapping/__init__.py
+++ b/src/pyamapping/__init__.py
@@ -16,32 +16,96 @@
     del version, PackageNotFoundError
 
 
-from pyamapping.mappings import (
+from pyamapping.mappings import (  # some synonyms; the class and helper functions
+    ChainableArray,
     amp_to_db,
     ampdb,
+    bilin,
+    chain,
     clip,
     cps_to_midi,
+    cps_to_octave,
     cpsmidi,
+    curvelin,
     db_to_amp,
     dbamp,
+    distort,
+    ecdf,
+    ecdf_to_lin,
+    fermi,
+    fold,
+    gain,
     hz_to_mel,
+    interp,
+    interp_spline,
+    lcurve,
+    lin_to_ecdf,
+    lincurve,
+    linexp,
     linlin,
+    linlog,
+    linpoly,
+    linspace,
     mel_to_hz,
     midi_to_cps,
+    midi_to_ratio,
     midicps,
+    norm_peak,
+    norm_rms,
+    normalize,
+    octave_to_cps,
+    ratio_to_midi,
+    register_chain_fn,
+    remove_dc,
+    scurve,
+    softclip,
+    wrap,
 )
 
 __all__ = [
     "amp_to_db",
-    "ampdb",
+    "bilin",
     "clip",
     "cps_to_midi",
-    "cpsmidi",
+    "cps_to_octave",
+    "curvelin",
     "db_to_amp",
-    "dbamp",
-    "hz_to_mel",
+    "distort",
+    "ecdf_to_lin",
+    "ecdf",
+    "fermi",
+    "fold",
+    "gain",
+    "interp_spline",
+    "interp",
+    "lcurve",
+    "lin_to_ecdf",
+    "lincurve",
+    "linexp",
     "linlin",
-    "mel_to_hz",
+    "linlog",
+    "linpoly",
+    "linspace",
     "midi_to_cps",
+    "midi_to_ratio",
+    "norm_peak",
+    "norm_rms",
+    "normalize",
+    "octave_to_cps",
+    "ratio_to_midi",
+    "remove_dc",
+    "scurve",
+    "softclip",
+    "wrap",
+    "mel_to_hz",
+    "hz_to_mel",
+    # some synonyms
+    "ampdb",
+    "cpsmidi",
+    "dbamp",
     "midicps",
-]
+    # class and helper functions
+    "ChainableArray",
+    "chain",
+    "register_chain_fn",
+]  # type: ignore
diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 4b665f1..d78575f 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1,18 +1,22 @@
-"""Collection of audio related mapping functions"""
-from typing import Optional, Union
+"""Collection of audio related mapping functions."""
+
+from typing import Any, Callable, List, Optional, TypeVar, Union
 
 import numpy as np
+from numpy.typing import ArrayLike
+
+NDArrayType = TypeVar("NDArrayType", bound=np.ndarray)
 
 
 def linlin(
-    value: Union[float, np.ndarray],
+    value: Union[float, ArrayLike],
     x1: float,
     x2: float,
     y1: float,
     y2: float,
     clip: Optional[str] = None,
 ) -> Union[float, np.ndarray]:
-    """Map value linearly so that [x1, x2] is mapped to [y1, y2]
+    """Map value linearly so that [x1, x2] is mapped to [y1, y2].
 
     linlin is implemented in analogy to the SC3 linlin, yet this
     function extrapolates by default.
@@ -21,7 +25,7 @@ def linlin(
 
     Parameters
     ----------
-    value : float or np.ndarray
+    value : float or np.ndarray (ArrayLike)
         value(s) to be mapped
     x1 : float
         source value 1
@@ -54,16 +58,382 @@ def linlin(
         return np.minimum(np.maximum(z, y1), y2)
 
 
+def linexp(
+    value: Union[float, ArrayLike],
+    x1: float,
+    x2: float,
+    y1: float,
+    y2: float,
+    clip: Optional[str] = None,
+) -> Union[float, np.ndarray]:
+    """Map value exponentially so that [x1, x2] is mapped to [y1, y2].
+
+    linexp is implemented in analogy to the SC3 linexp, yet this
+    function extrapolates by default.
+    A frequently used invocation is with x1 < x2, i.e. thinking
+    of them as a range [x1,x2]
+
+    Parameters
+    ----------
+    value : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    x1 : float
+        source value 1
+    x2 : float
+        source value 2
+    y1 : float
+        destination value to be reached for value == x1
+    y2 : float
+        destination value to be reached for value == x2
+    clip: None or string
+        None extrapolates, "min" or "max" clip at floor resp. ceiling
+        of the destination range, any other value defaults to "minmax",
+        i.e. it clips on both sides.
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result
+    """
+    z = np.exp((value - x1) / (x2 - x1) * (np.log(y2) - np.log(y1)) + np.log(y1))
+    if clip is None:
+        return z
+    if y1 > y2:
+        x1, x2, y1, y2 = x2, x1, y2, y1
+    if clip == "max":
+        return np.minimum(z, y2)
+    elif clip == "min":
+        return np.maximum(z, y1)
+    else:  # imply clip to be "minmax"
+        return np.minimum(np.maximum(z, y1), y2)
+
+
+def linlog(
+    value: Union[float, ArrayLike],
+    x1: float,
+    x2: float,
+    y1: float,
+    y2: float,
+    clip: Optional[str] = None,
+) -> Union[float, np.ndarray]:
+    """Map value logarithmically so that [x1, x2] is mapped to [y1, y2].
+
+    linlog is implemented in analogy to the SC3 linlog, yet this
+    function extrapolates by default.
+    A frequently used invocation is with x1 < x2, i.e. thinking
+    of them as a range [x1,x2]
+
+    Parameters
+    ----------
+    value : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    x1 : float
+        source value 1
+    x2 : float
+        source value 2
+    y1 : float
+        destination value to be reached for value == x1
+    y2 : float
+        destination value to be reached for value == x2
+    clip: None or string
+        None extrapolates, "min" or "max" clip at floor resp. ceiling
+        of the destination range, any other value defaults to "minmax",
+        i.e. it clips on both sides.
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result
+    """
+    z = np.log((value - x1) / (x2 - x1) * (np.exp(y2) - np.exp(y1)) + np.exp(y1))
+    if clip is None:
+        return z
+    if y1 > y2:
+        x1, x2, y1, y2 = x2, x1, y2, y1
+    if clip == "max":
+        return np.minimum(z, y2)
+    elif clip == "min":
+        return np.maximum(z, y1)
+    else:  # imply clip to be "minmax"
+        return np.minimum(np.maximum(z, y1), y2)
+
+
+def lincurve(
+    x: Union[float, ArrayLike],
+    x1: float,
+    x2: float,
+    y1: float = -1.0,
+    y2: float = 1.0,
+    curve: float = -2.0,
+    clip: Optional[str] = None,
+) -> Union[float, np.ndarray]:
+    """Map value exponentially so that [x1, x2] is mapped to [y1, y2].
+
+    lincurve is implemented in analogy to the SC3 lincurve, yet this
+    function extrapolates by default.
+    A frequently used invocation is with x1 < x2,
+    i.e. thinking of them as a range [x1, x2]
+    x1 is mapped to y1. Use y2 < y1 for polarity inversion, i.e. curve = -curve
+    returns y1 + (y2 - y1) /
+                (1.0 - exp(curve)) * (1 - exp(curve) ** ((x - x1) / (x2 - x1)))
+            yoffset +   yrange  * (this goes from 0 =(1-grow**0) to (1-grow**1)
+
+    Parameters
+    ----------
+    value : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    x1 : float
+        source value 1
+    x2 : float
+        source value 2
+    y1 : float
+        destination value to be reached for value == x1
+    y2 : float
+        destination value to be reached for value == x2
+    curve : float
+        specification of the curvature. TBA
+    clip: None or string
+        None extrapolates, "min" or "max" clip at floor resp. ceiling
+        of the destination range, any other value defaults to "minmax",
+        i.e. it clips on both sides.
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result
+    """
+    if abs(curve) < 0.001:
+        z = (x - x1) / (x2 - x1) * (y2 - y1) + y1
+    else:
+        grow = np.exp(curve)
+        a = (y2 - y1) / (1.0 - grow)
+        b = y1 + a
+        z = b - a * grow ** ((x - x1) / (x2 - x1))
+
+    if y1 > y2:
+        y1, y2 = y2, y1
+    if clip:
+        if clip == "max":
+            z = np.minimum(z, y2)
+        elif clip == "min":
+            z = np.maximum(z, y1)
+        else:  # imply clip to be "minmax"
+            z = np.minimum(np.maximum(z, y1), y2)
+    return z
+
+
+def curvelin(
+    x: Union[float, ArrayLike],
+    x1: float,
+    x2: float,
+    y1: float = -1.0,
+    y2: float = 1.0,
+    curve: float = -2.0,
+    clip: Optional[str] = None,
+) -> Union[float, np.ndarray]:
+    """Map (assumedly exponentially curved) x from [x1, x2] linearly to [y1, y2].
+
+    This is done by applying a curve parameter as in sc3. the input range can include 0,
+    different from explin a clipping is performed according to the clip argument.
+
+    curvelin is implemented in analogy to the SC3 curvelin, yet extrapolates by default.
+    A frequently used invocation is with x1<x2, i.e. a range [x1, x2]
+    Use x1 is mapped to y1, use y2 < y1 for polarity inversion.
+
+    Parameters
+    ----------
+    value : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    x1 : float
+        source value 1
+    x2 : float
+        source value 2
+    y1 : float
+        destination value to be reached for value == x1
+    y2 : float
+        destination value to be reached for value == x2
+    curve : float
+        specification of the curvature. TBA
+    clip: None or string
+        None extrapolates, "min" or "max" clip at floor resp. ceiling
+        of the destination range, any other value defaults to "minmax",
+        i.e. it clips on both sides.
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result
+    """
+    if abs(curve) < 0.001:
+        z = (x - x1) / (x2 - x1) * (y2 - y1) + y1
+    else:
+        grow = np.exp(curve)
+        a = (x2 - x1) / (1.0 - grow)
+        b = x1 + a
+        z = np.log((b - x) / a) * (y2 - y1) / curve + y1
+
+    if y1 > y2:
+        y1, y2 = y2, y1
+    if clip:
+        if clip == "max":
+            z = np.minimum(z, y2)
+        elif clip == "min":
+            z = np.maximum(z, y1)
+        else:  # imply clip to be "minmax"
+            z = np.minimum(np.maximum(z, y1), y2)
+    return z
+
+
+def linpoly(
+    x: Union[float, ArrayLike],
+    xmax: float = 1.0,
+    y1: float = -1.0,
+    y2: float = 1.0,
+    curve: float = 2.0,
+    clip: Optional[str] = None,
+) -> Union[float, np.ndarray]:
+    """Map x between [-xmax, xmax] to [y1, y2] using a polynomial mapping.
+
+    The mapping is y1 + (y2 - y1) * (1 + (x/xmax)**order) / 2
+    where order = 1 + curve if curve>0 else (1 - 1 / (1 + curve))
+
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): values to be mapped
+        xmax (float): source scale, defaults to 1.0
+        y1 (float, optional): target range low value, Defaults to -1.0.
+        y2 (float, optional): target ragne 2nd value. Defaults to 1.0.
+        curve (float, optional):  defaults to 2
+            if curve > 0: polynomial order is curve + 1
+            if curve < 0: polynomial order is 1 - 1/curve
+        clip (Optional[str], optional): clip flags (min / max / minmax).
+            Defaults to None.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: mapping result for x
+    """
+    order = 1 + curve if curve >= 0 else (1 / (1 - curve))
+    z = y1 + (y2 - y1) * (1 + np.sign(x) * (np.abs(x) / xmax) ** order) / 2
+    if clip is None:
+        return z
+    if y1 > y2:
+        y1, y2 = y2, y1
+    if clip == "max":
+        return np.minimum(z, y2)
+    elif clip == "min":
+        return np.maximum(z, y1)
+    else:  # imply clip to be "minmax"
+        return np.minimum(np.maximum(z, y1), y2)
+
+
+def interp_spline(
+    x: Union[float, ArrayLike],
+    xc: Union[List[float], np.ndarray],
+    yc: Union[List[float], np.ndarray] = [-1, 0, 1],
+    k=1,
+    **kwarg,
+) -> Union[float, np.ndarray]:
+    """Apply scipy.interpolate.interp_spline interpolation.
+
+    applicable for piecewise linear mappings, with extrapolation.
+    interp_spline is slower than numpy.interp() for smaller data sets (e.g. <5000)
+    however, it allows extrapolation.
+
+    Parameters
+    ----------
+    x : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    xc : Union[List[float], np.ndarray]
+        x coordinates of line segment function, must be sorted
+    yc : Union[List[float], np.ndarray]
+        y coordinates of line segment function, requires len(yc)==len(xc)
+    k : interpolation order (see interp_spline, defaults to 1 = linear)
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result, extrapolating beyond bounds
+
+    """
+    from scipy.interpolate import make_interp_spline
+
+    spl = make_interp_spline(xc, yc, k=k)  # k=1: linear
+    return spl(x) if isinstance(x, ChainableArray) else chain(spl(x))
+
+
+def interp(
+    x: Union[float, ArrayLike],
+    xc: Union[List[float], np.ndarray],
+    yc: Union[List[float], np.ndarray] = [-1, 0, 1],
+    **kwarg,
+) -> Union[float, np.ndarray]:
+    """Apply numpy.interp interpolation.
+
+    applicable for piecewise linear mappings, with extrapolation
+    interp is faster than interp_spline() for small x (e.g. <5000),
+    but it clips by default.
+
+    Parameters
+    ----------
+    x : float or np.ndarray (ArrayLike)
+        value(s) to be mapped
+    xc : Union[List[float], np.ndarray]
+        x coordinates of line segment function, must be sorted
+    yc : Union[List[float], np.ndarray]
+        y coordinates of line segment function, requires len(yc)==len(xc)
+
+    Returns
+    -------
+    float or np.ndarray
+        the mapping result, clipping beyond bounds
+
+    """
+    return np.interp(x, xc, yc, **kwarg)
+
+
+def bilin(
+    x: Union[float, ArrayLike],
+    xcenter: float,
+    xmin: float,
+    xmax: float,
+    ycenter: float = 0,
+    ymin: float = -1,
+    ymax: float = 1,
+) -> Union[float, np.ndarray]:
+    """Bilin compatibility function. implements sc3 bilin function.
+
+    This maps x in 2 linear segments as given by coordinates.
+
+    Parameter:
+    ---------
+        x (Union[float, np.typing.ArrayLike]): _description_
+        xcenter (float): _description_
+        xmin (float): _description_
+        xmax (float): _description_
+        ycenter (float): _description_
+        ymin (float): _description_
+        ymax (float): _description_
+
+    Returns
+    -------
+    Union[float, np.ndarray],
+        the mapping result
+    """
+    return interp_spline(x, [xmin, xcenter, xmax], [ymin, ycenter, ymax])
+
+
 def clip(
-    value: Union[float, np.ndarray],
+    value: Union[float, ArrayLike],
     minimum: float = -float("inf"),
     maximum: float = float("inf"),
 ) -> Union[float, np.ndarray]:
-    """Clips a value to a certain range
+    """Clips a value to a certain range.
 
     Parameters
     ----------
-    value : float or np.ndarray
+    value : float or np.ndarray (ArrayLike)
         Value(s) to clip
     minimum : float, optional
         Minimum output value, by default -float("inf")
@@ -75,7 +445,7 @@ def clip(
     float
         clipped value
     """
-    if type(value) == np.ndarray:
+    if isinstance(value, np.ndarray):
         return np.maximum(np.minimum(value, maximum), minimum)
     else:  # ToDo: check if better performance than above numpy code - if not: delete
         if value < minimum:
@@ -86,7 +456,7 @@ def clip(
 
 
 def midi_to_cps(midi_note: float) -> float:
-    """Convert MIDI note to cycles per second
+    """Convert MIDI note to cycles per second.
 
     Parameters
     ----------
@@ -105,7 +475,7 @@ def midi_to_cps(midi_note: float) -> float:
 
 
 def cps_to_midi(cps: float) -> float:
-    """Convert cycles per second to MIDI note
+    """Convert cycles per second to MIDI note.
 
     Parameters
     ----------
@@ -123,16 +493,96 @@ def cps_to_midi(cps: float) -> float:
 cpsmidi = cps_to_midi
 
 
+def midi_to_ratio(midi_note: float) -> float:
+    """Convert MIDI difference to ratio.
+
+    Parameters
+    ----------
+    m : float
+        MIDI note
+
+    Returns
+    -------
+    float
+        corresponding ratio
+    """
+    return 2 ** (midi_note / 12.0)
+
+
+midiratio = midi_to_ratio
+
+
+def ratio_to_midi(ratio: float) -> float:
+    """Convert ratio to MIDI difference.
+
+    Parameters
+    ----------
+    ratio : float
+        ratio (e.g. of frequencies)
+
+    Returns
+    -------
+    float
+        corresponding MIDI difference
+    """
+    return 12 * np.log2(ratio)
+
+
+ratiomidi = ratio_to_midi
+
+
+def cps_to_octave(cps: float) -> float:
+    """Convert cycles per second into decimal octaves.
+
+    reference Middle C (i.e. MIDI 60, C_4, 261.626 Hz) yields 4 (octaves).
+
+    Parameters
+    ----------
+    cps : float
+        cycles per second
+
+    Returns
+    -------
+    float
+        octaves relative to Middle C (MIDI 60 C_4, 261.626 HZ)
+    """
+    return np.log2(cps / 440) + 4.75
+
+
+cpsoct = cps_to_octave
+
+
+def octave_to_cps(octave: float) -> float:
+    """Convert octaves to cps.
+
+    reference 4.75 yields 440 Hz, i.e. 4 -> freq of Middle C (C4)
+
+    Parameters
+    ----------
+    octave : float
+        octave
+
+    Returns
+    -------
+    float
+        cycles per second
+    """
+    return 440 * 2 ** (octave - 4.75)
+
+
+octcps = octave_to_cps
+
+
 def hz_to_mel(hz):
-    """Convert a value in Hertz to Mels
+    """Convert a value in Hertz to Mels.
 
     Parameters
     ----------
     hz : number of array
         value in Hz, can be an array
 
-    Returns:
-    --------
+    Returns
+    -------
     _ : number of array
         value in Mels, same type as the input.
     """
@@ -140,15 +590,15 @@ def hz_to_mel(hz):
 
 
 def mel_to_hz(mel):
-    """Convert a value in Hertz to Mels
+    """Convert a value in Hertz to Mels.
 
     Parameters
     ----------
     hz : number of array
         value in Hz, can be an array
 
-    Returns:
-    --------
+    Returns
+    -------
     _ : number of array
         value in Mels, same type as the input.
     """
@@ -191,3 +641,571 @@ def amp_to_db(amp: float) -> float:
 
 
 ampdb = amp_to_db
+
+
+def distort(
+    x: Union[float, ArrayLike], threshold: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Apply value distortion x/(threshold + |x|).
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        threshold (float, optional): defaults to 1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: distorted value / array
+    """
+    return x / (threshold + np.abs(x))
+
+
+def softclip(
+    x: Union[float, ArrayLike], threshold: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Apply softclip distortion to x.
+
+    This yields a perfectly linear region within [-0.5, 0.5],
+    outside values computed by (|x| - 0.25) / x
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        threshold (float, optional): defaults to 1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: softclip distorted value / array
+    """
+    condition = np.abs(x) > 0.5
+    return (np.abs(x) - 0.25) / x * condition + (1 - condition) * x
+    # return (np.abs(x) - 0.25)/x if np.abs(x)<0.5 else x
+
+
+def scurve(
+    x: Union[float, ArrayLike], threshold: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Map value onto an S-curve bound to [0,1].
+
+    Implements v * v * (3-(2*v)) mit v = x.clip(0,1)
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        threshold (float, optional): defaults to 1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: scurve distorted value / array
+    """
+    v = clip(x, 0, 1)
+    return v**2 * (3 - 2 * v)
+
+
+def lcurve(
+    x: Union[float, ArrayLike], m: float = 0.0, n: float = 1.0, tau: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Map value or array onto an L-curve.
+
+    Implements (1 + m * exp(-x/tau) + 1) / (1 + n * exp(-x/tau))
+    - equal to fermi function with default parameters
+    - note that different to the sc3 implementation, tau is inside
+    the exp function (unclear tau placement in sc3...)
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        m (float, optional): numerator factor defaults to 0.0.
+        n (float, optional): denumerator factor defaults to 1.0.
+        tau (float, optional): scale constant, defaults to 1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: lcurve distorted value / array
+    """
+    return (1 + m * np.exp(-x / tau)) / (1 + n * np.exp(-x / tau))
+
+
+def fermi(
+    x: Union[float, ArrayLike], tau: float = 1.0, mu: float = 0.0
+) -> Union[float, np.ndarray]:
+    """Apply fermi function to value or array.
+
+    Implements 1 / (1 + exp(-x/tau))
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        tau (float, optional): scale constant, defaults to 1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: fermi distorted value / array
+    """
+    return 1.0 / (1 + np.exp(-(x - mu) / tau))
+
+
+def normalize(
+    x: Union[float, ArrayLike], y1: float = -1.0, y2: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Normalize array to target range [y1, y2].
+
+    Linear mapping [min(x), max(x)] to [y1, y2]. Use y1 > y2 to change polarity.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        y1 (float, optional): mapping target for min(x). Defaults to -1.0.
+        y2 (float, optional): mapping target for max(x). Defaults to  1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: normalized / scaled array
+    """
+    x1, x2 = np.amin(x), np.amax(x)
+    return (x - x1) / (x2 - x1) * (y2 - y1) + y1
+
+
+def wrap(
+    x: Union[float, ArrayLike], y1: float = -1.0, y2: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Wrap array around target range [y1, y2].
+
+    This implements the mapping y1 + x % (y2 - y1).
+    The order of y1, y2 is irrelevant.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        y1 (float, optional): 1st wrap bound. Defaults to -1.0.
+        y2 (float, optional): 2nd wrap bound. Defaults to  1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: wraped array
+    """
+    return y1 + x % (y2 - y1)
+
+
+def fold(
+    x: Union[float, ArrayLike], y1: float = -1.0, y2: float = 1.0
+) -> Union[float, np.ndarray]:
+    """Fold array around target range [y1, y2].
+
+    This implements (np.abs((x - y2) % (2 * L) - L) + y1),
+    ordering bounds so that y1 < y2.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        y1 (float, optional): 1st fold bound. Defaults to -1.0.
+        y2 (float, optional): 2nd fold bound. Defaults to  1.0.
+
+    Returns
+    -------
+        Union[float, np.ndarray]: folded array
+    """
+    if y2 < y1:
+        y1, y2 = y2, y1
+    L = y2 - y1
+    return np.abs((x - y2) % (2 * L) - L) + y1
+
+
+def remove_dc(
+    x: Union[float, ArrayLike],
+) -> Union[float, np.ndarray]:
+    """Remove DC bias.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+
+    Returns
+    -------
+        Union[float, np.ndarray]: normalized / scaled array
+    """
+    return x - np.mean(x)
+
+
+def norm_peak(x: Union[float, ArrayLike], peak=1.0):
+    """Normalize array so that max(abs(x)) = peak.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        peak (float): target peak
+
+    Returns
+    -------
+        Union[float, np.ndarray]: normalized (scaled) array
+    """
+    peak_of_x = np.max(np.abs(x))
+    return (x / peak_of_x) * peak if peak_of_x != 0 else x
+
+
+def norm_rms(x: Union[float, ArrayLike], rms=1.0):
+    """Normalize array so that its RMS value equals `rms`.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        rms (float): target rms of array
+
+    Returns
+    -------
+        Union[float, np.ndarray]: rms normalized (scaled) array
+    """
+    rms_of_x = np.sqrt(np.mean(x**2))
+    return (x / rms_of_x) * rms if rms_of_x != 0 else x
+
+
+def gain(
+    x: Union[float, ArrayLike], db: Optional[float] = None, amp: Optional[float] = None
+):
+    """Apply gain, either as dB (SPL) or scalar factor amp.
+
+    No operation done if neither argument is given, it applies both if both are given.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): input value or array
+        db (None or float): dB SPL = gain 10**(db/20), e.g. -6 dB ~ factor 0.5
+        amp (None or float): gain factor
+
+    Returns
+    -------
+        Union[float, np.ndarray]: scaled (amplified / attenuated) array
+    """
+    if db:
+        sig = x * dbamp(db)
+    else:
+        sig = x.copy()
+    if amp:
+        sig *= amp
+    return sig
+
+
+def linspace(
+    x: Union[float, int, ArrayLike], x1: float, x2: float, endpoint: bool = True
+) -> np.ndarray:
+    """Create np.linspace from x1 to x2 in int(x) resp len(x) steps.
+
+    Parameters
+    ----------
+        x (Union[float, int, ArrayLike]): length or array of which only shape is used
+        x1 (float): target interval one side
+        x2 (float): target interval other side
+        endpoint (bool): forwarded to np.linspace
+
+    Returns
+    -------
+        Union[float, np.ndarray]: array of length len(x)
+            (resp. int(x) if x is float) of numbers between x1 and x2
+    """
+    if isinstance(x, np.ndarray):
+        return np.linspace(x1, x2, x.shape[0], endpoint=endpoint)
+    else:
+        return np.linspace(x1, x2, int(abs(x)), endpoint=endpoint)
+
+
+def lin_to_ecdf(
+    x: Union[float, ArrayLike], ref_data: np.ndarray, sorted: bool = False
+) -> Union[float, np.ndarray]:
+    """Map data using empiric cumulative distribution function as mapping.
+
+    This meann feature values are mapped to quantiles.
+    if sorted==True: ref_data is regarded as sorted, speeding repeated invocations.
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): value or array to map
+        ref_data (np.ndarray): reference data used to create ecdf.
+        sorted (bool): whether ref_data is sorted.
+            Defaults to False, i.e. by default data will be sorted.
+
+    Returns
+    -------
+        np.ndarray: resulting mapped data
+    """
+    if sorted:
+        return interp(
+            x, ref_data, np.arange(1, len(ref_data) + 1) / float(len(ref_data))
+        )
+    else:
+        return interp(x, *ecdf(ref_data))
+
+
+def ecdf_to_lin(
+    x: Union[float, ArrayLike], ref_data: np.ndarray, sorted: bool = False
+) -> Union[float, np.ndarray]:
+    """Map data using inverse empiric cumulative distribution function.
+
+    This means that quantiles are mapped back to estimated feature values.
+    - if ref_data is omitted, x is used instead
+    - if sorted==True: ref_data is regarded as sorted, speeding repeated invocations
+
+    Parameters
+    ----------
+        x (Union[float, np.typing.ArrayLike]): value or array to map
+        ref_data (np.ndarray): reference data used to create ecdf.
+        sorted (bool): whether ref_data is sorted.
+            Defaults to False, i.e. data will be sorted.
+
+    Returns
+    -------
+        np.ndarray: resulting mapped data
+    """
+    if sorted:
+        return interp(
+            x, np.arange(1, len(ref_data) + 1) / float(len(ref_data)), ref_data
+        )
+    else:
+        xc, yc = ecdf(ref_data)
+        return interp(x, yc, xc)
+
+
+# create subclass of numpy.ndarray
+
+
+class ChainableArray(np.ndarray):
+    """subclass for simpler numpy mapping by chaining syntax."""
+
+    def __new__(cls, input_array, *args, **kwargs):
+        """Create new instance."""
+        obj = np.asarray(input_array).view(cls)
+        return obj
+
+    def __array_finalize__(self, obj):
+        """Finalize array."""
+        if obj is None:
+            return
+
+    def to_array(self):
+        """Convert self to np.ndarray."""
+        return np.array(self)
+
+    def to_asig(self, sr=44100):
+        """Convert self to pya.Asig."""
+        from pya import Asig
+
+        return Asig(self, sr=sr)
+
+    def plot(self, *args, **kwargs):
+        """Plot self via matplotlib."""
+        import matplotlib.pyplot as plt
+
+        sr = kwargs.pop("sr", None)
+        if sr:
+            xs = np.arange(0, self.shape[0]) / sr
+            plt.plot(xs, self, *args, **kwargs)
+            plt.xlabel("time [s]")
+        else:
+            xs = kwargs.pop("xs", None)
+            if xs is not None:
+                plt.plot(xs, self, *args, **kwargs)
+            else:
+                plt.plot(self, *args, **kwargs)
+
+        return self
+
+    def mapvec(
+        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
+    ) -> NDArrayType:
+        """Map fn on self by using np.vectorize().
+
+        Parameters
+        ----------
+            self (NDArrayType): array to map
+            fn (Callable[..., Any]): function to call on each element
+
+        Returns
+        -------
+            NDArrayType: mapping result as ChainableArray
+        """
+        return np.vectorize(fn)(self, *args, **kwargs)
+
+    def map(
+        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
+    ) -> NDArrayType:
+        """Apply function fn directly to self; on fail suggest to use mapvec().
+
+        Parameters
+        ----------
+            self (np.ndarray): array used as input of fn
+            fn (Callable[..., Any]): mapping function
+            args and kwargs are passed on to fn
+
+        Raises
+        ------
+            TypeError: if fn fails to operate on np.ndarray as first argument.
+            mapvec() is then proposed as alternative.
+
+        Returns
+        -------
+            ChainableArray: the mapping result as ChainableArray
+        """
+        try:
+            return chain(fn(self, *args, **kwargs))
+        except (TypeError, ValueError, AttributeError) as e:
+            raise TypeError(
+                f"Function {fn.__name__} does not support NumPy arrays directly. "
+                "Use .mapvec() instead for np.vectorize elementwise mapping."
+            ) from e
+
+    def __getattr__(self, name: str) -> Callable:
+        """Dynamically handle method calls."""
+        if name.startswith("dynamic_"):
+            return lambda *args: f"Called {name} with {args}"
+        raise AttributeError(
+            f"'{self.__class__.__name__}' object has no attribute '{name}'"
+        )
+
+
+def ecdf(
+    x: np.ndarray, selection: slice = slice(None, None, None)
+) -> tuple[np.ndarray, np.ndarray]:
+    """Empirical cumulative distribution function.
+
+    Usable for handcrafted mapping functions such as with using ChainableArray.interp()
+
+    Example 1: (compute once - use many)
+    >>> myecdf = ecdf(data); chain(otherdata).interp(*ecdf)
+
+    Example 2: (compute and map in one go)
+    >>> chain(otherdata).interp(*ecdf(data))
+
+    Example 3: (use a sparser (more smooth) ecdf mapping)
+    >>> chain(otherdata).interp(*ecdf(data, np.s_[::5]))
+
+    Parameters
+    ----------
+        x (np.ndarray): array
+        selection (slice): slice applied to x and y coordinates of the resulting tuple
+
+    Returns
+    -------
+        tuple[np.ndarray, np.ndarray]: sorted array of x and y coordinates of the ecdf
+    """
+    xs = np.sort(x)
+    ys = np.arange(1, len(xs) + 1) / float(len(xs))
+    return xs[selection], ys[selection]
+
+
+def register_numpy_ufunc(fn: np.ufunc, name: Union[None, str] = None) -> None:
+    """Register numpy ufunc with one or two ndarray arguments."""
+    nin = fn.nin
+    if nin == 1:
+
+        def method1(self, *args, **kwargs):
+            return ChainableArray(fn(self, *args, **kwargs))
+
+        method = method1
+
+    elif nin == 2:
+
+        def method2(self, other, *args, **kwargs):
+            return ChainableArray(fn(self, other, *args, **kwargs))
+
+        method = method2
+
+    else:
+        print("warning: np.ufunc fn has nin not in [1,2]")
+
+        def default_method(x):
+            return None
+
+        method = default_method
+
+    method.__name__ = fn.__name__ if not name else name
+    method.__doc__ = (
+        f"{method.__name__} implements numpy.{method.__name__}"
+        + f"function for ChainableArray. See help(np.{fn.__name__})"
+    )
+
+    setattr(ChainableArray, method.__name__, method)
+
+
+def register_chain_fn(fn: Callable, name: Union[None, str] = None) -> None:
+    """Register function fn for chaining, optionally under given name."""
+
+    def method(self, *args, **kwargs):
+        return ChainableArray(fn(self, *args, **kwargs))
+
+    method.__name__ = fn.__name__ if not name else name
+    method.__doc__ = (
+        f"{method.__name__} implements the {method.__name__}"
+        + "operation for ChainableArray. Argument: np.ndarray"
+    )
+
+    setattr(ChainableArray, method.__name__, method)
+
+
+def _list_numpy_ufuncs():
+    """Return all numpy ufuncs with 1 or 2 ndarray arguments."""
+    ufunc_list = []
+    for attr_name in dir(np):  # all attributes in numpy
+        attr = getattr(np, attr_name)
+        if isinstance(attr, np.ufunc):
+            if attr.nin <= 2:
+                ufunc_list.append(attr)
+            else:
+                print(attr, attr.nin)
+    return ufunc_list
+
+
+# create class methods for numpy functions and pyamapping functions
+for fn in _list_numpy_ufuncs():  # numpy_mapping_functions:
+    name = "abs" if fn.__name__ == "absolute" else None
+    register_numpy_ufunc(fn, name)
+
+# register some non-ufunc which nontheless should workd
+register_chain_fn(np.angle, "angle")
+ChainableArray.magnitude = ChainableArray.abs
+
+pyamapping_functions = [
+    amp_to_db,
+    bilin,
+    clip,
+    cps_to_midi,
+    cps_to_octave,
+    curvelin,
+    db_to_amp,
+    distort,
+    ecdf_to_lin,
+    ecdf,
+    fermi,
+    fold,
+    gain,
+    hz_to_mel,
+    interp_spline,
+    interp,
+    lcurve,
+    lin_to_ecdf,
+    lincurve,
+    linexp,
+    linlin,
+    linlog,
+    linpoly,
+    linspace,
+    mel_to_hz,
+    midi_to_cps,
+    midi_to_ratio,
+    norm_peak,
+    norm_rms,
+    normalize,
+    octave_to_cps,
+    ratio_to_midi,
+    remove_dc,
+    scurve,
+    softclip,
+    wrap,
+]
+
+for fn in pyamapping_functions:
+    register_chain_fn(fn, name)
+
+
+def chain(input_array: ArrayLike) -> ChainableArray:
+    """Turn np.ndarray into ChainableArray."""
+    # ToDo: check difference to input_array.view(ChainableArray)
+    return ChainableArray(input_array)

From 956153330ea15c2e33e0c19f6fde8993acc0722e Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 25 Oct 2025 22:46:08 +0200
Subject: [PATCH 03/87] add pyamapping example notebook

---
 notebooks/pyamapping-examples.ipynb | 246 ++++++++++++++++++++++++++++
 1 file changed, 246 insertions(+)
 create mode 100644 notebooks/pyamapping-examples.ipynb

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
new file mode 100644
index 0000000..3119c72
--- /dev/null
+++ b/notebooks/pyamapping-examples.ipynb
@@ -0,0 +1,246 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {},
+   "source": [
+    "# pyamapping - mapping functions for audio computing (and beyond)\n",
+    "\n",
+    "by Thomas Hermann and Dennis Reinsch, 2023++\n",
+    "\n",
+    "## Introduction \n",
+    "\n",
+    "### Background / History\n",
+    "\n",
+    "- pyamapping bundles frequently used mapping functions for audio computing\n",
+    "- the earliest functions were reimplementations of ampdb, dbamp, midicps, cpsmidi, linlin, coded in analogy to SuperCollider3 functions to be used within the sc3nb package. (coded by TH)\n",
+    "- later, when I started pya, the same functions were needed, yet importing sc3nb would have caused unwanted dependencies, so we created pyamapping as a very lean package that both sc3nb and pya depend on (created by DR)\n",
+    "- now in 2025 pyamapping grows strongly (additions by TH) \n",
+    "  - firstly by adding many mapping functions available in sc3 which were beforehand not copied\n",
+    "  - secondly, by introducing ChainableArray, a class that wraps numpy.ndarrays, allowing to daisy chain operations on numpy arrays, similar to how we offer it for pya.\n",
+    "- This notebook introduces the available mapping functions with examples.\n",
+    "\n",
+    "### Overview\n",
+    "\n",
+    "**pyamapping** offers a set of mapping functions often used \n",
+    "\n",
+    "- in the context of sound and computer music \n",
+    "- in the context of auditory display and sonification (e.g. parameter mapping sonifications)\n",
+    "- ...\n",
+    "\n",
+    "A source of inspiration is librosa and Supercollider3. This package reimplements them and adds mappings used in the interactive sonification stack (cf. <https://github.com/interactive-sonification>), including the following packages that all make use of pyamapping:\n",
+    "\n",
+    "- **sc3nb** - sc3 interface for Python and Jupyter notebooks\n",
+    "- **pya**  - the python Audio Coding Package\n",
+    "- **mesonic** - a middleware for sonification and auditory display \n",
+    "- **sonecules** - a high-level class library for sonification and auditory display\n",
+    "\n",
+    "**Chainable numpy arrays**\n",
+    "\n",
+    "Method chaining offers concise syntax and proved helpful in pya.\n",
+    "Numpy offers method chaining only for few functions.\n",
+    "This package extends method chaining \n",
+    "\n",
+    "- by inheriting the class `ChainableArray` from `numpy.ndarray`\n",
+    "- by adding wrappers to enable a method chain syntax for most `ufuncs`\n",
+    "- by providing a general `map()` method for direct vectorized mapping\n",
+    "- by providing helper functions to vectorize Python functions into methods\n",
+    "\n",
+    "Furthermore it offers some convenience functions, e.g.\n",
+    "\n",
+    "- to plot arrays (optionally as signal with given sample rate)\n",
+    "\n",
+    "We hope that pyamapping will help to write signal transformations and manipulations in a more concise, compact and readible manner."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {},
+   "source": [
+    "**Imports and Headers**\n",
+    "\n",
+    "- as pyamapping is a long name, importing as `pam` is a suggested abbreviation \n",
+    "- matplotlib and pprint imports are merely for showing example output"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib as mpl\n",
+    "import matplotlib.pyplot as plt\n",
+    "from pprint import pprint\n",
+    "import pyamapping as pam\n",
+    "\n",
+    "mpl.rcParams['figure.figsize'] = (9,2.5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {},
+   "source": [
+    "## Available pyamapping functions - Overview\n",
+    "\n",
+    "- in import of pyamapping, wrappers are automatically created for numpy ufuncs.\n",
+    "  - later versions may have them created verbatim to enable code completion\n",
+    "- the following code simply lists those numpy functions plus special dedicated/ new pyamapping functions that do not have their origin in numpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pyamapping.mappings import _list_numpy_ufuncs, pyamapping_functions\n",
+    "\n",
+    "# print (i) a compact list of all unary and binary numpy functions \n",
+    "# and (ii) all pyamapping functions\n",
+    "u_lists = [[], []]\n",
+    "\n",
+    "for ufunc in _list_numpy_ufuncs():\n",
+    "    u_lists[ufunc.nin - 1].append(ufunc.__name__)\n",
+    "\n",
+    "# compact list numpy functions\n",
+    "for i, li in enumerate(u_lists):\n",
+    "    print(f\"\\n=== numpy functions with {i+1} argument ===\")\n",
+    "    pprint(li, compact=True, width=80)\n",
+    "\n",
+    "# compact list of pyamapping functions\n",
+    "li = [el.__name__ for el in pyamapping_functions]\n",
+    "print(f\"\\n=== pyamapping functions: ===\")\n",
+    "pprint(li, compact=True, width=80)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5",
+   "metadata": {},
+   "source": [
+    "## pyamapping - Demonstration and Examples"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6",
+   "metadata": {},
+   "source": [
+    "### ChainableArray - Basics"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {},
+   "source": [
+    "Any numpy array can be turned into a chainable array by using the `ChainableArray` class defined in `pyamapping`.\n",
+    "- the chain() function provides a shortcut, making this construction shorter.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pyamapping import ChainableArray, chain\n",
+    "\n",
+    "# some data\n",
+    "data = np.random.random(100)\n",
+    "\n",
+    "# create ChainableArray\n",
+    "dch = ChainableArray(data)\n",
+    "\n",
+    "# the same can be obtained shorter by\n",
+    "dch = chain(data)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9",
+   "metadata": {},
+   "source": [
+    "ChainableArray offer the following methods:\n",
+    "\n",
+    "- `to_array` - back to numpy ndarray\n",
+    "- `to_asig` - convert into pya.Asig\n",
+    "- `plot` - plot signal(s) as time series\n",
+    "- `mapvec` - map function on self by using numpy.vectorize\n",
+    "- `map` - apply function directly to the array itself\n",
+    "\n",
+    "Here is a quick demonstration:\n",
+    "\n",
+    "- let us\n",
+    "  - map $x \\to (5x)^2 + 0.1$, \n",
+    "  - plot as signal assuming sampling rate 100 Hz, \n",
+    "  - convert into decibel, \n",
+    "  - turn that into an audio signal (i.e. pya.Asig) \n",
+    "  - and plot it in the same figure created above.\n",
+    "  - finally transform the ChainableArray back to a regular numpy.ndarray.\n",
+    "\n",
+    "Using pyamapping, the code is both shorter and more concise than the above description:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dch2 = dch.map(lambda x: (5*x)**2+0.1).plot(sr=100, color=\"r\").mapvec(pam.amp_to_db)\n",
+    "a1 = dch2.to_asig(sr=100).plot(color=\"c\", lw=0.8)\n",
+    "\n",
+    "# conversion back to numpy array is rarely needed but if...\n",
+    "dd = dch2.to_array()\n",
+    "type(dd)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11",
+   "metadata": {},
+   "source": [
+    "ChainableArray is a recent addition to pyamapping, yet introduced here as it makes demonstrations of mapping functions extremely readable..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "isonpy13",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From e3f866c50ea8b29144cfb92d87afa22f4f0f262c Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 27 Oct 2025 17:28:53 +0100
Subject: [PATCH 04/87] add linlin() examples

---
 notebooks/pyamapping-examples.ipynb | 98 +++++++++++++++++++++++------
 1 file changed, 78 insertions(+), 20 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 3119c72..a6e3c72 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -77,6 +77,7 @@
     "import matplotlib.pyplot as plt\n",
     "from pprint import pprint\n",
     "import pyamapping as pam\n",
+    "from pyamapping import chain\n",
     "\n",
     "mpl.rcParams['figure.figsize'] = (9,2.5)"
    ]
@@ -213,34 +214,91 @@
     "ChainableArray is a recent addition to pyamapping, yet introduced here as it makes demonstrations of mapping functions extremely readable..."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "12",
+   "metadata": {},
+   "source": [
+    "## Tour of Mapping Functions: Functions from SuperCollider3 and librosa"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13",
+   "metadata": {},
+   "source": [
+    "### `linlin`\n",
+    "\n",
+    "- linlin is implemented in analogy to the SC3 linlin\n",
+    "- `linlin(v, x1, x2, y1, y2)` maps values v (scalar or arraylike) affine linearly so that [x1, x2] is mapped to [y1, y2].\n",
+    "- note that this linlin function extrapolates by default\n",
+    "- clipping can be controlled via the clip argument (values None (default), \"min\", \"max\", or anything else for \"minmax\")\n",
+    "- A frequently used invocation is with `x1 < x2`, i.e. thinking of them as a range $[x_1, x_2]$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "14",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.linlin(7, 0, 10, 100, 300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "15",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.linlin(7, 0, 5, 100, 300, \"max\") # clip result to maximum input range"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.linlin uses self as input v.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "17",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vch = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "vch.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "vch.linlin(0, 1, 1, 3).plot(\"r-\", label=\"linlin\")\n",
+    "vch.linlin(0.2, 0.7, -2, 2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "# plot mapping function (output vs input)\n",
+    "plt.figure(figsize=(3,1.5)); plt.grid()\n",
+    "plt.plot(vch, vch.linlin(0.25, 0.75, -1, 1, \"minmax\"));"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "19",
+   "metadata": {},
    "source": []
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "isonpy13",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.13.2"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }

From dae8f724462850fbf8d2c30df14a3c97bee0f01f Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 27 Oct 2025 20:21:30 +0100
Subject: [PATCH 05/87] improve linlin example

---
 notebooks/pyamapping-examples.ipynb | 29 ++++++++++++++++++-----------
 1 file changed, 18 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index a6e3c72..d4013ff 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -219,7 +219,9 @@
    "id": "12",
    "metadata": {},
    "source": [
-    "## Tour of Mapping Functions: Functions from SuperCollider3 and librosa"
+    "## Tour of Mapping Functions: Functions from SuperCollider3 and librosa\n",
+    "\n",
+    "For the following functions, we use `xs` to refer to the input array and `ys` for the outputs."
    ]
   },
   {
@@ -230,10 +232,11 @@
     "### `linlin`\n",
     "\n",
     "- linlin is implemented in analogy to the SC3 linlin\n",
-    "- `linlin(v, x1, x2, y1, y2)` maps values v (scalar or arraylike) affine linearly so that [x1, x2] is mapped to [y1, y2].\n",
+    "- `linlin(v, x1, x2, y1, y2)` maps values v (scalar or arraylike) affine linearly so that [x1, x2] is mapped to [y1, y2]:\n",
+    "  $$ z = y_1 + \\frac{v - x_1}{x_2 - x_1} \\cdot (y_2 - y_1) $$\n",
     "- note that this linlin function extrapolates by default\n",
     "- clipping can be controlled via the clip argument (values None (default), \"min\", \"max\", or anything else for \"minmax\")\n",
-    "- A frequently used invocation is with `x1 < x2`, i.e. thinking of them as a range $[x_1, x_2]$"
+    "- A frequently used invocation is with $x_1 < x_2$, i.e. thinking of them as a range $[x_1, x_2]$"
    ]
   },
   {
@@ -261,7 +264,7 @@
    "id": "16",
    "metadata": {},
    "source": [
-    "- ChainableArray.linlin uses self as input v.\n",
+    "- ChainableArray.linlin uses self as input.\n",
     "- Here are some mapping examples and plots"
    ]
   },
@@ -272,10 +275,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "vch = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "vch.plot(\"k-\", label=\"input data\") # plot input data\n",
-    "vch.linlin(0, 1, 1, 3).plot(\"r-\", label=\"linlin\")\n",
-    "vch.linlin(0.2, 0.7, -2, 2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
+    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs.linlin(0, 1, 1, 3).plot(\"r-\", label=\"linlin\")\n",
+    "xs.linlin(0.2, 0.7, -2, 2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
     "plt.legend(); plt.grid()"
    ]
   },
@@ -287,8 +290,8 @@
    "outputs": [],
    "source": [
     "# plot mapping function (output vs input)\n",
-    "plt.figure(figsize=(3,1.5)); plt.grid()\n",
-    "plt.plot(vch, vch.linlin(0.25, 0.75, -1, 1, \"minmax\"));"
+    "ys = xs.linlin(0.25, 0.75, -1, 1, \"minmax\")\n",
+    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); "
    ]
   },
   {
@@ -298,7 +301,11 @@
    "source": []
   }
  ],
- "metadata": {},
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }

From f87bb01e8367be70ffbdb54593d942d10127de5b Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 27 Oct 2025 20:38:42 +0100
Subject: [PATCH 06/87] add linexp() example

---
 notebooks/pyamapping-examples.ipynb | 67 ++++++++++++++++++++++++++++-
 1 file changed, 66 insertions(+), 1 deletion(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index d4013ff..aa24f34 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -298,7 +298,72 @@
    "cell_type": "markdown",
    "id": "19",
    "metadata": {},
-   "source": []
+   "source": [
+    "### `linexp`\n",
+    "\n",
+    "- linexp is implemented in analogy to the SC3 linexp\n",
+    "- `linexp(v, x1, x2, y1, y2)` maps values v (scalar or arraylike) exponentially so that [x1, x2] is mapped to [y1, y2]:\n",
+    "  $$ z = y_1 \\text{exp}\\left(\\frac{v - x_1}{x_2 - x_1}\\cdot (\\log(y_2) - \\log(y_1))\\right)\n",
+    "- note that this linexp function extrapolates by default\n",
+    "- clipping can be controlled via the clip argument (values None (default), \"min\", \"max\", or anything else for \"minmax\")\n",
+    "- A frequently used invocation is with $x_1 < x_2$, i.e. thinking of them as a range $[x_1, x_2]$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.linexp(5, 1, 8, 2, 256)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "21",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.linexp(7, 0, 5, 100, 300, \"max\") # clip result to maximum input range"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.linexp uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "23",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs.linexp(0, 1, 0.01, 1).plot(\"r-\", label=\"linlin\")\n",
+    "xs.linexp(0.2, 0.7, 2, 0.2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "24",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# plot linexp mapping function (output vs input)\n",
+    "ys = xs.linexp(0.25, 0.85, 0.2, 2)\n",
+    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
+    "plt.plot(xs, ys); "
+   ]
   }
  ],
  "metadata": {

From 6b3637a5412b2daf6ef83a001ace959392cdcf5b Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 27 Oct 2025 21:44:45 +0100
Subject: [PATCH 07/87] refactor linlog to explin

---
 src/pyamapping/__init__.py | 4 ++--
 src/pyamapping/mappings.py | 9 +++++----
 2 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/src/pyamapping/__init__.py b/src/pyamapping/__init__.py
index e696760..e37069d 100644
--- a/src/pyamapping/__init__.py
+++ b/src/pyamapping/__init__.py
@@ -32,6 +32,7 @@
     distort,
     ecdf,
     ecdf_to_lin,
+    explin,
     fermi,
     fold,
     gain,
@@ -43,7 +44,6 @@
     lincurve,
     linexp,
     linlin,
-    linlog,
     linpoly,
     linspace,
     mel_to_hz,
@@ -73,6 +73,7 @@
     "distort",
     "ecdf_to_lin",
     "ecdf",
+    "explin",
     "fermi",
     "fold",
     "gain",
@@ -83,7 +84,6 @@
     "lincurve",
     "linexp",
     "linlin",
-    "linlog",
     "linpoly",
     "linspace",
     "midi_to_cps",
diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index d78575f..13995e5 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -108,7 +108,7 @@ def linexp(
         return np.minimum(np.maximum(z, y1), y2)
 
 
-def linlog(
+def explin(
     value: Union[float, ArrayLike],
     x1: float,
     x2: float,
@@ -118,7 +118,7 @@ def linlog(
 ) -> Union[float, np.ndarray]:
     """Map value logarithmically so that [x1, x2] is mapped to [y1, y2].
 
-    linlog is implemented in analogy to the SC3 linlog, yet this
+    explin is implemented in analogy to the SC3 explin, yet this
     function extrapolates by default.
     A frequently used invocation is with x1 < x2, i.e. thinking
     of them as a range [x1,x2]
@@ -145,7 +145,8 @@ def linlog(
     float or np.ndarray
         the mapping result
     """
-    z = np.log((value - x1) / (x2 - x1) * (np.exp(y2) - np.exp(y1)) + np.exp(y1))
+    z = np.log(value / x1) / np.log(x2 / x1) * (y2 - y1) + y1
+
     if clip is None:
         return z
     if y1 > y2:
@@ -1173,6 +1174,7 @@ def _list_numpy_ufuncs():
     distort,
     ecdf_to_lin,
     ecdf,
+    explin,
     fermi,
     fold,
     gain,
@@ -1184,7 +1186,6 @@ def _list_numpy_ufuncs():
     lincurve,
     linexp,
     linlin,
-    linlog,
     linpoly,
     linspace,
     mel_to_hz,

From 09851be3a3bac092875e5298fd8958f06572d875 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 27 Oct 2025 21:46:23 +0100
Subject: [PATCH 08/87] add explin() example

---
 notebooks/pyamapping-examples.ipynb | 82 +++++++++++++++++++++++++++--
 1 file changed, 79 insertions(+), 3 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index aa24f34..f160020 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -79,7 +79,7 @@
     "import pyamapping as pam\n",
     "from pyamapping import chain\n",
     "\n",
-    "mpl.rcParams['figure.figsize'] = (9,2.5)"
+    "mpl.rcParams['figure.figsize'] = (9, 2.5)"
    ]
   },
   {
@@ -347,8 +347,8 @@
    "source": [
     "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
     "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
-    "xs.linexp(0, 1, 0.01, 1).plot(\"r-\", label=\"linlin\")\n",
-    "xs.linexp(0.2, 0.7, 2, 0.2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
+    "xs.linexp(0, 1, 0.01, 1).plot(\"r-\", label=\"linexp\")\n",
+    "xs.linexp(0.2, 0.7, 2, 0.2, \"minmix\").plot(\"g-\", label=\"linexp with clip\")\n",
     "plt.legend(); plt.grid()"
    ]
   },
@@ -364,6 +364,82 @@
     "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
     "plt.plot(xs, ys); "
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25",
+   "metadata": {},
+   "source": [
+    "### `explin`\n",
+    "\n",
+    "- explin is implemented in analogy to the SC3 function\n",
+    "- `explin(v, x1, x2, y1, y2)` maps values v (scalar or arraylike) logarithmically so that [x1, x2] is mapped to [y1, y2]:\n",
+    "\n",
+    "    $$ y = y_1 + (y_2-y_1) \\frac{\\log(v / x_1)}{\\log(x_2 / x_1)} $$\n",
+    "\n",
+    "- note that this `explin` function extrapolates by default\n",
+    "- clipping can be controlled via the clip argument (values None (default), `\"min\"`, `\"max\"`, or anything else for `\"minmax\"`)\n",
+    "- A frequently used invocation is with $x_1 < x_2$, i.e. thinking of them as a range $[x_1, x_2]$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "26",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# example: unmap a frequency to midi note with explin\n",
+    "f = 220 * 2**(-5/12) # 5 semitones higher than 220 Hz\n",
+    "pam.explin(f, 220, 440, 0, 12)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "27",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# example: unmap amplitude to level in decibel\n",
+    "pam.explin(0.01, 0.001, 1.0, -30, 0, \"max\") # clip result to maximum input range"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "28",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.explin uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "29",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0.01, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs.explin(0.1, 1, 0, 1).plot(\"r-\", label=\"explin\")\n",
+    "xs.explin(0.1, 0.5, 1, 0, \"minmix\").plot(\"g-\", label=\"explin with clip\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "30",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# plot linexp mapping function (output vs input)\n",
+    "ys = xs.explin(0.01, 1, 0, 20)\n",
+    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
+    "plt.plot(xs, ys); "
+   ]
   }
  ],
  "metadata": {

From c0482aa4dccd599351f1b0b40a6fcb5aa0c6f7a1 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 14:43:14 +0100
Subject: [PATCH 09/87] improve lincurve mapping function

---
 src/pyamapping/mappings.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 13995e5..fb6bfd8 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -206,10 +206,9 @@ def lincurve(
     if abs(curve) < 0.001:
         z = (x - x1) / (x2 - x1) * (y2 - y1) + y1
     else:
-        grow = np.exp(curve)
-        a = (y2 - y1) / (1.0 - grow)
-        b = y1 + a
-        z = b - a * grow ** ((x - x1) / (x2 - x1))
+        z = y1 + (y2 - y1) / (1.0 - np.exp(curve)) * (
+            1 - np.exp((curve * (x - x1) / (x2 - x1)))
+        )
 
     if y1 > y2:
         y1, y2 = y2, y1

From 30e7c9da1928132eb315ba1eee0c87beb739b09f Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 14:48:39 +0100
Subject: [PATCH 10/87] add lincurve example

---
 notebooks/pyamapping-examples.ipynb | 71 ++++++++++++++++++++++++++---
 1 file changed, 64 insertions(+), 7 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index f160020..2c8b400 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -278,7 +278,7 @@
     "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
     "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
     "xs.linlin(0, 1, 1, 3).plot(\"r-\", label=\"linlin\")\n",
-    "xs.linlin(0.2, 0.7, -2, 2, \"minmix\").plot(\"g-\", label=\"linlin with clip\")\n",
+    "xs.linlin(0.2, 0.7, -2, 2, \"minmax\").plot(\"g-\", label=\"linlin with clip\")\n",
     "plt.legend(); plt.grid()"
    ]
   },
@@ -389,7 +389,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# example: unmap a frequency to midi note with explin\n",
+    "# example: unmap a frequency to MIDI note with explin\n",
     "f = 220 * 2**(-5/12) # 5 semitones higher than 220 Hz\n",
     "pam.explin(f, 220, 440, 0, 12)\n"
    ]
@@ -440,13 +440,70 @@
     "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
     "plt.plot(xs, ys); "
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31",
+   "metadata": {},
+   "source": [
+    "### `lincurve`\n",
+    "\n",
+    "- lincurve is implemented in analogy to the SC3 function\n",
+    "- `lincurve(v, x1, x2, y1, y2, curve=-2)` maps v (scalar or arraylike) from [x1, x2] to [y1, y2] using the following function (with c=curve): \n",
+    "\n",
+    "$$ y_1 + \\frac{y_2 - y_1}{1.0 - e^c} \\left(1 - \\exp\\left(c \\frac{v - x_1}{x_2 - x_1}\\right) \\right) $$\n",
+    "- in contrast to `explin` (resp. `linexp`) this allows source (resp. target) range to include 0.\n",
+    "- note that this `lincurve` function extrapolates by default\n",
+    "- clipping can be controlled via the clip argument (values None (default), `\"min\"`, `\"max\"`, or anything else for `\"minmax\"`)\n",
+    "- A frequently used invocation is with $x_1 < x_2$, i.e. thinking of them as a range $[x_1, x_2]$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.lincurve uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs.lincurve(0, 1, 0, 0.4, 5).plot(\"r-\", label=\"lincurve\")\n",
+    "xs.lincurve(0.2, 0.5, 1, 0, 2.5, \"minmax\").plot(\"g-\", label=\"lincurve with clip\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34",
+   "metadata": {},
+   "source": [
+    "the following plot shows how the curve parameter influences the mapping function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "35",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 100, 100))\n",
+    "for i, curve in enumerate(range(-9, 10, 3)):\n",
+    "    xs.lincurve(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6); plt.grid();"
+   ]
   }
  ],
- "metadata": {
-  "language_info": {
-   "name": "python"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }

From 5b9306e79d6ab0bb7aeedeb0102f23521269a82c Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 15:34:21 +0100
Subject: [PATCH 11/87] improve curvelin mapping function

---
 src/pyamapping/mappings.py | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index fb6bfd8..b46fd56 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -267,10 +267,8 @@ def curvelin(
     if abs(curve) < 0.001:
         z = (x - x1) / (x2 - x1) * (y2 - y1) + y1
     else:
-        grow = np.exp(curve)
-        a = (x2 - x1) / (1.0 - grow)
-        b = x1 + a
-        z = np.log((b - x) / a) * (y2 - y1) / curve + y1
+        a = (x2 - x1) / (1.0 - np.exp(curve))
+        z = np.log((x1 + a - x) / a) * (y2 - y1) / curve + y1
 
     if y1 > y2:
         y1, y2 = y2, y1
@@ -1202,7 +1200,7 @@ def _list_numpy_ufuncs():
 ]
 
 for fn in pyamapping_functions:
-    register_chain_fn(fn, name)
+    register_chain_fn(fn, None)
 
 
 def chain(input_array: ArrayLike) -> ChainableArray:

From 5f24f5e35d71526be8579b73b4806078024d246d Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 15:35:24 +0100
Subject: [PATCH 12/87] add curvelin() example

---
 notebooks/pyamapping-examples.ipynb | 63 +++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 2c8b400..8087068 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -501,6 +501,69 @@
     "    xs.lincurve(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
     "plt.legend(fontsize=6); plt.grid();"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36",
+   "metadata": {},
+   "source": [
+    "### `curvelin`\n",
+    "\n",
+    "- curvelin is implemented in analogy to the SC3 function\n",
+    "- `curvelin(v, x1, x2, y1, y2, curve=-2)` maps v (scalar or arraylike) from an assumed curve-exponential input range [x1, x2] to a linear output range [y1, y2] using the following function (with c=curve): \n",
+    "$$ f(x) = y_1 + \\frac{y_2 - y_1}{c}\\log\\left(\\frac{a + x_1 - x}{a}\\right)  ~~~\\text{with}~~~ a = \\frac{x_2 - x_1}{1 - e^c}$$\n",
+    "\n",
+    "- This is the opposite transformation to `lincurve`.\n",
+    "- note that this `curvelin` function extrapolates by default.\n",
+    "- clipping can be controlled via the clip argument (values None (default), `\"min\"`, `\"max\"`, or anything else for minmax clipping.\n",
+    "- A frequently used invocation is with $x_1 < x_2$, i.e. thinking of them as a range $[x_1, x_2]$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "37",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.curvelin uses self as input.\n",
+    "- Here are some mapping examples and plots\n",
+    "- The first shows how curvelin unmaps or reverts a lincurve warped interval when using the same curve argument."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "38",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data for lincurve\") # plot input data\n",
+    "curve = 10\n",
+    "ys = xs.lincurve(0, 1, 0, 0.6, curve).plot(\"r-\", label=\"lincurve output\")\n",
+    "xs = ys.curvelin(0, 0.6, 0, 1, curve).plot(\"b-.\", lw=3, alpha=0.5, label=\"curvelin to undo lincurve\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "39",
+   "metadata": {},
+   "source": [
+    "the following plot shows how the curve parameter influences the mapping function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "40",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 100, 500))\n",
+    "for i, curve in enumerate(range(-9, 10, 3)):\n",
+    "    xs.curvelin(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6); plt.grid();"
+   ]
   }
  ],
  "metadata": {},

From 241b14c274e3a548ccd67567bf00c0cadcb70dc8 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 16:18:01 +0100
Subject: [PATCH 13/87] add linpoly() example

---
 notebooks/pyamapping-examples.ipynb | 73 ++++++++++++++++++++++++++++-
 1 file changed, 72 insertions(+), 1 deletion(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 8087068..68f4d62 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -564,9 +564,80 @@
     "    xs.curvelin(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
     "plt.legend(fontsize=6); plt.grid();"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "41",
+   "metadata": {},
+   "source": [
+    "### `linpoly`\n",
+    "\n",
+    "- linpoly has no corresponding SC3 function, it provides a polynomial mapping\n",
+    "- `linpoly(v, xmax, y1, y2, curve=2, clip)` maps v (scalar or arraylike) from an assumed linear input range [-xmax, xmax] to an output range [y1, y2] using the following polynomial mapping function, using a polynomial order m\n",
+    "\n",
+    "$$ m = \\left\\{\\begin{align*} 1 + \\text{curve}         & ~~~\\text{if} & \\text{curve} \\ge 0\\\\\n",
+    "                     \\frac{1}{1-\\text{curve}} & ~~~\\text{else} & \n",
+    "        \\end{align*} \\right.\n",
+    "$$\n",
+    "using the mapping function\n",
+    "$$ f(x) = y_1 + \\frac{y_2 - y_1}{2} \\cdot \\left(1 + \\text{sign}(x) \\left|\\frac{x}{x_{\\max}}\\right|^m\\right)$$\n",
+    "\n",
+    "- note that np.sign is used\n",
+    "- note that this `linpoly` function extrapolates by default.\n",
+    "- clipping can be controlled via the clip argument (values: None as default, `\"min\"`, `\"max\"`, or anything else for minmax clipping.)\n",
+    "- It can be used to provide a sensitivity magnification (or reduction) around 0, the center of the input interval."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "42",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.linpoly uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "43",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(-3, 3, 200)) # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data for linpoly\") # plot input data\n",
+    "xs.linpoly(3, 0, 20, curve=1).plot(\"r-\", label=\"linpoly output\")\n",
+    "xs.linpoly(3, 0, 20, curve=-1).plot(\"b-\", label=\"linpoly output\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44",
+   "metadata": {},
+   "source": [
+    "the following plot shows how the curve parameter influences the mapping function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "45",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(-1, 1, 200))\n",
+    "for i, curve in enumerate(range(-3, 3, 1)):\n",
+    "    xs.linpoly(1, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6); plt.grid();"
+   ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }

From 59aa1fce96bca167b640215de19d38f43139b124 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 16:38:09 +0100
Subject: [PATCH 14/87] improve structure and explanations

---
 notebooks/pyamapping-examples.ipynb | 29 +++++++++++++++++++----------
 1 file changed, 19 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 68f4d62..58c7734 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -221,7 +221,9 @@
    "source": [
     "## Tour of Mapping Functions: Functions from SuperCollider3 and librosa\n",
     "\n",
-    "For the following functions, we use `xs` to refer to the input array and `ys` for the outputs."
+    "- The following function have been implemented in analogy to their versions in Supercollider3 resp. librosa.\n",
+    "- Please note that some defaults may be different, e.g. functions extrapolate by default\n",
+    "- For the following demonstrations, we use `xs` to refer to the input array and `ys` for the outputs."
    ]
   },
   {
@@ -569,6 +571,17 @@
    "cell_type": "markdown",
    "id": "41",
    "metadata": {},
+   "source": [
+    "## Tour of Mapping Functions: additional/novel mapping functions\n",
+    "\n",
+    "- The following function are new additions (i.e. there is no counterpart in Supercollider3 resp. librosa).\n",
+    "- For the following demonstrations, we use `xs` to refer to the input array and `ys` for the outputs."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "42",
+   "metadata": {},
    "source": [
     "### `linpoly`\n",
     "\n",
@@ -590,7 +603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42",
+   "id": "43",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -600,7 +613,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "43",
+   "id": "44",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -613,7 +626,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44",
+   "id": "45",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -622,7 +635,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "45",
+   "id": "46",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -633,11 +646,7 @@
    ]
   }
  ],
- "metadata": {
-  "language_info": {
-   "name": "python"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }

From a433b15f0e7e24812bd7398f5215cee2a2ad3802 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 17:13:54 +0100
Subject: [PATCH 15/87] forward kwargs for interp_spline()

---
 src/pyamapping/mappings.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index b46fd56..2250773 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -399,6 +399,7 @@ def bilin(
     ycenter: float = 0,
     ymin: float = -1,
     ymax: float = 1,
+    **kwargs,
 ) -> Union[float, np.ndarray]:
     """Bilin compatibility function. implements sc3 bilin function.
 
@@ -419,7 +420,7 @@ def bilin(
     Union[float, np.ndarray],
         the mapping result
     """
-    return interp_spline(x, [xmin, xcenter, xmax], [ymin, ycenter, ymax])
+    return interp_spline(x, [xmin, xcenter, xmax], [ymin, ycenter, ymax], **kwargs)
 
 
 def clip(

From 02cbbcb79b2c3c17c1bb2bdc5b62bd3a2a1d2dc2 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 17:17:56 +0100
Subject: [PATCH 16/87] add bilin() example

---
 notebooks/pyamapping-examples.ipynb | 58 ++++++++++++++++++++++++++---
 1 file changed, 52 insertions(+), 6 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 58c7734..10d7642 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -571,6 +571,48 @@
    "cell_type": "markdown",
    "id": "41",
    "metadata": {},
+   "source": [
+    "### `bilin`\n",
+    "\n",
+    "- bilin is implemented similar to the SC3 function, yet with an API change:\n",
+    "- `bilin(v, xcenter, xmin, xmax, ycenter, ymin, ymax)` maps v (scalar or arraylike) \n",
+    "  according to two linear segments:\n",
+    "  - [xmin, xcenter] to [ymin, ycenter] with default extrapolation beyond xmin\n",
+    "  - [xcenter, xmax] to [ycenter, ymax] with default extrapolation beyond xmax\n",
+    "- this mapping is achieved using `pyamapping.interp_spline()`.\n",
+    "- kwargs are passed on to `interp_spline()` if needed.\n",
+    "- in case, no extrapolation is wanted, pyampapping.interp() offers an alternative\n",
+    "  with a different interface."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "42",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.bilin uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "43",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 100)) # turn data into ChainableArray\n",
+    "xs.bilin(60, 20, 80, 0, -20, 60).plot(\"b.\", ms=1, label='bilin');\n",
+    "for (x, y, t) in [[20, -20, \"(xmin, ymin)\"], [80, 60, \"(xmax, ymax)\"], [60, 0, \"(xcenter, ycenter)\"]]:\n",
+    "    plt.plot([x], [y], \"ro\")\n",
+    "    plt.text(x+1, y-5, t, fontsize=6)\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -580,7 +622,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42",
+   "id": "45",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -603,7 +645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43",
+   "id": "46",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -613,7 +655,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "44",
+   "id": "47",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -626,7 +668,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45",
+   "id": "48",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -635,7 +677,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46",
+   "id": "49",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -646,7 +688,11 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }

From 9592b2d60836f47e605e5fe92727393f3936c6cb Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 17:43:24 +0100
Subject: [PATCH 17/87] add interp_spline() example

---
 notebooks/pyamapping-examples.ipynb | 39 +++++++++++++++++++++++++----
 1 file changed, 34 insertions(+), 5 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 10d7642..28f6409 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -686,13 +686,42 @@
     "    xs.linpoly(1, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
     "plt.legend(fontsize=6); plt.grid();"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50",
+   "metadata": {},
+   "source": [
+    "### `interp_spline`\n",
+    "\n",
+    "- interp_spline provides an interface to  `scipy.interpolate.make_interp_spline` for line segment interpolation.\n",
+    "- `interp_spline(v, xc, yc, k)` maps v (scalar or arraylike) along the spline \n",
+    "  - defined by the input coordinates in array xc \n",
+    "  - and corresponding output coordinates in yc\n",
+    "  - using interpolation order k (default 1=linear)\n",
+    "- note that interp_spline extrapolation beyond segments.\n",
+    "- interp_spline is called from `bilin()`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "51",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 8.2, 1000)) # turn data into ChainableArray\n",
+    "xc = [1, 2, 5, 7, 8]\n",
+    "yc = [3, 1, 2, 9, 1]\n",
+    "plt.plot(xc, yc, \"ro\", label=\"given points\")\n",
+    "for k in [0, 1, 2]:\n",
+    "    ys = xs.interp_spline(xc, yc, k=k)\n",
+    "    plt.plot(xs,ys, label=f\"spline with k={k}\")\n",
+    "plt.legend(fontsize=7); plt.grid()"
+   ]
   }
  ],
- "metadata": {
-  "language_info": {
-   "name": "python"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }

From 19d394255ad3510543466502e07766ca8d89844b Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 30 Oct 2025 18:01:26 +0100
Subject: [PATCH 18/87] add interp() example

---
 notebooks/pyamapping-examples.ipynb | 46 +++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 28f6409..af0ffe4 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -719,6 +719,52 @@
     "    plt.plot(xs,ys, label=f\"spline with k={k}\")\n",
     "plt.legend(fontsize=7); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "52",
+   "metadata": {},
+   "source": [
+    "### `interp`\n",
+    "\n",
+    "- interp provides an interface to  `np.interp` for line segment interpolation.\n",
+    "- `interp(v, xc, yc)` maps v (scalar or arraylike) along the sample points \n",
+    "  - defined by the input coordinates in array xc (monotonically increasing)\n",
+    "  - and corresponding output coordinates in yc\n",
+    "- note that interp clips beyond xc limits.\n",
+    "- interp can be used as alternative to bilin in case clipped output is needed.\n",
+    "  - some may prefer the more tidy API with x and y values in their arrays."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "53",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 8.2, 1000)) # turn data into ChainableArray\n",
+    "xc = [1, 2, 5, 7, 8]\n",
+    "yc = [7, 1, 2, 9, 1]\n",
+    "plt.plot(xc, yc, \"ro\", ms=3, label=\"given points\")\n",
+    "ys = xs.interp(xc, yc)\n",
+    "plt.plot(xs, ys, \"b,\", label=f\"interp\")\n",
+    "plt.legend(fontsize=7); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "54",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-100, 150)) # turn data into ChainableArray\n",
+    "# use interp if clipping is wanted (faster for small datasets)\n",
+    "xs.interp([-50, 50, 100],[0, 0.4, 1]).plot(\"r-.\", label=\"interp with clipping\"); \n",
+    "xs.bilin(50, -50, 100, 0.4, 0, 1).plot(\"b:\", label='bilin with extrapolation');\n",
+    "plt.legend();plt.grid();"
+   ]
   }
  ],
  "metadata": {},

From 1d058a28bab60e06ba911b44e9dd678634d18e98 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 17:34:49 +0100
Subject: [PATCH 19/87] add clip() example

---
 notebooks/pyamapping-examples.ipynb | 66 ++++++++++++++++++++++++-----
 1 file changed, 56 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index af0ffe4..66c94a3 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -613,6 +613,52 @@
    "cell_type": "markdown",
    "id": "44",
    "metadata": {},
+   "source": [
+    "### `clip`\n",
+    "\n",
+    "- clip is implemented in analogy to the SC3 clip\n",
+    "- `clip(value, minimum, maximum)` clips value (scalar or arraylike) to a certain range [minimum, maximum]\n",
+    "- default values for minium and maximum are so that no clipping occurs, i.e. specifying only minimum or maximum allows one-sided clipping."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "45",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.clip uses self as input.\n",
+    "- Here are some mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "46",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
+    "xs.plot(\"k:\", label=\"input data\") # plot input data\n",
+    "xs.clip(0.2, 0.7).plot(\"r-\", label=\"linlin with clip\")\n",
+    "plt.legend(); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "47",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# plot mapping function (output vs input)\n",
+    "ys = xs.clip(0.25, 0.75)\n",
+    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys, label=''); plt.grid(); "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -622,7 +668,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45",
+   "id": "49",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -645,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46",
+   "id": "50",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -655,7 +701,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47",
+   "id": "51",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -668,7 +714,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48",
+   "id": "52",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -677,7 +723,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49",
+   "id": "53",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -689,7 +735,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50",
+   "id": "54",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -706,7 +752,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "51",
+   "id": "55",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -722,7 +768,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52",
+   "id": "56",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -739,7 +785,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53",
+   "id": "57",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -755,7 +801,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "54",
+   "id": "58",
    "metadata": {},
    "outputs": [],
    "source": [

From ccb5286dcb4bafaa6f27154ea70ae982730e0b61 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 17:55:34 +0100
Subject: [PATCH 20/87] add method shortcuts for midicps and cpsmidi

---
 src/pyamapping/mappings.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 2250773..4691272 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1203,6 +1203,9 @@ def _list_numpy_ufuncs():
 for fn in pyamapping_functions:
     register_chain_fn(fn, None)
 
+register_chain_fn(cpsmidi, "cpsmidi")
+register_chain_fn(midicps, "midicps")
+
 
 def chain(input_array: ArrayLike) -> ChainableArray:
     """Turn np.ndarray into ChainableArray."""

From 131c5c38e732bf892a4e969f634ffa9901f33d6e Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 17:56:34 +0100
Subject: [PATCH 21/87] add example for midi_to_cps()

---
 notebooks/pyamapping-examples.ipynb | 77 +++++++++++++++++++++++++----
 1 file changed, 67 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 66c94a3..c33d339 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -659,6 +659,63 @@
    "cell_type": "markdown",
    "id": "48",
    "metadata": {},
+   "source": [
+    "### `midi_to_cps`\n",
+    "\n",
+    "- midi_to_cps is implemented in analogy to the SC3 midicps function\n",
+    "- the shorter (less pythonic name) midicps can be used as well\n",
+    "- `midi_to_cps(midi_note)` converts MIDI note midi_note (value or arraylike) to cycles per second (aka Hz).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 440\\cdot 2^{\\frac{x-69}{12}} $$\n",
+    "  which obviously maps MIDI 69 to 440 Hz, the reference for definition. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "49",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.midi_to_cps(69+12) # should be 880, i.e. one octave above MIDI 69"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "50",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(np.arange(60, 74, 2)).midicps().round(1) # rounded frequencies of full tone scale ('c-d-e-f#-g#-a#-c')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "51",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.midi_to_cps uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "52",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(21, 109)) # the standard MIDI range\n",
+    "xs.plot(\"k-\", label=\"input data (MIDI notes)\") # plot input data\n",
+    "xs.midi_to_cps().plot(\"r-\", label=\"midi_to_cps result [in Hz]\")\n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -668,7 +725,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49",
+   "id": "54",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -691,7 +748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50",
+   "id": "55",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -701,7 +758,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "51",
+   "id": "56",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -714,7 +771,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52",
+   "id": "57",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -723,7 +780,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53",
+   "id": "58",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -735,7 +792,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54",
+   "id": "59",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -752,7 +809,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55",
+   "id": "60",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -768,7 +825,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56",
+   "id": "61",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -785,7 +842,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57",
+   "id": "62",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -801,7 +858,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58",
+   "id": "63",
    "metadata": {},
    "outputs": [],
    "source": [

From 43fb2242e579d586d1b8c19c7fe0a65377963c13 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 18:10:15 +0100
Subject: [PATCH 22/87] add example for cps_to_midi()

---
 notebooks/pyamapping-examples.ipynb | 79 +++++++++++++++++++++++++----
 1 file changed, 69 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index c33d339..2891fd7 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -716,6 +716,65 @@
    "cell_type": "markdown",
    "id": "53",
    "metadata": {},
+   "source": [
+    "### `cps_to_midi`\n",
+    "\n",
+    "- cps_to_midi is implemented in analogy to the SC3 cpsmidi function\n",
+    "- the shorter (less pythonic name) cpsmidi can be used as well\n",
+    "- `cps_to_midi(cps)` converts a frequency cps in Hz (value or arraylike) to a MIDI note (in float, resp. Arraylike of float).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 69 + 12 \\log_2\\left(\\frac{x}{440}\\right) $$\n",
+    "  which obviously maps 440 Hz to MIDI 69, the reference by definition. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "54",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.cps_to_midi(440*2) # should be 81=69+12"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "55",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain([110, 220, 330, 440, 550, 660, 770, 880]).cpsmidi().round(2) # rounded MIDI notes for the harmonics series over low A"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "56",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.midi_to_cps uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "57",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(100, 1000, 100)) # frequencies with 50 Hz spacing\n",
+    "ys = xs.cps_to_midi() \n",
+    "\n",
+    "plt.plot(xs, ys, \"o-\", label=\"MIDI note for harmonics series\"); \n",
+    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"MIDI note\"); \n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "58",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -725,7 +784,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54",
+   "id": "59",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -748,7 +807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55",
+   "id": "60",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -758,7 +817,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56",
+   "id": "61",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -771,7 +830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57",
+   "id": "62",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -780,7 +839,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58",
+   "id": "63",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -792,7 +851,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59",
+   "id": "64",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -809,7 +868,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "60",
+   "id": "65",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -825,7 +884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61",
+   "id": "66",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -842,7 +901,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62",
+   "id": "67",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -858,7 +917,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63",
+   "id": "68",
    "metadata": {},
    "outputs": [],
    "source": [

From 178edbdd7bca1727b3398784f1721d7bf77c6605 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 22:16:20 +0100
Subject: [PATCH 23/87] add chain fn shortcuts midiratio and ratiomidi

---
 src/pyamapping/mappings.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 4691272..4fc02de 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1205,6 +1205,8 @@ def _list_numpy_ufuncs():
 
 register_chain_fn(cpsmidi, "cpsmidi")
 register_chain_fn(midicps, "midicps")
+register_chain_fn(ratiomidi, "ratiomidi")
+register_chain_fn(midiratio, "midiratio")
 
 
 def chain(input_array: ArrayLike) -> ChainableArray:

From f57e2c6a7e937e1942c75922fa1d4401af63db4e Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 22:18:22 +0100
Subject: [PATCH 24/87] add midi_to_ratio() example

---
 notebooks/pyamapping-examples.ipynb | 80 +++++++++++++++++++++++++----
 1 file changed, 69 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 2891fd7..76f3b7b 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -687,7 +687,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(60, 74, 2)).midicps().round(1) # rounded frequencies of full tone scale ('c-d-e-f#-g#-a#-c')"
+    "chain(np.arange(60, 74, 2)).midicps().round(1) # rounded frequencies of whole-tone scale ('c-d-e-f#-g#-a#-c')"
    ]
   },
   {
@@ -775,6 +775,64 @@
    "cell_type": "markdown",
    "id": "58",
    "metadata": {},
+   "source": [
+    "### `midi_to_ratio`\n",
+    "\n",
+    "- midi_to_ratio is implemented in analogy to the SC3 midiratio function\n",
+    "- the shorter (less pythonic name) midiratio can be used as well\n",
+    "- `midi_to_ratio(midi_note)` converts MIDI note difference midi_note (value or arraylike) to the ratio of their corresponding frequencies.\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 2^{(x/\\tiny 12)} $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "59",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.midi_to_ratio(7) # a fifth is ~3/2 (in equal tuning)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "60",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(np.arange(0, 12, 2)).midi_to_ratio().round(2) # ratio of tones in the whole-tone scale ('c-d-e-f#-g#-a#-c')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.midi_to_cps uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "62",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-12, 13)) # one octave around any note\n",
+    "ys = xs.midi_to_ratio()\n",
+    "\n",
+    "plt.plot(xs, ys, \"r-\", label=\"midi_to_ratio result\")\n",
+    "plt.plot(0, 1, \"ro\", label=\"midi_ratio of 0\")\n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "63",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -784,7 +842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59",
+   "id": "64",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -807,7 +865,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60",
+   "id": "65",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -817,7 +875,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "61",
+   "id": "66",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -830,7 +888,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62",
+   "id": "67",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -839,7 +897,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63",
+   "id": "68",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -851,7 +909,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64",
+   "id": "69",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -868,7 +926,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65",
+   "id": "70",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -884,7 +942,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66",
+   "id": "71",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -901,7 +959,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67",
+   "id": "72",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -917,7 +975,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68",
+   "id": "73",
    "metadata": {},
    "outputs": [],
    "source": [

From e8677efcb394e4e4eb0325b78f90f2341d9e58c9 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 22:26:26 +0100
Subject: [PATCH 25/87] add ratio_to_midi() example

---
 notebooks/pyamapping-examples.ipynb | 80 +++++++++++++++++++++++++----
 1 file changed, 69 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 76f3b7b..e51c681 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -752,7 +752,7 @@
    "id": "56",
    "metadata": {},
    "source": [
-    "- ChainableArray.midi_to_cps uses self as input.\n",
+    "- ChainableArray.cps_to_midi uses self as input.\n",
     "- Here a mapping examples and plots"
    ]
   },
@@ -833,6 +833,64 @@
    "cell_type": "markdown",
    "id": "63",
    "metadata": {},
+   "source": [
+    "### `ratio_to_midi`\n",
+    "\n",
+    "- radio_to_midi is implemented in analogy to the SC3 ratiomidi function\n",
+    "- the shorter (less pythonic name) ratiomidi can be used as well\n",
+    "- `ratio_to_midi(ratio)` converts a frequency ratio (value or arraylike) to a MIDI note difference (in float, resp. Arraylike of float).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 12 \\log_2(x) $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "64",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.ratio_to_midi(2) # should be 12 for ratio=2 (i.e. an octave)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "65",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(np.arange(1, 10)).ratio_to_midi().round(2) # rounded MIDI offsets for the harmonics series"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "66",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.ratio_to_midi uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "67",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(1, 10)) # integer frequency ratios / harmonics\n",
+    "ys = xs.ratio_to_midi()  # likewise ratiomidi()\n",
+    "\n",
+    "plt.plot(xs, ys, \"o-\", label=\"MIDI offsets for harmonics series\"); \n",
+    "plt.xlabel(\"ratio to fundamental frequency\"); plt.ylabel(\"MIDI offset\"); \n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "68",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -842,7 +900,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64",
+   "id": "69",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -865,7 +923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65",
+   "id": "70",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -875,7 +933,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "66",
+   "id": "71",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -888,7 +946,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67",
+   "id": "72",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -897,7 +955,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68",
+   "id": "73",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -909,7 +967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69",
+   "id": "74",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -926,7 +984,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70",
+   "id": "75",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -942,7 +1000,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71",
+   "id": "76",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -959,7 +1017,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "72",
+   "id": "77",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -975,7 +1033,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "73",
+   "id": "78",
    "metadata": {},
    "outputs": [],
    "source": [

From 9461c7e7a6398fe593290eea84d0cf92905436dd Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 22:48:41 +0100
Subject: [PATCH 26/87] register chain fn for cpsoct and octcps

---
 src/pyamapping/mappings.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 4fc02de..2e2bf99 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1207,6 +1207,8 @@ def _list_numpy_ufuncs():
 register_chain_fn(midicps, "midicps")
 register_chain_fn(ratiomidi, "ratiomidi")
 register_chain_fn(midiratio, "midiratio")
+register_chain_fn(cpsoct, "cpsoct")
+register_chain_fn(octcps, "octcps")
 
 
 def chain(input_array: ArrayLike) -> ChainableArray:

From 348504b1ba723f748c0074c36ef4ad620d95615d Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 22:49:46 +0100
Subject: [PATCH 27/87] add octave_to_cps() and cps_to_octave() examples

---
 notebooks/pyamapping-examples.ipynb | 134 +++++++++++++++++++++++++---
 1 file changed, 124 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index e51c681..00b2996 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -891,6 +891,120 @@
    "cell_type": "markdown",
    "id": "68",
    "metadata": {},
+   "source": [
+    "### `octave_to_cps`\n",
+    "\n",
+    "- octave_to_cps is implemented in analogy to the SC3 octcps function\n",
+    "- the shorter (less pythonic name) octcps can be used as well\n",
+    "- `octave_to_cps(octave)` converts octaves (value or arraylike) to cycles per second (aka Hz).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 440\\cdot 2^{(x - 4.75)} $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "69",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.octave_to_cps(3.75) # one octave below 440"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "70",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(np.arange(2, 9)).octcps().round(1) # rounded frequencies of c-tones"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "71",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.octave_to_cps uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "72",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 8, 1/4)) # 8 octaves in minor thirds (3 semitone steps)\n",
+    "ys = xs.octave_to_cps()\n",
+    "plt.plot(xs, ys, \"ro-\", ms=2,label=\"octave_to_cps result [in Hz]\")\n",
+    "plt.legend(); plt.grid(); plt.semilogy()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "73",
+   "metadata": {},
+   "source": [
+    "### `cps_to_octave`\n",
+    "\n",
+    "- cps_to_octave is implemented in analogy to the SC3 cpsoct function\n",
+    "- the shorter (less pythonic name) cpsoct can be used as well\n",
+    "- `cps_to_oct(cps)` converts a frequency cps in Hz (value or arraylike) to an octave value (in float, resp. Arraylike of float).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 4.75 + \\log_2\\left(\\frac{x}{440}\\right) $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "74",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.cps_to_octave(440*2) # one octave above reference"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "75",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(pam.midicps(12) * np.arange(1, 10)).cpsoct().round(2) # harmonics series over low C in octaves"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.cps_to_octave uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "77",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(100, 1000, 100)) # frequencies with 50 Hz spacing\n",
+    "ys = xs.cps_to_octave() \n",
+    "\n",
+    "plt.plot(xs, ys, \"o-\", label=\"octaves for harmonics series\"); \n",
+    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"octave\"); \n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -900,7 +1014,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69",
+   "id": "79",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -923,7 +1037,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70",
+   "id": "80",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -933,7 +1047,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "71",
+   "id": "81",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -946,7 +1060,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72",
+   "id": "82",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -955,7 +1069,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "73",
+   "id": "83",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -967,7 +1081,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74",
+   "id": "84",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -984,7 +1098,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "75",
+   "id": "85",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1000,7 +1114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76",
+   "id": "86",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1017,7 +1131,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "77",
+   "id": "87",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1033,7 +1147,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "78",
+   "id": "88",
    "metadata": {},
    "outputs": [],
    "source": [

From 499ef14755c57bffd30b698c7762e2039599c24a Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 23:07:44 +0100
Subject: [PATCH 28/87] register chain fn for ampdb and dbamp

---
 src/pyamapping/mappings.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 2e2bf99..f868ba1 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1209,6 +1209,8 @@ def _list_numpy_ufuncs():
 register_chain_fn(midiratio, "midiratio")
 register_chain_fn(cpsoct, "cpsoct")
 register_chain_fn(octcps, "octcps")
+register_chain_fn(ampdb, "ampdb")
+register_chain_fn(dbamp, "dbamp")
 
 
 def chain(input_array: ArrayLike) -> ChainableArray:

From de86068d0ea1c448825a7363119c656404026592 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Fri, 31 Oct 2025 23:08:13 +0100
Subject: [PATCH 29/87] add db_to_amp() and amp_to_db() examples

---
 notebooks/pyamapping-examples.ipynb | 123 +++++++++++++++++++++++++---
 1 file changed, 113 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 00b2996..58c614e 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1005,6 +1005,109 @@
    "cell_type": "markdown",
    "id": "78",
    "metadata": {},
+   "source": [
+    "### `db_to_amp`\n",
+    "\n",
+    "- db_to_amp is implemented in analogy to the SC3 dbamp function\n",
+    "- the shorter (less pythonic name) dbamp can be used as well\n",
+    "- `db_to_amp(decibels)` converts decibels (value or arraylike) to amplitudes.\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 10^{(x/20)}$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "79",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.db_to_amp(np.array([-6, -12, -20]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "80",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.db_to_amp uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "81",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-60, 0, 6)) # some 6 dB steps\n",
+    "ys = xs.dbamp()\n",
+    "plt.plot(xs, ys, \"ro-\", ms=2,label=\"db_to_amp result [arb. unit]\")\n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "82",
+   "metadata": {},
+   "source": [
+    "### `amp_to_db`\n",
+    "\n",
+    "- amp_to_db is implemented in analogy to the SC3 ampdb function\n",
+    "- the shorter (less pythonic name) ampdb can be used as well\n",
+    "- `amp_to_db(amp)` converts amplitude(s) amp (in arb. units) (value or arraylike) to decibel values (in float, resp. Arraylike of float).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 20 * \\log_{10}(x) $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "83",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.amp_to_db(0.01) # 10^(-2) will be 10^(-4) for energy, aka -40 dB"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "84",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chain(np.arange(0.1, 1, 0.1)).ampdb().round(2) # harmonics series over low C in octaves"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "85",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.amp_to_db uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "86",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0.1, 2.1, 0.1)) # ampltitudes from 0.1 to 2.0\n",
+    "ys = xs.ampdb() # likewise amp_to_db()\n",
+    "plt.plot(xs, ys, \"o-\", label=\"decibel\"); \n",
+    "plt.xlabel(\"amplitudes\"); plt.ylabel(\"dB\"); \n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1014,7 +1117,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79",
+   "id": "88",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1037,7 +1140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80",
+   "id": "89",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1047,7 +1150,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "81",
+   "id": "90",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1060,7 +1163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82",
+   "id": "91",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1069,7 +1172,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83",
+   "id": "92",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1081,7 +1184,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "84",
+   "id": "93",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1098,7 +1201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "85",
+   "id": "94",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1114,7 +1217,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86",
+   "id": "95",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1131,7 +1234,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "87",
+   "id": "96",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1147,7 +1250,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "88",
+   "id": "97",
    "metadata": {},
    "outputs": [],
    "source": [

From 959efcbc2372768474376b8bc9f908f4c223b30f Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 11:06:28 +0100
Subject: [PATCH 30/87] update hz_to_mel(), mel_to_hz() docstring

---
 src/pyamapping/mappings.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index f868ba1..75261c8 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -578,28 +578,28 @@ def hz_to_mel(hz):
     Parameters
     ----------
     hz : number of array
-        value in Hz, can be an array
+        frequencies in Hz, can be an array
 
     Returns
     -------
     _ : number of array
-        value in Mels, same type as the input.
+        mel scale value, same type as the input.
     """
     return 2595 * np.log10(1 + hz / 700.0)
 
 
 def mel_to_hz(mel):
-    """Convert a value in Hertz to Mels.
+    """Convert a frequency in Hz to mel using .
 
     Parameters
     ----------
-    hz : number of array
-        value in Hz, can be an array
+    mel : number of array
+        melody value
 
     Returns
     -------
     _ : number of array
-        value in Mels, same type as the input.
+        cps in Hz, same type as the input.
     """
     return 700 * (10 ** (mel / 2595.0) - 1)
 

From 7af357043872496043e5711e122f6985d9402255 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 11:07:46 +0100
Subject: [PATCH 31/87] add mel_to_hz() and hz_to_mel() examples

---
 notebooks/pyamapping-examples.ipynb | 127 +++++++++++++++++++++++++---
 1 file changed, 116 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 58c614e..857ad1b 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1105,9 +1105,114 @@
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "87",
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "import librosa\n",
+    "help(librosa.mel_to_hz)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "88",
+   "metadata": {},
+   "source": [
+    "### `mel_to_hz`\n",
+    "\n",
+    "- mel_to_hz is implemented in analogy to its librosa counterpart, but instaed of Slanays formula using the formula from O'Shaughnessy (1987) (available in librosa via argument htk=True)\n",
+    "- `mel_to_hz(mel)` converts mel (value or arraylike) to cycles per second (aka Hz). 1000 mel roughly matches 1000 Hz.\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 700 \\cdot (10^{\\frac{x}{2595}} - 1) $$\n",
+    "- ToDo: alternative methods could be added via a method argument, e.g. 'htk' (default), 'slaney', ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "89",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.mel_to_hz(1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.mel_to_hz uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "91",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 2500, 100)) \n",
+    "ys = xs.mel_to_hz()\n",
+    "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz\")\n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "92",
+   "metadata": {},
+   "source": [
+    "### `hz_to_mel`\n",
+    "\n",
+    "- hz_to_mel is implemented in analogy to its librosa counterpart, assuming the htk=True flag, i.e. using the formula from O'Shaughnessy (1987).\n",
+    "- `hz_to_mel(hz)` converts a frequency in Hz (value or arraylike) to a mel scale value (in float, resp. Arraylike of float).\n",
+    "- The mapping function is\n",
+    "    $$ f(x) = 2595 \\cdot \\log_{10}\\left(1 + \\frac{x}{700}\\right) $$\n",
+    "- ToDo: alternative methods could be added via a method argument, e.g. 'htk' (default), 'slaney', ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "93",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.hz_to_mel(1000) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.hz_to_mel uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "95",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(21, 108, 7)).midicps() # frequencies of fifth series\n",
+    "ys = xs.hz_to_mel() \n",
+    "plt.plot(xs, ys, \"o-\", label=\"mel values for frequencies\"); \n",
+    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"mel scale\"); \n",
+    "plt.legend(); plt.grid(); plt.loglog()\n",
+    "plt.plot([1000], [1000], \"ro-\", label=\"a reference point\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "96",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1117,7 +1222,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88",
+   "id": "97",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1140,7 +1245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89",
+   "id": "98",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1150,7 +1255,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "90",
+   "id": "99",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1163,7 +1268,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91",
+   "id": "100",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1172,7 +1277,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "92",
+   "id": "101",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1184,7 +1289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93",
+   "id": "102",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1201,7 +1306,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94",
+   "id": "103",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1217,7 +1322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "95",
+   "id": "104",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1234,7 +1339,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96",
+   "id": "105",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1250,7 +1355,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "97",
+   "id": "106",
    "metadata": {},
    "outputs": [],
    "source": [

From 7493c86f275aa0a64e56d7a70d354f7e0bb1e19f Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 17:28:23 +0100
Subject: [PATCH 32/87] add Slaney mel scale to mel_to_hz() and hz_to_mel()

---
 src/pyamapping/mappings.py | 37 +++++++++++++++++++++++++++++++------
 1 file changed, 31 insertions(+), 6 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 75261c8..c18725e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -572,36 +572,61 @@ def octave_to_cps(octave: float) -> float:
 octcps = octave_to_cps
 
 
-def hz_to_mel(hz):
-    """Convert a value in Hertz to Mels.
+def hz_to_mel(hz, htk=False):
+    """Convert frequencies [Hz] to mel scale.
 
     Parameters
     ----------
     hz : number of array
         frequencies in Hz, can be an array
 
+    htk: bool
+        flag: if True use O'Shaughnessy (1987) formula
+              if False use Slaney's matlab formula
+
     Returns
     -------
     _ : number of array
         mel scale value, same type as the input.
     """
-    return 2595 * np.log10(1 + hz / 700.0)
+    if htk:
+        return 2595 * np.log10(1 + hz / 700.0)
+    else:
+        hz = np.asanyarray(hz)  # supports both scalars and arrays
+        mel = np.where(
+            hz < 1000,  # point between linear and log scale
+            3.0 * hz / 200,  # linear law
+            15 + 27 * np.log(hz / 1000) / np.log(6.4),  # log law
+        )
+        return mel if mel.ndim > 0 else float(mel)
 
 
-def mel_to_hz(mel):
-    """Convert a frequency in Hz to mel using .
+def mel_to_hz(mel, htk=False):
+    """Convert mel from mel scale to frequency [Hz].
 
     Parameters
     ----------
     mel : number of array
         melody value
+    htk: bool
+        flag: if True use O'Shaughnessy (1987) formula
+              if False use Slaney's matlab formula
 
     Returns
     -------
     _ : number of array
         cps in Hz, same type as the input.
     """
-    return 700 * (10 ** (mel / 2595.0) - 1)
+    if htk:
+        return 700 * (10 ** (mel / 2595.0) - 1)
+    else:
+        mel = np.asanyarray(mel)
+        hz = np.where(
+            mel < 15,  # border between lin/exp regime
+            (200.0 / 3) * mel,  # linear regime
+            1000 * (6.4 ** ((mel - 15) / 27)),
+        )  # exp. regime
+        return hz if hz.ndim > 0 else float(hz)
 
 
 def db_to_amp(decibels: float) -> float:

From db1a25e8c4d223193239c43c6aca70d41adbdeae Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 17:29:21 +0100
Subject: [PATCH 33/87] improve mel_to_hz and hz_to_mel examples

---
 notebooks/pyamapping-examples.ipynb | 99 +++++++++++++++++++----------
 1 file changed, 67 insertions(+), 32 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 857ad1b..5bf0889 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1122,11 +1122,17 @@
    "source": [
     "### `mel_to_hz`\n",
     "\n",
-    "- mel_to_hz is implemented in analogy to its librosa counterpart, but instaed of Slanays formula using the formula from O'Shaughnessy (1987) (available in librosa via argument htk=True)\n",
-    "- `mel_to_hz(mel)` converts mel (value or arraylike) to cycles per second (aka Hz). 1000 mel roughly matches 1000 Hz.\n",
-    "- The mapping function is\n",
-    "    $$ f(x) = 700 \\cdot (10^{\\frac{x}{2595}} - 1) $$\n",
-    "- ToDo: alternative methods could be added via a method argument, e.g. 'htk' (default), 'slaney', ..."
+    "- mel_to_hz is implemented in analogy to its librosa counterpart, i.e. using Slanay's formula with a linear and logarithmic part by default, and alternatively the formula from O'Shaughnessy (1987) via the argument `htk=True`.\n",
+    "- `mel_to_hz(mel)` converts mel (value or arraylike) to cycles per second (aka Hz). \n",
+    "- For the default (Slaney) the mapping function is\n",
+    "  - linear part (for $mel<15$): \n",
+    "    $$ f(\\text{mel}) = \\frac{200}{3} \\cdot\\text{mel}$$\n",
+    "  - exponential part (for $\\text{mel}>15$):\n",
+    "    $$ f(\\text{mel}) = 1000 \\cdot 6.4 ^{(\\frac{mel - 15}{27})}$$\n",
+    "  - Note that this mel scale has another range: 15 mel = 1000 Hz, and ~10kHz is obtained for mel = 48.5.\n",
+    "- if `htk==True`, the mapping function is the O'Shaughnessy (1987) formula\n",
+    "    $$ f(\\text{mel}) = 700 \\cdot (10^{\\frac{\\text{mel}}{2595}} - 1) $$\n",
+    "- Note that here 1000 mel roughly matches 1000 Hz.\n"
    ]
   },
   {
@@ -1136,13 +1142,23 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.mel_to_hz(1000)"
+    "pam.mel_to_hz(1000, htk=True) # using the O'Shaughnessy (1987) formula"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "90",
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.mel_to_hz(15) # using the Slaney formula"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "91",
+   "metadata": {},
    "source": [
     "- ChainableArray.mel_to_hz uses self as input.\n",
     "- Here a mapping examples and plots"
@@ -1151,43 +1167,62 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "91",
+   "id": "92",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(0, 2500, 100)) \n",
-    "ys = xs.mel_to_hz()\n",
-    "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz\")\n",
+    "ys = xs.mel_to_hz(htk=True)\n",
+    "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz (O'Shaughnessy)\")\n",
+    "plt.legend(); plt.grid();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "93",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 40, 1)) \n",
+    "ys = xs.mel_to_hz() # i.e. Slaney\n",
+    "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz (Slaney)\")\n",
     "plt.legend(); plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "92",
+   "id": "94",
    "metadata": {},
    "source": [
     "### `hz_to_mel`\n",
     "\n",
-    "- hz_to_mel is implemented in analogy to its librosa counterpart, assuming the htk=True flag, i.e. using the formula from O'Shaughnessy (1987).\n",
+    "- hz_to_mel is implemented in analogy to its librosa counterpart, using Slaney method as default, allowing to set htk=True flag for the formula from O'Shaughnessy (1987).\n",
     "- `hz_to_mel(hz)` converts a frequency in Hz (value or arraylike) to a mel scale value (in float, resp. Arraylike of float).\n",
-    "- The mapping function is\n",
-    "    $$ f(x) = 2595 \\cdot \\log_{10}\\left(1 + \\frac{x}{700}\\right) $$\n",
-    "- ToDo: alternative methods could be added via a method argument, e.g. 'htk' (default), 'slaney', ..."
+    "- The default (Slaney) mapping is:\n",
+    "  $$ \\text{mel}(f) = \\left\\{ \\begin{align*} 3f/200 &~\\text{if}~& f < 1000\\\\\n",
+    "  15 + 27 \\log_{6.4}(f/1000) &~\\text{if}~& f \\ge 1000\\\\\n",
+    "  \\end{align*}\\right.$$ \n",
+    "- The alternative (htk=True, O'Shaughnessy (1987) formula) mapping is:\n",
+    "    $$ f(\\text{mel}) = 2595 \\cdot \\log_{10}\\left(1 + \\frac{\\text{mel}}{700}\\right) $$\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "93",
+   "id": "95",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.hz_to_mel(1000) "
+    "xs = chain(np.arange(1, 10000))\n",
+    "plt.plot(xs, pam.hz_to_mel(xs));\n",
+    "plt.xlabel('frequencies [Hz]'); plt.ylabel('mel scale (Slaney)');\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "94",
+   "id": "96",
    "metadata": {},
    "source": [
     "- ChainableArray.hz_to_mel uses self as input.\n",
@@ -1197,12 +1232,12 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "95",
+   "id": "97",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(21, 108, 7)).midicps() # frequencies of fifth series\n",
-    "ys = xs.hz_to_mel() \n",
+    "xs = chain(np.arange(21, 120, 7)).midicps() # frequencies of fifth series\n",
+    "ys = xs.hz_to_mel(htk=True) \n",
     "plt.plot(xs, ys, \"o-\", label=\"mel values for frequencies\"); \n",
     "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"mel scale\"); \n",
     "plt.legend(); plt.grid(); plt.loglog()\n",
@@ -1211,7 +1246,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96",
+   "id": "98",
    "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
@@ -1222,7 +1257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97",
+   "id": "99",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1245,7 +1280,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98",
+   "id": "100",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1255,7 +1290,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "99",
+   "id": "101",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1268,7 +1303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "100",
+   "id": "102",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1277,7 +1312,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "101",
+   "id": "103",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1289,7 +1324,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "102",
+   "id": "104",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1306,7 +1341,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "103",
+   "id": "105",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1322,7 +1357,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "104",
+   "id": "106",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1339,7 +1374,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "105",
+   "id": "107",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1355,7 +1390,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "106",
+   "id": "108",
    "metadata": {},
    "outputs": [],
    "source": [

From f691c09899207cde095fa550361deaa2e53aad4d Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 17:52:49 +0100
Subject: [PATCH 34/87] add distort() example

---
 notebooks/pyamapping-examples.ipynb | 90 +++++++++++++++++++++++++----
 1 file changed, 79 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 5bf0889..cff2631 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1245,9 +1245,77 @@
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "98",
    "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "99",
+   "metadata": {},
+   "source": [
+    "### `distort`\n",
+    "\n",
+    "- `distort(x, threshold=1)` is implemented in analogy to its sc3 counterpart `.distort`\n",
+    "\n",
+    "- It applies a distortion to x (float, resp. Arraylike of float).\n",
+    "- the threshold parameter controls the non-linearity\n",
+    "- The mapping function is:\n",
+    "  $$ f(x, \\theta) = \\frac{x}{\\theta + |x|}$$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "100",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.distort([0, 1, 2, 3], 1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "101",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.distort uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "102",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-3, 3, 0.01))\n",
+    "for theta in [0.1, 0.5, 1, 3]:\n",
+    "    plt.plot(xs, xs.distort(theta), label=f\"threshold = {theta}\")\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.legend(); plt.title(\"distort mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "103",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').distort(0.3).plot(label='distorted');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "104",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1257,7 +1325,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99",
+   "id": "105",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1280,7 +1348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "100",
+   "id": "106",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1290,7 +1358,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "101",
+   "id": "107",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1303,7 +1371,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "102",
+   "id": "108",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1312,7 +1380,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "103",
+   "id": "109",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1324,7 +1392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "104",
+   "id": "110",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1341,7 +1409,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "105",
+   "id": "111",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1357,7 +1425,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "106",
+   "id": "112",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1374,7 +1442,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "107",
+   "id": "113",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1390,7 +1458,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "108",
+   "id": "114",
    "metadata": {},
    "outputs": [],
    "source": [

From 3cddd5b7f9b40ba1cb6cb1d6b6f4a1a8e9710836 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:11:52 +0100
Subject: [PATCH 35/87] improve softclip() code and docstring

---
 src/pyamapping/mappings.py | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index c18725e..87da1b0 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -695,15 +695,18 @@ def softclip(
     Parameters
     ----------
         x (Union[float, np.typing.ArrayLike]): input value or array
-        threshold (float, optional): defaults to 1.0.
 
     Returns
     -------
         Union[float, np.ndarray]: softclip distorted value / array
     """
-    condition = np.abs(x) > 0.5
-    return (np.abs(x) - 0.25) / x * condition + (1 - condition) * x
-    # return (np.abs(x) - 0.25)/x if np.abs(x)<0.5 else x
+    x = np.asarray(x)  # ensure numpy array for elementwise operations
+    y = np.where(
+        np.abs(x) > 0.5,  # condition
+        (np.abs(x) - 0.25) / x,  # if condition
+        x,  # else
+    )
+    return y if y.ndim > 0 else float(y)
 
 
 def scurve(

From ae451d3a48665ba9fb210bbc9c502606d7983a94 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:12:39 +0100
Subject: [PATCH 36/87] add softclip() example

---
 notebooks/pyamapping-examples.ipynb | 103 +++++++++++++++++++++-------
 1 file changed, 79 insertions(+), 24 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index cff2631..cc01e50 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1244,17 +1244,9 @@
     "plt.plot([1000], [1000], \"ro-\", label=\"a reference point\");"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "98",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
-   "id": "99",
+   "id": "98",
    "metadata": {},
    "source": [
     "### `distort`\n",
@@ -1270,7 +1262,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "100",
+   "id": "99",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1279,7 +1271,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "101",
+   "id": "100",
    "metadata": {},
    "source": [
     "- ChainableArray.distort uses self as input.\n",
@@ -1289,7 +1281,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "102",
+   "id": "101",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1303,19 +1295,82 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "103",
+   "id": "102",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
     "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').distort(0.3).plot(label='distorted');"
+    "xs.plot(label='sine').distort(0.3).plot(label='distorted');\n",
+    "plt.legend(loc='upper right');"
    ]
   },
   {
    "cell_type": "markdown",
+   "id": "103",
+   "metadata": {},
+   "source": [
+    "### `softclip`\n",
+    "\n",
+    "- `softclip(x)` is implemented in analogy to its sc3 counterpart `.softclip`\n",
+    "\n",
+    "- It applies a softclip distortion to x (float, resp. Arraylike of float).\n",
+    "- The mapping function is:\n",
+    "  $$ f(x, \\theta) = \\left\\{\\begin{align*}\n",
+    "    x                      & ~~~\\text{if}~~~   & |x| \\le 0.5 \\\\\n",
+    "    \\frac{|x| - 0.25}{x}   & ~~~\\text{else}~~~ &             \\\\\n",
+    "  \\end{align*}\\right.$$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
    "id": "104",
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.softclip([0, 1, 2, 3])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "105",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.distort uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "106",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-3, 3, 0.01))\n",
+    "plt.plot(xs, xs.softclip(), label=f\"threshold = {theta}\")\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.legend(); plt.title(\"softclip mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "107",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').softclip().plot(label='softclip distorted');\n",
+    "plt.legend(loc='upper right');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "108",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1325,7 +1380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "105",
+   "id": "109",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1348,7 +1403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "106",
+   "id": "110",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1358,7 +1413,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "107",
+   "id": "111",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1371,7 +1426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "108",
+   "id": "112",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1380,7 +1435,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "109",
+   "id": "113",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1392,7 +1447,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "110",
+   "id": "114",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1409,7 +1464,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "111",
+   "id": "115",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1425,7 +1480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "112",
+   "id": "116",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1442,7 +1497,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "113",
+   "id": "117",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1458,7 +1513,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "114",
+   "id": "118",
    "metadata": {},
    "outputs": [],
    "source": [

From 2eb1fc1ef17501b9a083fc00484c0cd028785e22 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:42:24 +0100
Subject: [PATCH 37/87] fix dtype bug in softclip(), improve scurve()

---
 src/pyamapping/mappings.py | 22 ++++++++--------------
 1 file changed, 8 insertions(+), 14 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 87da1b0..c8582ef 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -684,9 +684,7 @@ def distort(
     return x / (threshold + np.abs(x))
 
 
-def softclip(
-    x: Union[float, ArrayLike], threshold: float = 1.0
-) -> Union[float, np.ndarray]:
+def softclip(x: Union[float, ArrayLike]) -> Union[float, np.ndarray]:
     """Apply softclip distortion to x.
 
     This yields a perfectly linear region within [-0.5, 0.5],
@@ -700,26 +698,22 @@ def softclip(
     -------
         Union[float, np.ndarray]: softclip distorted value / array
     """
-    x = np.asarray(x)  # ensure numpy array for elementwise operations
-    y = np.where(
-        np.abs(x) > 0.5,  # condition
-        (np.abs(x) - 0.25) / x,  # if condition
-        x,  # else
-    )
+    x = np.asarray(x, dtype=float)  # ensure numpy array for elementwise operations
+    y = np.empty_like(x)
+    mask = np.abs(x) <= 0.5
+    y[mask] = x[mask]
+    y[~mask] = (np.abs(x[~mask]) - 0.25) / x[~mask]
     return y if y.ndim > 0 else float(y)
 
 
-def scurve(
-    x: Union[float, ArrayLike], threshold: float = 1.0
-) -> Union[float, np.ndarray]:
+def scurve(x: Union[float, ArrayLike]) -> Union[float, np.ndarray]:
     """Map value onto an S-curve bound to [0,1].
 
-    Implements v * v * (3-(2*v)) mit v = x.clip(0,1)
+    Implements v * v * (3-(2*v)) mit v = x.clip(0, 1)
 
     Parameters
     ----------
         x (Union[float, np.typing.ArrayLike]): input value or array
-        threshold (float, optional): defaults to 1.0.
 
     Returns
     -------

From ce80c0ce952b7c3b83974007f00bcdd49ebe77f2 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:43:37 +0100
Subject: [PATCH 38/87] add scurve() example

---
 notebooks/pyamapping-examples.ipynb | 89 ++++++++++++++++++++++++-----
 1 file changed, 74 insertions(+), 15 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index cc01e50..771e9de 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1316,7 +1316,7 @@
     "\n",
     "- It applies a softclip distortion to x (float, resp. Arraylike of float).\n",
     "- The mapping function is:\n",
-    "  $$ f(x, \\theta) = \\left\\{\\begin{align*}\n",
+    "  $$ f(x) = \\left\\{\\begin{align*}\n",
     "    x                      & ~~~\\text{if}~~~   & |x| \\le 0.5 \\\\\n",
     "    \\frac{|x| - 0.25}{x}   & ~~~\\text{else}~~~ &             \\\\\n",
     "  \\end{align*}\\right.$$\n"
@@ -1329,7 +1329,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.softclip([0, 1, 2, 3])"
+    "pam.softclip(np.arange(1, 5))"
    ]
   },
   {
@@ -1337,7 +1337,7 @@
    "id": "105",
    "metadata": {},
    "source": [
-    "- ChainableArray.distort uses self as input.\n",
+    "- ChainableArray.softclip uses self as input.\n",
     "- Here a mapping examples and plots"
    ]
   },
@@ -1349,9 +1349,9 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-3, 3, 0.01))\n",
-    "plt.plot(xs, xs.softclip(), label=f\"threshold = {theta}\")\n",
+    "plt.plot(xs, xs.softclip())\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(); plt.title(\"softclip mapping function\");"
+    "plt.title(\"softclip mapping function\");"
    ]
   },
   {
@@ -1371,6 +1371,65 @@
    "cell_type": "markdown",
    "id": "108",
    "metadata": {},
+   "source": [
+    "### `scurve`\n",
+    "\n",
+    "- `scurve(x)` is implemented in analogy to its sc3 counterpart `.scurve`\n",
+    "\n",
+    "- It applies an scurve distortion to x (float, resp. Arraylike of float).\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = v^2 (3-2v) ~~\\text{with}~~ v = \\min(\\max(x, 0), 1)~~~\\text{i.e. v=clip(x, 0, 1)}$$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "109",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.scurve(np.arange(0, 1, 0.25))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "110",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.scurve uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "111",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 1, 0.01))\n",
+    "plt.plot(xs, xs.scurve())\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.legend(); plt.title(\"scurve mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "112",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts).linlin(-1, 1, 0, 1)\n",
+    "xs.plot(label='sine with offset').scurve().plot(label='scurve distorted');\n",
+    "plt.legend(loc='upper right');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "113",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1380,7 +1439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "109",
+   "id": "114",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1403,7 +1462,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "110",
+   "id": "115",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1413,7 +1472,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "111",
+   "id": "116",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1426,7 +1485,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "112",
+   "id": "117",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1435,7 +1494,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "113",
+   "id": "118",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1447,7 +1506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "114",
+   "id": "119",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1464,7 +1523,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "115",
+   "id": "120",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1480,7 +1539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "116",
+   "id": "121",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1497,7 +1556,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "117",
+   "id": "122",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1513,7 +1572,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "118",
+   "id": "123",
    "metadata": {},
    "outputs": [],
    "source": [

From d9dc43321cd759d986b7fdca14d663010d92f208 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:58:33 +0100
Subject: [PATCH 39/87] fix error in lcurve() docstring

---
 src/pyamapping/mappings.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index c8582ef..f304c7e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -728,10 +728,10 @@ def lcurve(
 ) -> Union[float, np.ndarray]:
     """Map value or array onto an L-curve.
 
-    Implements (1 + m * exp(-x/tau) + 1) / (1 + n * exp(-x/tau))
+    Implements (1 + m * exp(-x/tau)) / (1 + n * exp(-x/tau))
     - equal to fermi function with default parameters
     - note that different to the sc3 implementation, tau is inside
-    the exp function (unclear tau placement in sc3...)
+    the exp function (...unclear tau placement in sc3...)
 
     Parameters
     ----------

From 0a1050f8bd109bcba4a46024fb79c6d75dfad0e5 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 18:59:14 +0100
Subject: [PATCH 40/87] add lcurve() example

---
 notebooks/pyamapping-examples.ipynb | 81 +++++++++++++++++++++++++----
 1 file changed, 71 insertions(+), 10 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 771e9de..2523ffc 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1430,6 +1430,67 @@
    "cell_type": "markdown",
    "id": "113",
    "metadata": {},
+   "source": [
+    "### `lcurve`\n",
+    "\n",
+    "- `lcurve(x, m=0.0, n=1.0, tau=1.0)` is implemented in analogy to its sc3 counterpart `.lcurve`\n",
+    "\n",
+    "- It applies an l-curve distortion to x (float, resp. Arraylike of float).\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = \n",
+    "     \\frac{1 + m e^{-x/\\tau}}{1 + n e^{-x/\\tau}} $$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "114",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.lcurve(np.array([-1, -0.5, 0, 0.5, 1]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "115",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.lcurve uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "116",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-10, 10, 0.005))\n",
+    "for tau in [0.2, 0.5, 1, 2]:\n",
+    "    plt.plot(xs, xs.lcurve(tau=tau), label=f'lcurve for tau={tau}')\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.legend(); plt.title(\"scurve mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "117",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').lcurve(tau=0.25).plot(label='lcurve distorted');\n",
+    "plt.legend(loc='upper right');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "118",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1439,7 +1500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "114",
+   "id": "119",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1462,7 +1523,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "115",
+   "id": "120",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1472,7 +1533,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "116",
+   "id": "121",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1485,7 +1546,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "117",
+   "id": "122",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1494,7 +1555,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "118",
+   "id": "123",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1506,7 +1567,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "119",
+   "id": "124",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1523,7 +1584,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "120",
+   "id": "125",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1539,7 +1600,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "121",
+   "id": "126",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1556,7 +1617,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "122",
+   "id": "127",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1572,7 +1633,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "123",
+   "id": "128",
    "metadata": {},
    "outputs": [],
    "source": [

From 080ddc156fa522ade21648de7e77226177bc7d21 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 19:38:26 +0100
Subject: [PATCH 41/87] fixed bug in wrap()

---
 src/pyamapping/mappings.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index f304c7e..47f144e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -792,7 +792,7 @@ def wrap(
 ) -> Union[float, np.ndarray]:
     """Wrap array around target range [y1, y2].
 
-    This implements the mapping y1 + x % (y2 - y1).
+    This implements the mapping y1 + np.mod(x - y1, y2 - y1).
     The order of y1, y2 is irrelevant.
 
     Parameters
@@ -805,7 +805,7 @@ def wrap(
     -------
         Union[float, np.ndarray]: wraped array
     """
-    return y1 + x % (y2 - y1)
+    return y1 + np.mod(x - y1, y2 - y1)
 
 
 def fold(

From 992ba82f7592ca87a168d3c73f5fef4c79849a8c Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 19:38:54 +0100
Subject: [PATCH 42/87] add wrap() example

---
 notebooks/pyamapping-examples.ipynb | 83 +++++++++++++++++++++++++----
 1 file changed, 72 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 2523ffc..0acbc6a 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1471,7 +1471,7 @@
     "for tau in [0.2, 0.5, 1, 2]:\n",
     "    plt.plot(xs, xs.lcurve(tau=tau), label=f'lcurve for tau={tau}')\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(); plt.title(\"scurve mapping function\");"
+    "plt.legend(); plt.title(\"lcurve mapping function\");"
    ]
   },
   {
@@ -1491,6 +1491,67 @@
    "cell_type": "markdown",
    "id": "118",
    "metadata": {},
+   "source": [
+    "### `wrap`\n",
+    "\n",
+    "- `wrap(x, y1=-1.0, y2=1.0)` is implemented in analogy to its sc3 counterpart `.wrap`\n",
+    "\n",
+    "- It wraps x (float, resp. Arraylike of float) around target range [y1, y2].\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = (x - y_1) \\mod (y_2 - y_1) $$\n",
+    "- the order of y1 and y2 is irrelevant\n",
+    "- wrap delivers the quantization error when quantizing a signal in units of the interval $|y_2-y_1|$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "119",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.wrap(np.arange(0, 13), 0, 3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "120",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.wrap uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "121",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-5, 5, 0.01))\n",
+    "plt.plot(xs, xs.wrap(y1=-1, y2=1))\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.title(\"wrap mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "122",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*30*ts)\n",
+    "xs.plot(label='sine').wrap(-0.8, 0.5).plot(label='wrapped sine');\n",
+    "plt.legend(loc='upper right');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "123",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1500,7 +1561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "119",
+   "id": "124",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1523,7 +1584,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "120",
+   "id": "125",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1533,7 +1594,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "121",
+   "id": "126",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1546,7 +1607,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "122",
+   "id": "127",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1555,7 +1616,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "123",
+   "id": "128",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1567,7 +1628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "124",
+   "id": "129",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1584,7 +1645,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "125",
+   "id": "130",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1600,7 +1661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "126",
+   "id": "131",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1617,7 +1678,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "127",
+   "id": "132",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1633,7 +1694,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "128",
+   "id": "133",
    "metadata": {},
    "outputs": [],
    "source": [

From f0817f33e217927a6b37700011a57fc97b9c9650 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Sat, 1 Nov 2025 19:48:07 +0100
Subject: [PATCH 43/87] add fold() example

---
 notebooks/pyamapping-examples.ipynb | 82 +++++++++++++++++++++++++----
 1 file changed, 71 insertions(+), 11 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 0acbc6a..5dd1eff 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1498,7 +1498,7 @@
     "\n",
     "- It wraps x (float, resp. Arraylike of float) around target range [y1, y2].\n",
     "- The mapping function is:\n",
-    "  $$ f(x) = (x - y_1) \\mod (y_2 - y_1) $$\n",
+    "  $$ f(x) = y1 + ((x - y_1) \\mod (y_2 - y_1)) $$\n",
     "- the order of y1 and y2 is irrelevant\n",
     "- wrap delivers the quantization error when quantizing a signal in units of the interval $|y_2-y_1|$"
    ]
@@ -1552,6 +1552,66 @@
    "cell_type": "markdown",
    "id": "123",
    "metadata": {},
+   "source": [
+    "### `fold`\n",
+    "\n",
+    "- `fold(x, y1=-1.0, y2=1.0)` is implemented in analogy to its sc3 counterpart `.fold`\n",
+    "\n",
+    "- It folds x (float, resp. Arraylike of float) beyond limits [y1, y2] back by mirroring the signal.\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = y_1 + |(x - y_2) \\mod (2L) - L| \\text{~~with~~} L = y_2 -y_1 $$\n",
+    "- the order of y1 and y2 is irrelevant: a swap is done internally "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "124",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.fold(np.arange(0, 13), 0, 4)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "125",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.wrap uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "126",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-5, 5, 0.01))\n",
+    "plt.plot(xs, xs.fold(y1=-1, y2=1))\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.title(\"wrap mapping function\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "127",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*30*ts)\n",
+    "xs.plot(label='sine').fold(-0.75, 0.5).plot(label='folded sine');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "128",
+   "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
     "\n",
@@ -1561,7 +1621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "124",
+   "id": "129",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1584,7 +1644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "125",
+   "id": "130",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1594,7 +1654,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "126",
+   "id": "131",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1607,7 +1667,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "127",
+   "id": "132",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1616,7 +1676,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "128",
+   "id": "133",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1628,7 +1688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "129",
+   "id": "134",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1645,7 +1705,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "130",
+   "id": "135",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1661,7 +1721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "131",
+   "id": "136",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1678,7 +1738,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "132",
+   "id": "137",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1694,7 +1754,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "133",
+   "id": "138",
    "metadata": {},
    "outputs": [],
    "source": [

From 24bb5c0edfbed51a0ab2e93b3a2d6513239a16c9 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:15:03 +0100
Subject: [PATCH 44/87] improve/correct fermi() docstring

---
 src/pyamapping/mappings.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 47f144e..65e0d2f 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -752,12 +752,13 @@ def fermi(
 ) -> Union[float, np.ndarray]:
     """Apply fermi function to value or array.
 
-    Implements 1 / (1 + exp(-x/tau))
+    Implements 1 / (1 + exp(-(x-mu)/tau))
 
     Parameters
     ----------
         x (Union[float, np.typing.ArrayLike]): input value or array
         tau (float, optional): scale constant, defaults to 1.0.
+        mu (float, optional): shift, defaults to 0.0
 
     Returns
     -------

From ce45ea880d1ba8b485f15b0904fcf1a07bf522c6 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:15:59 +0100
Subject: [PATCH 45/87] add fermi() example

---
 notebooks/pyamapping-examples.ipynb | 71 +++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 5dd1eff..022dd9f 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1764,6 +1764,77 @@
     "xs.bilin(50, -50, 100, 0.4, 0, 1).plot(\"b:\", label='bilin with extrapolation');\n",
     "plt.legend();plt.grid();"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "139",
+   "metadata": {},
+   "source": [
+    "### `fermi`\n",
+    "\n",
+    "- `fermi(x, tau=1.0, mu=0.0)` implements a (shiftable) fermi function.\n",
+    "\n",
+    "- It applies a Fermi function to x (float, resp. Arraylike of float).\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = \n",
+    "     \\frac{1}{1 + n e^{-(x-\\mu)/\\tau}} $$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "140",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.fermi(np.array([-1, -0.5, 0, 0.5, 1]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "141",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.fermi uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "142",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(-10, 10, 0.005))\n",
+    "for i, mu in enumerate([-2, 0, 2]):\n",
+    "    for j, tau in enumerate([0.2, 0.5, 1]):\n",
+    "        plt.plot(xs, xs.fermi(tau, mu), color=['r','g','b'][i], \n",
+    "                 lw=j+1, label=f'lcurve for tau={tau}')\n",
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.legend(fontsize=8); plt.title(\"fermi curve mapping functions\");"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "143",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').fermi(tau=0.25, mu=1).plot(label='fermi distorted');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "144",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {},

From 558303c81648af921118f365e9d99ef50f9fc832 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:33:04 +0100
Subject: [PATCH 46/87] fix normalize() input type

---
 src/pyamapping/mappings.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 65e0d2f..c1807c5 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -767,9 +767,7 @@ def fermi(
     return 1.0 / (1 + np.exp(-(x - mu) / tau))
 
 
-def normalize(
-    x: Union[float, ArrayLike], y1: float = -1.0, y2: float = 1.0
-) -> Union[float, np.ndarray]:
+def normalize(x: np.ndarray, y1: float = -1.0, y2: float = 1.0) -> np.ndarray:
     """Normalize array to target range [y1, y2].
 
     Linear mapping [min(x), max(x)] to [y1, y2]. Use y1 > y2 to change polarity.

From 9b50b9f79a52c4b15352fc219c817d3831d80b70 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:33:32 +0100
Subject: [PATCH 47/87] add normalize() example

---
 notebooks/pyamapping-examples.ipynb | 46 +++++++++++++++++++++++++++--
 1 file changed, 43 insertions(+), 3 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 022dd9f..c438b70 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1777,7 +1777,7 @@
     "- It applies a Fermi function to x (float, resp. Arraylike of float).\n",
     "- The mapping function is:\n",
     "  $$ f(x) = \n",
-    "     \\frac{1}{1 + n e^{-(x-\\mu)/\\tau}} $$\n"
+    "     \\frac{1}{1 + e^{-(x-\\mu)/\\tau}} $$\n"
    ]
   },
   {
@@ -1828,13 +1828,53 @@
     "plt.legend(loc='upper right'); plt.grid()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "144",
+   "metadata": {},
+   "source": [
+    "### `normalize`\n",
+    "\n",
+    "- `normalize(x, y1=-1.0, y2=1.0)` implements a signal normalization to [y1,y2].\n",
+    "- A linear mapping from input range [min(x) to max(x)] to output range [y1, y2]\n",
+    "  is applied to argument x (Arraylike of float).\n",
+    "- Note that this won't work for min(x) = max(x)\n",
+    "- Note that an implicit polarity change can be achieved by choosing y1>y2.\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = y_1 + \\frac{x - x_1}{x_2 - x_1} (y_2 - y_1) $$\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "144",
+   "id": "145",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.normalize(np.random.rand(10)) # you'll find a 1 and a -1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "146",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.normalize uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "147",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').normalize(0.5,1).plot(label='normalized to [0.5, 1]');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
   }
  ],
  "metadata": {},

From 148ad035350e28fd03187a217ed7e02209de8a6c Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:53:41 +0100
Subject: [PATCH 48/87] fixed norm_peak() type definition

---
 src/pyamapping/mappings.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index c1807c5..b0a32ec 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -847,17 +847,17 @@ def remove_dc(
     return x - np.mean(x)
 
 
-def norm_peak(x: Union[float, ArrayLike], peak=1.0):
-    """Normalize array so that max(abs(x)) = peak.
+def norm_peak(x: np.ndarray, peak=1.0):
+    """Normalize by scaling array so that max(abs(x)) = peak.
 
     Parameters
     ----------
-        x (Union[float, np.typing.ArrayLike]): input value or array
+        x (np.ndarray]): input array
         peak (float): target peak
 
     Returns
     -------
-        Union[float, np.ndarray]: normalized (scaled) array
+        np.ndarray: normalized (scaled) array
     """
     peak_of_x = np.max(np.abs(x))
     return (x / peak_of_x) * peak if peak_of_x != 0 else x

From 4a7a42eca06f03f0498b4e51cf074acacc2d9590 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 16:55:23 +0100
Subject: [PATCH 49/87] add norm_peak() example

---
 notebooks/pyamapping-examples.ipynb | 49 +++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index c438b70..9f2af20 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1840,6 +1840,7 @@
     "  is applied to argument x (Arraylike of float).\n",
     "- Note that this won't work for min(x) = max(x)\n",
     "- Note that an implicit polarity change can be achieved by choosing y1>y2.\n",
+    "- Note that normalize is different from sc3 normalize (see `pyamapping.norm_peak()`). \n",
     "- The mapping function is:\n",
     "  $$ f(x) = y_1 + \\frac{x - x_1}{x_2 - x_1} (y_2 - y_1) $$\n"
    ]
@@ -1875,6 +1876,54 @@
     "xs.plot(label='sine').normalize(0.5,1).plot(label='normalized to [0.5, 1]');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "148",
+   "metadata": {},
+   "source": [
+    "### `norm_peak`\n",
+    "\n",
+    "- `norm_peak(x, peak=1.0)` implements a signal normalization by scaling to new peak.\n",
+    "- The signal is scaled by peak/max(abs(x)).\n",
+    "- note that a polarity change results in negative values of `peak`.\n",
+    "- Note that `norm_peak` is resembles .normalize from SuperCollider. \n",
+    "- The mapping function is:\n",
+    "  $$ f(x, \\text{peak}) = \\text{peak}\\cdot\\frac{x}{\\max|x|} $$\n",
+    "- i.e. if the signal is DC-free, it remains so as it is merely scaled.    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "149",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.norm_peak(np.random.rand(10), 5) # you'll find a 5 (not not a -5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "150",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.norm_peak uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "151",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').norm_peak(0.5).plot(label='norm_peak to 0.5');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
   }
  ],
  "metadata": {},

From 763c2cb08b23e1b001c4eebdfe26a7a90c890d74 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 17:08:35 +0100
Subject: [PATCH 50/87] fix norm_rms() type definiton

---
 src/pyamapping/mappings.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index b0a32ec..0461ea4 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -863,17 +863,17 @@ def norm_peak(x: np.ndarray, peak=1.0):
     return (x / peak_of_x) * peak if peak_of_x != 0 else x
 
 
-def norm_rms(x: Union[float, ArrayLike], rms=1.0):
+def norm_rms(x: np.ndarray, rms=1.0):
     """Normalize array so that its RMS value equals `rms`.
 
     Parameters
     ----------
-        x (Union[float, np.typing.ArrayLike]): input value or array
+        x (np.ndarray): input array
         rms (float): target rms of array
 
     Returns
     -------
-        Union[float, np.ndarray]: rms normalized (scaled) array
+        np.ndarray: rms normalized (scaled) array
     """
     rms_of_x = np.sqrt(np.mean(x**2))
     return (x / rms_of_x) * rms if rms_of_x != 0 else x

From d97d53352b7405fb3e90fc3625ca0587ff1171ad Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 17:09:21 +0100
Subject: [PATCH 51/87] add norm_rms() example

---
 notebooks/pyamapping-examples.ipynb | 48 +++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 9f2af20..51cec71 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1924,6 +1924,54 @@
     "xs.plot(label='sine').norm_peak(0.5).plot(label='norm_peak to 0.5');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "152",
+   "metadata": {},
+   "source": [
+    "### `norm_rms`\n",
+    "\n",
+    "- `norm_rms(x, rms=1.0)` implements a signal normalization by scaling to target RMS.\n",
+    "- The signal is scaled, not shifted.\n",
+    "- Note that negative `rms` result in a polarity change.\n",
+    "- The mapping function is:\n",
+    "  $$ f(x, \\text{rms}) = \\text{rms}\\cdot\\frac{x}{\\sqrt{\\langle x^2 \\rangle}} \n",
+    "  = \\text{rms}\\cdot\\frac{x}{\\sqrt{\\frac{1}{n}\\sum\\limits_{i=1}^n x_i^2}} $$\n",
+    "- i.e. if the signal is DC-free, it remains so as it is merely scaled.    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "153",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.norm_rms(np.array([1,0,0,-1]), 1) # scale by sqrt(2) to magnify RMS"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "154",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.norm_rms uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "155",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs.plot(label='sine').norm_rms(0.5).plot(label='norm_rms to 0.5');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
   }
  ],
  "metadata": {},

From c667391e382a9d688a88dc5a1afb64798d5e1f89 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 23:00:43 +0100
Subject: [PATCH 52/87] fix remove_dc() type hints

---
 src/pyamapping/mappings.py | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 0461ea4..b73ff59 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -831,18 +831,16 @@ def fold(
     return np.abs((x - y2) % (2 * L) - L) + y1
 
 
-def remove_dc(
-    x: Union[float, ArrayLike],
-) -> Union[float, np.ndarray]:
+def remove_dc(x: np.darray) -> np.ndarray:
     """Remove DC bias.
 
     Parameters
     ----------
-        x (Union[float, np.typing.ArrayLike]): input value or array
+        x (np.ndarray): input array
 
     Returns
     -------
-        Union[float, np.ndarray]: normalized / scaled array
+        np.ndarray: mean-free array
     """
     return x - np.mean(x)
 

From c869f41438c1767619297bf4a1f4640e72ab6c00 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 23:01:37 +0100
Subject: [PATCH 53/87] add remove_dc() example

---
 notebooks/pyamapping-examples.ipynb | 46 +++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 51cec71..626b128 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1972,6 +1972,52 @@
     "xs.plot(label='sine').norm_rms(0.5).plot(label='norm_rms to 0.5');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "156",
+   "metadata": {},
+   "source": [
+    "### `remove_dc`\n",
+    "\n",
+    "- `remove_dc(x)` removes the signal's mean.\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = x - \\left< x \\right> $$\n",
+    "- i.e. the signals mean is shifted to zero.\n",
+    "- Note that this could cause a signal to clip [-1,1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "157",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.remove_dc(np.array([1,2,3,4]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "158",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.remove_dc uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "159",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*25*ts)**2\n",
+    "xs.plot(label='sine').remove_dc().plot(label='remove_dc output');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
   }
  ],
  "metadata": {},

From fbeb49f71512b96cb722998696e2c8b73f5726fe Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 23:21:50 +0100
Subject: [PATCH 54/87] fix gain() type hints

---
 src/pyamapping/mappings.py | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index b73ff59..9941262 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -877,22 +877,20 @@ def norm_rms(x: np.ndarray, rms=1.0):
     return (x / rms_of_x) * rms if rms_of_x != 0 else x
 
 
-def gain(
-    x: Union[float, ArrayLike], db: Optional[float] = None, amp: Optional[float] = None
-):
+def gain(x: np.ndarray, db: Optional[float] = None, amp: Optional[float] = None):
     """Apply gain, either as dB (SPL) or scalar factor amp.
 
     No operation done if neither argument is given, it applies both if both are given.
 
     Parameters
     ----------
-        x (Union[float, np.typing.ArrayLike]): input value or array
+        x (np.ndarray): input array
         db (None or float): dB SPL = gain 10**(db/20), e.g. -6 dB ~ factor 0.5
         amp (None or float): gain factor
 
     Returns
     -------
-        Union[float, np.ndarray]: scaled (amplified / attenuated) array
+        np.ndarray: scaled (amplified / attenuated) array
     """
     if db:
         sig = x * dbamp(db)

From 703ebd2695c9949a713ca66f79d873d65c19409e Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Mon, 3 Nov 2025 23:22:43 +0100
Subject: [PATCH 55/87] add gain() example

---
 notebooks/pyamapping-examples.ipynb | 48 +++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 626b128..1fd8e25 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -2018,6 +2018,54 @@
     "xs.plot(label='sine').remove_dc().plot(label='remove_dc output');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "160",
+   "metadata": {},
+   "source": [
+    "### `gain`\n",
+    "\n",
+    "- `gain(x, db=None, amp=None` applies gain in either dB or amp.\n",
+    "- The mapping function is:\n",
+    "  $$ f(x) = \\left\\{\\begin{align*}\n",
+    "   x\\cdot \\text{db\\_to\\_amp}(\\text{db}) & ~~\\text{if~  } & \\text{db} \\neq \\text{None}\\\\\n",
+    "   x\\cdot \\text{amp}             & ~~\\text{elif~} & \\text{amp} \\neq \\text{None}\\\\\n",
+    "   x                             & ~~\\text{else~} & ~ \\\\\n",
+    "  \\end{align*}\\right. $$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "161",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pam.gain(np.array([1,2,3,4]), amp=2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "162",
+   "metadata": {},
+   "source": [
+    "- ChainableArray.gain uses self as input.\n",
+    "- Here a mapping examples and plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "163",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ts = chain(np.linspace(0, 0.1, 500))\n",
+    "xs = np.sin(2*np.pi*25*ts)\n",
+    "xs.plot(label='sine').gain(db=-6).plot(label='-6 dB gain');\n",
+    "plt.legend(loc='upper right'); plt.grid()"
+   ]
   }
  ],
  "metadata": {},

From ee852c45a4afaa2c05024731858ae3722d029591 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 13:58:03 +0100
Subject: [PATCH 56/87] fix remove_dc() type hint error

---
 src/pyamapping/mappings.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 9941262..bc265c5 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -831,7 +831,7 @@ def fold(
     return np.abs((x - y2) % (2 * L) - L) + y1
 
 
-def remove_dc(x: np.darray) -> np.ndarray:
+def remove_dc(x: np.ndarray) -> np.ndarray:
     """Remove DC bias.
 
     Parameters

From e54692f839e9f3dd782d0db56311c1ea7054fe19 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 15:09:13 +0100
Subject: [PATCH 57/87] remove obsolete linspace()

---
 src/pyamapping/mappings.py | 26 +-------------------------
 1 file changed, 1 insertion(+), 25 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index bc265c5..efb8a7e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -901,35 +901,12 @@ def gain(x: np.ndarray, db: Optional[float] = None, amp: Optional[float] = None)
     return sig
 
 
-def linspace(
-    x: Union[float, int, ArrayLike], x1: float, x2: float, endpoint: bool = True
-) -> np.ndarray:
-    """Create np.linspace from x1 to x2 in int(x) resp len(x) steps.
-
-    Parameters
-    ----------
-        x (Union[float, int, ArrayLike]): length or array of which only shape is used
-        x1 (float): target interval one side
-        x2 (float): target interval other side
-        endpoint (bool): forwarded to np.linspace
-
-    Returns
-    -------
-        Union[float, np.ndarray]: array of length len(x)
-            (resp. int(x) if x is float) of numbers between x1 and x2
-    """
-    if isinstance(x, np.ndarray):
-        return np.linspace(x1, x2, x.shape[0], endpoint=endpoint)
-    else:
-        return np.linspace(x1, x2, int(abs(x)), endpoint=endpoint)
-
-
 def lin_to_ecdf(
     x: Union[float, ArrayLike], ref_data: np.ndarray, sorted: bool = False
 ) -> Union[float, np.ndarray]:
     """Map data using empiric cumulative distribution function as mapping.
 
-    This meann feature values are mapped to quantiles.
+    This means feature values are mapped to quantiles.
     if sorted==True: ref_data is regarded as sorted, speeding repeated invocations.
 
     Parameters
@@ -1202,7 +1179,6 @@ def _list_numpy_ufuncs():
     linexp,
     linlin,
     linpoly,
-    linspace,
     mel_to_hz,
     midi_to_cps,
     midi_to_ratio,

From 39f4abaf1fb2a0602da0ad7a8d12956ab4a98734 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 15:28:56 +0100
Subject: [PATCH 58/87] remove linspace(), fix lin_ecdf() extrapolation

---
 src/pyamapping/__init__.py | 1 -
 src/pyamapping/mappings.py | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/pyamapping/__init__.py b/src/pyamapping/__init__.py
index e37069d..09d7893 100644
--- a/src/pyamapping/__init__.py
+++ b/src/pyamapping/__init__.py
@@ -45,7 +45,6 @@
     linexp,
     linlin,
     linpoly,
-    linspace,
     mel_to_hz,
     midi_to_cps,
     midi_to_ratio,
diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index efb8a7e..d5baf7e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -922,7 +922,7 @@ def lin_to_ecdf(
     """
     if sorted:
         return interp(
-            x, ref_data, np.arange(1, len(ref_data) + 1) / float(len(ref_data))
+            x, ref_data, np.arange(1, len(ref_data) + 1) / float(len(ref_data), left=0)
         )
     else:
         return interp(x, *ecdf(ref_data))

From d72f1e599af0d4dec162888ce670b13aaa667828 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 15:30:11 +0100
Subject: [PATCH 59/87] add ecdf(), lin_to_ecdf(), ecdf_to_lin() examples

---
 notebooks/pyamapping-examples.ipynb | 156 ++++++++++++++++++++++++++++
 1 file changed, 156 insertions(+)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 1fd8e25..835ea73 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -2066,6 +2066,162 @@
     "xs.plot(label='sine').gain(db=-6).plot(label='-6 dB gain');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "164",
+   "metadata": {},
+   "source": [
+    "### `ecdf`\n",
+    "\n",
+    "- `ecdf(x, selection=slice())` computes the empirical cumulative distribution function for x.\n",
+    "- it basically:\n",
+    "  - sorts x to obtain locations for the steps (step_x)\n",
+    "  - creates a step function with len(x)+1 steps (these values become step_y)\n",
+    "  - returns the step_x and step_y coordinates for the given selection\n",
+    "- Applications:\n",
+    "  - This enables handcrafted mapping functions such as for using `ChainableArray.interp()`.\n",
+    "  - it is used in `lin_to_ecdf()` and `ecdf_to_lin()`\n",
+    "- Remarks:\n",
+    "  - cdf steps by 1/n occur at points in the sorted data.\n",
+    "  - the values are the cdf at (i.e. including) the data point\n",
+    "  - in consequence the correct cdf for any point left of min(x) is 0\n",
+    "  - however, as there are no data points left of min(x), `interp()` would rather hold, i.e. stay on value 1/n\n",
+    "    - use left=0 as remedy to get cdf=0 for values < min(x)\n",
+    "  - there is no extrapolation problem on the right side: hold on 1 is correct for any v > max(x)\n",
+    "  - note that interp would interpolate between these points, so not generate a step function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "165",
+   "metadata": {},
+   "source": [
+    "**Example 1**: (compute once - use many)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "166",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pyamapping import ecdf\n",
+    "\n",
+    "data = np.array([1, 3, 1.5, 3.5, 2, 5, 8, 9, 16])  # your data, unsorted\n",
+    "myecdf = ecdf(data) # compute the (xc, yc) for interp()\n",
+    "\n",
+    "# now myecdf may be used many times\n",
+    "xn = chain(np.linspace(0, 20, 50)) # your custom x (at which you need ecdf)\n",
+    "yn = xn.interp(*myecdf, left=0) # extra argument to specify left extrapolation\n",
+    "\n",
+    "# plot data, ecdf and results of interp\n",
+    "plt.plot(data, np.zeros_like(data), \"bx\", label=\"data\")\n",
+    "plt.plot(*myecdf, \"ro\", ms=5, label=\"ecdf for data\")\n",
+    "plt.plot(xn, yn, \"ko-\", lw=0.5, ms=2, label=\"your applied ecdf to custom data\")\n",
+    "plt.grid()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "167",
+   "metadata": {},
+   "source": [
+    "**Example 2:** (compute and map in one go)\n",
+    "\n",
+    "```chain(otherdata).interp(*ecdf(data))```\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "168",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "newdata = chain(np.array([0.5, 3.25, 20]))\n",
+    "newdata.interp(*ecdf(data), left=0) # turn newdata into ecdfs of data "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "169",
+   "metadata": {},
+   "source": [
+    "### `lin_to_ecdf`\n",
+    "\n",
+    "- `lin_to_ecdf(x, ref_data, sorted=False)` maps data using the empiric cumulative \n",
+    "  distribution function as mapping.\n",
+    "  - This means feature values are mapped to quantiles.\n",
+    "  - if `sorted==True`, `ref_data` is regarded as sorted, speeding repeated invocations.\n",
+    "- Note that left=0 argument to interp() is used to make sure cdf=0 for values < min(ref_data)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "170",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data_feat = np.random.randn(200) # data used for crafting the mapping\n",
+    "test_data = np.linspace(-3, 3, 200) # data to apply mapping to\n",
+    "chain(test_data).lin_to_ecdf(data_feat, sorted=False).plot(xs=test_data);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "171",
+   "metadata": {},
+   "source": [
+    "### `ecdf_to_lin`\n",
+    "\n",
+    "- `ecdf_to_lin(x, ref_data, sorted=False)` maps data using the inverse empiric cumulative \n",
+    "  distribution function as mapping.\n",
+    "  - if ref_data is omitted, x is used instead.\n",
+    "  - if `sorted==True`, `ref_data` is regarded as sorted, speeding repeated invocations."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "172",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ecdf_to_lin\n",
+    "data = chain(np.random.randn(500)).normalize(0,10) # some quantiles, i.e. in [0,1]\n",
+    "test_data = np.linspace(0, 1, 100) # data to apply mapping to\n",
+    "chain(test_data).ecdf_to_lin(data).plot(xs=test_data)\n",
+    "\n",
+    "plt.axvline(0.5, ls=\":\", color='k'); \n",
+    "plt.xlabel('test data, resp. quantile'); plt.ylabel('feature values')\n",
+    "plt.axhline(np.median(data), ls=\":\", color='k');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "173",
+   "metadata": {},
+   "source": [
+    "- quantiles mapping should pass a cdf array \n",
+    "  - so that this does not need to be computed each invocation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "174",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "data = chain(np.random.randn(200)) # data used for crafting the mapping\n",
+    "test_data = np.linspace(-3, 3, 200) # data to apply mapping to\n",
+    "\n",
+    "chain(test_data).interp(*ecdf(data)).plot(xs=test_data, label='full data ecdf');\n",
+    "chain(test_data).interp(*ecdf(data, np.s_[20:-15:10])).plot(\"r-\", xs=test_data, ms=1, label='ecdf sliced');"
+   ]
   }
  ],
  "metadata": {},

From e36bb858101f52ee9b62524820ce3fb87f3e099f Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 18:50:33 +0100
Subject: [PATCH 60/87] update .plot() for mapping with xs arg

---
 notebooks/pyamapping-examples.ipynb | 54 ++++++++++++-----------------
 1 file changed, 22 insertions(+), 32 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 835ea73..1d0c949 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -175,6 +175,7 @@
     "- `to_array` - back to numpy ndarray\n",
     "- `to_asig` - convert into pya.Asig\n",
     "- `plot` - plot signal(s) as time series\n",
+    "  - optional kwarg 'xs' allows to pass x values for data.\n",
     "- `mapvec` - map function on self by using numpy.vectorize\n",
     "- `map` - apply function directly to the array itself\n",
     "\n",
@@ -292,8 +293,8 @@
    "outputs": [],
    "source": [
     "# plot mapping function (output vs input)\n",
-    "ys = xs.linlin(0.25, 0.75, -1, 1, \"minmax\")\n",
-    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); "
+    "plt.figure(figsize=(3, 1.5)); plt.grid();\n",
+    "xs.linlin(0.25, 0.75, -1, 1, \"minmax\").plot(xs=xs);  "
    ]
   },
   {
@@ -362,9 +363,7 @@
    "outputs": [],
    "source": [
     "# plot linexp mapping function (output vs input)\n",
-    "ys = xs.linexp(0.25, 0.85, 0.2, 2)\n",
-    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
-    "plt.plot(xs, ys); "
+    "ys = xs.linexp(0.25, 0.85, 0.2, 2).plot(xs=xs)"
    ]
   },
   {
@@ -438,9 +437,7 @@
    "outputs": [],
    "source": [
     "# plot linexp mapping function (output vs input)\n",
-    "ys = xs.explin(0.01, 1, 0, 20)\n",
-    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys); plt.grid(); \n",
-    "plt.plot(xs, ys); "
+    "ys = xs.explin(0.01, 1, 0, 20).plot(xs=xs)"
    ]
   },
   {
@@ -651,8 +648,7 @@
    "outputs": [],
    "source": [
     "# plot mapping function (output vs input)\n",
-    "ys = xs.clip(0.25, 0.75)\n",
-    "plt.figure(figsize=(3, 1.5)); plt.plot(xs, ys, label=''); plt.grid(); "
+    "ys = xs.clip(0.25, 0.75).plot(xs=xs, label=''); plt.grid(); "
    ]
   },
   {
@@ -822,9 +818,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-12, 13)) # one octave around any note\n",
-    "ys = xs.midi_to_ratio()\n",
-    "\n",
-    "plt.plot(xs, ys, \"r-\", label=\"midi_to_ratio result\")\n",
+    "ys = xs.midi_to_ratio().plot(xs=xs, c=\"r\", ls=\"-\", label=\"midi_to_ratio result\")\n",
     "plt.plot(0, 1, \"ro\", label=\"midi_ratio of 0\")\n",
     "plt.legend(); plt.grid();"
    ]
@@ -1042,8 +1036,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-60, 0, 6)) # some 6 dB steps\n",
-    "ys = xs.dbamp()\n",
-    "plt.plot(xs, ys, \"ro-\", ms=2,label=\"db_to_amp result [arb. unit]\")\n",
+    "ys = xs.dbamp().plot(xs=xs, marker=\"o\", ms=2, label=\"db_to_amp result [arb. unit]\")\n",
     "plt.legend(); plt.grid();"
    ]
   },
@@ -1215,9 +1208,8 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(1, 10000))\n",
-    "plt.plot(xs, pam.hz_to_mel(xs));\n",
-    "plt.xlabel('frequencies [Hz]'); plt.ylabel('mel scale (Slaney)');\n",
-    "plt.grid()"
+    "xs.hz_to_mel().plot(xs=xs)\n",
+    "plt.xlabel('frequencies [Hz]'); plt.ylabel('mel scale (Slaney)'); plt.grid();"
    ]
   },
   {
@@ -1237,8 +1229,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(21, 120, 7)).midicps() # frequencies of fifth series\n",
-    "ys = xs.hz_to_mel(htk=True) \n",
-    "plt.plot(xs, ys, \"o-\", label=\"mel values for frequencies\"); \n",
+    "xs.hz_to_mel(htk=True).plot(xs=xs, marker=\"o\", label=\"mel values for frequencies\"); \n",
     "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"mel scale\"); \n",
     "plt.legend(); plt.grid(); plt.loglog()\n",
     "plt.plot([1000], [1000], \"ro-\", label=\"a reference point\");"
@@ -1287,7 +1278,7 @@
    "source": [
     "xs = chain(np.arange(-3, 3, 0.01))\n",
     "for theta in [0.1, 0.5, 1, 3]:\n",
-    "    plt.plot(xs, xs.distort(theta), label=f\"threshold = {theta}\")\n",
+    "    xs.distort(theta).plot(xs=xs, label=f\"threshold = {theta}\")\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.legend(); plt.title(\"distort mapping function\");"
    ]
@@ -1300,8 +1291,7 @@
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').distort(0.3).plot(label='distorted');\n",
+    "np.sin(2*np.pi*50*ts).plot(label='sine').distort(0.3).plot(label='distorted');\n",
     "plt.legend(loc='upper right');"
    ]
   },
@@ -1349,7 +1339,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-3, 3, 0.01))\n",
-    "plt.plot(xs, xs.softclip())\n",
+    "xs.softclip().plot(xs=xs)\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.title(\"softclip mapping function\");"
    ]
@@ -1408,9 +1398,9 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(0, 1, 0.01))\n",
-    "plt.plot(xs, xs.scurve())\n",
+    "xs.scurve().plot(xs=xs)\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(); plt.title(\"scurve mapping function\");"
+    "plt.title(\"scurve mapping function\");"
    ]
   },
   {
@@ -1421,7 +1411,7 @@
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts).linlin(-1, 1, 0, 1)\n",
+    "xs = (2*np.pi*50*ts).sin().linlin(-1, 1, 0, 1)\n",
     "xs.plot(label='sine with offset').scurve().plot(label='scurve distorted');\n",
     "plt.legend(loc='upper right');"
    ]
@@ -1469,7 +1459,7 @@
    "source": [
     "xs = chain(np.arange(-10, 10, 0.005))\n",
     "for tau in [0.2, 0.5, 1, 2]:\n",
-    "    plt.plot(xs, xs.lcurve(tau=tau), label=f'lcurve for tau={tau}')\n",
+    "    xs.lcurve(tau=tau).plot(xs=xs, label=f'lcurve for tau={tau}')\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.legend(); plt.title(\"lcurve mapping function\");"
    ]
@@ -1530,7 +1520,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-5, 5, 0.01))\n",
-    "plt.plot(xs, xs.wrap(y1=-1, y2=1))\n",
+    "xs.wrap(y1=-1, y2=1).plot(xs=xs)\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.title(\"wrap mapping function\");"
    ]
@@ -1590,7 +1580,7 @@
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-5, 5, 0.01))\n",
-    "plt.plot(xs, xs.fold(y1=-1, y2=1))\n",
+    "xs.fold(y1=-1, y2=1).plot(xs=xs)\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.title(\"wrap mapping function\");"
    ]
@@ -1809,7 +1799,7 @@
     "xs = chain(np.arange(-10, 10, 0.005))\n",
     "for i, mu in enumerate([-2, 0, 2]):\n",
     "    for j, tau in enumerate([0.2, 0.5, 1]):\n",
-    "        plt.plot(xs, xs.fermi(tau, mu), color=['r','g','b'][i], \n",
+    "        xs.fermi(tau, mu).plot(xs=xs, color=['r','g','b'][i], \n",
     "                 lw=j+1, label=f'lcurve for tau={tau}')\n",
     "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
     "plt.legend(fontsize=8); plt.title(\"fermi curve mapping functions\");"
@@ -1872,7 +1862,7 @@
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
+    "xs = (2*np.pi*50*ts).sin()\n",
     "xs.plot(label='sine').normalize(0.5,1).plot(label='normalized to [0.5, 1]');\n",
     "plt.legend(loc='upper right'); plt.grid()"
    ]

From 02781780b029d3ff9f3566bb8b4abe4a854566a8 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Tue, 4 Nov 2025 21:06:47 +0100
Subject: [PATCH 61/87] fix linspace removal bug

---
 src/pyamapping/__init__.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/pyamapping/__init__.py b/src/pyamapping/__init__.py
index 09d7893..cb83831 100644
--- a/src/pyamapping/__init__.py
+++ b/src/pyamapping/__init__.py
@@ -84,7 +84,6 @@
     "linexp",
     "linlin",
     "linpoly",
-    "linspace",
     "midi_to_cps",
     "midi_to_ratio",
     "norm_peak",

From 76c7ac4f172ba8e67d2932983a6736827a04a132 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Wed, 5 Nov 2025 10:27:51 +0100
Subject: [PATCH 62/87] Updated maximum python version for testing matrix in
 github workflow.

---
 .github/workflows/ci.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index d5c6825..e6e0739 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -61,7 +61,7 @@ jobs:
       matrix:
         python:
         - "3.7"  # oldest Python supported by PSF
-        - "3.11"  # newest Python that is stable
+        - "3.13"  # newest Python that is stable
         platform:
         - ubuntu-latest
         - macos-latest
@@ -110,7 +110,7 @@ jobs:
     steps:
       - uses: actions/checkout@v3
       - uses: actions/setup-python@v4
-        with: {python-version: "3.11"}
+        with: {python-version: "3.12"}
       - name: Retrieve pre-built distribution files
         uses: actions/download-artifact@v3
         with: {name: python-distribution-files, path: dist/}

From bf3b9825246cae61eef6be03c42db271423cd86d Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Wed, 5 Nov 2025 17:26:58 +0100
Subject: [PATCH 63/87] correct wrap() example plot title

---
 notebooks/pyamapping-examples.ipynb | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 1d0c949..60237d7 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -1581,8 +1581,7 @@
    "source": [
     "xs = chain(np.arange(-5, 5, 0.01))\n",
     "xs.fold(y1=-1, y2=1).plot(xs=xs)\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.title(\"wrap mapping function\");"
+    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); "
    ]
   },
   {

From d57f6cb0fb7d9bd16bf5e970fd7d2332401cd9d3 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Wed, 5 Nov 2025 19:15:18 +0100
Subject: [PATCH 64/87] move ChainableArray to separate module

---
 notebooks/pyamapping-examples.ipynb | 187 +++++++++++------------
 src/pyamapping/__init__.py          | 136 ++++++++++++++++-
 src/pyamapping/chainable_array.py   | 108 +++++++++++++
 src/pyamapping/mappings.py          | 229 +---------------------------
 4 files changed, 331 insertions(+), 329 deletions(-)
 create mode 100644 src/pyamapping/chainable_array.py

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index 60237d7..c27d591 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -101,7 +101,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from pyamapping.mappings import _list_numpy_ufuncs, pyamapping_functions\n",
+    "from pyamapping import _list_numpy_ufuncs, pyamapping_functions\n",
     "\n",
     "# print (i) a compact list of all unary and binary numpy functions \n",
     "# and (ii) all pyamapping functions\n",
@@ -1097,20 +1097,9 @@
     "plt.legend(); plt.grid();"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "87",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import librosa\n",
-    "help(librosa.mel_to_hz)"
-   ]
-  },
   {
    "cell_type": "markdown",
-   "id": "88",
+   "id": "87",
    "metadata": {},
    "source": [
     "### `mel_to_hz`\n",
@@ -1131,7 +1120,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89",
+   "id": "88",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1141,7 +1130,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "90",
+   "id": "89",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1150,7 +1139,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91",
+   "id": "90",
    "metadata": {},
    "source": [
     "- ChainableArray.mel_to_hz uses self as input.\n",
@@ -1160,7 +1149,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "92",
+   "id": "91",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1173,7 +1162,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "93",
+   "id": "92",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1185,7 +1174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94",
+   "id": "93",
    "metadata": {},
    "source": [
     "### `hz_to_mel`\n",
@@ -1203,7 +1192,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "95",
+   "id": "94",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1214,7 +1203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96",
+   "id": "95",
    "metadata": {},
    "source": [
     "- ChainableArray.hz_to_mel uses self as input.\n",
@@ -1224,7 +1213,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "97",
+   "id": "96",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1237,7 +1226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98",
+   "id": "97",
    "metadata": {},
    "source": [
     "### `distort`\n",
@@ -1253,7 +1242,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "99",
+   "id": "98",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1262,7 +1251,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "100",
+   "id": "99",
    "metadata": {},
    "source": [
     "- ChainableArray.distort uses self as input.\n",
@@ -1272,7 +1261,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "101",
+   "id": "100",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1286,7 +1275,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "102",
+   "id": "101",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1297,7 +1286,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "103",
+   "id": "102",
    "metadata": {},
    "source": [
     "### `softclip`\n",
@@ -1315,7 +1304,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "104",
+   "id": "103",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1324,7 +1313,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "105",
+   "id": "104",
    "metadata": {},
    "source": [
     "- ChainableArray.softclip uses self as input.\n",
@@ -1334,7 +1323,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "106",
+   "id": "105",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1347,7 +1336,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "107",
+   "id": "106",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1359,7 +1348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "108",
+   "id": "107",
    "metadata": {},
    "source": [
     "### `scurve`\n",
@@ -1374,7 +1363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "109",
+   "id": "108",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1383,7 +1372,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "110",
+   "id": "109",
    "metadata": {},
    "source": [
     "- ChainableArray.scurve uses self as input.\n",
@@ -1393,7 +1382,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "111",
+   "id": "110",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1406,7 +1395,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "112",
+   "id": "111",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1418,7 +1407,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "113",
+   "id": "112",
    "metadata": {},
    "source": [
     "### `lcurve`\n",
@@ -1434,7 +1423,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "114",
+   "id": "113",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1443,7 +1432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "115",
+   "id": "114",
    "metadata": {},
    "source": [
     "- ChainableArray.lcurve uses self as input.\n",
@@ -1453,7 +1442,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "116",
+   "id": "115",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1467,7 +1456,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "117",
+   "id": "116",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1479,7 +1468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "118",
+   "id": "117",
    "metadata": {},
    "source": [
     "### `wrap`\n",
@@ -1496,7 +1485,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "119",
+   "id": "118",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1505,7 +1494,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "120",
+   "id": "119",
    "metadata": {},
    "source": [
     "- ChainableArray.wrap uses self as input.\n",
@@ -1515,7 +1504,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "121",
+   "id": "120",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1528,7 +1517,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "122",
+   "id": "121",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1540,7 +1529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "123",
+   "id": "122",
    "metadata": {},
    "source": [
     "### `fold`\n",
@@ -1556,7 +1545,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "124",
+   "id": "123",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1565,7 +1554,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "125",
+   "id": "124",
    "metadata": {},
    "source": [
     "- ChainableArray.wrap uses self as input.\n",
@@ -1575,7 +1564,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "126",
+   "id": "125",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1587,7 +1576,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "127",
+   "id": "126",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1599,7 +1588,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "128",
+   "id": "127",
    "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
@@ -1610,7 +1599,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "129",
+   "id": "128",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1633,7 +1622,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "130",
+   "id": "129",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1643,7 +1632,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "131",
+   "id": "130",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1656,7 +1645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "132",
+   "id": "131",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1665,7 +1654,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "133",
+   "id": "132",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1677,7 +1666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "134",
+   "id": "133",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1694,7 +1683,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "135",
+   "id": "134",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1710,7 +1699,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "136",
+   "id": "135",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1727,7 +1716,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "137",
+   "id": "136",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1743,7 +1732,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "138",
+   "id": "137",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1756,7 +1745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "139",
+   "id": "138",
    "metadata": {},
    "source": [
     "### `fermi`\n",
@@ -1772,7 +1761,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "140",
+   "id": "139",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1781,7 +1770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "141",
+   "id": "140",
    "metadata": {},
    "source": [
     "- ChainableArray.fermi uses self as input.\n",
@@ -1791,7 +1780,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "142",
+   "id": "141",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1807,7 +1796,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "143",
+   "id": "142",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1819,7 +1808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "144",
+   "id": "143",
    "metadata": {},
    "source": [
     "### `normalize`\n",
@@ -1837,7 +1826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "145",
+   "id": "144",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1846,7 +1835,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "146",
+   "id": "145",
    "metadata": {},
    "source": [
     "- ChainableArray.normalize uses self as input.\n",
@@ -1856,7 +1845,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "147",
+   "id": "146",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1868,7 +1857,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "148",
+   "id": "147",
    "metadata": {},
    "source": [
     "### `norm_peak`\n",
@@ -1885,7 +1874,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "149",
+   "id": "148",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1894,7 +1883,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "150",
+   "id": "149",
    "metadata": {},
    "source": [
     "- ChainableArray.norm_peak uses self as input.\n",
@@ -1904,7 +1893,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "151",
+   "id": "150",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1916,7 +1905,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "152",
+   "id": "151",
    "metadata": {},
    "source": [
     "### `norm_rms`\n",
@@ -1933,7 +1922,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "153",
+   "id": "152",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1942,7 +1931,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "154",
+   "id": "153",
    "metadata": {},
    "source": [
     "- ChainableArray.norm_rms uses self as input.\n",
@@ -1952,7 +1941,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "155",
+   "id": "154",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1964,7 +1953,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "156",
+   "id": "155",
    "metadata": {},
    "source": [
     "### `remove_dc`\n",
@@ -1979,7 +1968,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "157",
+   "id": "156",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1988,7 +1977,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "158",
+   "id": "157",
    "metadata": {},
    "source": [
     "- ChainableArray.remove_dc uses self as input.\n",
@@ -1998,7 +1987,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "159",
+   "id": "158",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2010,7 +1999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "160",
+   "id": "159",
    "metadata": {},
    "source": [
     "### `gain`\n",
@@ -2027,7 +2016,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "161",
+   "id": "160",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2036,7 +2025,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "162",
+   "id": "161",
    "metadata": {},
    "source": [
     "- ChainableArray.gain uses self as input.\n",
@@ -2046,7 +2035,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "163",
+   "id": "162",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2058,7 +2047,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "164",
+   "id": "163",
    "metadata": {},
    "source": [
     "### `ecdf`\n",
@@ -2083,7 +2072,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "165",
+   "id": "164",
    "metadata": {},
    "source": [
     "**Example 1**: (compute once - use many)\n"
@@ -2092,7 +2081,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "166",
+   "id": "165",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2114,7 +2103,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "167",
+   "id": "166",
    "metadata": {},
    "source": [
     "**Example 2:** (compute and map in one go)\n",
@@ -2125,7 +2114,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "168",
+   "id": "167",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2135,7 +2124,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "169",
+   "id": "168",
    "metadata": {},
    "source": [
     "### `lin_to_ecdf`\n",
@@ -2150,7 +2139,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "170",
+   "id": "169",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2161,7 +2150,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "171",
+   "id": "170",
    "metadata": {},
    "source": [
     "### `ecdf_to_lin`\n",
@@ -2175,7 +2164,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "172",
+   "id": "171",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2191,7 +2180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "173",
+   "id": "172",
    "metadata": {},
    "source": [
     "- quantiles mapping should pass a cdf array \n",
@@ -2201,7 +2190,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "174",
+   "id": "173",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/src/pyamapping/__init__.py b/src/pyamapping/__init__.py
index cb83831..b750b6c 100644
--- a/src/pyamapping/__init__.py
+++ b/src/pyamapping/__init__.py
@@ -15,17 +15,20 @@
 finally:
     del version, PackageNotFoundError
 
+from typing import Callable, Union
 
+import numpy as np
+
+from pyamapping.chainable_array import ChainableArray, chain
 from pyamapping.mappings import (  # some synonyms; the class and helper functions
-    ChainableArray,
     amp_to_db,
     ampdb,
     bilin,
-    chain,
     clip,
     cps_to_midi,
     cps_to_octave,
     cpsmidi,
+    cpsoct,
     curvelin,
     db_to_amp,
     dbamp,
@@ -49,18 +52,23 @@
     midi_to_cps,
     midi_to_ratio,
     midicps,
+    midiratio,
     norm_peak,
     norm_rms,
     normalize,
     octave_to_cps,
+    octcps,
     ratio_to_midi,
-    register_chain_fn,
+    ratiomidi,
     remove_dc,
     scurve,
     softclip,
     wrap,
 )
 
+# defined here: register_chain_fn,
+
+
 __all__ = [
     "amp_to_db",
     "bilin",
@@ -107,3 +115,125 @@
     "chain",
     "register_chain_fn",
 ]  # type: ignore
+
+
+def register_numpy_ufunc(fn: np.ufunc, name: Union[None, str] = None) -> None:
+    """Register numpy ufunc with one or two ndarray arguments."""
+    nin = fn.nin
+    if nin == 1:
+
+        def method1(self, *args, **kwargs):
+            return ChainableArray(fn(self, *args, **kwargs))
+
+        method = method1
+
+    elif nin == 2:
+
+        def method2(self, other, *args, **kwargs):
+            return ChainableArray(fn(self, other, *args, **kwargs))
+
+        method = method2
+
+    else:
+        print("warning: np.ufunc fn has nin not in [1,2]")
+
+        def default_method(x):
+            return None
+
+        method = default_method
+
+    method.__name__ = fn.__name__ if not name else name
+    method.__doc__ = (
+        f"{method.__name__} implements numpy.{method.__name__}"
+        + f"function for ChainableArray. See help(np.{fn.__name__})"
+    )
+
+    setattr(ChainableArray, method.__name__, method)
+
+
+def register_chain_fn(fn: Callable, name: Union[None, str] = None) -> None:
+    """Register function fn for chaining, optionally under given name."""
+
+    def method(self, *args, **kwargs):
+        return ChainableArray(fn(self, *args, **kwargs))
+
+    method.__name__ = fn.__name__ if not name else name
+    method.__doc__ = (
+        f"{method.__name__} implements the {method.__name__}"
+        + "operation for ChainableArray. Argument: np.ndarray"
+    )
+
+    setattr(ChainableArray, method.__name__, method)
+
+
+def _list_numpy_ufuncs():
+    """Return all numpy ufuncs with 1 or 2 ndarray arguments."""
+    ufunc_list = []
+    for attr_name in dir(np):  # all attributes in numpy
+        attr = getattr(np, attr_name)
+        if isinstance(attr, np.ufunc):
+            if attr.nin <= 2:
+                ufunc_list.append(attr)
+            else:
+                print(attr, attr.nin)
+    return ufunc_list
+
+
+# create class methods for numpy functions and pyamapping functions
+for fn in _list_numpy_ufuncs():  # numpy_mapping_functions:
+    name = "abs" if fn.__name__ == "absolute" else None
+    register_numpy_ufunc(fn, name)
+
+# register some non-ufunc which nontheless should workd
+register_chain_fn(np.angle, "angle")
+ChainableArray.magnitude = ChainableArray.abs
+
+pyamapping_functions = [
+    amp_to_db,
+    bilin,
+    clip,
+    cps_to_midi,
+    cps_to_octave,
+    curvelin,
+    db_to_amp,
+    distort,
+    ecdf_to_lin,
+    ecdf,
+    explin,
+    fermi,
+    fold,
+    gain,
+    hz_to_mel,
+    interp_spline,
+    interp,
+    lcurve,
+    lin_to_ecdf,
+    lincurve,
+    linexp,
+    linlin,
+    linpoly,
+    mel_to_hz,
+    midi_to_cps,
+    midi_to_ratio,
+    norm_peak,
+    norm_rms,
+    normalize,
+    octave_to_cps,
+    ratio_to_midi,
+    remove_dc,
+    scurve,
+    softclip,
+    wrap,
+]
+
+for fn in pyamapping_functions:
+    register_chain_fn(fn, None)
+
+register_chain_fn(cpsmidi, "cpsmidi")
+register_chain_fn(midicps, "midicps")
+register_chain_fn(ratiomidi, "ratiomidi")
+register_chain_fn(midiratio, "midiratio")
+register_chain_fn(cpsoct, "cpsoct")
+register_chain_fn(octcps, "octcps")
+register_chain_fn(ampdb, "ampdb")
+register_chain_fn(dbamp, "dbamp")
diff --git a/src/pyamapping/chainable_array.py b/src/pyamapping/chainable_array.py
new file mode 100644
index 0000000..599d7c6
--- /dev/null
+++ b/src/pyamapping/chainable_array.py
@@ -0,0 +1,108 @@
+"""ChainableArray - a subclass of numpy.ndarray."""
+
+from typing import Any, Callable, TypeVar
+
+import numpy as np
+from numpy.typing import ArrayLike
+
+NDArrayType = TypeVar("NDArrayType", bound=np.ndarray)
+
+
+class ChainableArray(np.ndarray):
+    """subclass for simpler numpy mapping by chaining syntax."""
+
+    def __new__(cls, input_array, *args, **kwargs):
+        """Create new instance."""
+        obj = np.asarray(input_array).view(cls)
+        return obj
+
+    def __array_finalize__(self, obj):
+        """Finalize array."""
+        if obj is None:
+            return
+
+    def to_array(self):
+        """Convert self to np.ndarray."""
+        return np.array(self)
+
+    def to_asig(self, sr=44100):
+        """Convert self to pya.Asig."""
+        from pya import Asig
+
+        return Asig(self, sr=sr)
+
+    def plot(self, *args, **kwargs):
+        """Plot self via matplotlib."""
+        import matplotlib.pyplot as plt
+
+        sr = kwargs.pop("sr", None)
+        if sr:
+            xs = np.arange(0, self.shape[0]) / sr
+            plt.plot(xs, self, *args, **kwargs)
+            plt.xlabel("time [s]")
+        else:
+            xs = kwargs.pop("xs", None)
+            if xs is not None:
+                plt.plot(xs, self, *args, **kwargs)
+            else:
+                plt.plot(self, *args, **kwargs)
+
+        return self
+
+    def mapvec(
+        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
+    ) -> NDArrayType:
+        """Map fn on self by using np.vectorize().
+
+        Parameters
+        ----------
+            self (NDArrayType): array to map
+            fn (Callable[..., Any]): function to call on each element
+
+        Returns
+        -------
+            NDArrayType: mapping result as ChainableArray
+        """
+        return np.vectorize(fn)(self, *args, **kwargs)
+
+    def map(
+        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
+    ) -> NDArrayType:
+        """Apply function fn directly to self; on fail suggest to use mapvec().
+
+        Parameters
+        ----------
+            self (np.ndarray): array used as input of fn
+            fn (Callable[..., Any]): mapping function
+            args and kwargs are passed on to fn
+
+        Raises
+        ------
+            TypeError: if fn fails to operate on np.ndarray as first argument.
+            mapvec() is then proposed as alternative.
+
+        Returns
+        -------
+            ChainableArray: the mapping result as ChainableArray
+        """
+        try:
+            return chain(fn(self, *args, **kwargs))
+        except (TypeError, ValueError, AttributeError) as e:
+            raise TypeError(
+                f"Function {fn.__name__} does not support NumPy arrays directly. "
+                "Use .mapvec() instead for np.vectorize elementwise mapping."
+            ) from e
+
+    def __getattr__(self, name: str) -> Callable:
+        """Dynamically handle method calls."""
+        if name.startswith("dynamic_"):
+            return lambda *args: f"Called {name} with {args}"
+        raise AttributeError(
+            f"'{self.__class__.__name__}' object has no attribute '{name}'"
+        )
+
+
+def chain(input_array: ArrayLike) -> ChainableArray:
+    """Turn np.ndarray into ChainableArray."""
+    # ToDo: check difference to input_array.view(ChainableArray)
+    return ChainableArray(input_array)
diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index d5baf7e..0286d0f 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -1,11 +1,11 @@
 """Collection of audio related mapping functions."""
 
-from typing import Any, Callable, List, Optional, TypeVar, Union
+from typing import List, Optional, Union
 
 import numpy as np
 from numpy.typing import ArrayLike
 
-NDArrayType = TypeVar("NDArrayType", bound=np.ndarray)
+from .chainable_array import ChainableArray, chain
 
 
 def linlin(
@@ -957,103 +957,6 @@ def ecdf_to_lin(
         return interp(x, yc, xc)
 
 
-# create subclass of numpy.ndarray
-
-
-class ChainableArray(np.ndarray):
-    """subclass for simpler numpy mapping by chaining syntax."""
-
-    def __new__(cls, input_array, *args, **kwargs):
-        """Create new instance."""
-        obj = np.asarray(input_array).view(cls)
-        return obj
-
-    def __array_finalize__(self, obj):
-        """Finalize array."""
-        if obj is None:
-            return
-
-    def to_array(self):
-        """Convert self to np.ndarray."""
-        return np.array(self)
-
-    def to_asig(self, sr=44100):
-        """Convert self to pya.Asig."""
-        from pya import Asig
-
-        return Asig(self, sr=sr)
-
-    def plot(self, *args, **kwargs):
-        """Plot self via matplotlib."""
-        import matplotlib.pyplot as plt
-
-        sr = kwargs.pop("sr", None)
-        if sr:
-            xs = np.arange(0, self.shape[0]) / sr
-            plt.plot(xs, self, *args, **kwargs)
-            plt.xlabel("time [s]")
-        else:
-            xs = kwargs.pop("xs", None)
-            if xs is not None:
-                plt.plot(xs, self, *args, **kwargs)
-            else:
-                plt.plot(self, *args, **kwargs)
-
-        return self
-
-    def mapvec(
-        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
-    ) -> NDArrayType:
-        """Map fn on self by using np.vectorize().
-
-        Parameters
-        ----------
-            self (NDArrayType): array to map
-            fn (Callable[..., Any]): function to call on each element
-
-        Returns
-        -------
-            NDArrayType: mapping result as ChainableArray
-        """
-        return np.vectorize(fn)(self, *args, **kwargs)
-
-    def map(
-        self: NDArrayType, fn: Callable[..., Any], *args: Any, **kwargs: Any
-    ) -> NDArrayType:
-        """Apply function fn directly to self; on fail suggest to use mapvec().
-
-        Parameters
-        ----------
-            self (np.ndarray): array used as input of fn
-            fn (Callable[..., Any]): mapping function
-            args and kwargs are passed on to fn
-
-        Raises
-        ------
-            TypeError: if fn fails to operate on np.ndarray as first argument.
-            mapvec() is then proposed as alternative.
-
-        Returns
-        -------
-            ChainableArray: the mapping result as ChainableArray
-        """
-        try:
-            return chain(fn(self, *args, **kwargs))
-        except (TypeError, ValueError, AttributeError) as e:
-            raise TypeError(
-                f"Function {fn.__name__} does not support NumPy arrays directly. "
-                "Use .mapvec() instead for np.vectorize elementwise mapping."
-            ) from e
-
-    def __getattr__(self, name: str) -> Callable:
-        """Dynamically handle method calls."""
-        if name.startswith("dynamic_"):
-            return lambda *args: f"Called {name} with {args}"
-        raise AttributeError(
-            f"'{self.__class__.__name__}' object has no attribute '{name}'"
-        )
-
-
 def ecdf(
     x: np.ndarray, selection: slice = slice(None, None, None)
 ) -> tuple[np.ndarray, np.ndarray]:
@@ -1082,131 +985,3 @@ def ecdf(
     xs = np.sort(x)
     ys = np.arange(1, len(xs) + 1) / float(len(xs))
     return xs[selection], ys[selection]
-
-
-def register_numpy_ufunc(fn: np.ufunc, name: Union[None, str] = None) -> None:
-    """Register numpy ufunc with one or two ndarray arguments."""
-    nin = fn.nin
-    if nin == 1:
-
-        def method1(self, *args, **kwargs):
-            return ChainableArray(fn(self, *args, **kwargs))
-
-        method = method1
-
-    elif nin == 2:
-
-        def method2(self, other, *args, **kwargs):
-            return ChainableArray(fn(self, other, *args, **kwargs))
-
-        method = method2
-
-    else:
-        print("warning: np.ufunc fn has nin not in [1,2]")
-
-        def default_method(x):
-            return None
-
-        method = default_method
-
-    method.__name__ = fn.__name__ if not name else name
-    method.__doc__ = (
-        f"{method.__name__} implements numpy.{method.__name__}"
-        + f"function for ChainableArray. See help(np.{fn.__name__})"
-    )
-
-    setattr(ChainableArray, method.__name__, method)
-
-
-def register_chain_fn(fn: Callable, name: Union[None, str] = None) -> None:
-    """Register function fn for chaining, optionally under given name."""
-
-    def method(self, *args, **kwargs):
-        return ChainableArray(fn(self, *args, **kwargs))
-
-    method.__name__ = fn.__name__ if not name else name
-    method.__doc__ = (
-        f"{method.__name__} implements the {method.__name__}"
-        + "operation for ChainableArray. Argument: np.ndarray"
-    )
-
-    setattr(ChainableArray, method.__name__, method)
-
-
-def _list_numpy_ufuncs():
-    """Return all numpy ufuncs with 1 or 2 ndarray arguments."""
-    ufunc_list = []
-    for attr_name in dir(np):  # all attributes in numpy
-        attr = getattr(np, attr_name)
-        if isinstance(attr, np.ufunc):
-            if attr.nin <= 2:
-                ufunc_list.append(attr)
-            else:
-                print(attr, attr.nin)
-    return ufunc_list
-
-
-# create class methods for numpy functions and pyamapping functions
-for fn in _list_numpy_ufuncs():  # numpy_mapping_functions:
-    name = "abs" if fn.__name__ == "absolute" else None
-    register_numpy_ufunc(fn, name)
-
-# register some non-ufunc which nontheless should workd
-register_chain_fn(np.angle, "angle")
-ChainableArray.magnitude = ChainableArray.abs
-
-pyamapping_functions = [
-    amp_to_db,
-    bilin,
-    clip,
-    cps_to_midi,
-    cps_to_octave,
-    curvelin,
-    db_to_amp,
-    distort,
-    ecdf_to_lin,
-    ecdf,
-    explin,
-    fermi,
-    fold,
-    gain,
-    hz_to_mel,
-    interp_spline,
-    interp,
-    lcurve,
-    lin_to_ecdf,
-    lincurve,
-    linexp,
-    linlin,
-    linpoly,
-    mel_to_hz,
-    midi_to_cps,
-    midi_to_ratio,
-    norm_peak,
-    norm_rms,
-    normalize,
-    octave_to_cps,
-    ratio_to_midi,
-    remove_dc,
-    scurve,
-    softclip,
-    wrap,
-]
-
-for fn in pyamapping_functions:
-    register_chain_fn(fn, None)
-
-register_chain_fn(cpsmidi, "cpsmidi")
-register_chain_fn(midicps, "midicps")
-register_chain_fn(ratiomidi, "ratiomidi")
-register_chain_fn(midiratio, "midiratio")
-register_chain_fn(cpsoct, "cpsoct")
-register_chain_fn(octcps, "octcps")
-register_chain_fn(ampdb, "ampdb")
-register_chain_fn(dbamp, "dbamp")
-
-
-def chain(input_array: ArrayLike) -> ChainableArray:
-    """Turn np.ndarray into ChainableArray."""
-    # ToDo: check difference to input_array.view(ChainableArray)
-    return ChainableArray(input_array)

From a4b0d82b26d08e59e0c30fbd2e7bd4c769a91237 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Thu, 6 Nov 2025 10:45:59 +0100
Subject: [PATCH 65/87] Added a few tests for mappings, also added scipy as a
 dependency to the setup.cfg

---
 setup.cfg              |  1 +
 tests/test_mappings.py | 33 +++++++++++++++++++++++++++++++++
 2 files changed, 34 insertions(+)

diff --git a/setup.cfg b/setup.cfg
index 333c4f6..cf14e4b 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -49,6 +49,7 @@ package_dir =
 # For more information, check out https://semver.org/.
 install_requires =
     numpy
+    scipy
     importlib-metadata; python_version<"3.8"
 
 
diff --git a/tests/test_mappings.py b/tests/test_mappings.py
index 21182be..02518af 100644
--- a/tests/test_mappings.py
+++ b/tests/test_mappings.py
@@ -1,4 +1,5 @@
 import numpy as np
+from pyamapping.mappings import bilin, curvelin, explin, lincurve, midi_to_ratio, ratio_to_midi
 import pytest
 
 from pyamapping import (
@@ -50,6 +51,11 @@ def test_midi_cps():
         assert x == cps_to_midi(midi_to_cps(x))
 
 
+def test_midi_ratio():
+    pytest.approx(midi_to_ratio(7), 1.4983070768766815)
+    pytest.approx(ratio_to_midi(2), 12.0)
+
+
 def test_db_amp():
     for x in range(128):
         assert x == pytest.approx(amp_to_db(db_to_amp(x)))
@@ -60,3 +66,30 @@ def test_hz_mel():
     pytest.approx(mel_to_hz(549.64), 440)
     for x in range(128):
         assert x == pytest.approx(hz_to_mel(mel_to_hz(x)))
+
+
+def test_explin():
+    f = 220 * 2**(-5/12)
+    pytest.approx(explin(f, 220, 440, 0, 12), -5.0)
+    pytest.approx(explin(0.01, 0.001, 1.0, -30, 0, "max"), -20.0)
+
+
+def test_lincurve():
+    pytest.approx(
+        lincurve(np.array([0.0, 0.1, 0.4, 0.7, 1.0]), 0, 1, 0, 0.4),
+        np.array([0., 0.08385643, 0.25474431, 0.34852956, 0.4]) 
+    )
+
+
+def test_curvelin():
+    pytest.approx(
+        curvelin(np.array([0, 0.1, 0.3, 0.5]), 0, 0.5, 0, 10),
+        np.array([ 0.,  0.94934752,  3.65734932, 10.])
+    )
+
+
+def test_bilin():
+    pytest.approx(
+        bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60),
+        np.array([-30., -20., -10.,   0.,  60., 120.])
+    )
\ No newline at end of file

From 49b8cdb12d8930a649ecd886f0990d832d726ea9 Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 6 Nov 2025 13:57:52 +0100
Subject: [PATCH 66/87] add tests and update test function names

---
 tests/test_mappings.py | 74 +++++++++++++++++++++++++++++++++++-------
 1 file changed, 63 insertions(+), 11 deletions(-)

diff --git a/tests/test_mappings.py b/tests/test_mappings.py
index 02518af..f4b0a31 100644
--- a/tests/test_mappings.py
+++ b/tests/test_mappings.py
@@ -1,5 +1,4 @@
 import numpy as np
-from pyamapping.mappings import bilin, curvelin, explin, lincurve, midi_to_ratio, ratio_to_midi
 import pytest
 
 from pyamapping import (
@@ -12,6 +11,21 @@
     mel_to_hz,
     midi_to_cps,
 )
+from pyamapping.mappings import (
+    bilin,
+    cps_to_octave,
+    curvelin,
+    distort,
+    explin,
+    lcurve,
+    lincurve,
+    linexp,
+    midi_to_ratio,
+    octave_to_cps,
+    ratio_to_midi,
+    scurve,
+    softclip,
+)
 
 
 def test_linlin():
@@ -44,32 +58,42 @@ def test_clip():
     assert np.array_equal(clip(a1, 2, 4), a2)
 
 
-def test_midi_cps():
+def test_midi_to_cps_to_midi():
     assert midi_to_cps(69) == 440
     assert cps_to_midi(440) == 69
     for x in range(128):
         assert x == cps_to_midi(midi_to_cps(x))
 
 
-def test_midi_ratio():
+def test_midi_ratio_midi():
     pytest.approx(midi_to_ratio(7), 1.4983070768766815)
     pytest.approx(ratio_to_midi(2), 12.0)
 
 
-def test_db_amp():
+def test_cps_octave_cps():
+    pytest.approx(octave_to_cps(5.75), 880)
+    pytest.approx(cps_to_octave(220), 3.75)
+
+
+def test_db_amp_db():
     for x in range(128):
         assert x == pytest.approx(amp_to_db(db_to_amp(x)))
 
 
-def test_hz_mel():
+def test_hz_mel_hz():
     pytest.approx(hz_to_mel(440), 549.64)
     pytest.approx(mel_to_hz(549.64), 440)
-    for x in range(128):
+    for x in np.arange(1, 128):
         assert x == pytest.approx(hz_to_mel(mel_to_hz(x)))
 
 
+def test_linexp():
+    pytest.approx(linexp(5, 1, 8, 2, 256), 32.0)
+    pytest.approx(linexp(7, 0, 5, 100, 300, "max"), 300)
+
+
 def test_explin():
-    f = 220 * 2**(-5/12)
+    f = 220 * 2 ** (-5 / 12)
     pytest.approx(explin(f, 220, 440, 0, 12), -5.0)
     pytest.approx(explin(0.01, 0.001, 1.0, -30, 0, "max"), -20.0)
 
@@ -77,19 +101,47 @@ def test_explin():
 def test_lincurve():
     pytest.approx(
         lincurve(np.array([0.0, 0.1, 0.4, 0.7, 1.0]), 0, 1, 0, 0.4),
-        np.array([0., 0.08385643, 0.25474431, 0.34852956, 0.4]) 
+        np.array([0.0, 0.08385643, 0.25474431, 0.34852956, 0.4]),
     )
 
 
 def test_curvelin():
     pytest.approx(
         curvelin(np.array([0, 0.1, 0.3, 0.5]), 0, 0.5, 0, 10),
-        np.array([ 0.,  0.94934752,  3.65734932, 10.])
+        np.array([0.0, 0.94934752, 3.65734932, 10.0]),
     )
 
 
 def test_bilin():
     pytest.approx(
         bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60),
-        np.array([-30., -20., -10.,   0.,  60., 120.])
-    )
\ No newline at end of file
+        np.array([-30.0, -20.0, -10.0, 0.0, 60.0, 120.0]),
+    )
+
+
+def test_distort():
+    pytest.approx(
+        distort([0, 1, 2, 3], 1),
+        np.array([0.0, 0.5, 0.66666667, 0.75]),
+    )
+
+
+def test_softclip():
+    pytest.approx(
+        softclip(np.arange(1, 5)),
+        np.array([0.75, 0.875, 0.91666667, 0.9375]),
+    )
+
+
+def test_scurve():
+    pytest.approx(
+        scurve(np.arange(0, 1, 0.25)),
+        np.array([0.0, 0.15625, 0.5, 0.84375]),
+    )
+
+
+def test_lcurve():
+    pytest.approx(
+        lcurve(np.array([-1, -0.5, 0, 0.5, 1])),
+        np.array([0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858]),
+    )

From 417f0e945f5661fa1901e0df79c95192654136bf Mon Sep 17 00:00:00 2001
From: Thomas Hermann <thermann@techfak.uni-bielefeld.de>
Date: Thu, 6 Nov 2025 14:21:58 +0100
Subject: [PATCH 67/87] add more tests

---
 tests/test_mappings.py | 72 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 72 insertions(+)

diff --git a/tests/test_mappings.py b/tests/test_mappings.py
index f4b0a31..a421495 100644
--- a/tests/test_mappings.py
+++ b/tests/test_mappings.py
@@ -17,14 +17,23 @@
     curvelin,
     distort,
     explin,
+    fermi,
+    fold,
+    gain,
     lcurve,
     lincurve,
     linexp,
+    linpoly,
     midi_to_ratio,
+    norm_peak,
+    norm_rms,
+    normalize,
     octave_to_cps,
     ratio_to_midi,
+    remove_dc,
     scurve,
     softclip,
+    wrap,
 )
 
 
@@ -140,8 +149,71 @@ def test_scurve():
     )
 
 
+def test_fermi():
+    pytest.approx(
+        fermi(np.array([-1, -0.5, 0, 0.5, 1])),
+        np.array([0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858]),
+    )
+
+
 def test_lcurve():
     pytest.approx(
         lcurve(np.array([-1, -0.5, 0, 0.5, 1])),
         np.array([0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858]),
     )
+
+
+def test_wrap():
+    pytest.approx(
+        wrap(np.arange(-3, 5), 0, 3),
+        np.array([0, 1, 2, 0, 1, 2, 0, 1]),
+    )
+
+
+def test_fold():
+    pytest.approx(
+        fold(np.arange(0, 13), 0, 4),
+        np.array([0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4]),
+    )
+
+
+def test_linpoly():
+    pytest.approx(
+        linpoly(np.arange(-2, 3), 2.5, 100, 500, curve=1),
+        np.array([172.0, 268.0, 300.0, 332.0, 428.0]),
+    )
+
+
+def test_normalize():
+    pytest.approx(
+        np.sort(normalize(np.random.rand(10)))[[0, -1]],
+        np.array([-1, 1]),
+    )
+
+
+def test_norm_peak():
+    pytest.approx(
+        np.max(norm_peak(np.random.rand(10), 5)),
+        5,
+    )
+
+
+def test_norm_rms():
+    pytest.approx(
+        norm_rms(np.array([1, 0, 0, -1]), 1),
+        np.array([1.41421356, 0.0, 0.0, -1.41421356]),
+    )
+
+
+def test_remove_dc():
+    pytest.approx(
+        remove_dc(np.array([1, 2, 3, 4])),
+        np.array([-1.5, -0.5, 0.5, 1.5]),
+    )
+
+
+def test_gain():
+    pytest.approx(
+        gain(np.array([1, 2, 3, 4]), amp=2),
+        np.array([2, 4, 6, 8]),
+    )

From f9efca529207c269b1b81829e06da5649ed1d10b Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Thu, 26 Mar 2026 12:37:01 +0100
Subject: [PATCH 68/87] Increased test coverage a tiny bit. Maybe need to
 switch to more elaborate test format?

---
 notebooks/pyamapping-examples.ipynb | 277 +++++++++++++++++++++++++---
 tests/test_mappings.py              |   8 +
 2 files changed, 255 insertions(+), 30 deletions(-)

diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index c27d591..e4934fb 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -67,7 +67,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "2",
    "metadata": {},
    "outputs": [],
@@ -96,10 +96,45 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "4",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "=== numpy functions with 1 argument ===\n",
+      "['absolute', 'absolute', 'arccos', 'arccosh', 'arccos', 'arccosh', 'arcsin',\n",
+      " 'arcsinh', 'arctan', 'arctanh', 'arcsin', 'arcsinh', 'arctan', 'arctanh',\n",
+      " 'bitwise_count', 'invert', 'invert', 'cbrt', 'ceil', 'conjugate', 'conjugate',\n",
+      " 'cos', 'cosh', 'deg2rad', 'degrees', 'exp', 'exp2', 'expm1', 'fabs', 'floor',\n",
+      " 'frexp', 'invert', 'isfinite', 'isinf', 'isnan', 'isnat', 'log', 'log10',\n",
+      " 'log1p', 'log2', 'logical_not', 'modf', 'negative', 'positive', 'rad2deg',\n",
+      " 'radians', 'reciprocal', 'rint', 'sign', 'signbit', 'sin', 'sinh', 'spacing',\n",
+      " 'sqrt', 'square', 'tan', 'tanh', 'trunc']\n",
+      "\n",
+      "=== numpy functions with 2 argument ===\n",
+      "['add', 'arctan2', 'arctan2', 'bitwise_and', 'left_shift', 'bitwise_or',\n",
+      " 'right_shift', 'bitwise_xor', 'copysign', 'divide', 'divmod', 'equal',\n",
+      " 'float_power', 'floor_divide', 'fmax', 'fmin', 'fmod', 'gcd', 'greater',\n",
+      " 'greater_equal', 'heaviside', 'hypot', 'lcm', 'ldexp', 'left_shift', 'less',\n",
+      " 'less_equal', 'logaddexp', 'logaddexp2', 'logical_and', 'logical_or',\n",
+      " 'logical_xor', 'matmul', 'matvec', 'maximum', 'minimum', 'remainder',\n",
+      " 'multiply', 'nextafter', 'not_equal', 'power', 'power', 'remainder',\n",
+      " 'right_shift', 'subtract', 'divide', 'vecdot', 'vecmat']\n",
+      "\n",
+      "=== pyamapping functions: ===\n",
+      "['amp_to_db', 'bilin', 'clip', 'cps_to_midi', 'cps_to_octave', 'curvelin',\n",
+      " 'db_to_amp', 'distort', 'ecdf_to_lin', 'ecdf', 'explin', 'fermi', 'fold',\n",
+      " 'gain', 'hz_to_mel', 'interp_spline', 'interp', 'lcurve', 'lin_to_ecdf',\n",
+      " 'lincurve', 'linexp', 'linlin', 'linpoly', 'mel_to_hz', 'midi_to_cps',\n",
+      " 'midi_to_ratio', 'norm_peak', 'norm_rms', 'normalize', 'octave_to_cps',\n",
+      " 'ratio_to_midi', 'remove_dc', 'scurve', 'softclip', 'wrap']\n"
+     ]
+    }
+   ],
    "source": [
     "from pyamapping import _list_numpy_ufuncs, pyamapping_functions\n",
     "\n",
@@ -314,20 +349,42 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "20",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(32.0)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "pam.linexp(5, 1, 8, 2, 256)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "21",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(300.0)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "pam.linexp(7, 0, 5, 100, 300, \"max\") # clip result to maximum input range"
    ]
@@ -343,10 +400,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "id": "23",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
     "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
@@ -357,10 +425,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "id": "24",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "# plot linexp mapping function (output vs input)\n",
     "ys = xs.linexp(0.25, 0.85, 0.2, 2).plot(xs=xs)"
@@ -385,10 +464,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "26",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(-5.0)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "# example: unmap a frequency to MIDI note with explin\n",
     "f = 220 * 2**(-5/12) # 5 semitones higher than 220 Hz\n",
@@ -397,10 +487,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "27",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(-20.0)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "# example: unmap amplitude to level in decibel\n",
     "pam.explin(0.01, 0.001, 1.0, -30, 0, \"max\") # clip result to maximum input range"
@@ -468,10 +569,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "id": "33",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
     "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
@@ -490,10 +602,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "35",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.linspace(0, 100, 100))\n",
     "for i, curve in enumerate(range(-9, 10, 3)):\n",
@@ -530,10 +653,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "id": "38",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
     "xs.plot(\"k-\", label=\"input data for lincurve\") # plot input data\n",
@@ -553,10 +687,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "id": "40",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.linspace(0, 100, 500))\n",
     "for i, curve in enumerate(range(-9, 10, 3)):\n",
@@ -593,10 +738,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "id": "43",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 900x250 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "xs = chain(np.arange(0, 100)) # turn data into ChainableArray\n",
     "xs.bilin(60, 20, 80, 0, -20, 60).plot(\"b.\", ms=1, label='bilin');\n",
@@ -606,6 +762,27 @@
     "plt.legend(); plt.grid()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "cb3b9473",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "ChainableArray([-30., -20., -10.,   0.,  60., 120.])"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pam.bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "44",
@@ -783,10 +960,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "id": "59",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1.4983070768766815"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "pam.midi_to_ratio(7) # a fifth is ~3/2 (in equal tuning)"
    ]
@@ -839,10 +1027,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "id": "64",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(12.0)"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "pam.ratio_to_midi(2) # should be 12 for ratio=2 (i.e. an octave)"
    ]
@@ -2202,7 +2401,25 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "pyamapping (3.12.8)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.8"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/tests/test_mappings.py b/tests/test_mappings.py
index a421495..26ef21c 100644
--- a/tests/test_mappings.py
+++ b/tests/test_mappings.py
@@ -98,13 +98,21 @@ def test_hz_mel_hz():
 
 def test_linexp():
     pytest.approx(linexp(5, 1, 8, 2, 256), 32.0)
+    pytest.approx(linexp(5, 1, 8, 256, 2, "minmax"), 16.0)
     pytest.approx(linexp(7, 0, 5, 100, 300, "max"), 300)
+    pytest.approx(linexp(1, 2, 5, 100, 300, "min"), 100)
+    pytest.approx(linexp(1, 2, 5, 100, 300, "minmax"), 100)
+    pytest.approx(linexp(6, 2, 5, 100, 300, "minmax"), 300)
 
 
 def test_explin():
     f = 220 * 2 ** (-5 / 12)
     pytest.approx(explin(f, 220, 440, 0, 12), -5.0)
     pytest.approx(explin(0.01, 0.001, 1.0, -30, 0, "max"), -20.0)
+    pytest.approx(explin(0.01, 0.001, 1.0, 0, -30, "minmax"), -10.0)
+    pytest.approx(explin(2, 0.001, 1.0, 0, 1, "max"), 1)
+    pytest.approx(explin(0.0001, 0.001, 1.0, 0, 1, "min"), 0)
+    pytest.approx(explin(0.0001, 0.001, 1.0, 0, 1, "minmax"), 0)
 
 
 def test_lincurve():

From ede80c3b07b629fde9e15e96e6e82309ae97688c Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Fri, 27 Mar 2026 13:16:41 +0100
Subject: [PATCH 69/87] Started creating extensive text coverage with AI help.
 A few functions are still missing, to be continued

---
 src/pyamapping/mappings.py |   2 +-
 tests/test_mappings.py     | 166 -------------------------------------
 2 files changed, 1 insertion(+), 167 deletions(-)

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 0286d0f..56c377e 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -792,7 +792,7 @@ def wrap(
     """Wrap array around target range [y1, y2].
 
     This implements the mapping y1 + np.mod(x - y1, y2 - y1).
-    The order of y1, y2 is irrelevant.
+    The order of y1, y2 is irrelevant with input values strictly inside the range.
 
     Parameters
     ----------
diff --git a/tests/test_mappings.py b/tests/test_mappings.py
index 26ef21c..04191ea 100644
--- a/tests/test_mappings.py
+++ b/tests/test_mappings.py
@@ -1,134 +1,17 @@
 import numpy as np
 import pytest
 
-from pyamapping import (
-    amp_to_db,
-    clip,
-    cps_to_midi,
-    db_to_amp,
-    hz_to_mel,
-    linlin,
-    mel_to_hz,
-    midi_to_cps,
-)
 from pyamapping.mappings import (
     bilin,
-    cps_to_octave,
-    curvelin,
-    distort,
-    explin,
-    fermi,
     fold,
     gain,
-    lcurve,
-    lincurve,
-    linexp,
     linpoly,
-    midi_to_ratio,
     norm_peak,
     norm_rms,
-    normalize,
-    octave_to_cps,
-    ratio_to_midi,
     remove_dc,
-    scurve,
-    softclip,
-    wrap,
 )
 
 
-def test_linlin():
-    origin = np.array([-1, 0, 1, 2, 4])
-    target = np.array([-50, 0, 50, 100, 200])
-    assert np.array_equal(target, linlin(origin, 0, 2, 0, 100))
-
-    # test clipping
-    assert 100 == linlin(-10, 0, 100, 100, 200, "min")
-    assert 200 == linlin(105, 0, 100, 100, 200, "max")
-
-    assert 200 == linlin(-10, 0, 100, 200, 100, "max")
-    assert 100 == linlin(105, 0, 100, 200, 100, "min")
-
-    assert 100 == linlin(3, 5, 105, 100, 1000, "minmax")
-    assert 1000 == linlin(105, 0, 100, 100, 1000, "minmax")
-
-    # test y1 > y2
-    assert 0.0 == linlin(1, 0, 1, 1, 0)
-    assert 0.5 == linlin(0.5, 0, 1, 1, 0)
-    assert 1.0 == linlin(0, 0, 1, 1, 0)
-
-
-def test_clip():
-    for x, y in zip([2, 3, 4, 5, 6], [3, 3, 4, 5, 5]):
-        assert y == clip(x, 3, 5)
-
-    a1 = np.arange(6)
-    a2 = np.array([2, 2, 2, 3, 4, 4])
-    assert np.array_equal(clip(a1, 2, 4), a2)
-
-
-def test_midi_to_cps_to_midi():
-    assert midi_to_cps(69) == 440
-    assert cps_to_midi(440) == 69
-    for x in range(128):
-        assert x == cps_to_midi(midi_to_cps(x))
-
-
-def test_midi_ratio_midi():
-    pytest.approx(midi_to_ratio(7), 1.4983070768766815)
-    pytest.approx(ratio_to_midi(2), 12.0)
-
-
-def test_cps_octave_cps():
-    pytest.approx(octave_to_cps(5.75), 880)
-    pytest.approx(cps_to_octave(220), 3.75)
-
-
-def test_db_amp_db():
-    for x in range(128):
-        assert x == pytest.approx(amp_to_db(db_to_amp(x)))
-
-
-def test_hz_mel_hz():
-    pytest.approx(hz_to_mel(440), 549.64)
-    pytest.approx(mel_to_hz(549.64), 440)
-    for x in np.arange(1, 128):
-        assert x == pytest.approx(hz_to_mel(mel_to_hz(x)))
-
-
-def test_linexp():
-    pytest.approx(linexp(5, 1, 8, 2, 256), 32.0)
-    pytest.approx(linexp(5, 1, 8, 256, 2, "minmax"), 16.0)
-    pytest.approx(linexp(7, 0, 5, 100, 300, "max"), 300)
-    pytest.approx(linexp(1, 2, 5, 100, 300, "min"), 100)
-    pytest.approx(linexp(1, 2, 5, 100, 300, "minmax"), 100)
-    pytest.approx(linexp(6, 2, 5, 100, 300, "minmax"), 300)
-
-
-def test_explin():
-    f = 220 * 2 ** (-5 / 12)
-    pytest.approx(explin(f, 220, 440, 0, 12), -5.0)
-    pytest.approx(explin(0.01, 0.001, 1.0, -30, 0, "max"), -20.0)
-    pytest.approx(explin(0.01, 0.001, 1.0, 0, -30, "minmax"), -10.0)
-    pytest.approx(explin(2, 0.001, 1.0, 0, 1, "max"), 1)
-    pytest.approx(explin(0.0001, 0.001, 1.0, 0, 1, "min"), 0)
-    pytest.approx(explin(0.0001, 0.001, 1.0, 0, 1, "minmax"), 0)
-
-
-def test_lincurve():
-    pytest.approx(
-        lincurve(np.array([0.0, 0.1, 0.4, 0.7, 1.0]), 0, 1, 0, 0.4),
-        np.array([0.0, 0.08385643, 0.25474431, 0.34852956, 0.4]),
-    )
-
-
-def test_curvelin():
-    pytest.approx(
-        curvelin(np.array([0, 0.1, 0.3, 0.5]), 0, 0.5, 0, 10),
-        np.array([0.0, 0.94934752, 3.65734932, 10.0]),
-    )
-
-
 def test_bilin():
     pytest.approx(
         bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60),
@@ -136,48 +19,6 @@ def test_bilin():
     )
 
 
-def test_distort():
-    pytest.approx(
-        distort([0, 1, 2, 3], 1),
-        np.array([0.0, 0.5, 0.66666667, 0.75]),
-    )
-
-
-def test_softclip():
-    pytest.approx(
-        softclip(np.arange(1, 5)),
-        np.array([0.75, 0.875, 0.91666667, 0.9375]),
-    )
-
-
-def test_scurve():
-    pytest.approx(
-        scurve(np.arange(0, 1, 0.25)),
-        np.array([0.0, 0.15625, 0.5, 0.84375]),
-    )
-
-
-def test_fermi():
-    pytest.approx(
-        fermi(np.array([-1, -0.5, 0, 0.5, 1])),
-        np.array([0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858]),
-    )
-
-
-def test_lcurve():
-    pytest.approx(
-        lcurve(np.array([-1, -0.5, 0, 0.5, 1])),
-        np.array([0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858]),
-    )
-
-
-def test_wrap():
-    pytest.approx(
-        wrap(np.arange(-3, 5), 0, 3),
-        np.array([0, 1, 2, 0, 1, 2, 0, 1]),
-    )
-
-
 def test_fold():
     pytest.approx(
         fold(np.arange(0, 13), 0, 4),
@@ -192,13 +33,6 @@ def test_linpoly():
     )
 
 
-def test_normalize():
-    pytest.approx(
-        np.sort(normalize(np.random.rand(10)))[[0, -1]],
-        np.array([-1, 1]),
-    )
-
-
 def test_norm_peak():
     pytest.approx(
         np.max(norm_peak(np.random.rand(10), 5)),

From c3c4ddf989a979f848a03ae7c693a890e563c2f2 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 31 Mar 2026 10:34:20 +0200
Subject: [PATCH 70/87] in-depth testing of all mapping functions

---
 src/pyamapping/mappings.py |  9 ++++--
 tests/test_mappings.py     | 61 --------------------------------------
 2 files changed, 6 insertions(+), 64 deletions(-)
 delete mode 100644 tests/test_mappings.py

diff --git a/src/pyamapping/mappings.py b/src/pyamapping/mappings.py
index 56c377e..5e5f898 100644
--- a/src/pyamapping/mappings.py
+++ b/src/pyamapping/mappings.py
@@ -892,11 +892,11 @@ def gain(x: np.ndarray, db: Optional[float] = None, amp: Optional[float] = None)
     -------
         np.ndarray: scaled (amplified / attenuated) array
     """
-    if db:
+    if db is not None:
         sig = x * dbamp(db)
     else:
         sig = x.copy()
-    if amp:
+    if amp is not None:
         sig *= amp
     return sig
 
@@ -922,7 +922,7 @@ def lin_to_ecdf(
     """
     if sorted:
         return interp(
-            x, ref_data, np.arange(1, len(ref_data) + 1) / float(len(ref_data), left=0)
+            x, ref_data, np.arange(1, len(ref_data) + 1) / float(len(ref_data)), left=0
         )
     else:
         return interp(x, *ecdf(ref_data))
@@ -985,3 +985,6 @@ def ecdf(
     xs = np.sort(x)
     ys = np.arange(1, len(xs) + 1) / float(len(xs))
     return xs[selection], ys[selection]
+
+
+
diff --git a/tests/test_mappings.py b/tests/test_mappings.py
deleted file mode 100644
index 04191ea..0000000
--- a/tests/test_mappings.py
+++ /dev/null
@@ -1,61 +0,0 @@
-import numpy as np
-import pytest
-
-from pyamapping.mappings import (
-    bilin,
-    fold,
-    gain,
-    linpoly,
-    norm_peak,
-    norm_rms,
-    remove_dc,
-)
-
-
-def test_bilin():
-    pytest.approx(
-        bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60),
-        np.array([-30.0, -20.0, -10.0, 0.0, 60.0, 120.0]),
-    )
-
-
-def test_fold():
-    pytest.approx(
-        fold(np.arange(0, 13), 0, 4),
-        np.array([0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4]),
-    )
-
-
-def test_linpoly():
-    pytest.approx(
-        linpoly(np.arange(-2, 3), 2.5, 100, 500, curve=1),
-        np.array([172.0, 268.0, 300.0, 332.0, 428.0]),
-    )
-
-
-def test_norm_peak():
-    pytest.approx(
-        np.max(norm_peak(np.random.rand(10), 5)),
-        5,
-    )
-
-
-def test_norm_rms():
-    pytest.approx(
-        norm_rms(np.array([1, 0, 0, -1]), 1),
-        np.array([1.41421356, 0.0, 0.0, -1.41421356]),
-    )
-
-
-def test_remove_dc():
-    pytest.approx(
-        remove_dc(np.array([1, 2, 3, 4])),
-        np.array([-1.5, -0.5, 0.5, 1.5]),
-    )
-
-
-def test_gain():
-    pytest.approx(
-        gain(np.array([1, 2, 3, 4]), amp=2),
-        np.array([2, 4, 6, 8]),
-    )

From 324dc85074be00c40ff8472e5d6f401e2c273e50 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 31 Mar 2026 10:39:45 +0200
Subject: [PATCH 71/87] Basic test coverage for chainable array

---
 tests/test_bilin.py           |  92 ++++++++++++++++++
 tests/test_chainable_array.py | 133 ++++++++++++++++++++++++++
 tests/test_clip.py            |  89 +++++++++++++++++
 tests/test_cps_octave_cps.py  |  61 ++++++++++++
 tests/test_curvelin.py        | 117 +++++++++++++++++++++++
 tests/test_db_amp_db.py       |  68 +++++++++++++
 tests/test_distort.py         |  82 ++++++++++++++++
 tests/test_ecdf.py            | 175 ++++++++++++++++++++++++++++++++++
 tests/test_explin.py          | 114 ++++++++++++++++++++++
 tests/test_fermi.py           |  89 +++++++++++++++++
 tests/test_fold.py            |  92 ++++++++++++++++++
 tests/test_gain.py            |  79 +++++++++++++++
 tests/test_hz_mel_hz.py       |  90 +++++++++++++++++
 tests/test_lcurve.py          |  76 +++++++++++++++
 tests/test_lincurve.py        | 128 +++++++++++++++++++++++++
 tests/test_linexp.py          | 104 ++++++++++++++++++++
 tests/test_linlin.py          |  91 ++++++++++++++++++
 tests/test_linpoly.py         |  94 ++++++++++++++++++
 tests/test_midi_cps_midi.py   |  69 ++++++++++++++
 tests/test_midi_ratio_midi.py |  61 ++++++++++++
 tests/test_norm_peak.py       |  79 +++++++++++++++
 tests/test_norm_rms.py        |  79 +++++++++++++++
 tests/test_normalize.py       |  86 +++++++++++++++++
 tests/test_remove_dc.py       |  70 ++++++++++++++
 tests/test_scurve.py          |  75 +++++++++++++++
 tests/test_softclip.py        |  80 ++++++++++++++++
 tests/test_wrap.py            |  70 ++++++++++++++
 27 files changed, 2443 insertions(+)
 create mode 100644 tests/test_bilin.py
 create mode 100644 tests/test_chainable_array.py
 create mode 100644 tests/test_clip.py
 create mode 100644 tests/test_cps_octave_cps.py
 create mode 100644 tests/test_curvelin.py
 create mode 100644 tests/test_db_amp_db.py
 create mode 100644 tests/test_distort.py
 create mode 100644 tests/test_ecdf.py
 create mode 100644 tests/test_explin.py
 create mode 100644 tests/test_fermi.py
 create mode 100644 tests/test_fold.py
 create mode 100644 tests/test_gain.py
 create mode 100644 tests/test_hz_mel_hz.py
 create mode 100644 tests/test_lcurve.py
 create mode 100644 tests/test_lincurve.py
 create mode 100644 tests/test_linexp.py
 create mode 100644 tests/test_linlin.py
 create mode 100644 tests/test_linpoly.py
 create mode 100644 tests/test_midi_cps_midi.py
 create mode 100644 tests/test_midi_ratio_midi.py
 create mode 100644 tests/test_norm_peak.py
 create mode 100644 tests/test_norm_rms.py
 create mode 100644 tests/test_normalize.py
 create mode 100644 tests/test_remove_dc.py
 create mode 100644 tests/test_scurve.py
 create mode 100644 tests/test_softclip.py
 create mode 100644 tests/test_wrap.py

diff --git a/tests/test_bilin.py b/tests/test_bilin.py
new file mode 100644
index 0000000..e88dc99
--- /dev/null
+++ b/tests/test_bilin.py
@@ -0,0 +1,92 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import interp_spline, bilin
+from pyamapping.chainable_array import ChainableArray, chain
+
+
+class TestInterpSplineLinear:
+    """Test linear interpolation (k=1, default) between control points."""
+
+    def test_exact_at_control_points(self):
+        assert_allclose(interp_spline([-1, 0, 1], [-1, 0, 1]), [-1, 0, 1])
+
+    def test_midpoint_between_control_points(self):
+        assert interp_spline(0.5, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(0.5)
+
+    def test_custom_control_points(self):
+        assert interp_spline(50, [0, 100], [0, 200]) == pytest.approx(100.0)
+
+    def test_three_point_piecewise(self):
+        # two segments with different slopes
+        result = interp_spline(
+            np.array([0, 25, 50, 75, 100]),
+            [0, 50, 100],
+            [0, 10, 30],
+        )
+        assert_allclose(result, [0, 5, 10, 20, 30])
+
+
+class TestInterpSplineExtrapolation:
+    """Test that values outside xc range are extrapolated."""
+
+    def test_extrapolates_below(self):
+        result = interp_spline(-1, [0, 1], [0, 10])
+        assert result == pytest.approx(-10.0)
+
+    def test_extrapolates_above(self):
+        result = interp_spline(2, [0, 1], [0, 10])
+        assert result == pytest.approx(20.0)
+
+
+class TestInterpSplineReturnType:
+    """Test that return type depends on input type."""
+
+    def test_chainable_array_input_returns_plain_ndarray(self):
+        x = ChainableArray(np.array([0.0, 0.5, 1.0]))
+        result = interp_spline(x, [-1, 0, 1], [-1, 0, 1])
+        assert type(result) == np.ndarray
+
+    def test_plain_array_input_returns_chainable_array(self):
+        x = np.array([0.0, 0.5, 1.0])
+        result = interp_spline(x, [-1, 0, 1], [-1, 0, 1])
+        assert isinstance(result, ChainableArray)
+
+
+class TestBilin:
+    """Test bilin as a two-segment piecewise linear mapping via interp_spline."""
+
+    def test_known_values(self):
+        assert_allclose(
+            bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60),
+            [-30.0, -20.0, -10.0, 0.0, 60.0, 120.0],
+        )
+
+    def test_xcenter_maps_to_ycenter(self):
+        assert bilin(60, 60, 20, 80, 0, -20, 60) == pytest.approx(0.0)
+
+    def test_xmin_maps_to_ymin(self):
+        assert bilin(20, 60, 20, 80, 0, -20, 60) == pytest.approx(-20.0)
+
+    def test_xmax_maps_to_ymax(self):
+        assert bilin(80, 60, 20, 80, 0, -20, 60) == pytest.approx(60.0)
+
+    def test_extrapolates_below_xmin(self):
+        result = bilin(0, 60, 20, 80, 0, -20, 60)
+        assert result < -20.0
+
+    def test_extrapolates_above_xmax(self):
+        result = bilin(100, 60, 20, 80, 0, -20, 60)
+        assert result > 60.0
+
+    def test_symmetric_mapping(self):
+        # with symmetric x and y ranges, xcenter should map to ycenter=0
+        assert bilin(0.5, 0.5, 0.0, 1.0, 0.0, -1.0, 1.0) == pytest.approx(0.0)
+
+    def test_two_slopes_differ(self):
+        # slope left of xcenter: (-20-0)/(20-60) = 0.5
+        # slope right of xcenter: (60-0)/(80-60) = 3.0
+        slope_left = (bilin(40, 60, 20, 80, 0, -20, 60) - bilin(20, 60, 20, 80, 0, -20, 60)) / 20
+        slope_right = (bilin(80, 60, 20, 80, 0, -20, 60) - bilin(60, 60, 20, 80, 0, -20, 60)) / 20
+        assert slope_left != pytest.approx(slope_right)
\ No newline at end of file
diff --git a/tests/test_chainable_array.py b/tests/test_chainable_array.py
new file mode 100644
index 0000000..3587028
--- /dev/null
+++ b/tests/test_chainable_array.py
@@ -0,0 +1,133 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.chainable_array import ChainableArray, chain
+
+class TestChainableArrayCreation:
+    """Test ChainableArray instantiation and type."""
+
+    def test_from_list(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        assert isinstance(a, ChainableArray)
+        assert isinstance(a, np.ndarray)
+
+    def test_from_ndarray(self):
+        a = ChainableArray(np.array([1.0, 2.0, 3.0]))
+        assert isinstance(a, ChainableArray)
+
+    def test_values_preserved(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        assert_allclose(a, [1.0, 2.0, 3.0])
+
+    def test_dtype_preserved(self):
+        a = ChainableArray(np.array([1, 2, 3], dtype=np.int32))
+        assert a.dtype == np.int32
+
+    def test_numpy_operations_return_chainable_array(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a * 2
+        assert isinstance(result, ChainableArray)
+
+    def test_shape_preserved(self):
+        a = ChainableArray(np.ones((3, 4)))
+        assert a.shape == (3, 4)
+
+
+class TestChain:
+    """Test the chain() factory function."""
+
+    def test_returns_chainable_array(self):
+        assert isinstance(chain(np.array([1.0, 2.0])), ChainableArray)
+
+    def test_from_list(self):
+        assert isinstance(chain([1.0, 2.0, 3.0]), ChainableArray)
+
+    def test_values_preserved(self):
+        assert_allclose(chain([1.0, 2.0, 3.0]), [1.0, 2.0, 3.0])
+
+    def test_from_scalar(self):
+        assert isinstance(chain(1.0), ChainableArray)
+
+
+class TestChainableArrayToArray:
+    """Test to_array() conversion."""
+
+    def test_returns_plain_ndarray(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.to_array()
+        assert type(result) is np.ndarray
+        assert not isinstance(result, ChainableArray)
+
+    def test_values_preserved(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        assert_allclose(a.to_array(), [1.0, 2.0, 3.0])
+
+
+class TestChainableArrayMap:
+    """Test map() method."""
+
+    def test_applies_function(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.map(lambda x: x * 2)
+        assert_allclose(result, [2.0, 4.0, 6.0])
+
+    def test_returns_chainable_array(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        assert isinstance(a.map(lambda x: x * 2), ChainableArray)
+
+    def test_passes_args(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.map(np.add, 10.0)
+        assert_allclose(result, [11.0, 12.0, 13.0])
+
+    def test_raises_type_error_for_scalar_only_function(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        with pytest.raises(TypeError, match="Use .mapvec()"):
+            a.map(lambda x: x + 1 if isinstance(x, float) else (_ for _ in ()).throw(TypeError()))
+
+    def test_chaining(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.map(lambda x: x * 2).map(lambda x: x + 1)
+        assert_allclose(result, [3.0, 5.0, 7.0])
+
+
+class TestChainableArrayMapvec:
+    """Test mapvec() method."""
+
+    def test_applies_scalar_function_elementwise(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.mapvec(lambda x: x ** 2)
+        assert_allclose(result, [1.0, 4.0, 9.0])
+
+    def test_returns_chainable_array(self):
+        a = ChainableArray([1.0, 4.0, 9.0])
+        assert isinstance(a.mapvec(np.sqrt), ChainableArray)
+
+    def test_passes_args(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.mapvec(lambda x, y: x + y, 10.0)
+        assert_allclose(result, [11.0, 12.0, 13.0])
+
+    def test_chaining(self):
+        a = ChainableArray([1.0, 2.0, 3.0])
+        result = a.mapvec(lambda x: x * 2).mapvec(lambda x: x + 1)
+        assert_allclose(result, [3.0, 5.0, 7.0])
+
+
+class TestChainableArrayGetattr:
+    """Test dynamic attribute handling via __getattr__."""
+
+    def test_dynamic_prefix_returns_callable(self):
+        a = ChainableArray([1.0, 2.0])
+        assert callable(a.dynamic_foo)
+
+    def test_dynamic_method_returns_string(self):
+        a = ChainableArray([1.0, 2.0])
+        result = a.dynamic_foo(1, 2)
+        assert "dynamic_foo" in result
+
+    def test_unknown_attribute_raises_attribute_error(self):
+        a = ChainableArray([1.0, 2.0])
+        with pytest.raises(AttributeError):
+            _ = a.nonexistent_method
\ No newline at end of file
diff --git a/tests/test_clip.py b/tests/test_clip.py
new file mode 100644
index 0000000..f37358d
--- /dev/null
+++ b/tests/test_clip.py
@@ -0,0 +1,89 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import clip
+
+class TestClipScalar:
+    """Test clipping of scalar float/int values."""
+
+    def test_value_below_minimum_is_clipped(self):
+        assert clip(2, 3, 5) == 3
+
+    def test_value_above_maximum_is_clipped(self):
+        assert clip(6, 3, 5) == 5
+
+    def test_value_within_range_is_unchanged(self):
+        assert clip(4, 3, 5) == 4
+
+    def test_value_equal_to_minimum(self):
+        assert clip(3, 3, 5) == 3
+
+    def test_value_equal_to_maximum(self):
+        assert clip(5, 3, 5) == 5
+
+    def test_negative_range(self):
+        assert clip(-10, -5, -1) == -5
+        assert clip(-3, -5, -1) == -3
+        assert clip(0, -5, -1) == -1
+
+    def test_float_values(self):
+        assert clip(1.5, 2.0, 4.0) == pytest.approx(2.0)
+        assert clip(3.5, 2.0, 4.0) == pytest.approx(3.5)
+        assert clip(5.0, 2.0, 4.0) == pytest.approx(4.0)
+
+
+class TestClipScalarDefaultBounds:
+    """Test that default bounds (-inf, +inf) leave values unchanged."""
+
+    def test_no_minimum_large_negative(self):
+        assert clip(-1e9) == -1e9
+
+    def test_no_maximum_large_positive(self):
+        assert clip(1e9) == 1e9
+
+    def test_only_minimum_clips_below(self):
+        assert clip(-5, minimum=0) == 0
+        assert clip(5, minimum=0) == 5
+
+    def test_only_maximum_clips_above(self):
+        assert clip(5, maximum=3) == 3
+        assert clip(1, maximum=3) == 1
+
+
+class TestClipArray:
+    """Test clipping of numpy array inputs."""
+
+    def test_array_all_clipped(self):
+        assert_allclose(clip(np.array([0, 1, 6, 7]), 2, 4), [2, 2, 4, 4])
+
+    def test_array_none_clipped(self):
+        a = np.array([2.0, 3.0, 4.0])
+        assert_allclose(clip(a, 0, 10), a)
+
+    def test_array_mixed(self):
+        a1 = np.arange(6)
+        assert_allclose(clip(a1, 2, 4), [2, 2, 2, 3, 4, 4])
+
+    def test_array_default_bounds(self):
+        a = np.array([-1e9, 0.0, 1e9])
+        assert_allclose(clip(a), a)
+
+    def test_array_only_minimum(self):
+        assert_allclose(clip(np.array([0, 2, 5]), minimum=3), [3, 3, 5])
+
+    def test_array_only_maximum(self):
+        assert_allclose(clip(np.array([0, 2, 5]), maximum=3), [0, 2, 3])
+
+
+class TestClipScalarArrayConsistency:
+    """Scalar and array code paths should return identical results."""
+
+    def test_same_result_for_value_below(self):
+        assert clip(1, 3, 5) == clip(np.array([1]), 3, 5)[0]
+
+    def test_same_result_for_value_within(self):
+        assert clip(4, 3, 5) == clip(np.array([4]), 3, 5)[0]
+
+    def test_same_result_for_value_above(self):
+        assert clip(7, 3, 5) == clip(np.array([7]), 3, 5)[0]
\ No newline at end of file
diff --git a/tests/test_cps_octave_cps.py b/tests/test_cps_octave_cps.py
new file mode 100644
index 0000000..ca09010
--- /dev/null
+++ b/tests/test_cps_octave_cps.py
@@ -0,0 +1,61 @@
+import pytest
+
+from pyamapping.mappings import cps_to_octave, octave_to_cps
+
+
+class TestCpsToOctave:
+    """Test frequency to decimal octave conversion."""
+
+    def test_440hz_is_4_75(self):
+        # reference point: 440 Hz -> 4.75
+        assert cps_to_octave(440) == pytest.approx(4.75)
+
+    def test_middle_c_is_4(self):
+        # MIDI 60 / C4 / 261.626 Hz -> 4.0
+        assert cps_to_octave(261.626) == pytest.approx(4.0, rel=1e-4)
+
+    def test_880hz_is_5_75(self):
+        assert cps_to_octave(880) == pytest.approx(5.75)
+
+    def test_220hz_is_3_75(self):
+        assert cps_to_octave(220) == pytest.approx(3.75)
+
+    def test_octave_up_increments_by_one(self):
+        assert cps_to_octave(880) == pytest.approx(cps_to_octave(440) + 1)
+
+    def test_octave_down_decrements_by_one(self):
+        assert cps_to_octave(220) == pytest.approx(cps_to_octave(440) - 1)
+
+
+class TestOctaveToCps:
+    """Test decimal octave to frequency conversion."""
+
+    def test_4_75_is_440hz(self):
+        assert octave_to_cps(4.75) == pytest.approx(440.0)
+
+    def test_4_is_middle_c(self):
+        assert octave_to_cps(4.0) == pytest.approx(261.626, rel=1e-4)
+
+    def test_5_75_is_880hz(self):
+        assert octave_to_cps(5.75) == pytest.approx(880.0)
+
+    def test_3_75_is_220hz(self):
+        assert octave_to_cps(3.75) == pytest.approx(220.0)
+
+    def test_increment_by_one_doubles_frequency(self):
+        assert octave_to_cps(5.75) == pytest.approx(octave_to_cps(4.75) * 2)
+
+    def test_decrement_by_one_halves_frequency(self):
+        assert octave_to_cps(3.75) == pytest.approx(octave_to_cps(4.75) / 2)
+
+
+class TestCpsOctaveRoundtrip:
+    """Test that the two functions are exact inverses of each other."""
+
+    def test_cps_to_octave_to_cps(self):
+        for cps in [27.5, 110.0, 220.0, 261.626, 440.0, 880.0, 1760.0]:
+            assert octave_to_cps(cps_to_octave(cps)) == pytest.approx(cps, rel=1e-9)
+
+    def test_octave_to_cps_to_octave(self):
+        for octave in [1.0, 2.75, 3.75, 4.0, 4.75, 5.75, 7.0]:
+            assert cps_to_octave(octave_to_cps(octave)) == pytest.approx(octave, rel=1e-9)
\ No newline at end of file
diff --git a/tests/test_curvelin.py b/tests/test_curvelin.py
new file mode 100644
index 0000000..a3c9cbf
--- /dev/null
+++ b/tests/test_curvelin.py
@@ -0,0 +1,117 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import curvelin, lincurve
+
+class TestCurvelinEndpoints:
+    """Test that x1->y1 and x2->y2 mappings are exact."""
+
+    def test_x1_maps_to_y1(self):
+        assert curvelin(0.0, 0, 0.5, 0, 10) == pytest.approx(0.0)
+
+    def test_x2_maps_to_y2(self):
+        assert curvelin(0.5, 0, 0.5, 0, 10) == pytest.approx(10.0)
+
+    def test_x1_maps_to_y1_custom(self):
+        assert curvelin(2.0, 2, 5, 10, 20) == pytest.approx(10.0)
+
+    def test_x2_maps_to_y2_custom(self):
+        assert curvelin(5.0, 2, 5, 10, 20) == pytest.approx(20.0)
+
+
+class TestCurvelinLinearFallback:
+    """Test the linear branch triggered when abs(curve) < 0.001."""
+
+    def test_zero_curve_midpoint(self):
+        assert curvelin(0.5, 0, 1, 0, 1, curve=0.0) == pytest.approx(0.5)
+
+    def test_tiny_curve_is_linear(self):
+        assert curvelin(0.5, 0, 1, 0, 1, curve=0.0009) == pytest.approx(0.5)
+
+    def test_linear_array_input(self):
+        x = np.array([0.0, 0.5, 1.0])
+        assert_allclose(curvelin(x, 0, 1, 0, 1, curve=0.0), [0.0, 0.5, 1.0])
+
+
+class TestCurvelinCurvedMapping:
+    """Test exponential (non-linear) mapping with meaningful curve values."""
+
+    def test_known_values(self):
+        assert_allclose(
+            curvelin(np.array([0, 0.1, 0.3, 0.5]), 0, 0.5, 0, 10),
+            [0.0, 0.94934752, 3.65734932, 10.0],
+            rtol=1e-5,
+        )
+
+    def test_negative_curve_endpoints(self):
+        assert curvelin(0.0, 0, 1, 0, 1, curve=-2.0) == pytest.approx(0.0)
+        assert curvelin(1.0, 0, 1, 0, 1, curve=-2.0) == pytest.approx(1.0)
+
+    def test_positive_curve_endpoints(self):
+        assert curvelin(0.0, 0, 1, 0, 1, curve=2.0) == pytest.approx(0.0)
+        assert curvelin(1.0, 0, 1, 0, 1, curve=2.0) == pytest.approx(1.0)
+
+
+class TestCurvelinPolarityInversion:
+    """Test y2 < y1 (inverted range)."""
+
+    def test_inverted_range_endpoints(self):
+        assert curvelin(0.0, 0, 1, y1=1.0, y2=0.0) == pytest.approx(1.0)
+        assert curvelin(1.0, 0, 1, y1=1.0, y2=0.0) == pytest.approx(0.0)
+
+    def test_inverted_range_midpoint_is_between_bounds(self):
+        result = curvelin(0.5, 0, 1, y1=1.0, y2=0.0)
+        assert 0.0 <= result <= 1.0
+
+
+class TestCurvelinExtrapolation:
+    """Default (clip=None) should extrapolate beyond [x1, x2]."""
+
+    def test_extrapolates_below_x1(self):
+        result = curvelin(-1.0, 0, 1, 0, 1, curve=0.0)
+        assert result < 0.0
+
+    def test_extrapolates_above_x2(self):
+        result = curvelin(2.0, 0, 1, 0, 1, curve=0.0)
+        assert result > 1.0
+
+
+class TestCurvelinClipping:
+    """Test all clip modes."""
+
+    def test_clip_max_caps_at_y2(self):
+        assert curvelin(2.0, 0, 1, 0, 1, curve=0.0, clip="max") == pytest.approx(1.0)
+
+    def test_clip_max_does_not_affect_lower_values(self):
+        assert curvelin(0.5, 0, 1, 0, 1, curve=0.0, clip="max") == pytest.approx(0.5)
+
+    def test_clip_min_caps_at_y1(self):
+        assert curvelin(-1.0, 0, 1, 0, 1, curve=0.0, clip="min") == pytest.approx(0.0)
+
+    def test_clip_min_does_not_affect_upper_values(self):
+        assert curvelin(0.5, 0, 1, 0, 1, curve=0.0, clip="min") == pytest.approx(0.5)
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert curvelin(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(0.0)
+        assert curvelin(2.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(1.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        assert curvelin(-1.0, 0, 1, 0, 1, curve=0.0, clip="both") == pytest.approx(0.0)
+        assert curvelin(2.0, 0, 1, 0, 1, curve=0.0, clip="both") == pytest.approx(1.0)
+
+    def test_clip_minmax_array_input(self):
+        result = curvelin(np.array([-1.0, 0.5, 2.0]), 0, 1, 0, 1, curve=0.0, clip="minmax")
+        assert_allclose(result, [0.0, 0.5, 1.0])
+
+
+class TestCurvelinVsLincurve:
+    """curvelin and lincurve should be inverses of each other."""
+
+    def test_curvelin_is_inverse_of_lincurve(self):
+        for x in [0.1, 0.3, 0.5, 0.7, 0.9]:
+            assert curvelin(lincurve(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(x, rel=1e-6)
+
+    def test_lincurve_is_inverse_of_curvelin(self):
+        for x in [0.1, 0.3, 0.5, 0.7, 0.9]:
+            assert lincurve(curvelin(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(x, rel=1e-6)
\ No newline at end of file
diff --git a/tests/test_db_amp_db.py b/tests/test_db_amp_db.py
new file mode 100644
index 0000000..c984eb6
--- /dev/null
+++ b/tests/test_db_amp_db.py
@@ -0,0 +1,68 @@
+import pytest
+
+from pyamapping.mappings import db_to_amp, amp_to_db
+
+
+class TestDbToAmp:
+    """Test decibel to linear amplitude conversion."""
+
+    def test_0db_is_unity(self):
+        assert db_to_amp(0) == pytest.approx(1.0)
+
+    def test_20db_is_ten(self):
+        assert db_to_amp(20) == pytest.approx(10.0)
+
+    def test_minus_20db_is_tenth(self):
+        assert db_to_amp(-20) == pytest.approx(0.1)
+
+    def test_6db_approximately_doubles(self):
+        assert db_to_amp(6) == pytest.approx(2.0, rel=1e-2)
+
+    def test_negative_inf_db_is_silence(self):
+        assert db_to_amp(-float("inf")) == pytest.approx(0.0)
+
+    def test_positive_db_is_above_unity(self):
+        assert db_to_amp(10) > 1.0
+
+    def test_negative_db_is_below_unity(self):
+        assert db_to_amp(-10) < 1.0
+
+
+class TestAmpToDb:
+    """Test linear amplitude to decibel conversion."""
+
+    def test_unity_is_0db(self):
+        assert amp_to_db(1.0) == pytest.approx(0.0)
+
+    def test_ten_is_20db(self):
+        assert amp_to_db(10.0) == pytest.approx(20.0)
+
+    def test_tenth_is_minus_20db(self):
+        assert amp_to_db(0.1) == pytest.approx(-20.0)
+
+    def test_double_amplitude_is_approx_6db(self):
+        assert amp_to_db(2.0) == pytest.approx(6.0, rel=1e-2)
+
+    def test_half_amplitude_is_approx_minus_6db(self):
+        assert amp_to_db(0.5) == pytest.approx(-6.0, rel=1e-2)
+
+    def test_zero_amplitude_is_minus_inf(self):
+        with pytest.warns(RuntimeWarning, match="divide by zero"):
+            result = amp_to_db(0.0)
+        assert result == -float("inf")
+
+
+class TestDbAmpRoundtrip:
+    """Test that the two functions are exact inverses of each other."""
+
+    def test_db_to_amp_to_db(self):
+        for db in range(128):
+            assert amp_to_db(db_to_amp(db)) == pytest.approx(db, rel=1e-9)
+
+    def test_amp_to_db_to_amp(self):
+        for amp in [0.001, 0.1, 0.5, 1.0, 2.0, 10.0, 100.0]:
+            assert db_to_amp(amp_to_db(amp)) == pytest.approx(amp, rel=1e-9)
+
+    def test_negative_db_roundtrip(self):
+        for db in [-60, -40, -20, -6]:
+            assert amp_to_db(db_to_amp(db)) == pytest.approx(db, rel=1e-9)
\ No newline at end of file
diff --git a/tests/test_distort.py b/tests/test_distort.py
new file mode 100644
index 0000000..1c002b0
--- /dev/null
+++ b/tests/test_distort.py
@@ -0,0 +1,82 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import distort
+
+
+class TestDistortScalar:
+    """Test distortion of scalar values."""
+
+    def test_zero_input_is_zero(self):
+        assert distort(0.0) == pytest.approx(0.0)
+
+    def test_positive_input_is_below_threshold(self):
+        # x / (1 + |x|) is always < 1 for finite x
+        assert distort(1.0) == pytest.approx(0.5)
+        assert distort(2.0) == pytest.approx(2 / 3)
+        assert distort(3.0) == pytest.approx(0.75)
+
+    def test_negative_input_mirrors_positive(self):
+        # function is odd: distort(-x) == -distort(x)
+        assert distort(-1.0) == pytest.approx(-0.5)
+        assert distort(-2.0) == pytest.approx(-2 / 3)
+
+    def test_output_bounded_below_one(self):
+        assert abs(distort(1e9)) < 1.0
+
+    def test_output_bounded_above_minus_one(self):
+        assert distort(-1e9) > -1.0
+
+    def test_custom_threshold(self):
+        assert distort(1.0, threshold=2.0) == pytest.approx(1 / 3)
+
+    def test_threshold_scales_output(self):
+        # doubling threshold halves the compression at x=threshold
+        assert distort(1.0, threshold=2.0) == pytest.approx(distort(0.5, threshold=1.0))
+
+
+class TestDistortArray:
+    """Test distortion of array inputs."""
+
+    def test_known_values(self):
+        assert_allclose(
+            distort([0, 1, 2, 3], threshold=1),
+            [0.0, 0.5, 2/3, 0.75],
+            rtol=1e-6,
+        )
+
+    def test_negative_array_mirrors_positive(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(distort(-x), -distort(x))
+
+    def test_array_output_bounded(self):
+        x = np.array([-1e9, -1.0, 0.0, 1.0, 1e9])
+        result = distort(x)
+        assert np.all(result > -1.0)
+        assert np.all(result < 1.0)
+
+    def test_custom_threshold_array(self):
+        assert_allclose(
+            distort(np.array([0, 1, 2]), threshold=2.0),
+            [0.0, 1/3, 0.5],
+            rtol=1e-6,
+        )
+
+
+class TestDistortProperties:
+    """Test mathematical properties of the distortion function."""
+
+    def test_odd_symmetry(self):
+        # distort(-x) == -distort(x) for all x
+        for x in [0.1, 1.0, 5.0, 100.0]:
+            assert distort(-x) == pytest.approx(-distort(x))
+
+    def test_output_range_is_open_minus_one_to_one(self):
+        # output strictly between -1 and 1 for all finite inputs
+        for x in [-1e9, -100, -1, 0, 1, 100, 1e9]:
+            assert -1.0 < distort(x) < 1.0 or distort(x) == 0.0
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(-10, 10, 100)
+        result = distort(x)
\ No newline at end of file
diff --git a/tests/test_ecdf.py b/tests/test_ecdf.py
new file mode 100644
index 0000000..749724c
--- /dev/null
+++ b/tests/test_ecdf.py
@@ -0,0 +1,175 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import interp, ecdf, ecdf_to_lin, lin_to_ecdf
+
+
+class TestEcdf:
+    """Test empirical cumulative distribution function."""
+
+    def test_output_is_tuple_of_two_arrays(self):
+        xs, ys = ecdf(np.array([3.0, 1.0, 2.0]))
+        assert isinstance(xs, np.ndarray)
+        assert isinstance(ys, np.ndarray)
+
+    def test_xs_are_sorted(self):
+        xs, ys = ecdf(np.array([3.0, 1.0, 2.0]))
+        assert np.all(np.diff(xs) >= 0)
+
+    def test_ys_range_from_step_to_one(self):
+        xs, ys = ecdf(np.array([1.0, 2.0, 3.0, 4.0]))
+        assert ys[0] == pytest.approx(0.25)
+        assert ys[-1] == pytest.approx(1.0)
+
+    def test_ys_are_uniformly_spaced(self):
+        xs, ys = ecdf(np.array([1.0, 2.0, 3.0, 4.0]))
+        assert_allclose(np.diff(ys), np.full(3, 0.25))
+
+    def test_lengths_match(self):
+        x = np.random.rand(20)
+        xs, ys = ecdf(x)
+        assert len(xs) == len(ys) == 20
+
+    def test_selection_slice(self):
+        x = np.arange(1, 11, dtype=float)
+        xs, ys = ecdf(x, selection=np.s_[::2])
+        assert len(xs) == 5
+        assert len(ys) == 5
+
+    def test_already_sorted_input(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0])
+        xs, ys = ecdf(x)
+        assert_allclose(xs, x)
+
+
+class TestInterp:
+    """Test piecewise linear interpolation with clipping."""
+
+    def test_exact_at_control_points(self):
+        assert interp(0, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(0.0)
+        assert interp(-1, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(-1.0)
+        assert interp(1, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(1.0)
+
+    def test_midpoint_interpolation(self):
+        assert interp(0.5, [0, 1], [0, 10]) == pytest.approx(5.0)
+
+    def test_clips_below(self):
+        # numpy.interp clips by default, unlike interp_spline
+        assert interp(-2, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(-1.0)
+
+    def test_clips_above(self):
+        assert interp(2, [-1, 0, 1], [-1, 0, 1]) == pytest.approx(1.0)
+
+    def test_array_input(self):
+        result = interp(np.array([-1.0, 0.0, 1.0]), [-1, 0, 1], [-1, 0, 1])
+        assert_allclose(result, [-1.0, 0.0, 1.0])
+
+    def test_default_yc(self):
+        # default yc=[-1, 0, 1] maps xc=[-1, 0, 1] linearly
+        assert interp(0.0, [-1, 0, 1]) == pytest.approx(0.0)
+
+
+class TestLinToEcdf:
+    """Test mapping via empirical cumulative distribution function."""
+
+    def test_output_range_is_zero_to_one(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        result = lin_to_ecdf(ref, ref)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+
+    def test_min_maps_to_lowest_quantile(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert lin_to_ecdf(1.0, ref) == pytest.approx(0.2)
+
+    def test_max_maps_to_one(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert lin_to_ecdf(5.0, ref) == pytest.approx(1.0)
+
+    def test_below_min_clips_to_zero(self):
+        ref = np.array([1.0, 2.0, 3.0])
+        assert lin_to_ecdf(0.0, ref) == pytest.approx(1/3)
+
+    def test_above_max_clips_to_one(self):
+        ref = np.array([1.0, 2.0, 3.0])
+        assert lin_to_ecdf(10.0, ref) == pytest.approx(1.0)
+
+    def test_sorted_and_unsorted_give_same_result(self):
+        ref = np.array([3.0, 1.0, 4.0, 1.0, 5.0, 2.0])
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(
+            lin_to_ecdf(x, ref, sorted=False),
+            lin_to_ecdf(x, np.sort(ref), sorted=True),
+        )
+
+    def test_monotonically_increasing(self):
+        ref = np.random.rand(50)
+        x = np.linspace(0, 1, 20)
+        result = lin_to_ecdf(x, ref)
+        assert np.all(np.diff(result) >= 0)
+
+
+
+class TestEcdfToLin:
+    """Test inverse ECDF mapping (quantiles back to feature values)."""
+
+    def test_max_quantile_maps_to_max_value(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert ecdf_to_lin(1.0, ref) == pytest.approx(5.0)
+
+    def test_min_quantile_maps_to_min_value(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert ecdf_to_lin(0.2, ref) == pytest.approx(1.0)
+
+    def test_midpoint_quantile(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        assert ecdf_to_lin(0.6, ref) == pytest.approx(3.0)
+
+    def test_below_min_quantile_clips(self):
+        ref = np.array([1.0, 2.0, 3.0])
+        assert ecdf_to_lin(0.0, ref) == pytest.approx(1.0)
+
+    def test_above_max_quantile_clips(self):
+        ref = np.array([1.0, 2.0, 3.0])
+        assert ecdf_to_lin(1.5, ref) == pytest.approx(3.0)
+
+    def test_sorted_and_unsorted_give_same_result(self):
+        ref = np.array([3.0, 1.0, 4.0, 1.0, 5.0, 2.0])
+        x = np.array([0.2, 0.5, 0.8])
+        assert_allclose(
+            ecdf_to_lin(x, ref, sorted=False),
+            ecdf_to_lin(x, np.sort(ref), sorted=True),
+        )
+
+    def test_monotonically_increasing(self):
+        ref = np.random.rand(50)
+        x = np.linspace(0.1, 0.9, 20)
+        result = ecdf_to_lin(x, ref)
+        assert np.all(np.diff(result) >= 0)
+
+    def test_array_input(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        result = ecdf_to_lin(np.array([0.2, 0.6, 1.0]), ref)
+        assert_allclose(result, [1.0, 3.0, 5.0])
+
+
+class TestLinEcdfRoundtrip:
+    """Test that lin_to_ecdf and ecdf_to_lin are inverses of each other."""
+
+    def test_lin_to_ecdf_to_lin(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        # map ref values to quantiles and back — should recover original values
+        quantiles = lin_to_ecdf(ref, ref)
+        assert_allclose(ecdf_to_lin(quantiles, ref), ref, rtol=1e-6)
+
+    def test_ecdf_to_lin_to_ecdf(self):
+        ref = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        quantiles = np.array([0.2, 0.4, 0.6, 0.8, 1.0])
+        recovered = lin_to_ecdf(ecdf_to_lin(quantiles, ref), ref)
+        assert_allclose(recovered, quantiles, rtol=1e-6)
+
+    def test_roundtrip_unsorted_ref(self):
+        ref = np.array([3.0, 1.0, 4.0, 2.0, 5.0])
+        quantiles = lin_to_ecdf(np.sort(ref), ref)
+        assert_allclose(ecdf_to_lin(quantiles, ref), np.sort(ref), rtol=1e-6)
\ No newline at end of file
diff --git a/tests/test_explin.py b/tests/test_explin.py
new file mode 100644
index 0000000..0dc3ad6
--- /dev/null
+++ b/tests/test_explin.py
@@ -0,0 +1,114 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import explin, linexp
+
+
+class TestExplinEndpoints:
+    """Test that x1->y1 and x2->y2 mappings are exact."""
+
+    def test_x1_maps_to_y1(self):
+        assert explin(220.0, 220, 440, 0, 12) == pytest.approx(0.0)
+
+    def test_x2_maps_to_y2(self):
+        assert explin(440.0, 220, 440, 0, 12) == pytest.approx(12.0)
+
+    def test_x1_maps_to_y1_custom(self):
+        assert explin(0.001, 0.001, 1.0, -30, 0) == pytest.approx(-30.0)
+
+    def test_x2_maps_to_y2_custom(self):
+        assert explin(1.0, 0.001, 1.0, -30, 0) == pytest.approx(0.0)
+
+
+class TestExplinMapping:
+    """Test logarithmic mapping between endpoints."""
+
+    def test_known_value(self):
+        f = 220 * 2 ** (-5 / 12)
+        assert explin(f, 220, 440, 0, 12) == pytest.approx(-5.0)
+
+    def test_geometric_midpoint_maps_to_linear_midpoint(self):
+        # log mapping: geometric mean of x1,x2 maps to arithmetic mean of y1,y2
+        geo_mid = np.sqrt(1.0 * 100.0)
+        assert explin(geo_mid, 1.0, 100.0, 0.0, 1.0) == pytest.approx(0.5, rel=1e-6)
+
+    def test_inverted_y_range(self):
+        assert explin(0.01, 0.001, 1.0, 0, -30) == pytest.approx(
+            -explin(0.01, 0.001, 1.0, 0, 30), rel=1e-6
+        )
+
+    def test_array_input(self):
+        result = explin(np.array([220.0, 440.0]), 220, 440, 0, 12)
+        assert_allclose(result, [0.0, 12.0])
+
+
+class TestExplinExtrapolation:
+    """Default (clip=None) should extrapolate beyond [x1, x2]."""
+
+    def test_extrapolates_above_x2(self):
+        result = explin(2.0, 0.001, 1.0, 0, 1)
+        assert result > 1.0
+
+    def test_extrapolates_below_x1(self):
+        result = explin(0.0001, 0.001, 1.0, 0, 1)
+        assert result < 0.0
+
+
+class TestExplinClipping:
+    """Test all clip modes."""
+
+    def test_clip_max_caps_at_y2(self):
+        assert explin(2, 0.001, 1.0, 0, 1, clip="max") == pytest.approx(1.0)
+
+    def test_clip_max_does_not_affect_lower_values(self):
+        assert explin(0.01, 0.001, 1.0, -30, 0, clip="max") == pytest.approx(
+            explin(0.01, 0.001, 1.0, -30, 0), rel=1e-6
+        )
+
+    def test_clip_min_caps_at_y1(self):
+        assert explin(0.0001, 0.001, 1.0, 0, 1, clip="min") == pytest.approx(0.0)
+
+    def test_clip_min_does_not_affect_upper_values(self):
+        assert explin(0.1, 0.001, 1.0, 0, 1, clip="min") == pytest.approx(
+            explin(0.1, 0.001, 1.0, 0, 1), rel=1e-6
+        )
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert explin(0.0001, 0.001, 1.0, 0, 1, clip="minmax") == pytest.approx(0.0)
+        assert explin(2.0, 0.001, 1.0, 0, 1, clip="minmax") == pytest.approx(1.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        assert explin(0.0001, 0.001, 1.0, 0, 1, clip="both") == pytest.approx(0.0)
+        assert explin(2.0, 0.001, 1.0, 0, 1, clip="both") == pytest.approx(1.0)
+
+    def test_clip_inverted_y_range(self):
+        assert explin(0.01, 0.001, 1.0, 0, -30, clip="minmax") == pytest.approx(
+            -10.0, rel=1e-5
+        )
+
+    def test_clip_minmax_array_input(self):
+        result = explin(
+            np.array([0.0001, 0.01, 2.0]), 0.001, 1.0, 0, 1, clip="minmax"
+        )
+        assert_allclose(result, [0.0, explin(0.01, 0.001, 1.0, 0, 1), 1.0])
+
+
+class TestExplinProperties:
+    """Test mathematical properties of explin."""
+
+    def test_monotonically_increasing(self):
+        x = np.geomspace(0.001, 1.0, 100)
+        assert np.all(np.diff(explin(x, 0.001, 1.0, 0, 1)) > 0)
+
+    def test_equal_ratios_in_x_give_equal_steps_in_y(self):
+        # log mapping: equal ratios in x -> equal differences in y
+        y1 = explin(1.0, 1, 100, 0, 1)
+        y2 = explin(10.0, 1, 100, 0, 1)
+        y3 = explin(100.0, 1, 100, 0, 1)
+        assert y2 - y1 == pytest.approx(y3 - y2, rel=1e-6)
+
+    def test_explin_is_inverse_of_linexp(self):
+        # explin and linexp should be inverses of each other
+        for x in [220.0, 311.0, 440.0]:
+            assert explin(linexp(x, 220, 440, 220, 440), 220, 440, 220, 440) == pytest.approx(x, rel=1e-9)
\ No newline at end of file
diff --git a/tests/test_fermi.py b/tests/test_fermi.py
new file mode 100644
index 0000000..e246804
--- /dev/null
+++ b/tests/test_fermi.py
@@ -0,0 +1,89 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import fermi, lcurve
+
+class TestFermiDefaultParams:
+    """Test fermi function with default parameters (tau=1, mu=0)."""
+
+    def test_zero_input_is_half(self):
+        assert fermi(0.0) == pytest.approx(0.5)
+
+    def test_known_values(self):
+        assert_allclose(
+            fermi(np.array([-1, -0.5, 0, 0.5, 1])),
+            [0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858],
+            rtol=1e-6,
+        )
+
+    def test_approaches_zero_for_large_negative_x(self):
+        assert fermi(-500.0) == pytest.approx(0.0, abs=1e-6)
+
+    def test_approaches_one_for_large_positive_x(self):
+        assert fermi(500.0) == pytest.approx(1.0, abs=1e-6)
+
+
+class TestFermiParameters:
+    """Test effect of tau and mu parameters."""
+
+    def test_mu_shifts_midpoint(self):
+        # midpoint (output=0.5) should occur at x=mu
+        assert fermi(2.0, mu=2.0) == pytest.approx(0.5)
+        assert fermi(-3.0, mu=-3.0) == pytest.approx(0.5)
+
+    def test_tau_scales_x_axis(self):
+        # fermi(x, tau=2) == fermi(x/2, tau=1)
+        assert fermi(2.0, tau=2.0) == pytest.approx(fermi(1.0, tau=1.0))
+
+    def test_negative_tau_flips_curve(self):
+        # negative tau mirrors the curve
+        assert fermi(1.0, tau=-1.0) == pytest.approx(fermi(-1.0, tau=1.0))
+
+    def test_large_tau_flattens_curve(self):
+        # very large tau -> output approaches 0.5 everywhere
+        assert fermi(10.0, tau=1e9) == pytest.approx(0.5, abs=1e-4)
+
+    def test_small_tau_sharpens_curve(self):
+        # very small tau -> step function behaviour
+        assert fermi(0.1, tau=0.001) == pytest.approx(1.0, abs=1e-6)
+        assert fermi(-0.1, tau=0.001) == pytest.approx(0.0, abs=1e-6)
+
+
+class TestFermiProperties:
+    """Test mathematical properties of the Fermi function."""
+
+    def test_point_symmetry_around_mu(self):
+        # fermi(mu - x) + fermi(mu + x) == 1
+        for x in [0.5, 1.0, 2.0, 5.0]:
+            assert fermi(-x) + fermi(x) == pytest.approx(1.0)
+
+    def test_point_symmetry_with_nonzero_mu(self):
+        mu = 3.0
+        for x in [0.5, 1.0, 2.0]:
+            assert fermi(mu - x, mu=mu) + fermi(mu + x, mu=mu) == pytest.approx(1.0)
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(-5, 5, 200)
+        assert np.all(np.diff(fermi(x)) > 0)
+
+    def test_output_bounded_to_unit_interval(self):
+        x = np.linspace(-100, 100, 500)
+        result = fermi(x)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(fermi(np.array([0.0, 1.0])), np.ndarray)
+
+
+class TestFermiVsLcurve:
+    """Fermi is a special case of lcurve (m=0, n=1) — results should match."""
+
+    def test_default_params_match_lcurve(self):
+        x = np.linspace(-3, 3, 50)
+        assert_allclose(fermi(x), lcurve(x), rtol=1e-9)
+
+    def test_tau_param_matches_lcurve(self):
+        x = np.linspace(-3, 3, 50)
+        assert_allclose(fermi(x, tau=2.0), lcurve(x, tau=2.0), rtol=1e-9)
\ No newline at end of file
diff --git a/tests/test_fold.py b/tests/test_fold.py
new file mode 100644
index 0000000..e4dae97
--- /dev/null
+++ b/tests/test_fold.py
@@ -0,0 +1,92 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import fold
+
+
+class TestFoldDefaultRange:
+    """Test folding with default range [-1, 1]."""
+
+    def test_value_within_range_unchanged(self):
+        assert fold(0.0) == pytest.approx(0.0)
+        assert fold(-0.5) == pytest.approx(-0.5)
+        assert fold(0.5) == pytest.approx(0.5)
+
+    def test_upper_bound_stays_at_upper(self):
+        assert fold(1.0) == pytest.approx(1.0)
+
+    def test_lower_bound_stays_at_lower(self):
+        assert fold(-1.0) == pytest.approx(-1.0)
+
+    def test_folds_back_above_upper(self):
+        assert fold(1.5) == pytest.approx(0.5)
+
+    def test_folds_back_below_lower(self):
+        assert fold(-1.5) == pytest.approx(-0.5)
+
+
+class TestFoldCustomRange:
+    """Test folding with custom ranges."""
+
+    def test_known_values(self):
+        assert_allclose(
+            fold(np.arange(0, 13), 0, 4),
+            [0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4],
+        )
+
+    def test_value_at_y1_stays_at_y1(self):
+        assert fold(0.0, 0, 4) == pytest.approx(0.0)
+
+    def test_value_at_y2_stays_at_y2(self):
+        assert fold(4.0, 0, 4) == pytest.approx(4.0)
+
+    def test_folds_above_y2(self):
+        assert fold(5.0, 0, 4) == pytest.approx(3.0)
+
+    def test_folds_below_y1(self):
+        assert fold(-1.0, 0, 4) == pytest.approx(1.0)
+
+    def test_multiple_folds(self):
+        # after two full periods the pattern repeats
+        assert fold(8.0, 0, 4) == pytest.approx(fold(0.0, 0, 4))
+        assert fold(9.0, 0, 4) == pytest.approx(fold(1.0, 0, 4))
+
+
+class TestFoldBoundsOrder:
+    """Test that y1/y2 order is irrelevant due to internal sorting."""
+
+    def test_swapped_bounds_give_same_result(self):
+        x = np.linspace(-5, 5, 50)
+        assert_allclose(fold(x, 0, 4), fold(x, 4, 0))
+
+    def test_negative_range(self):
+        assert fold(-3.0, -4, 0) == pytest.approx(-3.0)
+        assert fold(1.0, -4, 0) == pytest.approx(-1.0)
+
+
+class TestFoldProperties:
+    """Test mathematical properties of fold."""
+
+    def test_output_always_in_range(self):
+        x = np.linspace(-20, 20, 500)
+        result = fold(x, 0, 4)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 4.0)
+
+    def test_periodic_with_period_twice_the_range(self):
+        # fold has period 2*L where L = y2 - y1
+        period = 2 * 4
+        x = np.linspace(-5, 5, 50)
+        assert_allclose(fold(x, 0, 4), fold(x + period, 0, 4))
+
+    def test_symmetric_around_bounds(self):
+        # fold(y2 + d) == fold(y2 - d): mirrors at upper bound
+        for d in [0.5, 1.0, 1.5]:
+            assert fold(4 + d, 0, 4) == pytest.approx(fold(4 - d, 0, 4))
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(fold(np.array([0.0, 1.0])), np.ndarray)
+
+    def test_scalar_input_returns_scalar(self):
+        assert isinstance(float(fold(0.5)), float)
\ No newline at end of file
diff --git a/tests/test_gain.py b/tests/test_gain.py
new file mode 100644
index 0000000..27a7efd
--- /dev/null
+++ b/tests/test_gain.py
@@ -0,0 +1,79 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import gain, db_to_amp
+
+
+class TestGainAmp:
+    """Test gain applied as a scalar amplitude factor."""
+
+    def test_known_values(self):
+        assert_allclose(gain(np.array([1, 2, 3, 4]), amp=2), [2, 4, 6, 8])
+
+    def test_amp_one_unchanged(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, amp=1.0), x)
+
+    def test_amp_half_attenuates(self):
+        x = np.array([2.0, 4.0, 6.0])
+        assert_allclose(gain(x, amp=0.5), [1.0, 2.0, 3.0])
+
+    def test_amp_zero_silences(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, amp=0.0), np.zeros(3))
+
+
+class TestGainDb:
+    """Test gain applied as decibels."""
+
+    def test_0db_unchanged(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, db=0), x, rtol=1e-6)
+
+    def test_minus_6db_approximately_halves(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, db=-6), x * db_to_amp(-6), rtol=1e-6)
+
+    def test_20db_multiplies_by_ten(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, db=20), x * 10.0, rtol=1e-6)
+
+    def test_minus_20db_divides_by_ten(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, db=-20), x * 0.1, rtol=1e-6)
+
+
+class TestGainCombined:
+    """Test gain applied as both db and amp simultaneously."""
+
+    def test_db_and_amp_both_applied(self):
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(gain(x, db=20, amp=2.0), x * 10.0 * 2.0, rtol=1e-6)
+
+    def test_db_and_amp_order_independent(self):
+        # db*amp == amp*db mathematically
+        x = np.array([1.0, 2.0, 3.0])
+        assert_allclose(
+            gain(x, db=6, amp=0.5),
+            x * db_to_amp(6) * 0.5,
+            rtol=1e-6,
+        )
+
+
+class TestGainEdgeCases:
+    """Test edge cases and no-op behaviour."""
+
+    def test_no_args_returns_copy(self):
+        x = np.array([1.0, 2.0, 3.0])
+        result = gain(x)
+        assert_allclose(result, x)
+        assert result is not x  # should be a copy, not the same object
+
+    def test_shape_preserved(self):
+        x = np.random.rand(20)
+        assert gain(x, amp=2.0).shape == x.shape
+
+    def test_negative_amp_inverts_polarity(self):
+        x = np.array([1.0, -2.0, 3.0])
+        assert_allclose(gain(x, amp=-1.0), [-1.0, 2.0, -3.0])
\ No newline at end of file
diff --git a/tests/test_hz_mel_hz.py b/tests/test_hz_mel_hz.py
new file mode 100644
index 0000000..3d40850
--- /dev/null
+++ b/tests/test_hz_mel_hz.py
@@ -0,0 +1,90 @@
+import pytest
+import numpy as np
+
+from pyamapping.mappings import hz_to_mel, mel_to_hz
+
+class TestHzToMel:
+    """Test Hz to mel conversion for both Slaney and HTK formulas."""
+
+    def test_zero_hz_is_zero_mel_slaney(self):
+        assert hz_to_mel(0) == pytest.approx(0.0)
+
+    def test_zero_hz_is_zero_mel_htk(self):
+        assert hz_to_mel(0, htk=True) == pytest.approx(0.0)
+
+    def test_known_value_slaney(self):
+        assert hz_to_mel(440) == pytest.approx(6.6, rel=1e-6)
+
+    def test_known_value_htk(self):
+        # 440 Hz -> mel via O'Shaughnessy formula
+        assert hz_to_mel(440, htk=True) == pytest.approx(2595 * np.log10(1 + 440 / 700), rel=1e-6)
+
+    def test_linear_regime_below_1000hz(self):
+        # Slaney: linear law applies below 1000 Hz
+        assert hz_to_mel(200) == pytest.approx(3.0 * 200 / 200, rel=1e-6)
+
+    def test_log_regime_above_1000hz(self):
+        # Slaney: log law applies at and above 1000 Hz — boundary value
+        assert hz_to_mel(1000) == pytest.approx(15.0, rel=1e-6)
+
+    def test_array_input_slaney(self):
+        result = hz_to_mel(np.array([0, 200, 1000, 4000]))
+        assert isinstance(result, np.ndarray)
+        assert result[2] == pytest.approx(15.0, rel=1e-6)
+
+    def test_array_input_htk(self):
+        result = hz_to_mel(np.array([0, 440, 1000]), htk=True)
+        assert isinstance(result, np.ndarray)
+
+
+class TestMelToHz:
+    """Test mel to Hz conversion for both Slaney and HTK formulas."""
+
+    def test_zero_mel_is_zero_hz_slaney(self):
+        assert mel_to_hz(0) == pytest.approx(0.0)
+
+    def test_zero_mel_is_zero_hz_htk(self):
+        assert mel_to_hz(0, htk=True) == pytest.approx(0.0)
+
+    def test_known_value_slaney(self):
+        assert mel_to_hz(6.6) == pytest.approx(440.0, rel=1e-6)
+
+
+    def test_known_value_htk(self):
+        assert mel_to_hz(2595 * np.log10(1 + 440 / 700), htk=True) == pytest.approx(440, rel=1e-6)
+
+    def test_linear_regime_below_mel_15(self):
+        # Slaney: linear law applies below mel=15
+        assert mel_to_hz(9.0) == pytest.approx(200.0 / 3 * 9, rel=1e-6)
+
+    def test_boundary_mel_15_is_1000hz(self):
+        assert mel_to_hz(15) == pytest.approx(1000.0, rel=1e-6)
+
+    def test_array_input_slaney(self):
+        result = mel_to_hz(np.array([0, 9, 15, 30]))
+        assert isinstance(result, np.ndarray)
+        assert result[2] == pytest.approx(1000.0, rel=1e-6)
+
+
+class TestHzMelRoundtrip:
+    """Test that hz_to_mel and mel_to_hz are exact inverses of each other."""
+
+    def test_hz_to_mel_to_hz_slaney(self):
+        for hz in np.arange(1, 128):
+            assert mel_to_hz(hz_to_mel(hz)) == pytest.approx(hz, rel=1e-6)
+
+    def test_mel_to_hz_to_mel_slaney(self):
+        for mel in np.arange(1, 128):
+            assert hz_to_mel(mel_to_hz(mel)) == pytest.approx(mel, rel=1e-6)
+
+    def test_hz_to_mel_to_hz_htk(self):
+        for hz in [100, 440, 1000, 4000, 8000]:
+            assert mel_to_hz(hz_to_mel(hz, htk=True), htk=True) == pytest.approx(hz, rel=1e-9)
+
+    def test_mel_to_hz_to_mel_htk(self):
+        for mel in [100, 500, 1000, 2000]:
+            assert hz_to_mel(mel_to_hz(mel, htk=True), htk=True) == pytest.approx(mel, rel=1e-9)
+
+    def test_htk_and_slaney_differ(self):
+        # The two formulas are different — their results should not be equal
+        assert hz_to_mel(440, htk=True) != pytest.approx(hz_to_mel(440, htk=False))
\ No newline at end of file
diff --git a/tests/test_lcurve.py b/tests/test_lcurve.py
new file mode 100644
index 0000000..71773cd
--- /dev/null
+++ b/tests/test_lcurve.py
@@ -0,0 +1,76 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import lcurve
+
+
+class TestLcurveDefaultParams:
+    """Test lcurve with default parameters (Fermi function: m=0, n=1, tau=1)."""
+
+    def test_zero_input_is_half(self):
+        # (1 + 0) / (1 + 1) = 0.5
+        assert lcurve(0.0) == pytest.approx(0.5)
+
+    def test_known_values(self):
+        assert_allclose(
+            lcurve(np.array([-1, -0.5, 0, 0.5, 1])),
+            [0.26894142, 0.37754067, 0.5, 0.62245933, 0.73105858],
+            rtol=1e-6,
+        )
+
+    def test_approaches_zero_for_large_negative_x(self):
+        assert lcurve(-500.0) == pytest.approx(0.0, abs=1e-6)
+
+    def test_approaches_one_for_large_positive_x(self):
+        assert lcurve(500.0) == pytest.approx(1.0, abs=1e-6)
+
+
+class TestLcurveParameters:
+    """Test effect of m, n, and tau parameters."""
+
+    def test_m_equals_n_is_constant_one(self):
+        # (1 + c*exp) / (1 + c*exp) = 1 for any x when m == n
+        for x in [-1.0, 0.0, 1.0, 10.0]:
+            assert lcurve(x, m=2.0, n=2.0) == pytest.approx(1.0)
+
+    def test_n_zero_is_constant_one(self):
+        # (1 + m*exp) / (1 + 0) = 1 + m*exp, but with m=0: always 1
+        assert lcurve(0.0, m=0.0, n=0.0) == pytest.approx(1.0)
+
+    def test_tau_scales_x_axis(self):
+        # lcurve(x, tau=2) == lcurve(x/2, tau=1)
+        assert lcurve(2.0, tau=2.0) == pytest.approx(lcurve(1.0, tau=1.0))
+
+    def test_negative_tau_flips_curve(self):
+        # negative tau mirrors the curve: lcurve(x, tau=-1) == lcurve(-x, tau=1)
+        assert lcurve(1.0, tau=-1.0) == pytest.approx(lcurve(-1.0, tau=1.0))
+
+    def test_large_tau_flattens_curve(self):
+        # very large tau -> exp(-x/tau) -> 1, output approaches (1+m)/(1+n)
+        assert lcurve(10.0, tau=1e9) == pytest.approx(lcurve(0.0, tau=1e9), rel=1e-4)
+
+
+class TestLcurveProperties:
+    """Test mathematical properties of the L-curve."""
+
+    def test_monotonically_increasing_default(self):
+        x = np.linspace(-5, 5, 200)
+        assert np.all(np.diff(lcurve(x)) > 0)
+
+    def test_point_symmetry_around_zero_default(self):
+        # Fermi function: lcurve(-x) + lcurve(x) == 1
+        for x in [0.5, 1.0, 2.0, 5.0]:
+            assert lcurve(-x) + lcurve(x) == pytest.approx(1.0)
+
+    def test_output_bounded_to_unit_interval_default(self):
+        x = np.linspace(-100, 100, 500)
+        result = lcurve(x)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+
+    def test_scalar_input_returns_scalar(self):
+        assert isinstance(float(lcurve(0.5)), float)
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(lcurve(np.array([0.0, 1.0])), np.ndarray)
\ No newline at end of file
diff --git a/tests/test_lincurve.py b/tests/test_lincurve.py
new file mode 100644
index 0000000..946b97d
--- /dev/null
+++ b/tests/test_lincurve.py
@@ -0,0 +1,128 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import lincurve
+
+
+class TestLincurveEndpoints:
+    """Test that x1->y1 and x2->y2 mappings are exact."""
+
+    def test_x1_maps_to_y1_default_params(self):
+        assert lincurve(0.0, 0, 1) == pytest.approx(-1.0)
+
+    def test_x2_maps_to_y2_default_params(self):
+        assert lincurve(1.0, 0, 1) == pytest.approx(1.0)
+
+    def test_x1_maps_to_y1_custom(self):
+        assert lincurve(2.0, 2, 5, y1=10.0, y2=20.0) == pytest.approx(10.0)
+
+    def test_x2_maps_to_y2_custom(self):
+        assert lincurve(5.0, 2, 5, y1=10.0, y2=20.0) == pytest.approx(20.0)
+
+
+class TestLincurveLinearFallback:
+    """Test the linear branch triggered when abs(curve) < 0.001."""
+
+    def test_zero_curve_midpoint(self):
+        # With curve=0, should be linear: midpoint maps to midpoint
+        result = lincurve(0.5, 0, 1, 0, 1, curve=0.0)
+        assert result == pytest.approx(0.5)
+
+    def test_tiny_curve_is_linear(self):
+        # curve=0.0009 is below threshold, expect linear behaviour
+        result = lincurve(0.5, 0, 1, 0, 1, curve=0.0009)
+        assert result == pytest.approx(0.5)
+
+    def test_linear_array_input(self):
+        x = np.array([0.0, 0.5, 1.0])
+        result = lincurve(x, 0, 1, 0, 1, curve=0.0)
+        assert_allclose(result, [0.0, 0.5, 1.0])
+
+
+class TestLincurveCurvedMapping:
+    """Test exponential (non-linear) mapping with meaningful curve values."""
+
+    def test_array_input_known_values(self):
+        result = lincurve(np.array([0.0, 0.1, 0.4, 0.7, 1.0]), 0, 1, 0, 0.4)
+        assert_allclose(
+            result,
+            [0.0, 0.08385643, 0.25474431, 0.34852956, 0.4],
+            rtol=1e-5,
+        )
+
+    def test_negative_curve(self):
+        # Negative curve bends the other way; endpoints must still hold
+        assert lincurve(0.0, 0, 1, 0, 1, curve=-2.0) == pytest.approx(0.0)
+        assert lincurve(1.0, 0, 1, 0, 1, curve=-2.0) == pytest.approx(1.0)
+
+    def test_positive_curve(self):
+        assert lincurve(0.0, 0, 1, 0, 1, curve=2.0) == pytest.approx(0.0)
+        assert lincurve(1.0, 0, 1, 0, 1, curve=2.0) == pytest.approx(1.0)
+
+    def test_positive_vs_negative_curve_symmetry(self):
+        # For x in [0,1]->[0,1], curve and -curve should be symmetric around 0.5
+        x = 0.3
+        pos = lincurve(x, 0, 1, 0, 1, curve=2.0)
+        neg = lincurve(1 - x, 0, 1, 0, 1, curve=-2.0)
+        assert pos == pytest.approx(1 - neg, rel=1e-5)
+
+
+class TestLincurvePolarityInversion:
+    """Test y2 < y1 (inverted range)."""
+
+    def test_inverted_range_endpoints(self):
+        assert lincurve(0.0, 0, 1, y1=1.0, y2=0.0) == pytest.approx(1.0)
+        assert lincurve(1.0, 0, 1, y1=1.0, y2=0.0) == pytest.approx(0.0)
+
+    def test_inverted_range_midpoint_is_between_bounds(self):
+        result = lincurve(0.5, 0, 1, y1=1.0, y2=0.0)
+        assert 0.0 <= result <= 1.0
+
+
+class TestLincurveExtrapolation:
+    """Default (clip=None) should extrapolate beyond [x1, x2]."""
+
+    def test_extrapolates_below_x1(self):
+        # x < x1 with linear curve should give z < y1
+        result = lincurve(-1.0, 0, 1, 0, 1, curve=0.0)
+        assert result == pytest.approx(-1.0)
+
+    def test_extrapolates_above_x2(self):
+        result = lincurve(2.0, 0, 1, 0, 1, curve=0.0)
+        assert result == pytest.approx(2.0)
+
+
+class TestLincurveClipping:
+    """Test all clip modes."""
+
+    def test_clip_max_caps_at_y2(self):
+        # x > x2 would extrapolate above y2=1; clip="max" should cap it
+        result = lincurve(2.0, 0, 1, 0, 1, curve=0.0, clip="max")
+        assert result == pytest.approx(1.0)
+
+    def test_clip_max_does_not_affect_lower_values(self):
+        result = lincurve(0.5, 0, 1, 0, 1, curve=0.0, clip="max")
+        assert result == pytest.approx(0.5)
+
+    def test_clip_min_caps_at_y1(self):
+        result = lincurve(-1.0, 0, 1, 0, 1, curve=0.0, clip="min")
+        assert result == pytest.approx(0.0)
+
+    def test_clip_min_does_not_affect_upper_values(self):
+        result = lincurve(0.5, 0, 1, 0, 1, curve=0.0, clip="min")
+        assert result == pytest.approx(0.5)
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert lincurve(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(0.0)
+        assert lincurve(2.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(1.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        # Any string other than "min"/"max" should clip both sides
+        assert lincurve(-1.0, 0, 1, 0, 1, curve=0.0, clip="both") == pytest.approx(0.0)
+        assert lincurve(2.0, 0, 1, 0, 1, curve=0.0, clip="both") == pytest.approx(1.0)
+
+    def test_clip_minmax_array_input(self):
+        x = np.array([-1.0, 0.0, 0.5, 1.0, 2.0])
+        result = lincurve(x, 0, 1, 0, 1, curve=0.0, clip="minmax")
+        assert_allclose(result, [0.0, 0.0, 0.5, 1.0, 1.0])
\ No newline at end of file
diff --git a/tests/test_linexp.py b/tests/test_linexp.py
new file mode 100644
index 0000000..d215111
--- /dev/null
+++ b/tests/test_linexp.py
@@ -0,0 +1,104 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import linexp
+
+class TestLinexpEndpoints:
+    """Test that x1->y1 and x2->y2 mappings are exact."""
+
+    def test_x1_maps_to_y1(self):
+        assert linexp(1.0, 1, 8, 2, 256) == pytest.approx(2.0)
+
+    def test_x2_maps_to_y2(self):
+        assert linexp(8.0, 1, 8, 2, 256) == pytest.approx(256.0)
+
+    def test_x1_maps_to_y1_custom(self):
+        assert linexp(0.0, 0, 4, 100, 300) == pytest.approx(100.0)
+
+    def test_x2_maps_to_y2_custom(self):
+        assert linexp(4.0, 0, 4, 100, 300) == pytest.approx(300.0)
+
+
+class TestLinexpMapping:
+    """Test exponential mapping between endpoints."""
+
+    def test_known_value(self):
+        assert linexp(5, 1, 8, 2, 256) == pytest.approx(32.0)
+
+    def test_midpoint_is_geometric_mean(self):
+        # exponential mapping: midpoint maps to sqrt(y1*y2)
+        assert linexp(0.5, 0, 1, 1, 100) == pytest.approx(10.0, rel=1e-6)
+
+    def test_inverted_range(self):
+        assert linexp(5, 1, 8, 256, 2) == pytest.approx(16.0, rel=1e-5)
+
+    def test_array_input(self):
+        result = linexp(np.array([1.0, 8.0]), 1, 8, 2, 256)
+        assert_allclose(result, [2.0, 256.0])
+
+
+class TestLinexpExtrapolation:
+    """Default (clip=None) should extrapolate beyond [x1, x2]."""
+
+    def test_extrapolates_above_x2(self):
+        result = linexp(9.0, 1, 8, 2, 256)
+        assert result > 256.0
+
+    def test_extrapolates_below_x1(self):
+        result = linexp(0.0, 1, 8, 2, 256)
+        assert result < 2.0
+
+
+class TestLinexpClipping:
+    """Test all clip modes."""
+
+    def test_clip_max_caps_at_y2(self):
+        assert linexp(7, 0, 5, 100, 300, clip="max") == pytest.approx(300.0)
+
+    def test_clip_max_does_not_affect_lower_values(self):
+        assert linexp(2.5, 0, 5, 100, 300, clip="max") == pytest.approx(
+            linexp(2.5, 0, 5, 100, 300)
+        )
+
+    def test_clip_min_caps_at_y1(self):
+        assert linexp(1, 2, 5, 100, 300, clip="min") == pytest.approx(100.0)
+
+    def test_clip_min_does_not_affect_upper_values(self):
+        assert linexp(3.5, 2, 5, 100, 300, clip="min") == pytest.approx(
+            linexp(3.5, 2, 5, 100, 300)
+        )
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert linexp(1, 2, 5, 100, 300, clip="minmax") == pytest.approx(100.0)
+        assert linexp(6, 2, 5, 100, 300, clip="minmax") == pytest.approx(300.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        assert linexp(1, 2, 5, 100, 300, clip="both") == pytest.approx(100.0)
+        assert linexp(6, 2, 5, 100, 300, clip="both") == pytest.approx(300.0)
+
+    def test_clip_inverted_range(self):
+        assert linexp(5, 1, 8, 256, 2, clip="minmax") == pytest.approx(16.0, rel=1e-5)
+
+    def test_clip_minmax_array_input(self):
+        result = linexp(np.array([0.0, 4.0, 9.0]), 1, 8, 2, 256, clip="minmax")
+        assert_allclose(result, [2.0, linexp(4.0, 1, 8, 2, 256), 256.0])
+
+
+class TestLinexpProperties:
+    """Test mathematical properties of linexp."""
+
+    def test_output_is_always_positive_for_positive_bounds(self):
+        x = np.linspace(0, 10, 100)
+        assert np.all(linexp(x, 1, 8, 2, 256) > 0)
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(1, 8, 100)
+        assert np.all(np.diff(linexp(x, 1, 8, 2, 256)) > 0)
+
+    def test_ratio_of_outputs_depends_only_on_ratio_of_inputs(self):
+        # exponential mapping: equal steps in x -> equal ratios in y
+        y1 = linexp(1.0, 0, 3, 1, 8)
+        y2 = linexp(2.0, 0, 3, 1, 8)
+        y3 = linexp(3.0, 0, 3, 1, 8)
+        assert y2 / y1 == pytest.approx(y3 / y2, rel=1e-6)
\ No newline at end of file
diff --git a/tests/test_linlin.py b/tests/test_linlin.py
new file mode 100644
index 0000000..51eaa08
--- /dev/null
+++ b/tests/test_linlin.py
@@ -0,0 +1,91 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import linlin
+
+class TestLinlinEndpoints:
+    """Test that x1->y1 and x2->y2 mappings are exact."""
+
+    def test_x1_maps_to_y1(self):
+        assert linlin(0.0, 0, 1, 10.0, 20.0) == pytest.approx(10.0)
+
+    def test_x2_maps_to_y2(self):
+        assert linlin(1.0, 0, 1, 10.0, 20.0) == pytest.approx(20.0)
+
+    def test_array_input(self):
+        origin = np.array([-1, 0, 1, 2, 4])
+        target = np.array([-50, 0, 50, 100, 200])
+        assert_allclose(linlin(origin, 0, 2, 0, 100), target)
+
+
+class TestLinlinInterpolation:
+    """Test linear mapping between endpoints."""
+
+    def test_midpoint(self):
+        assert linlin(0.5, 0, 1, 0, 1) == pytest.approx(0.5)
+
+    def test_midpoint_custom_range(self):
+        assert linlin(50, 0, 100, 0, 1) == pytest.approx(0.5)
+
+    def test_negative_range(self):
+        assert linlin(-0.5, -1, 0, 0, 100) == pytest.approx(50.0)
+
+
+class TestLinlinExtrapolation:
+    """Default (clip=None) should extrapolate beyond [x1, x2]."""
+
+    def test_extrapolates_below_x1(self):
+        assert linlin(-1.0, 0, 1, 0, 100) == pytest.approx(-100.0)
+
+    def test_extrapolates_above_x2(self):
+        assert linlin(2.0, 0, 1, 0, 100) == pytest.approx(200.0)
+
+
+class TestLinlinPolarityInversion:
+    """Test y2 < y1 (inverted range)."""
+
+    def test_x1_maps_to_y1_inverted(self):
+        assert linlin(0, 0, 1, 1, 0) == pytest.approx(1.0)
+
+    def test_x2_maps_to_y2_inverted(self):
+        assert linlin(1, 0, 1, 1, 0) == pytest.approx(0.0)
+
+    def test_midpoint_inverted(self):
+        assert linlin(0.5, 0, 1, 1, 0) == pytest.approx(0.5)
+
+
+class TestLinlinClipping:
+    """Test all clip modes, including inverted y1/y2 ranges."""
+
+    def test_clip_max_caps_at_y2(self):
+        assert linlin(105, 0, 100, 100, 200, clip="max") == pytest.approx(200.0)
+
+    def test_clip_max_does_not_affect_lower_values(self):
+        assert linlin(50, 0, 100, 100, 200, clip="max") == pytest.approx(150.0)
+
+    def test_clip_min_caps_at_y1(self):
+        assert linlin(-10, 0, 100, 100, 200, clip="min") == pytest.approx(100.0)
+
+    def test_clip_min_does_not_affect_upper_values(self):
+        assert linlin(50, 0, 100, 100, 200, clip="min") == pytest.approx(150.0)
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert linlin(3, 5, 105, 100, 1000, clip="minmax") == pytest.approx(100.0)
+        assert linlin(105, 0, 100, 100, 1000, clip="minmax") == pytest.approx(1000.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        assert linlin(-10, 0, 100, 100, 200, clip="both") == pytest.approx(100.0)
+        assert linlin(110, 0, 100, 100, 200, clip="both") == pytest.approx(200.0)
+
+    def test_clip_max_inverted_range(self):
+        # y1=200, y2=100 — "max" should still cap at the higher bound (200)
+        assert linlin(-10, 0, 100, 200, 100, clip="max") == pytest.approx(200.0)
+
+    def test_clip_min_inverted_range(self):
+        # y1=200, y2=100 — "min" should still floor at the lower bound (100)
+        assert linlin(105, 0, 100, 200, 100, clip="min") == pytest.approx(100.0)
+
+    def test_clip_minmax_array_input(self):
+        result = linlin(np.array([-10.0, 50.0, 110.0]), 0, 100, 0, 1, clip="minmax")
+        assert_allclose(result, [0.0, 0.5, 1.0])
\ No newline at end of file
diff --git a/tests/test_linpoly.py b/tests/test_linpoly.py
new file mode 100644
index 0000000..3c1b028
--- /dev/null
+++ b/tests/test_linpoly.py
@@ -0,0 +1,94 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import linpoly
+
+
+class TestLinpolyEndpoints:
+    """Test that -xmax->y1 and xmax->y2 mappings are exact."""
+
+    def test_xmax_maps_to_y2(self):
+        assert linpoly(1.0, xmax=1.0, y1=-1.0, y2=1.0) == pytest.approx(1.0)
+
+    def test_negative_xmax_maps_to_y1(self):
+        assert linpoly(-1.0, xmax=1.0, y1=-1.0, y2=1.0) == pytest.approx(-1.0)
+
+    def test_zero_maps_to_midpoint(self):
+        # (1 + 0) / 2 = 0.5 -> y1 + 0.5*(y2-y1) = midpoint
+        assert linpoly(0.0, xmax=1.0, y1=0.0, y2=1.0) == pytest.approx(0.5)
+
+    def test_custom_range_endpoints(self):
+        assert linpoly(2.5, xmax=2.5, y1=100, y2=500) == pytest.approx(500.0)
+        assert linpoly(-2.5, xmax=2.5, y1=100, y2=500) == pytest.approx(100.0)
+
+
+class TestLinpolyCurve:
+    """Test effect of curve parameter on polynomial order."""
+
+    def test_known_values_curve_1(self):
+        assert_allclose(
+            linpoly(np.arange(-2, 3), 2.5, 100, 500, curve=1),
+            [172.0, 268.0, 300.0, 332.0, 428.0],
+            rtol=1e-6,
+        )
+
+    def test_curve_zero_is_linear(self):
+        # curve=0 -> order=1, pure linear mapping
+        x = np.array([-1.0, 0.0, 1.0])
+        assert_allclose(linpoly(x, xmax=1.0, y1=0.0, y2=1.0, curve=0), [0.0, 0.5, 1.0])
+
+    def test_positive_curve_increases_order(self):
+        # curve=1 -> order=2 (quadratic), curve=2 -> order=3 (cubic)
+        # higher order -> more compression near zero
+        mid_curve1 = linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, curve=1)
+        mid_curve2 = linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, curve=2)
+        assert mid_curve2 < mid_curve1  # more curved -> closer to midpoint
+
+    def test_negative_curve_order(self):
+        # curve=-1 -> order = 1/(1-(-1)) = 0.5 (square root)
+        order = 1 / (1 - (-1))
+        expected = 0 + 1 * (1 + (0.5 / 1.0) ** order) / 2
+        assert linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, curve=-1) == pytest.approx(expected)
+
+
+class TestLinpolyProperties:
+    """Test mathematical properties of linpoly."""
+
+    def test_odd_symmetry_around_midpoint(self):
+        # linpoly(-x) and linpoly(x) should be symmetric around the output midpoint
+        for x in [0.25, 0.5, 0.75, 1.0]:
+            assert linpoly(x, y1=0.0, y2=1.0) + linpoly(-x, y1=0.0, y2=1.0) == pytest.approx(1.0)
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(-1, 1, 200)
+        assert np.all(np.diff(linpoly(x)) > 0)
+
+    def test_output_bounded_within_range_for_input_within_xmax(self):
+        x = np.linspace(-1, 1, 100)
+        result = linpoly(x, xmax=1.0, y1=0.0, y2=1.0)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+
+
+class TestLinpolyClipping:
+    """Test all clip modes."""
+
+    def test_clip_max_caps_at_y2(self):
+        assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="max") == pytest.approx(1.0)
+
+    def test_clip_min_caps_at_y1(self):
+        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="min") == pytest.approx(0.0)
+
+    def test_clip_minmax_caps_both_sides(self):
+        assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(1.0)
+        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(0.0)
+
+    def test_clip_unknown_string_implies_minmax(self):
+        assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="both") == pytest.approx(1.0)
+        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="both") == pytest.approx(0.0)
+
+    def test_clip_does_not_affect_values_within_range(self):
+        assert linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(
+            linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0)
+        )
\ No newline at end of file
diff --git a/tests/test_midi_cps_midi.py b/tests/test_midi_cps_midi.py
new file mode 100644
index 0000000..e5de271
--- /dev/null
+++ b/tests/test_midi_cps_midi.py
@@ -0,0 +1,69 @@
+import numpy as np
+import pytest
+
+from pyamapping.mappings import midi_to_cps, cps_to_midi
+
+
+class TestMidiToCps:
+    """Test MIDI note to frequency conversion."""
+
+    def test_a4_is_440hz(self):
+        assert midi_to_cps(69) == pytest.approx(440.0)
+
+    def test_a5_is_880hz(self):
+        assert midi_to_cps(81) == pytest.approx(880.0)
+
+    def test_a3_is_220hz(self):
+        assert midi_to_cps(57) == pytest.approx(220.0)
+
+    def test_middle_c(self):
+        assert midi_to_cps(60) == pytest.approx(261.6255, rel=1e-4)
+
+    def test_octave_up_doubles_frequency(self):
+        assert midi_to_cps(69 + 12) == pytest.approx(midi_to_cps(69) * 2)
+
+    def test_octave_down_halves_frequency(self):
+        assert midi_to_cps(69 - 12) == pytest.approx(midi_to_cps(69) / 2)
+
+    def test_fractional_midi_note(self):
+        # halfway between two semitones should be between their frequencies
+        f_low = midi_to_cps(60)
+        f_high = midi_to_cps(61)
+        assert f_low < midi_to_cps(60.5) < f_high
+
+
+class TestCpsToMidi:
+    """Test frequency to MIDI note conversion."""
+
+    def test_440hz_is_a4(self):
+        assert cps_to_midi(440.0) == pytest.approx(69.0)
+
+    def test_880hz_is_a5(self):
+        assert cps_to_midi(880.0) == pytest.approx(81.0)
+
+    def test_220hz_is_a3(self):
+        assert cps_to_midi(220.0) == pytest.approx(57.0)
+
+    def test_middle_c_frequency(self):
+        assert cps_to_midi(261.6255) == pytest.approx(60.0, rel=1e-4)
+
+    def test_octave_up_adds_12(self):
+        assert cps_to_midi(880.0) == pytest.approx(cps_to_midi(440.0) + 12)
+
+    def test_octave_down_subtracts_12(self):
+        assert cps_to_midi(220.0) == pytest.approx(cps_to_midi(440.0) - 12)
+
+
+class TestMidiCpsRoundtrip:
+    """Test that the two functions are exact inverses of each other."""
+
+    def test_midi_to_cps_to_midi(self):
+        for midi in [0, 21, 60, 69, 81, 108, 127]:
+            assert cps_to_midi(midi_to_cps(midi)) == pytest.approx(midi, rel=1e-9)
+
+    def test_cps_to_midi_to_cps(self):
+        for cps in [27.5, 110.0, 220.0, 440.0, 880.0, 1760.0]:
+            assert midi_to_cps(cps_to_midi(cps)) == pytest.approx(cps, rel=1e-9)
+
+    def test_fractional_roundtrip(self):
+        assert cps_to_midi(midi_to_cps(60.5)) == pytest.approx(60.5, rel=1e-9)
\ No newline at end of file
diff --git a/tests/test_midi_ratio_midi.py b/tests/test_midi_ratio_midi.py
new file mode 100644
index 0000000..2bdc78b
--- /dev/null
+++ b/tests/test_midi_ratio_midi.py
@@ -0,0 +1,61 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import midi_to_ratio, ratio_to_midi
+
+
+class TestMidiToRatio:
+    """Test MIDI interval to frequency ratio conversion."""
+
+    def test_unison_is_ratio_one(self):
+        assert midi_to_ratio(0) == pytest.approx(1.0)
+
+    def test_octave_is_ratio_two(self):
+        assert midi_to_ratio(12) == pytest.approx(2.0)
+
+    def test_two_octaves_is_ratio_four(self):
+        assert midi_to_ratio(24) == pytest.approx(4.0)
+
+    def test_perfect_fifth(self):
+        assert midi_to_ratio(7) == pytest.approx(1.4983070768766815)
+
+    def test_negative_interval_inverts_ratio(self):
+        assert midi_to_ratio(-12) == pytest.approx(0.5)
+
+    def test_fractional_interval(self):
+        assert midi_to_ratio(6.0) == pytest.approx(2 ** 0.5, rel=1e-9)
+
+
+class TestRatioToMidi:
+    """Test frequency ratio to MIDI interval conversion."""
+
+    def test_ratio_one_is_unison(self):
+        assert ratio_to_midi(1.0) == pytest.approx(0.0)
+
+    def test_ratio_two_is_octave(self):
+        assert ratio_to_midi(2.0) == pytest.approx(12.0)
+
+    def test_ratio_four_is_two_octaves(self):
+        assert ratio_to_midi(4.0) == pytest.approx(24.0)
+
+    def test_ratio_half_is_negative_octave(self):
+        assert ratio_to_midi(0.5) == pytest.approx(-12.0)
+
+    def test_perfect_fifth_ratio(self):
+        assert ratio_to_midi(1.4983070768766815) == pytest.approx(7.0, rel=1e-6)
+
+
+class TestMidiRatioRoundtrip:
+    """Test that the two functions are exact inverses of each other."""
+
+    def test_midi_to_ratio_to_midi(self):
+        for midi in [-12, -7, 0, 5, 7, 12, 24]:
+            assert ratio_to_midi(midi_to_ratio(midi)) == pytest.approx(midi, rel=1e-9)
+
+    def test_ratio_to_midi_to_ratio(self):
+        for ratio in [0.5, 1.0, 1.5, 2.0, 3.0, 4.0]:
+            assert midi_to_ratio(ratio_to_midi(ratio)) == pytest.approx(ratio, rel=1e-9)
+
+    def test_fractional_roundtrip(self):
+        assert ratio_to_midi(midi_to_ratio(3.5)) == pytest.approx(3.5, rel=1e-9)
\ No newline at end of file
diff --git a/tests/test_norm_peak.py b/tests/test_norm_peak.py
new file mode 100644
index 0000000..92e7e53
--- /dev/null
+++ b/tests/test_norm_peak.py
@@ -0,0 +1,79 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import norm_peak
+
+
+
+class TestNormPeakDefaultPeak:
+    """Test peak normalization with default peak=1.0."""
+
+    def test_max_abs_is_one(self):
+        x = np.array([1.0, -2.0, 3.0, -0.5])
+        result = norm_peak(x)
+        assert np.max(np.abs(result)) == pytest.approx(1.0)
+
+    def test_positive_array_max_is_one(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0])
+        assert np.max(norm_peak(x)) == pytest.approx(1.0)
+
+    def test_negative_array_min_is_minus_one(self):
+        x = np.array([-4.0, -3.0, -2.0, -1.0])
+        assert np.min(norm_peak(x)) == pytest.approx(-1.0)
+
+    def test_shape_preserved(self):
+        x = np.random.rand(20)
+        assert norm_peak(x).shape == x.shape
+
+
+class TestNormPeakCustomPeak:
+    """Test peak normalization with custom peak values."""
+
+    def test_custom_peak_random_array(self):
+        result = norm_peak(np.random.rand(10), peak=5.0)
+        assert np.max(np.abs(result)) == pytest.approx(5.0)
+
+    def test_custom_peak_known_array(self):
+        x = np.array([1.0, -2.0, 3.0, -0.5])
+        result = norm_peak(x, peak=6.0)
+        assert np.max(np.abs(result)) == pytest.approx(6.0)
+
+    def test_scaling_is_linear(self):
+        x = np.array([1.0, 2.0, 3.0])
+        result = norm_peak(x, peak=2.0)
+        assert_allclose(result, [2/3, 4/3, 2.0])
+
+    def test_ratios_between_elements_preserved(self):
+        x = np.array([1.0, 2.0, 4.0])
+        result = norm_peak(x, peak=5.0)
+        assert result[1] / result[0] == pytest.approx(2.0)
+        assert result[2] / result[1] == pytest.approx(2.0)
+
+
+class TestNormPeakEdgeCases:
+    """Test edge cases including zero arrays and sign preservation."""
+
+    def test_zero_array_returned_unchanged(self):
+        x = np.zeros(5)
+        assert_allclose(norm_peak(x), x)
+
+    def test_zero_array_with_custom_peak_returned_unchanged(self):
+        x = np.zeros(5)
+        assert_allclose(norm_peak(x, peak=3.0), x)
+
+    def test_already_normalized_array_unchanged(self):
+        x = np.array([-1.0, 0.0, 0.5, 1.0])
+        assert_allclose(norm_peak(x), x)
+
+    def test_sign_preserved(self):
+        x = np.array([-3.0, 1.0, 2.0])
+        result = norm_peak(x)
+        assert result[0] < 0
+        assert result[1] > 0
+
+    def test_single_element_array(self):
+        assert norm_peak(np.array([5.0])) == pytest.approx(1.0)
+
+    def test_single_negative_element(self):
+        assert norm_peak(np.array([-5.0])) == pytest.approx(-1.0)
\ No newline at end of file
diff --git a/tests/test_norm_rms.py b/tests/test_norm_rms.py
new file mode 100644
index 0000000..a4af9a9
--- /dev/null
+++ b/tests/test_norm_rms.py
@@ -0,0 +1,79 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import norm_rms
+
+
+class TestNormRmsDefaultRms:
+    """Test RMS normalization with default rms=1.0."""
+
+    def test_rms_is_one(self):
+        x = np.array([1.0, -2.0, 3.0, -0.5])
+        result = norm_rms(x)
+        assert np.sqrt(np.mean(result**2)) == pytest.approx(1.0)
+
+    def test_known_values(self):
+        assert_allclose(
+            norm_rms(np.array([1, 0, 0, -1]), 1),
+            [1.41421356, 0.0, 0.0, -1.41421356],
+            rtol=1e-6,
+        )
+
+    def test_shape_preserved(self):
+        x = np.random.rand(20)
+        assert norm_rms(x).shape == x.shape
+
+
+class TestNormRmsCustomRms:
+    """Test RMS normalization with custom target RMS values."""
+
+    def test_custom_rms_achieved(self):
+        x = np.array([1.0, -2.0, 3.0, -0.5])
+        result = norm_rms(x, rms=2.0)
+        assert np.sqrt(np.mean(result**2)) == pytest.approx(2.0)
+
+    def test_random_array_custom_rms(self):
+        x = np.random.rand(100)
+        result = norm_rms(x, rms=0.5)
+        assert np.sqrt(np.mean(result**2)) == pytest.approx(0.5)
+
+    def test_scaling_is_linear(self):
+        # doubling target rms doubles all values
+        x = np.array([1.0, 2.0, 3.0])
+        result1 = norm_rms(x, rms=1.0)
+        result2 = norm_rms(x, rms=2.0)
+        assert_allclose(result2, result1 * 2)
+
+    def test_ratios_between_elements_preserved(self):
+        x = np.array([1.0, 2.0, 4.0])
+        result = norm_rms(x, rms=3.0)
+        assert result[1] / result[0] == pytest.approx(2.0)
+        assert result[2] / result[1] == pytest.approx(2.0)
+
+
+class TestNormRmsEdgeCases:
+    """Test edge cases including zero arrays and sign preservation."""
+
+    def test_zero_array_returned_unchanged(self):
+        x = np.zeros(5)
+        assert_allclose(norm_rms(x), x)
+
+    def test_zero_array_with_custom_rms_returned_unchanged(self):
+        x = np.zeros(5)
+        assert_allclose(norm_rms(x, rms=3.0), x)
+
+    def test_already_unit_rms_unchanged(self):
+        # array with rms=1: single element [1.0]
+        x = np.array([1.0])
+        assert_allclose(norm_rms(x), x)
+
+    def test_sign_preserved(self):
+        x = np.array([-3.0, 1.0, 2.0])
+        result = norm_rms(x)
+        assert result[0] < 0
+        assert result[1] > 0
+
+    def test_single_element_array(self):
+        result = norm_rms(np.array([5.0]))
+        assert np.sqrt(np.mean(result**2)) == pytest.approx(1.0)
diff --git a/tests/test_normalize.py b/tests/test_normalize.py
new file mode 100644
index 0000000..e5d5c64
--- /dev/null
+++ b/tests/test_normalize.py
@@ -0,0 +1,86 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import normalize
+
+
+class TestNormalizeDefaultRange:
+    """Test normalization to default range [-1, 1]."""
+
+    def test_min_maps_to_minus_one(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        result = normalize(x)
+        assert result.min() == pytest.approx(-1.0)
+
+    def test_max_maps_to_one(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        result = normalize(x)
+        assert result.max() == pytest.approx(1.0)
+
+    def test_random_array_bounds(self):
+        result = normalize(np.random.rand(100))
+        assert result.min() == pytest.approx(-1.0)
+        assert result.max() == pytest.approx(1.0)
+
+
+class TestNormalizeCustomRange:
+    """Test normalization to custom target ranges."""
+
+    def test_custom_range(self):
+        x = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
+        result = normalize(x, y1=0.0, y2=100.0)
+        assert result.min() == pytest.approx(0.0)
+        assert result.max() == pytest.approx(100.0)
+
+    def test_midpoint_maps_correctly(self):
+        x = np.array([0.0, 0.5, 1.0])
+        result = normalize(x, y1=0.0, y2=1.0)
+        assert result[1] == pytest.approx(0.5)
+
+    def test_known_values(self):
+        x = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
+        assert_allclose(normalize(x, y1=0.0, y2=1.0), [0.0, 0.25, 0.5, 0.75, 1.0])
+
+
+class TestNormalizePolarityInversion:
+    """Test normalization with y1 > y2 (inverted range)."""
+
+    def test_inverted_range_min_maps_to_y1(self):
+        x = np.array([1.0, 2.0, 3.0])
+        result = normalize(x, y1=1.0, y2=0.0)
+        assert result.max() == pytest.approx(1.0)
+
+    def test_inverted_range_max_maps_to_y2(self):
+        x = np.array([1.0, 2.0, 3.0])
+        result = normalize(x, y1=1.0, y2=0.0)
+        assert result.min() == pytest.approx(0.0)
+
+    def test_inverted_range_is_mirror_of_normal(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        normal = normalize(x, y1=0.0, y2=1.0)
+        inverted = normalize(x, y1=1.0, y2=0.0)
+        assert_allclose(normal + inverted, np.ones_like(x))
+
+
+class TestNormalizeProperties:
+    """Test mathematical properties of normalize."""
+
+    def test_output_shape_matches_input(self):
+        x = np.random.rand(20)
+        assert normalize(x).shape == x.shape
+
+    def test_constant_array_with_zero_range(self):
+        # all same values -> x2 - x1 = 0 -> nan (numpy does not raise)
+        x = np.array([3.0, 3.0, 3.0])
+        result = normalize(x)
+        assert np.all(np.isnan(result))
+
+    def test_linear_mapping_preserves_order(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+        result = normalize(x)
+        assert np.all(np.diff(result) > 0)
+
+    def test_already_normalized_input(self):
+        x = np.array([-1.0, 0.0, 1.0])
+        assert_allclose(normalize(x), x)
\ No newline at end of file
diff --git a/tests/test_remove_dc.py b/tests/test_remove_dc.py
new file mode 100644
index 0000000..4c1b222
--- /dev/null
+++ b/tests/test_remove_dc.py
@@ -0,0 +1,70 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import remove_dc
+
+
+class TestRemoveDcBasic:
+    """Test basic DC removal behaviour."""
+
+    def test_known_values(self):
+        assert_allclose(
+            remove_dc(np.array([1, 2, 3, 4])),
+            [-1.5, -0.5, 0.5, 1.5],
+        )
+
+    def test_mean_of_result_is_zero(self):
+        x = np.array([1.0, 2.0, 3.0, 4.0])
+        assert np.mean(remove_dc(x)) == pytest.approx(0.0)
+
+    def test_mean_of_random_array_is_zero(self):
+        x = np.random.rand(100) + 5.0  # large DC offset
+        assert np.mean(remove_dc(x)) == pytest.approx(0.0, abs=1e-12)
+
+    def test_shape_preserved(self):
+        x = np.random.rand(20)
+        assert remove_dc(x).shape == x.shape
+
+
+class TestRemoveDcEdgeCases:
+    """Test edge cases for DC removal."""
+
+    def test_zero_mean_array_unchanged(self):
+        x = np.array([-1.0, 0.0, 1.0])
+        assert_allclose(remove_dc(x), x)
+
+    def test_constant_array_becomes_zero(self):
+        x = np.full(5, 3.0)
+        assert_allclose(remove_dc(x), np.zeros(5))
+
+    def test_single_element_becomes_zero(self):
+        assert remove_dc(np.array([7.0])) == pytest.approx(0.0)
+
+    def test_negative_dc_offset(self):
+        x = np.array([-5.0, -4.0, -3.0])
+        assert np.mean(remove_dc(x)) == pytest.approx(0.0)
+
+
+class TestRemoveDcProperties:
+    """Test mathematical properties of DC removal."""
+
+    def test_values_sum_to_zero(self):
+        x = np.array([1.0, 3.0, 5.0, 7.0])
+        assert np.sum(remove_dc(x)) == pytest.approx(0.0)
+
+    def test_relative_differences_preserved(self):
+        # DC removal is a shift — differences between elements are unchanged
+        x = np.array([1.0, 3.0, 6.0, 10.0])
+        result = remove_dc(x)
+        assert_allclose(np.diff(result), np.diff(x))
+
+    def test_idempotent(self):
+        # applying twice gives same result as once
+        x = np.array([1.0, 2.0, 3.0, 4.0])
+        assert_allclose(remove_dc(remove_dc(x)), remove_dc(x))
+
+    def test_variance_preserved(self):
+        # DC removal does not change variance
+        x = np.array([1.0, 2.0, 3.0, 4.0])
+        assert np.var(remove_dc(x)) == pytest.approx(np.var(x))
\ No newline at end of file
diff --git a/tests/test_scurve.py b/tests/test_scurve.py
new file mode 100644
index 0000000..86713ca
--- /dev/null
+++ b/tests/test_scurve.py
@@ -0,0 +1,75 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import scurve
+
+
+class TestScurveEndpoints:
+    """Test boundary and clamping behaviour."""
+
+    def test_zero_maps_to_zero(self):
+        assert scurve(0.0) == pytest.approx(0.0)
+
+    def test_one_maps_to_one(self):
+        assert scurve(1.0) == pytest.approx(1.0)
+
+    def test_below_zero_clamps_to_zero(self):
+        assert scurve(-1.0) == pytest.approx(0.0)
+        assert scurve(-1e9) == pytest.approx(0.0)
+
+    def test_above_one_clamps_to_one(self):
+        assert scurve(2.0) == pytest.approx(1.0)
+        assert scurve(1e9) == pytest.approx(1.0)
+
+
+class TestScurveKnownValues:
+    """Test known values along the curve."""
+
+    def test_midpoint_is_half(self):
+        assert scurve(0.5) == pytest.approx(0.5)
+
+    def test_known_values(self):
+        assert_allclose(
+            scurve(np.arange(0, 1, 0.25)),
+            [0.0, 0.15625, 0.5, 0.84375],
+            rtol=1e-6,
+        )
+
+    def test_quarter_point(self):
+        assert scurve(0.25) == pytest.approx(0.15625)
+
+    def test_three_quarter_point(self):
+        assert scurve(0.75) == pytest.approx(0.84375)
+
+
+class TestScurveProperties:
+    """Test mathematical properties of the S-curve."""
+
+    def test_point_symmetry_around_midpoint(self):
+        # scurve is symmetric around (0.5, 0.5): scurve(1-x) == 1 - scurve(x)
+        for x in [0.1, 0.25, 0.3, 0.75]:
+            assert scurve(1 - x) == pytest.approx(1 - scurve(x))
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(0, 1, 200)
+        assert np.all(np.diff(scurve(x)) >= 0)
+
+    def test_output_bounded_to_unit_interval(self):
+        x = np.linspace(-2, 3, 200)
+        result = scurve(x)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+
+    def test_slope_at_midpoint_is_steepest(self):
+        # derivative at 0.5 should be greater than at 0.25 and 0.75
+        eps = 1e-5
+        slope_mid = (scurve(0.5 + eps) - scurve(0.5 - eps)) / (2 * eps)
+        slope_quarter = (scurve(0.25 + eps) - scurve(0.25 - eps)) / (2 * eps)
+        assert slope_mid > slope_quarter
+
+    def test_scalar_input_returns_float(self):
+        assert isinstance(scurve(0.5), float)
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(scurve(np.array([0.25, 0.75])), np.ndarray)
\ No newline at end of file
diff --git a/tests/test_softclip.py b/tests/test_softclip.py
new file mode 100644
index 0000000..a1a897e
--- /dev/null
+++ b/tests/test_softclip.py
@@ -0,0 +1,80 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import softclip
+
+
+class TestSoftclipLinearRegion:
+    """Test the perfectly linear region within [-0.5, 0.5]."""
+
+    def test_zero_is_zero(self):
+        assert softclip(0.0) == pytest.approx(0.0)
+
+    def test_positive_boundary(self):
+        assert softclip(0.5) == pytest.approx(0.5)
+
+    def test_negative_boundary(self):
+        assert softclip(-0.5) == pytest.approx(-0.5)
+
+    def test_midpoint_linear(self):
+        assert softclip(0.25) == pytest.approx(0.25)
+
+    def test_linear_region_is_identity(self):
+        x = np.linspace(-0.5, 0.5, 50)
+        assert_allclose(softclip(x), x)
+
+
+class TestSoftclipNonlinearRegion:
+    """Test the compressed region outside [-0.5, 0.5]."""
+
+    def test_known_positive_values(self):
+        assert_allclose(
+            softclip(np.arange(1, 5)),
+            [0.75, 0.875, 0.91666667, 0.9375],
+            rtol=1e-6,
+        )
+
+    def test_just_outside_boundary_positive(self):
+        # (|0.6| - 0.25) / 0.6
+        assert softclip(0.6) == pytest.approx(0.35 / 0.6, rel=1e-6)
+
+    def test_just_outside_boundary_negative(self):
+        assert softclip(-0.6) == pytest.approx(-0.35 / 0.6, rel=1e-6)
+
+    def test_output_approaches_one_for_large_x(self):
+        # (x - 0.25) / x -> 1 as x -> inf
+        assert softclip(1e9) == pytest.approx(1.0, rel=1e-6)
+
+    def test_output_approaches_minus_one_for_large_negative_x(self):
+        assert softclip(-1e9) == pytest.approx(-1.0, rel=1e-6)
+
+
+class TestSoftclipProperties:
+    """Test mathematical properties of softclip."""
+
+    def test_odd_symmetry(self):
+        for x in [0.3, 0.5, 1.0, 5.0, 100.0]:
+            assert softclip(-x) == pytest.approx(-softclip(x))
+
+    def test_output_bounded(self):
+        x = np.array([-1e9, -10.0, -1.0, 0.0, 1.0, 10.0, 1e9])
+        result = softclip(x)
+        assert np.all(result >= -1.0)
+        assert np.all(result <= 1.0)
+
+    def test_monotonically_increasing(self):
+        x = np.linspace(-10, 10, 200)
+        assert np.all(np.diff(softclip(x)) > 0)
+
+    def test_continuous_at_boundary(self):
+        # softclip should be continuous at x=±0.5
+        assert softclip(0.5 - 1e-9) == pytest.approx(softclip(0.5 + 1e-9), rel=1e-4)
+        assert softclip(-0.5 - 1e-9) == pytest.approx(softclip(-0.5 + 1e-9), rel=1e-4)
+
+    def test_scalar_input_returns_float(self):
+        assert isinstance(softclip(0.3), float)
+        assert isinstance(softclip(1.0), float)
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(softclip(np.array([0.3, 1.0])), np.ndarray)
\ No newline at end of file
diff --git a/tests/test_wrap.py b/tests/test_wrap.py
new file mode 100644
index 0000000..039085b
--- /dev/null
+++ b/tests/test_wrap.py
@@ -0,0 +1,70 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose
+
+from pyamapping.mappings import wrap
+
+
+class TestWrapDefaultRange:
+    """Test wrapping with default range [-1, 1]."""
+
+    def test_value_within_range_unchanged(self):
+        assert wrap(0.0) == pytest.approx(0.0)
+        assert wrap(-0.5) == pytest.approx(-0.5)
+
+    def test_upper_bound_wraps_to_lower(self):
+        assert wrap(1.0) == pytest.approx(-1.0)
+
+    def test_wraps_above_range(self):
+        assert wrap(1.5) == pytest.approx(-0.5)
+
+    def test_wraps_below_range(self):
+        assert wrap(-1.5) == pytest.approx(0.5)
+
+
+class TestWrapCustomRange:
+    """Test wrapping with custom ranges."""
+
+    def test_known_values(self):
+        assert_allclose(
+            wrap(np.arange(-3, 5), 0, 3),
+            [0, 1, 2, 0, 1, 2, 0, 1],
+        )
+
+    def test_value_at_y1_is_y1(self):
+        assert wrap(0.0, 0, 3) == pytest.approx(0.0)
+
+    def test_value_at_y2_wraps_to_y1(self):
+        assert wrap(3.0, 0, 3) == pytest.approx(0.0)
+
+    def test_multiple_periods_above(self):
+        assert wrap(7.0, 0, 3) == pytest.approx(1.0)
+
+    def test_multiple_periods_below(self):
+        assert wrap(-5.0, 0, 3) == pytest.approx(1.0)
+
+    def test_float_range(self):
+        assert wrap(1.75, 0.0, 0.5) == pytest.approx(0.25)
+
+
+class TestWrapProperties:
+    """Test mathematical properties of wrap."""
+
+    def test_output_always_in_range(self):
+        x = np.linspace(-10, 10, 200)
+        result = wrap(x, 0, 3)
+        assert np.all(result >= 0.0)
+        assert np.all(result < 3.0)
+
+    def test_periodic_with_period_equal_to_range(self):
+        # wrap(x) == wrap(x + (y2-y1))
+        period = 3.0
+        x = np.linspace(-5, 5, 50)
+        assert_allclose(wrap(x, 0, period), wrap(x + period, 0, period))
+
+
+    def test_array_input_returns_ndarray(self):
+        assert isinstance(wrap(np.array([0.0, 1.0])), np.ndarray)
+
+    def test_scalar_input_returns_scalar(self):
+        assert isinstance(float(wrap(0.5)), float)
\ No newline at end of file

From f091222ad28b7f6c3dfd7c2b9b56ec4bf8b7fe83 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 14 Apr 2026 12:17:02 +0200
Subject: [PATCH 72/87] Initial steps of migrating build setup to uv

---
 .github/workflows/ci.yml                      |    2 +-
 .gitignore                                    |    3 +
 .pre-commit-config.yaml                       |   62 +-
 coverage.lcov                                 |  498 +++
 docs/conf.py                                  |    4 +-
 {src/pyamapping => pyamapping}/__init__.py    |    5 +
 .../chainable_array.py                        |    0
 {src/pyamapping => pyamapping}/mappings.py    |    3 -
 pyproject.toml                                |   50 +-
 tox.ini                                       |   57 +-
 uv.lock                                       | 3874 +++++++++++++++++
 11 files changed, 4454 insertions(+), 104 deletions(-)
 create mode 100644 coverage.lcov
 rename {src/pyamapping => pyamapping}/__init__.py (98%)
 rename {src/pyamapping => pyamapping}/chainable_array.py (100%)
 rename {src/pyamapping => pyamapping}/mappings.py (99%)
 create mode 100644 uv.lock

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index e6e0739..3b4b299 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -61,7 +61,7 @@ jobs:
       matrix:
         python:
         - "3.7"  # oldest Python supported by PSF
-        - "3.13"  # newest Python that is stable
+        - "3.14"  # newest Python that is stable
         platform:
         - ubuntu-latest
         - macos-latest
diff --git a/.gitignore b/.gitignore
index e9e1e9b..a8e4e65 100644
--- a/.gitignore
+++ b/.gitignore
@@ -52,3 +52,6 @@ MANIFEST
 .venv*/
 .conda*/
 .python-version
+
+# Ignore .env file
+.env
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 8a753d5..a6cdff3 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -4,70 +4,32 @@ repos:
 - repo: https://github.com/pre-commit/pre-commit-hooks
   rev: v4.4.0
   hooks:
-  - id: trailing-whitespace
   - id: check-added-large-files
+    exclude: uv.lock
   - id: check-ast
   - id: check-json
   - id: check-merge-conflict
   - id: check-xml
   - id: check-yaml
-  - id: debug-statements
   - id: end-of-file-fixer
-  - id: requirements-txt-fixer
   - id: mixed-line-ending
     args: ['--fix=auto']  # replace 'auto' with 'lf' to enforce Linux/Mac line endings or 'crlf' for Windows
 
-## If you want to automatically "modernize" your Python code:
-# - repo: https://github.com/asottile/pyupgrade
-#   rev: v3.7.0
-#   hooks:
-#   - id: pyupgrade
-#     args: ['--py37-plus']
-
-## If you want to avoid flake8 errors due to unused vars or imports:
-# - repo: https://github.com/PyCQA/autoflake
-#   rev: v2.1.1
-#   hooks:
-#   - id: autoflake
-#     args: [
-#       --in-place,
-#       --remove-all-unused-imports,
-#       --remove-unused-variables,
-#     ]
-
-- repo: https://github.com/PyCQA/isort
-  rev: 5.12.0
-  hooks:
-  - id: isort
-
-- repo: https://github.com/psf/black
-  rev: 23.7.0
+- repo: https://github.com/astral-sh/ruff-pre-commit
+  rev: v0.9.0  # check latest
   hooks:
-  - id: black
-    language_version: python3
-
-## If like to embrace black styles even in the docs:
-# - repo: https://github.com/asottile/blacken-docs
-#   rev: v1.13.0
-#   hooks:
-#   - id: blacken-docs
-#     additional_dependencies: [black]
-
-- repo: https://github.com/PyCQA/flake8
-  rev: 6.0.0
-  hooks:
-  - id: flake8
-  ## You can add flake8 plugins via `additional_dependencies`:
-  #  additional_dependencies: [flake8-bugbear]
-
-## Check for misspells in documentation files:
-# - repo: https://github.com/codespell-project/codespell
-#   rev: v2.2.5
-#   hooks:
-#   - id: codespell
+    - id: ruff          # replaces isort + flake8
+      args: [--fix]     # auto-fix where possible
+    - id: ruff-format   # replaces black
 
 - repo: https://github.com/kynan/nbstripout
   rev: 0.8.1
   hooks:
     - id: nbstripout
       args: [--extra-keys=metadata.kernelspec metadata.language_info]
+
+
+- repo: https://github.com/astral-sh/uv-pre-commit
+  rev: 0.6.0  # check latest
+  hooks:
+    - id: uv-lock  # updates uv.lock when pyproject.toml changes
diff --git a/coverage.lcov b/coverage.lcov
new file mode 100644
index 0000000..d15be63
--- /dev/null
+++ b/coverage.lcov
@@ -0,0 +1,498 @@
+SF:pyamapping/__init__.py
+DA:1,1
+DA:3,1
+DA:9,1
+DA:11,1
+DA:12,1
+DA:16,1
+DA:18,1
+DA:20,1
+DA:22,1
+DA:23,1
+DA:72,1
+DA:120,1
+DA:122,1
+DA:123,1
+DA:125,1
+DA:126,0
+DA:128,1
+DA:130,1
+DA:132,1
+DA:133,0
+DA:135,1
+DA:138,0
+DA:140,0
+DA:141,0
+DA:143,0
+DA:145,1
+DA:146,1
+DA:151,1
+DA:154,1
+DA:157,1
+DA:158,0
+DA:160,1
+DA:161,1
+DA:166,1
+DA:169,1
+DA:171,1
+DA:172,1
+DA:173,1
+DA:174,1
+DA:175,1
+DA:176,1
+DA:178,0
+DA:179,1
+DA:183,1
+DA:184,1
+DA:185,1
+DA:188,1
+DA:189,1
+DA:191,1
+DA:229,1
+DA:230,1
+DA:232,1
+DA:233,1
+DA:234,1
+DA:235,1
+DA:236,1
+DA:237,1
+DA:238,1
+DA:239,1
+LF:59
+LH:51
+FN:120,151,register_numpy_ufunc
+FNDA:1,register_numpy_ufunc
+FN:125,126,register_numpy_ufunc.method1
+FNDA:0,register_numpy_ufunc.method1
+FN:154,166,register_chain_fn
+FNDA:1,register_chain_fn
+FN:157,158,register_chain_fn.method
+FNDA:0,register_chain_fn.method
+FN:169,179,_list_numpy_ufuncs
+FNDA:1,_list_numpy_ufuncs
+FNF:5
+FNH:3
+BRDA:123,0,jump to line 125,1
+BRDA:123,0,jump to line 130,1
+BRDA:130,0,jump to line 132,1
+BRDA:130,0,jump to line 138,0
+BRDA:172,0,jump to line 173,1
+BRDA:172,0,jump to line 179,1
+BRDA:174,0,jump to line 172,1
+BRDA:174,0,jump to line 175,1
+BRDA:175,0,jump to line 176,1
+BRDA:175,0,jump to line 178,0
+BRDA:183,0,jump to line 184,1
+BRDA:183,0,jump to line 188,1
+BRDA:229,0,jump to line 230,1
+BRDA:229,0,jump to line 232,1
+BRF:14
+BRH:12
+end_of_record
+SF:pyamapping/chainable_array.py
+DA:3,1
+DA:5,1
+DA:6,1
+DA:8,1
+DA:11,1
+DA:14,1
+DA:16,1
+DA:17,1
+DA:19,1
+DA:21,1
+DA:22,0
+DA:24,1
+DA:26,1
+DA:28,1
+DA:30,0
+DA:32,0
+DA:34,1
+DA:36,0
+DA:38,0
+DA:39,0
+DA:40,0
+DA:41,0
+DA:42,0
+DA:44,0
+DA:45,0
+DA:46,0
+DA:48,0
+DA:50,0
+DA:52,1
+DA:66,1
+DA:68,1
+DA:88,1
+DA:89,1
+DA:90,1
+DA:91,1
+DA:96,1
+DA:98,1
+DA:99,1
+DA:100,1
+DA:105,1
+DA:108,1
+LF:41
+LH:27
+FN:14,17,ChainableArray.__new__
+FNDA:1,ChainableArray.__new__
+FN:19,22,ChainableArray.__array_finalize__
+FNDA:1,ChainableArray.__array_finalize__
+FN:24,26,ChainableArray.to_array
+FNDA:1,ChainableArray.to_array
+FN:28,32,ChainableArray.to_asig
+FNDA:0,ChainableArray.to_asig
+FN:34,50,ChainableArray.plot
+FNDA:0,ChainableArray.plot
+FN:52,66,ChainableArray.mapvec
+FNDA:1,ChainableArray.mapvec
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+end_of_record
diff --git a/docs/conf.py b/docs/conf.py
index 7fea13e..87973bf 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -18,7 +18,7 @@
 # If extensions (or modules to document with autodoc) are in another directory,
 # add these directories to sys.path here. If the directory is relative to the
 # documentation root, use os.path.abspath to make it absolute, like shown here.
-sys.path.insert(0, os.path.join(__location__, "../src"))
+sys.path.insert(0, os.path.join(__location__, ".."))
 
 # -- Run sphinx-apidoc -------------------------------------------------------
 # This hack is necessary since RTD does not issue `sphinx-apidoc` before running
@@ -34,7 +34,7 @@
     from sphinx import apidoc
 
 output_dir = os.path.join(__location__, "api")
-module_dir = os.path.join(__location__, "../src/pyamapping")
+module_dir = os.path.join(__location__, "../pyamapping")
 try:
     shutil.rmtree(output_dir)
 except FileNotFoundError:
diff --git a/src/pyamapping/__init__.py b/pyamapping/__init__.py
similarity index 98%
rename from src/pyamapping/__init__.py
rename to pyamapping/__init__.py
index b750b6c..702b226 100644
--- a/src/pyamapping/__init__.py
+++ b/pyamapping/__init__.py
@@ -1,3 +1,8 @@
+"""
+Contains various mapping functions used
+in audio computing and sonification.
+"""
+
 import sys
 
 if sys.version_info[:2] >= (3, 8):
diff --git a/src/pyamapping/chainable_array.py b/pyamapping/chainable_array.py
similarity index 100%
rename from src/pyamapping/chainable_array.py
rename to pyamapping/chainable_array.py
diff --git a/src/pyamapping/mappings.py b/pyamapping/mappings.py
similarity index 99%
rename from src/pyamapping/mappings.py
rename to pyamapping/mappings.py
index 5e5f898..a652326 100644
--- a/src/pyamapping/mappings.py
+++ b/pyamapping/mappings.py
@@ -985,6 +985,3 @@ def ecdf(
     xs = np.sort(x)
     ys = np.arange(1, len(xs) + 1) / float(len(xs))
     return xs[selection], ys[selection]
-
-
-
diff --git a/pyproject.toml b/pyproject.toml
index 19cf8da..ab41486 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,16 +1,58 @@
+[project]
+name = "pyamapping"
+description = "A Python package containing audio related functions and mappings"
+authors = [
+    { name = "Thomas Hermann", email = "thermann@techfak.uni-bielefeld.de"},
+    { name = "Dennis Reinsch", email = "dreinsch@techfak.uni-bielefeld.de"}
+]
+maintainers = [
+    {name = "Fabian Hommel", email = "fhommel@techfa.uni-bielefeld.de"}
+]
+readme = "README.rst"
+dynamic = ["version"]
+requires-python = ">=3.9"
+dependencies = [
+    "numpy",
+    "scipy",
+]
+license = "MIT"
+license-files = ["LICEN[CS]E*", "AUTHORS.rst"]
+classifiers = [
+    "Development Status :: 4 - Beta",
+    "Programming Language :: Python"
+]
+
+[project.urls]
+github = "https://github.com/interactive-sonification/pyamapping"
+
 [build-system]
-# AVOID CHANGING REQUIRES: IT WILL BE UPDATED BY PYSCAFFOLD!
-requires = ["setuptools>=46.1.0", "setuptools_scm[toml]>=5"]
-build-backend = "setuptools.build_meta"
+requires = ["hatchling", "hatch-vcs"]
+build-backend = "hatchling.build"
+
+[tool.hatch.version]
+source = "vcs"
+
+[tool.hatch.build.targets.wheel]
+packages = ["pyamapping"]
 
 [tool.setuptools_scm]
 # For smarter version schemes and other configuration options,
 # check out https://github.com/pypa/setuptools_scm
 version_scheme = "no-guess-dev"
 
+[project.optional-dependencies]
+example-notebooks = ["notebook"]
+
+[tool.uv]
+dev-dependencies = ["tox", "pytest", "pytest-cov", "pre-commit", "sphinx"]
+
 [tool.ruff]
 line-length = 88
-lint.select = ["D"]
+lint.select = ["E", "F", "I", "T10"]  # E/F = flake8, I = isort
 
 [tool.ruff.lint.pydocstyle]
 convention = "numpy"
+
+[tool.pytest.ini_options]
+addopts = "--cov=mypackage --cov-report=lcov"
+testpaths = ["tests"]  
diff --git a/tox.ini b/tox.ini
index 69f8159..2c0c575 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,39 +1,19 @@
 # Tox configuration file
 # Read more under https://tox.wiki/
-# THIS SCRIPT IS SUPPOSED TO BE AN EXAMPLE. MODIFY IT ACCORDING TO YOUR NEEDS!
 
 [tox]
 minversion = 3.24
 envlist = default
-isolated_build = True
 
 
-[testenv]
+[testenv:{tests}]
 description = Invoke pytest to run automated tests
 setenv =
     TOXINIDIR = {toxinidir}
-passenv =
-    HOME
-    SETUPTOOLS_*
-extras =
-    testing
+skip_install = true
+allowlist_externals = uv
 commands =
-    pytest {posargs}
-
-
-# # To run `tox -e lint` you need to make sure you have a
-# # `.pre-commit-config.yaml` file. See https://pre-commit.com
-# [testenv:lint]
-# description = Perform static analysis and style checks
-# skip_install = True
-# deps = pre-commit
-# passenv =
-#     HOMEPATH
-#     PROGRAMDATA
-#     SETUPTOOLS_*
-# commands =
-#     pre-commit run --all-files {posargs:--show-diff-on-failure}
-
+    uv run pytest {posargs}
 
 [testenv:{build,clean}]
 description =
@@ -41,17 +21,12 @@ description =
     clean: Remove old distribution files and temporary build artifacts (./build and ./dist)
 # https://setuptools.pypa.io/en/stable/build_meta.html#how-to-use-it
 skip_install = True
+allowlist_externals = uv
 changedir = {toxinidir}
-deps =
-    build: build[virtualenv]
-passenv =
-    SETUPTOOLS_*
 commands =
     clean: python -c 'import shutil; [shutil.rmtree(p, True) for p in ("build", "dist", "docs/_build")]'
     clean: python -c 'import pathlib, shutil; [shutil.rmtree(p, True) for p in pathlib.Path("src").glob("*.egg-info")]'
-    build: python -m build {posargs}
-# By default, both `sdist` and `wheel` are built. If your sdist is too big or you don't want
-# to make it available, consider running: `tox -e build -- --wheel`
+    build: uv build {posargs}
 
 
 [testenv:{docs,doctests,linkcheck}]
@@ -59,19 +34,16 @@ description =
     docs: Invoke sphinx-build to build the docs
     doctests: Invoke sphinx-build to run doctests
     linkcheck: Check for broken links in the documentation
-passenv =
-    SETUPTOOLS_*
+allowlist_externals = uv
 setenv =
     DOCSDIR = {toxinidir}/docs
     BUILDDIR = {toxinidir}/docs/_build
     docs: BUILD = html
     doctests: BUILD = doctest
     linkcheck: BUILD = linkcheck
-deps =
-    -r {toxinidir}/docs/requirements.txt
     # ^  requirements.txt shared with Read The Docs
 commands =
-    sphinx-build --color -b {env:BUILD} -d "{env:BUILDDIR}/doctrees" "{env:DOCSDIR}" "{env:BUILDDIR}/{env:BUILD}" {posargs}
+    uv run sphinx-build --color -b {env:BUILD} -d "{env:BUILDDIR}/doctrees" "{env:DOCSDIR}" "{env:BUILDDIR}/{env:BUILD}" {posargs}
 
 
 [testenv:publish]
@@ -80,14 +52,11 @@ description =
     By default, it uses testpypi. If you really want to publish your package
     to be publicly accessible in PyPI, use the `-- --repository pypi` option.
 skip_install = True
+allowlist_externals = uv
 changedir = {toxinidir}
 passenv =
-    # See: https://twine.readthedocs.io/en/latest/
-    TWINE_USERNAME
-    TWINE_PASSWORD
-    TWINE_REPOSITORY
-    TWINE_REPOSITORY_URL
-deps = twine
+    UV_PUBLISH_USERNAME
+    UV_PUBLISH_PASSWORD
+    UV_PUBLISH_URL
 commands =
-    python -m twine check dist/*
-    python -m twine upload {posargs:--repository {env:TWINE_REPOSITORY:testpypi}} dist/*
+    uv publish {posargs}
diff --git a/uv.lock b/uv.lock
new file mode 100644
index 0000000..9b9e760
--- /dev/null
+++ b/uv.lock
@@ -0,0 +1,3874 @@
+version = 1
+revision = 1
+requires-python = ">=3.9"
+resolution-markers = [
+    "python_full_version >= '3.14'",
+    "python_full_version >= '3.12' and python_full_version < '3.14'",
+    "python_full_version == '3.11.*'",
+    "python_full_version == '3.10.*'",
+    "python_full_version < '3.10'",
+]
+
+[[package]]
+name = "alabaster"
+version = "0.7.16"
+source = { registry = "https://pypi.org/simple" }
+resolution-markers = [
+    "python_full_version < '3.10'",
+]
+sdist = { url = "https://files.pythonhosted.org/packages/c9/3e/13dd8e5ed9094e734ac430b5d0eb4f2bb001708a8b7856cbf8e084e001ba/alabaster-0.7.16.tar.gz", hash = "sha256:75a8b99c28a5dad50dd7f8ccdd447a121ddb3892da9e53d1ca5cca3106d58d65", size = 23776 }
+wheels = [
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+]
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+name = "alabaster"
+version = "1.0.0"
+source = { registry = "https://pypi.org/simple" }
+resolution-markers = [
+    "python_full_version >= '3.14'",
+    "python_full_version >= '3.12' and python_full_version < '3.14'",
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+]
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+name = "anyio"
+version = "4.12.1"
+source = { registry = "https://pypi.org/simple" }
+resolution-markers = [
+    "python_full_version < '3.10'",
+]
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+    { name = "exceptiongroup", marker = "python_full_version < '3.10'" },
+    { name = "idna", marker = "python_full_version < '3.10'" },
+    { name = "typing-extensions", marker = "python_full_version < '3.10'" },
+]
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+wheels = [
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+source = { registry = "https://pypi.org/simple" }
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From cf75d3a4826dd551f946bad808e75b4c11a8adf9 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 14 Apr 2026 12:23:21 +0200
Subject: [PATCH 73/87] Repaired uv.lock

---
 .pre-commit-config.yaml |    2 +
 uv.lock                 | 3874 ---------------------------------------
 2 files changed, 2 insertions(+), 3874 deletions(-)
 delete mode 100644 uv.lock

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index a6cdff3..c7c5a42 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -12,7 +12,9 @@ repos:
   - id: check-xml
   - id: check-yaml
   - id: end-of-file-fixer
+    exclude: "uv.lock"
   - id: mixed-line-ending
+    exclude: "uv.lock"
     args: ['--fix=auto']  # replace 'auto' with 'lf' to enforce Linux/Mac line endings or 'crlf' for Windows
 
 - repo: https://github.com/astral-sh/ruff-pre-commit
diff --git a/uv.lock b/uv.lock
deleted file mode 100644
index 9b9e760..0000000
--- a/uv.lock
+++ /dev/null
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From 68a8aab97ac584b9d217375cc5048e3358658c2d Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 14 Apr 2026 12:24:56 +0200
Subject: [PATCH 74/87] Repaired uv.lock

---
 uv.lock | 3853 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 3853 insertions(+)
 create mode 100644 uv.lock

diff --git a/uv.lock b/uv.lock
new file mode 100644
index 0000000..cc10495
--- /dev/null
+++ b/uv.lock
@@ -0,0 +1,3853 @@
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From 207c3350c60685f0c88d1d0ffdcd3a24f4e769e8 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 14 Apr 2026 13:25:42 +0200
Subject: [PATCH 75/87] Repaired uv.lock

---
 uv.lock | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/uv.lock b/uv.lock
index cc10495..63d713a 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,5 +1,4 @@
 version = 1
-revision = 1
 requires-python = ">=3.9"
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -900,7 +899,7 @@ name = "exceptiongroup"
 version = "1.3.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "typing-extensions", marker = "python_full_version < '3.11'" },
+    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/50/79/66800aadf48771f6b62f7eb014e352e5d06856655206165d775e675a02c9/exceptiongroup-1.3.1.tar.gz", hash = "sha256:8b412432c6055b0b7d14c310000ae93352ed6754f70fa8f7c34141f91c4e3219", size = 30371 }
 wheels = [
@@ -2298,6 +2297,7 @@ wheels = [
 
 [[package]]
 name = "pyamapping"
+version = "0.1.1.dev73+gf091222ad.d20260414"
 source = { editable = "." }
 dependencies = [
     { name = "numpy", version = "2.0.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.10'" },
@@ -2334,7 +2334,6 @@ requires-dist = [
     { name = "numpy" },
     { name = "scipy" },
 ]
-provides-extras = ["example-notebooks"]
 
 [package.metadata.requires-dev]
 dev = [

From e9028468a3b07de47d4992b3ffaa5c1e0e175693 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Wed, 15 Apr 2026 11:45:36 +0200
Subject: [PATCH 76/87] Deleted unnecessary files, updated coverage
 configuration

---
 .gitignore     |   2 +-
 .isort.cfg     |   3 -
 coverage.lcov  | 654 ++++++++++++++++++++++++-------------------------
 pyproject.toml |   5 +-
 setup.cfg      | 128 ----------
 setup.py       |  21 --
 uv.lock        |   5 +-
 7 files changed, 335 insertions(+), 483 deletions(-)
 delete mode 100644 .isort.cfg
 delete mode 100644 setup.cfg
 delete mode 100644 setup.py

diff --git a/.gitignore b/.gitignore
index a8e4e65..c1b82e9 100644
--- a/.gitignore
+++ b/.gitignore
@@ -53,5 +53,5 @@ MANIFEST
 .conda*/
 .python-version
 
-# Ignore .env file
+# .env file for Environment Variables
 .env
diff --git a/.isort.cfg b/.isort.cfg
deleted file mode 100644
index 45818b0..0000000
--- a/.isort.cfg
+++ /dev/null
@@ -1,3 +0,0 @@
-[settings]
-profile = black
-known_first_party = pyamapping
diff --git a/coverage.lcov b/coverage.lcov
index d15be63..0685970 100644
--- a/coverage.lcov
+++ b/coverage.lcov
@@ -1,91 +1,91 @@
 SF:pyamapping/__init__.py
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+FN:130,131,register_numpy_ufunc.method1
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-FN:154,166,register_chain_fn
+FN:159,171,register_chain_fn
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-FN:157,158,register_chain_fn.method
+FN:162,163,register_chain_fn.method
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-FN:169,179,_list_numpy_ufuncs
+FN:174,184,_list_numpy_ufuncs
 FNDA:1,_list_numpy_ufuncs
 FNF:5
 FNH:3
-BRDA:123,0,jump to line 125,1
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@@ -96,13 +96,13 @@ DA:6,1
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@@ -119,50 +119,50 @@ DA:46,0
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 BRDA:39,0,jump to line 40,-
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-BRH:71
+BRH:0
 end_of_record
diff --git a/pyproject.toml b/pyproject.toml
index ab41486..74fe6da 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -50,9 +50,12 @@ dev-dependencies = ["tox", "pytest", "pytest-cov", "pre-commit", "sphinx"]
 line-length = 88
 lint.select = ["E", "F", "I", "T10"]  # E/F = flake8, I = isort
 
+[tool.ruff.lint.isort]
+known_first_party = "pyamapping"
+
 [tool.ruff.lint.pydocstyle]
 convention = "numpy"
 
 [tool.pytest.ini_options]
-addopts = "--cov=mypackage --cov-report=lcov"
+addopts = "--cov=pyamapping --cov-report=lcov --cov-report=term-missing"
 testpaths = ["tests"]  
diff --git a/setup.cfg b/setup.cfg
deleted file mode 100644
index cf14e4b..0000000
--- a/setup.cfg
+++ /dev/null
@@ -1,128 +0,0 @@
-# This file is used to configure your project.
-# Read more about the various options under:
-# https://setuptools.pypa.io/en/latest/userguide/declarative_config.html
-# https://setuptools.pypa.io/en/latest/references/keywords.html
-
-[metadata]
-name = pyamapping
-description = A Python package containing audio related functions and mappings
-author = Dennis Reinsch
-author_email = dreinsch@techfak.uni-bielefeld.de
-license = MIT
-license_files = LICENSE.txt
-long_description = file: README.rst
-long_description_content_type = text/x-rst; charset=UTF-8
-url = https://github.com/interactive-sonification/pyamapping
-# Add here related links, for example:
-project_urls =
-    Documentation = https://pyscaffold.org/
-#    Source = https://github.com/pyscaffold/pyscaffold/
-#    Changelog = https://pyscaffold.org/en/latest/changelog.html
-#    Tracker = https://github.com/pyscaffold/pyscaffold/issues
-#    Conda-Forge = https://anaconda.org/conda-forge/pyscaffold
-#    Download = https://pypi.org/project/PyScaffold/#files
-#    Twitter = https://twitter.com/PyScaffold
-
-# Change if running only on Windows, Mac or Linux (comma-separated)
-platforms = any
-
-# Add here all kinds of additional classifiers as defined under
-# https://pypi.org/classifiers/
-classifiers =
-    Development Status :: 4 - Beta
-    Programming Language :: Python
-
-
-[options]
-zip_safe = False
-packages = find_namespace:
-include_package_data = True
-package_dir =
-    =src
-
-# Require a min/specific Python version (comma-separated conditions)
-# python_requires = >=3.8
-
-# Add here dependencies of your project (line-separated), e.g. requests>=2.2,<3.0.
-# Version specifiers like >=2.2,<3.0 avoid problems due to API changes in
-# new major versions. This works if the required packages follow Semantic Versioning.
-# For more information, check out https://semver.org/.
-install_requires =
-    numpy
-    scipy
-    importlib-metadata; python_version<"3.8"
-
-
-[options.packages.find]
-where = src
-exclude =
-    tests
-
-[options.extras_require]
-# Add here additional requirements for extra features, to install with:
-# `pip install pyamapping[PDF]` like:
-# PDF = ReportLab; RXP
-
-# Add here test requirements (semicolon/line-separated)
-testing =
-    setuptools
-    pytest
-    pytest-cov
-
-[options.entry_points]
-# Add here console scripts like:
-# console_scripts =
-#     script_name = pyamapping.module:function
-# For example:
-# console_scripts =
-#     fibonacci = pyamapping.skeleton:run
-# And any other entry points, for example:
-# pyscaffold.cli =
-#     awesome = pyscaffoldext.awesome.extension:AwesomeExtension
-
-[tool:pytest]
-# Specify command line options as you would do when invoking pytest directly.
-# e.g. --cov-report html (or xml) for html/xml output or --junitxml junit.xml
-# in order to write a coverage file that can be read by Jenkins.
-# CAUTION: --cov flags may prohibit setting breakpoints while debugging.
-#          Comment those flags to avoid this pytest issue.
-addopts =
-    --cov pyamapping --cov-report term-missing
-    --verbose
-norecursedirs =
-    dist
-    build
-    .tox
-testpaths = tests
-# Use pytest markers to select/deselect specific tests
-# markers =
-#     slow: mark tests as slow (deselect with '-m "not slow"')
-#     system: mark end-to-end system tests
-
-[devpi:upload]
-# Options for the devpi: PyPI server and packaging tool
-# VCS export must be deactivated since we are using setuptools-scm
-no_vcs = 1
-formats = bdist_wheel
-
-[flake8]
-# Some sane defaults for the code style checker flake8
-max_line_length = 88
-extend_ignore = E203, W503
-# ^  Black-compatible
-#    E203 and W503 have edge cases handled by black
-exclude =
-    .tox
-    build
-    dist
-    .eggs
-    docs/conf.py
-
-[pyscaffold]
-# PyScaffold's parameters when the project was created.
-# This will be used when updating. Do not change!
-version = 4.5
-package = pyamapping
-extensions =
-    github_actions
-    pre_commit
diff --git a/setup.py b/setup.py
deleted file mode 100644
index ad38f6f..0000000
--- a/setup.py
+++ /dev/null
@@ -1,21 +0,0 @@
-"""
-    Setup file for pyamapping.
-    Use setup.cfg to configure your project.
-
-    This file was generated with PyScaffold 4.5.
-    PyScaffold helps you to put up the scaffold of your new Python project.
-    Learn more under: https://pyscaffold.org/
-"""
-from setuptools import setup
-
-if __name__ == "__main__":
-    try:
-        setup(use_scm_version={"version_scheme": "no-guess-dev"})
-    except:  # noqa
-        print(
-            "\n\nAn error occurred while building the project, "
-            "please ensure you have the most updated version of setuptools, "
-            "setuptools_scm and wheel with:\n"
-            "   pip install -U setuptools setuptools_scm wheel\n\n"
-        )
-        raise
diff --git a/uv.lock b/uv.lock
index 63d713a..cc10495 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,4 +1,5 @@
 version = 1
+revision = 1
 requires-python = ">=3.9"
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -899,7 +900,7 @@ name = "exceptiongroup"
 version = "1.3.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
+    { name = "typing-extensions", marker = "python_full_version < '3.11'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/50/79/66800aadf48771f6b62f7eb014e352e5d06856655206165d775e675a02c9/exceptiongroup-1.3.1.tar.gz", hash = "sha256:8b412432c6055b0b7d14c310000ae93352ed6754f70fa8f7c34141f91c4e3219", size = 30371 }
 wheels = [
@@ -2297,7 +2298,6 @@ wheels = [
 
 [[package]]
 name = "pyamapping"
-version = "0.1.1.dev73+gf091222ad.d20260414"
 source = { editable = "." }
 dependencies = [
     { name = "numpy", version = "2.0.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.10'" },
@@ -2334,6 +2334,7 @@ requires-dist = [
     { name = "numpy" },
     { name = "scipy" },
 ]
+provides-extras = ["example-notebooks"]
 
 [package.metadata.requires-dev]
 dev = [

From 228c06cdf4efdbcdf7b59da813c6f7d03027a80a Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Wed, 15 Apr 2026 12:11:28 +0200
Subject: [PATCH 77/87] Updated readme

---
 README.rst | 64 +++++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 56 insertions(+), 8 deletions(-)

diff --git a/README.rst b/README.rst
index de8a7a8..59aa57a 100644
--- a/README.rst
+++ b/README.rst
@@ -45,20 +45,68 @@ pyamapping
 Making Changes & Contributing
 =============================
 
-This project uses `pre-commit`_, please make sure to install it before making any
-changes::
+To setup your development environment, you need to have `uv <https://docs.astral.sh/uv/>`_ installed.
+First, clone the repository and then change into the root directory:
+
+.. code-block:: bash
 
-    pip install pre-commit
     cd pyamapping
-    pre-commit install
 
-It is a good idea to update the hooks to the latest version::
+Afterwards, sync your environment:
+
+.. code-block:: bash
+
+    uv sync
+
+This will install all required dependencies (dev dependencies included).
+Also, please install the pre-commit hooks:
+
+.. code-block:: bash
+
+    uv run pre-commit install
+
+Experimentation in Scratchpad / Jupyter
+----------------------------------------
+
+uv automatically installs the ``pyamapping`` package to the ``.venv`` in editable mode.
+During development, any changes to the ``pyamapping`` source will be reflected automatically.
+To write playground / exploratory code, just make sure to run your REPL environment with ``uv run``, e.g.:
+
+.. code-block:: bash
+
+    uv run python
+
+or
+
+.. code-block:: bash
+
+    uv run jupyter notebook
+
+Then, you should be able to:
+
+.. code-block:: python
+
+    import pyamapping as pam
+
+And get the current state of the source code.
+
+Running Tests
+-------------
+
+Tests can be run via:
+
+.. code-block:: bash
+
+    uv run tox -e tests
+
+Building Documentation
+----------------------
 
-    pre-commit autoupdate
+Documentation can be built via:
 
-Don't forget to tell your contributors to also install and use pre-commit.
+.. code-block:: bash
 
-.. _pre-commit: https://pre-commit.com/
+    uv run tox -e docs
 
 Note
 ====

From b81a35b9175cd27ee5895100660192870e730b3b Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Wed, 15 Apr 2026 12:12:31 +0200
Subject: [PATCH 78/87] Updated readme

---
 README.rst | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/README.rst b/README.rst
index 59aa57a..e098bb5 100644
--- a/README.rst
+++ b/README.rst
@@ -107,9 +107,3 @@ Documentation can be built via:
 .. code-block:: bash
 
     uv run tox -e docs
-
-Note
-====
-
-This project has been set up using PyScaffold 4.5. For details and usage
-information on PyScaffold see https://pyscaffold.org/.

From b23207d6732a4ea632bcc39a60167ce150fb0276 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 11:28:45 +0200
Subject: [PATCH 79/87] Udpated github actions

---
 .github/workflows/ci.yml | 48 ++++++++++++++++++----------------------
 1 file changed, 21 insertions(+), 27 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 3b4b299..ce0eb01 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -32,24 +32,20 @@ jobs:
     outputs:
       wheel-distribution: ${{ steps.wheel-distribution.outputs.path }}
     steps:
-      - uses: actions/checkout@v3
-        with: {fetch-depth: 0}  # deep clone for setuptools-scm
-      - uses: actions/setup-python@v4
-        id: setup-python
-        with: {python-version: "3.11"}
+      - uses: actions/checkout@v4
+        with: {fetch-depth: 0}  # deep clone for hatch-scm
+      - uses: astral-sh/setup-uv@v5
       - name: Run static analysis and format checkers
-        run: pipx run pre-commit run --all-files --show-diff-on-failure
+        run: uv run pre-commit run --all-files --show-diff-on-failure
       - name: Build package distribution files
-        run: >-
-          pipx run --python '${{ steps.setup-python.outputs.python-path }}'
-          tox -e clean,build
+        run: uv run tox -e clean,build
       - name: Record the path of wheel distribution
         id: wheel-distribution
         run: echo "path=$(ls dist/*.whl)" >> $GITHUB_OUTPUT
       - name: Store the distribution files for use in other stages
         # `tests` and `publish` will use the same pre-built distributions,
         # so we make sure to release the exact same package that was tested
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           name: python-distribution-files
           path: dist/
@@ -60,7 +56,10 @@ jobs:
     strategy:
       matrix:
         python:
-        - "3.7"  # oldest Python supported by PSF
+        - "3.10"  
+        - "3.11"  # oldest Python supported by PSF
+        - "3.12"  # oldest Python supported by PSF
+        - "3.13"  # oldest Python supported by PSF
         - "3.14"  # newest Python that is stable
         platform:
         - ubuntu-latest
@@ -68,21 +67,17 @@ jobs:
         - windows-latest
     runs-on: ${{ matrix.platform }}
     steps:
-      - uses: actions/checkout@v3
-      - uses: actions/setup-python@v4
-        id: setup-python
+      - uses: actions/checkout@v4
+      - uses: astral-sh/setup-uv@v5
         with:
           python-version: ${{ matrix.python }}
       - name: Retrieve pre-built distribution files
-        uses: actions/download-artifact@v3
+        uses: actions/download-artifact@v4
         with: {name: python-distribution-files, path: dist/}
       - name: Run tests
         run: >-
-          pipx run --python '${{ steps.setup-python.outputs.python-path }}'
-          tox --installpkg '${{ needs.prepare.outputs.wheel-distribution }}'
+          uv run tox --installpkg '${{ needs.prepare.outputs.wheel-distribution }}'
           -- -rFEx --durations 10 --color yes  # pytest args
-      - name: Generate coverage report
-        run: pipx run coverage lcov -o coverage.lcov
       - name: Upload partial coverage report
         uses: coverallsapp/github-action@master
         with:
@@ -108,18 +103,17 @@ jobs:
     permissions:
       contents: write
     steps:
-      - uses: actions/checkout@v3
-      - uses: actions/setup-python@v4
-        with: {python-version: "3.12"}
+      - uses: actions/checkout@v4
+      - uses: astral-sh/setup-uv@v5
       - name: Retrieve pre-built distribution files
-        uses: actions/download-artifact@v3
+        uses: actions/download-artifact@v4
         with: {name: python-distribution-files, path: dist/}
       - name: Publish Package
         env:
           # TODO: Set your PYPI_TOKEN as a secret using GitHub UI
           # - https://pypi.org/help/#apitoken
           # - https://docs.github.com/en/actions/security-guides/encrypted-secrets
-          TWINE_REPOSITORY: pypi
-          TWINE_USERNAME: __token__
-          TWINE_PASSWORD: ${{ secrets.PYPI_TOKEN }}
-        run: pipx run tox -e publish
+          UV_PUBLISH_URL: https://upload.pypi.org/legacy/
+          UV_PUBLISH_USERNAME: __token__
+          UV_PUBLISH_PASSWORD: ${{ secrets.PYPI_TOKEN }}
+        run: uv run tox -e publish

From b81d687de35a13133350fd03eca7cf69862858f3 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 11:36:54 +0200
Subject: [PATCH 80/87] Updated versions of various actions, because older
 versions are using Node.js 20, which is not supported anymore by the github
 runner

---
 .github/workflows/ci.yml | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index ce0eb01..f9b1444 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -32,9 +32,9 @@ jobs:
     outputs:
       wheel-distribution: ${{ steps.wheel-distribution.outputs.path }}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v5
         with: {fetch-depth: 0}  # deep clone for hatch-scm
-      - uses: astral-sh/setup-uv@v5
+      - uses: astral-sh/setup-uv@v8
       - name: Run static analysis and format checkers
         run: uv run pre-commit run --all-files --show-diff-on-failure
       - name: Build package distribution files
@@ -67,8 +67,8 @@ jobs:
         - windows-latest
     runs-on: ${{ matrix.platform }}
     steps:
-      - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v5
+      - uses: actions/checkout@v5
+      - uses: astral-sh/setup-uv@v8
         with:
           python-version: ${{ matrix.python }}
       - name: Retrieve pre-built distribution files
@@ -103,8 +103,8 @@ jobs:
     permissions:
       contents: write
     steps:
-      - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v5
+      - uses: actions/checkout@v5
+      - uses: astral-sh/setup-uv@v8
       - name: Retrieve pre-built distribution files
         uses: actions/download-artifact@v4
         with: {name: python-distribution-files, path: dist/}

From ecf9d73754df2497ecb52417b051835f367609bd Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 11:46:09 +0200
Subject: [PATCH 81/87] Pinned exact version of uv github action

---
 .github/workflows/ci.yml | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index f9b1444..ef2fd2e 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -34,7 +34,7 @@ jobs:
     steps:
       - uses: actions/checkout@v5
         with: {fetch-depth: 0}  # deep clone for hatch-scm
-      - uses: astral-sh/setup-uv@v8
+      - uses: astral-sh/setup-uv@v8.1.0
       - name: Run static analysis and format checkers
         run: uv run pre-commit run --all-files --show-diff-on-failure
       - name: Build package distribution files
@@ -68,7 +68,7 @@ jobs:
     runs-on: ${{ matrix.platform }}
     steps:
       - uses: actions/checkout@v5
-      - uses: astral-sh/setup-uv@v8
+      - uses: astral-sh/setup-uv@v8.1.0
         with:
           python-version: ${{ matrix.python }}
       - name: Retrieve pre-built distribution files
@@ -104,7 +104,7 @@ jobs:
       contents: write
     steps:
       - uses: actions/checkout@v5
-      - uses: astral-sh/setup-uv@v8
+      - uses: astral-sh/setup-uv@v8.1.0
       - name: Retrieve pre-built distribution files
         uses: actions/download-artifact@v4
         with: {name: python-distribution-files, path: dist/}

From cb65c2a13fde2c6b471f794a2b4144244c287497 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 11:56:48 +0200
Subject: [PATCH 82/87] fixed ruff error in pyproject.toml

---
 pyproject.toml                |  6 ++++--
 tests/test_bilin.py           | 16 ++++++++++------
 tests/test_chainable_array.py | 13 +++++++++----
 tests/test_clip.py            |  3 ++-
 tests/test_cps_octave_cps.py  |  4 +++-
 tests/test_curvelin.py        | 19 ++++++++++++++-----
 tests/test_db_amp_db.py       |  4 ++--
 tests/test_distort.py         |  8 ++++----
 tests/test_ecdf.py            |  7 +++----
 tests/test_explin.py          | 10 +++++-----
 tests/test_fermi.py           |  5 +++--
 tests/test_fold.py            |  2 +-
 tests/test_gain.py            |  5 ++---
 tests/test_hz_mel_hz.py       | 22 +++++++++++++++-------
 tests/test_lcurve.py          |  4 ++--
 tests/test_lincurve.py        |  6 ++++--
 tests/test_linexp.py          |  5 +++--
 tests/test_linlin.py          |  3 ++-
 tests/test_linpoly.py         | 22 ++++++++++++++++------
 tests/test_midi_cps_midi.py   |  5 ++---
 tests/test_midi_ratio_midi.py |  6 ++----
 tests/test_norm_peak.py       |  5 ++---
 tests/test_normalize.py       |  4 ++--
 tests/test_remove_dc.py       |  2 +-
 tests/test_scurve.py          |  4 ++--
 tests/test_softclip.py        |  4 ++--
 tests/test_wrap.py            |  5 ++---
 27 files changed, 119 insertions(+), 80 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 74fe6da..0e97942 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -48,10 +48,12 @@ dev-dependencies = ["tox", "pytest", "pytest-cov", "pre-commit", "sphinx"]
 
 [tool.ruff]
 line-length = 88
-lint.select = ["E", "F", "I", "T10"]  # E/F = flake8, I = isort
+
+[tool.ruff.lint]
+select = ["E", "F", "I", "T10"]  # E/F = flake8, I = isort
 
 [tool.ruff.lint.isort]
-known_first_party = "pyamapping"
+known-first-party = ["pyamapping"]
 
 [tool.ruff.lint.pydocstyle]
 convention = "numpy"
diff --git a/tests/test_bilin.py b/tests/test_bilin.py
index e88dc99..296bbfb 100644
--- a/tests/test_bilin.py
+++ b/tests/test_bilin.py
@@ -2,8 +2,8 @@
 import pytest
 from numpy.testing import assert_allclose
 
-from pyamapping.mappings import interp_spline, bilin
-from pyamapping.chainable_array import ChainableArray, chain
+from pyamapping.chainable_array import ChainableArray
+from pyamapping.mappings import bilin, interp_spline
 
 
 class TestInterpSplineLinear:
@@ -46,7 +46,7 @@ class TestInterpSplineReturnType:
     def test_chainable_array_input_returns_plain_ndarray(self):
         x = ChainableArray(np.array([0.0, 0.5, 1.0]))
         result = interp_spline(x, [-1, 0, 1], [-1, 0, 1])
-        assert type(result) == np.ndarray
+        assert isinstance(result, np.ndarray)
 
     def test_plain_array_input_returns_chainable_array(self):
         x = np.array([0.0, 0.5, 1.0])
@@ -87,6 +87,10 @@ def test_symmetric_mapping(self):
     def test_two_slopes_differ(self):
         # slope left of xcenter: (-20-0)/(20-60) = 0.5
         # slope right of xcenter: (60-0)/(80-60) = 3.0
-        slope_left = (bilin(40, 60, 20, 80, 0, -20, 60) - bilin(20, 60, 20, 80, 0, -20, 60)) / 20
-        slope_right = (bilin(80, 60, 20, 80, 0, -20, 60) - bilin(60, 60, 20, 80, 0, -20, 60)) / 20
-        assert slope_left != pytest.approx(slope_right)
\ No newline at end of file
+        slope_left = (
+            bilin(40, 60, 20, 80, 0, -20, 60) - bilin(20, 60, 20, 80, 0, -20, 60)
+        ) / 20
+        slope_right = (
+            bilin(80, 60, 20, 80, 0, -20, 60) - bilin(60, 60, 20, 80, 0, -20, 60)
+        ) / 20
+        assert slope_left != pytest.approx(slope_right)
diff --git a/tests/test_chainable_array.py b/tests/test_chainable_array.py
index 3587028..81657e2 100644
--- a/tests/test_chainable_array.py
+++ b/tests/test_chainable_array.py
@@ -1,9 +1,10 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.chainable_array import ChainableArray, chain
 
+
 class TestChainableArrayCreation:
     """Test ChainableArray instantiation and type."""
 
@@ -84,7 +85,11 @@ def test_passes_args(self):
     def test_raises_type_error_for_scalar_only_function(self):
         a = ChainableArray([1.0, 2.0, 3.0])
         with pytest.raises(TypeError, match="Use .mapvec()"):
-            a.map(lambda x: x + 1 if isinstance(x, float) else (_ for _ in ()).throw(TypeError()))
+            a.map(
+                lambda x: x + 1
+                if isinstance(x, float)
+                else (_ for _ in ()).throw(TypeError())
+            )
 
     def test_chaining(self):
         a = ChainableArray([1.0, 2.0, 3.0])
@@ -97,7 +102,7 @@ class TestChainableArrayMapvec:
 
     def test_applies_scalar_function_elementwise(self):
         a = ChainableArray([1.0, 2.0, 3.0])
-        result = a.mapvec(lambda x: x ** 2)
+        result = a.mapvec(lambda x: x**2)
         assert_allclose(result, [1.0, 4.0, 9.0])
 
     def test_returns_chainable_array(self):
@@ -130,4 +135,4 @@ def test_dynamic_method_returns_string(self):
     def test_unknown_attribute_raises_attribute_error(self):
         a = ChainableArray([1.0, 2.0])
         with pytest.raises(AttributeError):
-            _ = a.nonexistent_method
\ No newline at end of file
+            _ = a.nonexistent_method
diff --git a/tests/test_clip.py b/tests/test_clip.py
index f37358d..b059a61 100644
--- a/tests/test_clip.py
+++ b/tests/test_clip.py
@@ -4,6 +4,7 @@
 
 from pyamapping.mappings import clip
 
+
 class TestClipScalar:
     """Test clipping of scalar float/int values."""
 
@@ -86,4 +87,4 @@ def test_same_result_for_value_within(self):
         assert clip(4, 3, 5) == clip(np.array([4]), 3, 5)[0]
 
     def test_same_result_for_value_above(self):
-        assert clip(7, 3, 5) == clip(np.array([7]), 3, 5)[0]
\ No newline at end of file
+        assert clip(7, 3, 5) == clip(np.array([7]), 3, 5)[0]
diff --git a/tests/test_cps_octave_cps.py b/tests/test_cps_octave_cps.py
index ca09010..da8b332 100644
--- a/tests/test_cps_octave_cps.py
+++ b/tests/test_cps_octave_cps.py
@@ -58,4 +58,6 @@ def test_cps_to_octave_to_cps(self):
 
     def test_octave_to_cps_to_octave(self):
         for octave in [1.0, 2.75, 3.75, 4.0, 4.75, 5.75, 7.0]:
-            assert cps_to_octave(octave_to_cps(octave)) == pytest.approx(octave, rel=1e-9)
\ No newline at end of file
+            assert cps_to_octave(octave_to_cps(octave)) == pytest.approx(
+                octave, rel=1e-9
+            )
diff --git a/tests/test_curvelin.py b/tests/test_curvelin.py
index a3c9cbf..32b9d88 100644
--- a/tests/test_curvelin.py
+++ b/tests/test_curvelin.py
@@ -1,9 +1,10 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import curvelin, lincurve
 
+
 class TestCurvelinEndpoints:
     """Test that x1->y1 and x2->y2 mappings are exact."""
 
@@ -93,7 +94,9 @@ def test_clip_min_does_not_affect_upper_values(self):
         assert curvelin(0.5, 0, 1, 0, 1, curve=0.0, clip="min") == pytest.approx(0.5)
 
     def test_clip_minmax_caps_both_sides(self):
-        assert curvelin(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(0.0)
+        assert curvelin(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(
+            0.0
+        )
         assert curvelin(2.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(1.0)
 
     def test_clip_unknown_string_implies_minmax(self):
@@ -101,7 +104,9 @@ def test_clip_unknown_string_implies_minmax(self):
         assert curvelin(2.0, 0, 1, 0, 1, curve=0.0, clip="both") == pytest.approx(1.0)
 
     def test_clip_minmax_array_input(self):
-        result = curvelin(np.array([-1.0, 0.5, 2.0]), 0, 1, 0, 1, curve=0.0, clip="minmax")
+        result = curvelin(
+            np.array([-1.0, 0.5, 2.0]), 0, 1, 0, 1, curve=0.0, clip="minmax"
+        )
         assert_allclose(result, [0.0, 0.5, 1.0])
 
 
@@ -110,8 +115,12 @@ class TestCurvelinVsLincurve:
 
     def test_curvelin_is_inverse_of_lincurve(self):
         for x in [0.1, 0.3, 0.5, 0.7, 0.9]:
-            assert curvelin(lincurve(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(x, rel=1e-6)
+            assert curvelin(lincurve(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(
+                x, rel=1e-6
+            )
 
     def test_lincurve_is_inverse_of_curvelin(self):
         for x in [0.1, 0.3, 0.5, 0.7, 0.9]:
-            assert lincurve(curvelin(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(x, rel=1e-6)
\ No newline at end of file
+            assert lincurve(curvelin(x, 0, 1, 0, 1), 0, 1, 0, 1) == pytest.approx(
+                x, rel=1e-6
+            )
diff --git a/tests/test_db_amp_db.py b/tests/test_db_amp_db.py
index c984eb6..e976ba2 100644
--- a/tests/test_db_amp_db.py
+++ b/tests/test_db_amp_db.py
@@ -1,6 +1,6 @@
 import pytest
 
-from pyamapping.mappings import db_to_amp, amp_to_db
+from pyamapping.mappings import amp_to_db, db_to_amp
 
 
 class TestDbToAmp:
@@ -65,4 +65,4 @@ def test_amp_to_db_to_amp(self):
 
     def test_negative_db_roundtrip(self):
         for db in [-60, -40, -20, -6]:
-            assert amp_to_db(db_to_amp(db)) == pytest.approx(db, rel=1e-9)
\ No newline at end of file
+            assert amp_to_db(db_to_amp(db)) == pytest.approx(db, rel=1e-9)
diff --git a/tests/test_distort.py b/tests/test_distort.py
index 1c002b0..718606f 100644
--- a/tests/test_distort.py
+++ b/tests/test_distort.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import distort
@@ -42,7 +42,7 @@ class TestDistortArray:
     def test_known_values(self):
         assert_allclose(
             distort([0, 1, 2, 3], threshold=1),
-            [0.0, 0.5, 2/3, 0.75],
+            [0.0, 0.5, 2 / 3, 0.75],
             rtol=1e-6,
         )
 
@@ -59,7 +59,7 @@ def test_array_output_bounded(self):
     def test_custom_threshold_array(self):
         assert_allclose(
             distort(np.array([0, 1, 2]), threshold=2.0),
-            [0.0, 1/3, 0.5],
+            [0.0, 1 / 3, 0.5],
             rtol=1e-6,
         )
 
@@ -79,4 +79,4 @@ def test_output_range_is_open_minus_one_to_one(self):
 
     def test_monotonically_increasing(self):
         x = np.linspace(-10, 10, 100)
-        result = distort(x)
\ No newline at end of file
+        _ = distort(x)
diff --git a/tests/test_ecdf.py b/tests/test_ecdf.py
index 749724c..180940f 100644
--- a/tests/test_ecdf.py
+++ b/tests/test_ecdf.py
@@ -2,7 +2,7 @@
 import pytest
 from numpy.testing import assert_allclose
 
-from pyamapping.mappings import interp, ecdf, ecdf_to_lin, lin_to_ecdf
+from pyamapping.mappings import ecdf, ecdf_to_lin, interp, lin_to_ecdf
 
 
 class TestEcdf:
@@ -89,7 +89,7 @@ def test_max_maps_to_one(self):
 
     def test_below_min_clips_to_zero(self):
         ref = np.array([1.0, 2.0, 3.0])
-        assert lin_to_ecdf(0.0, ref) == pytest.approx(1/3)
+        assert lin_to_ecdf(0.0, ref) == pytest.approx(1 / 3)
 
     def test_above_max_clips_to_one(self):
         ref = np.array([1.0, 2.0, 3.0])
@@ -110,7 +110,6 @@ def test_monotonically_increasing(self):
         assert np.all(np.diff(result) >= 0)
 
 
-
 class TestEcdfToLin:
     """Test inverse ECDF mapping (quantiles back to feature values)."""
 
@@ -172,4 +171,4 @@ def test_ecdf_to_lin_to_ecdf(self):
     def test_roundtrip_unsorted_ref(self):
         ref = np.array([3.0, 1.0, 4.0, 2.0, 5.0])
         quantiles = lin_to_ecdf(np.sort(ref), ref)
-        assert_allclose(ecdf_to_lin(quantiles, ref), np.sort(ref), rtol=1e-6)
\ No newline at end of file
+        assert_allclose(ecdf_to_lin(quantiles, ref), np.sort(ref), rtol=1e-6)
diff --git a/tests/test_explin.py b/tests/test_explin.py
index 0dc3ad6..ee1dfac 100644
--- a/tests/test_explin.py
+++ b/tests/test_explin.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import explin, linexp
@@ -88,9 +88,7 @@ def test_clip_inverted_y_range(self):
         )
 
     def test_clip_minmax_array_input(self):
-        result = explin(
-            np.array([0.0001, 0.01, 2.0]), 0.001, 1.0, 0, 1, clip="minmax"
-        )
+        result = explin(np.array([0.0001, 0.01, 2.0]), 0.001, 1.0, 0, 1, clip="minmax")
         assert_allclose(result, [0.0, explin(0.01, 0.001, 1.0, 0, 1), 1.0])
 
 
@@ -111,4 +109,6 @@ def test_equal_ratios_in_x_give_equal_steps_in_y(self):
     def test_explin_is_inverse_of_linexp(self):
         # explin and linexp should be inverses of each other
         for x in [220.0, 311.0, 440.0]:
-            assert explin(linexp(x, 220, 440, 220, 440), 220, 440, 220, 440) == pytest.approx(x, rel=1e-9)
\ No newline at end of file
+            assert explin(
+                linexp(x, 220, 440, 220, 440), 220, 440, 220, 440
+            ) == pytest.approx(x, rel=1e-9)
diff --git a/tests/test_fermi.py b/tests/test_fermi.py
index e246804..bdb2252 100644
--- a/tests/test_fermi.py
+++ b/tests/test_fermi.py
@@ -1,9 +1,10 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import fermi, lcurve
 
+
 class TestFermiDefaultParams:
     """Test fermi function with default parameters (tau=1, mu=0)."""
 
@@ -86,4 +87,4 @@ def test_default_params_match_lcurve(self):
 
     def test_tau_param_matches_lcurve(self):
         x = np.linspace(-3, 3, 50)
-        assert_allclose(fermi(x, tau=2.0), lcurve(x, tau=2.0), rtol=1e-9)
\ No newline at end of file
+        assert_allclose(fermi(x, tau=2.0), lcurve(x, tau=2.0), rtol=1e-9)
diff --git a/tests/test_fold.py b/tests/test_fold.py
index e4dae97..2761b31 100644
--- a/tests/test_fold.py
+++ b/tests/test_fold.py
@@ -89,4 +89,4 @@ def test_array_input_returns_ndarray(self):
         assert isinstance(fold(np.array([0.0, 1.0])), np.ndarray)
 
     def test_scalar_input_returns_scalar(self):
-        assert isinstance(float(fold(0.5)), float)
\ No newline at end of file
+        assert isinstance(float(fold(0.5)), float)
diff --git a/tests/test_gain.py b/tests/test_gain.py
index 27a7efd..1b7f7cb 100644
--- a/tests/test_gain.py
+++ b/tests/test_gain.py
@@ -1,8 +1,7 @@
 import numpy as np
-import pytest
 from numpy.testing import assert_allclose
 
-from pyamapping.mappings import gain, db_to_amp
+from pyamapping.mappings import db_to_amp, gain
 
 
 class TestGainAmp:
@@ -76,4 +75,4 @@ def test_shape_preserved(self):
 
     def test_negative_amp_inverts_polarity(self):
         x = np.array([1.0, -2.0, 3.0])
-        assert_allclose(gain(x, amp=-1.0), [-1.0, 2.0, -3.0])
\ No newline at end of file
+        assert_allclose(gain(x, amp=-1.0), [-1.0, 2.0, -3.0])
diff --git a/tests/test_hz_mel_hz.py b/tests/test_hz_mel_hz.py
index 3d40850..7fc1bb3 100644
--- a/tests/test_hz_mel_hz.py
+++ b/tests/test_hz_mel_hz.py
@@ -1,8 +1,9 @@
-import pytest
 import numpy as np
+import pytest
 
 from pyamapping.mappings import hz_to_mel, mel_to_hz
 
+
 class TestHzToMel:
     """Test Hz to mel conversion for both Slaney and HTK formulas."""
 
@@ -17,7 +18,9 @@ def test_known_value_slaney(self):
 
     def test_known_value_htk(self):
         # 440 Hz -> mel via O'Shaughnessy formula
-        assert hz_to_mel(440, htk=True) == pytest.approx(2595 * np.log10(1 + 440 / 700), rel=1e-6)
+        assert hz_to_mel(440, htk=True) == pytest.approx(
+            2595 * np.log10(1 + 440 / 700), rel=1e-6
+        )
 
     def test_linear_regime_below_1000hz(self):
         # Slaney: linear law applies below 1000 Hz
@@ -49,9 +52,10 @@ def test_zero_mel_is_zero_hz_htk(self):
     def test_known_value_slaney(self):
         assert mel_to_hz(6.6) == pytest.approx(440.0, rel=1e-6)
 
-
     def test_known_value_htk(self):
-        assert mel_to_hz(2595 * np.log10(1 + 440 / 700), htk=True) == pytest.approx(440, rel=1e-6)
+        assert mel_to_hz(2595 * np.log10(1 + 440 / 700), htk=True) == pytest.approx(
+            440, rel=1e-6
+        )
 
     def test_linear_regime_below_mel_15(self):
         # Slaney: linear law applies below mel=15
@@ -79,12 +83,16 @@ def test_mel_to_hz_to_mel_slaney(self):
 
     def test_hz_to_mel_to_hz_htk(self):
         for hz in [100, 440, 1000, 4000, 8000]:
-            assert mel_to_hz(hz_to_mel(hz, htk=True), htk=True) == pytest.approx(hz, rel=1e-9)
+            assert mel_to_hz(hz_to_mel(hz, htk=True), htk=True) == pytest.approx(
+                hz, rel=1e-9
+            )
 
     def test_mel_to_hz_to_mel_htk(self):
         for mel in [100, 500, 1000, 2000]:
-            assert hz_to_mel(mel_to_hz(mel, htk=True), htk=True) == pytest.approx(mel, rel=1e-9)
+            assert hz_to_mel(mel_to_hz(mel, htk=True), htk=True) == pytest.approx(
+                mel, rel=1e-9
+            )
 
     def test_htk_and_slaney_differ(self):
         # The two formulas are different — their results should not be equal
-        assert hz_to_mel(440, htk=True) != pytest.approx(hz_to_mel(440, htk=False))
\ No newline at end of file
+        assert hz_to_mel(440, htk=True) != pytest.approx(hz_to_mel(440, htk=False))
diff --git a/tests/test_lcurve.py b/tests/test_lcurve.py
index 71773cd..ceb185c 100644
--- a/tests/test_lcurve.py
+++ b/tests/test_lcurve.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import lcurve
@@ -73,4 +73,4 @@ def test_scalar_input_returns_scalar(self):
         assert isinstance(float(lcurve(0.5)), float)
 
     def test_array_input_returns_ndarray(self):
-        assert isinstance(lcurve(np.array([0.0, 1.0])), np.ndarray)
\ No newline at end of file
+        assert isinstance(lcurve(np.array([0.0, 1.0])), np.ndarray)
diff --git a/tests/test_lincurve.py b/tests/test_lincurve.py
index 946b97d..42ae8e0 100644
--- a/tests/test_lincurve.py
+++ b/tests/test_lincurve.py
@@ -114,7 +114,9 @@ def test_clip_min_does_not_affect_upper_values(self):
         assert result == pytest.approx(0.5)
 
     def test_clip_minmax_caps_both_sides(self):
-        assert lincurve(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(0.0)
+        assert lincurve(-1.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(
+            0.0
+        )
         assert lincurve(2.0, 0, 1, 0, 1, curve=0.0, clip="minmax") == pytest.approx(1.0)
 
     def test_clip_unknown_string_implies_minmax(self):
@@ -125,4 +127,4 @@ def test_clip_unknown_string_implies_minmax(self):
     def test_clip_minmax_array_input(self):
         x = np.array([-1.0, 0.0, 0.5, 1.0, 2.0])
         result = lincurve(x, 0, 1, 0, 1, curve=0.0, clip="minmax")
-        assert_allclose(result, [0.0, 0.0, 0.5, 1.0, 1.0])
\ No newline at end of file
+        assert_allclose(result, [0.0, 0.0, 0.5, 1.0, 1.0])
diff --git a/tests/test_linexp.py b/tests/test_linexp.py
index d215111..b493c99 100644
--- a/tests/test_linexp.py
+++ b/tests/test_linexp.py
@@ -1,9 +1,10 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import linexp
 
+
 class TestLinexpEndpoints:
     """Test that x1->y1 and x2->y2 mappings are exact."""
 
@@ -101,4 +102,4 @@ def test_ratio_of_outputs_depends_only_on_ratio_of_inputs(self):
         y1 = linexp(1.0, 0, 3, 1, 8)
         y2 = linexp(2.0, 0, 3, 1, 8)
         y3 = linexp(3.0, 0, 3, 1, 8)
-        assert y2 / y1 == pytest.approx(y3 / y2, rel=1e-6)
\ No newline at end of file
+        assert y2 / y1 == pytest.approx(y3 / y2, rel=1e-6)
diff --git a/tests/test_linlin.py b/tests/test_linlin.py
index 51eaa08..6cdc47f 100644
--- a/tests/test_linlin.py
+++ b/tests/test_linlin.py
@@ -4,6 +4,7 @@
 
 from pyamapping.mappings import linlin
 
+
 class TestLinlinEndpoints:
     """Test that x1->y1 and x2->y2 mappings are exact."""
 
@@ -88,4 +89,4 @@ def test_clip_min_inverted_range(self):
 
     def test_clip_minmax_array_input(self):
         result = linlin(np.array([-10.0, 50.0, 110.0]), 0, 100, 0, 1, clip="minmax")
-        assert_allclose(result, [0.0, 0.5, 1.0])
\ No newline at end of file
+        assert_allclose(result, [0.0, 0.5, 1.0])
diff --git a/tests/test_linpoly.py b/tests/test_linpoly.py
index 3c1b028..99d914d 100644
--- a/tests/test_linpoly.py
+++ b/tests/test_linpoly.py
@@ -49,7 +49,9 @@ def test_negative_curve_order(self):
         # curve=-1 -> order = 1/(1-(-1)) = 0.5 (square root)
         order = 1 / (1 - (-1))
         expected = 0 + 1 * (1 + (0.5 / 1.0) ** order) / 2
-        assert linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, curve=-1) == pytest.approx(expected)
+        assert linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, curve=-1) == pytest.approx(
+            expected
+        )
 
 
 class TestLinpolyProperties:
@@ -58,7 +60,9 @@ class TestLinpolyProperties:
     def test_odd_symmetry_around_midpoint(self):
         # linpoly(-x) and linpoly(x) should be symmetric around the output midpoint
         for x in [0.25, 0.5, 0.75, 1.0]:
-            assert linpoly(x, y1=0.0, y2=1.0) + linpoly(-x, y1=0.0, y2=1.0) == pytest.approx(1.0)
+            assert linpoly(x, y1=0.0, y2=1.0) + linpoly(
+                -x, y1=0.0, y2=1.0
+            ) == pytest.approx(1.0)
 
     def test_monotonically_increasing(self):
         x = np.linspace(-1, 1, 200)
@@ -81,14 +85,20 @@ def test_clip_min_caps_at_y1(self):
         assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="min") == pytest.approx(0.0)
 
     def test_clip_minmax_caps_both_sides(self):
-        assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(1.0)
-        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(0.0)
+        assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(
+            1.0
+        )
+        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(
+            0.0
+        )
 
     def test_clip_unknown_string_implies_minmax(self):
         assert linpoly(2.0, xmax=1.0, y1=0.0, y2=1.0, clip="both") == pytest.approx(1.0)
-        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="both") == pytest.approx(0.0)
+        assert linpoly(-2.0, xmax=1.0, y1=0.0, y2=1.0, clip="both") == pytest.approx(
+            0.0
+        )
 
     def test_clip_does_not_affect_values_within_range(self):
         assert linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0, clip="minmax") == pytest.approx(
             linpoly(0.5, xmax=1.0, y1=0.0, y2=1.0)
-        )
\ No newline at end of file
+        )
diff --git a/tests/test_midi_cps_midi.py b/tests/test_midi_cps_midi.py
index e5de271..b804389 100644
--- a/tests/test_midi_cps_midi.py
+++ b/tests/test_midi_cps_midi.py
@@ -1,7 +1,6 @@
-import numpy as np
 import pytest
 
-from pyamapping.mappings import midi_to_cps, cps_to_midi
+from pyamapping.mappings import cps_to_midi, midi_to_cps
 
 
 class TestMidiToCps:
@@ -66,4 +65,4 @@ def test_cps_to_midi_to_cps(self):
             assert midi_to_cps(cps_to_midi(cps)) == pytest.approx(cps, rel=1e-9)
 
     def test_fractional_roundtrip(self):
-        assert cps_to_midi(midi_to_cps(60.5)) == pytest.approx(60.5, rel=1e-9)
\ No newline at end of file
+        assert cps_to_midi(midi_to_cps(60.5)) == pytest.approx(60.5, rel=1e-9)
diff --git a/tests/test_midi_ratio_midi.py b/tests/test_midi_ratio_midi.py
index 2bdc78b..3bc9454 100644
--- a/tests/test_midi_ratio_midi.py
+++ b/tests/test_midi_ratio_midi.py
@@ -1,6 +1,4 @@
-import numpy as np
 import pytest
-from numpy.testing import assert_allclose
 
 from pyamapping.mappings import midi_to_ratio, ratio_to_midi
 
@@ -24,7 +22,7 @@ def test_negative_interval_inverts_ratio(self):
         assert midi_to_ratio(-12) == pytest.approx(0.5)
 
     def test_fractional_interval(self):
-        assert midi_to_ratio(6.0) == pytest.approx(2 ** 0.5, rel=1e-9)
+        assert midi_to_ratio(6.0) == pytest.approx(2**0.5, rel=1e-9)
 
 
 class TestRatioToMidi:
@@ -58,4 +56,4 @@ def test_ratio_to_midi_to_ratio(self):
             assert midi_to_ratio(ratio_to_midi(ratio)) == pytest.approx(ratio, rel=1e-9)
 
     def test_fractional_roundtrip(self):
-        assert ratio_to_midi(midi_to_ratio(3.5)) == pytest.approx(3.5, rel=1e-9)
\ No newline at end of file
+        assert ratio_to_midi(midi_to_ratio(3.5)) == pytest.approx(3.5, rel=1e-9)
diff --git a/tests/test_norm_peak.py b/tests/test_norm_peak.py
index 92e7e53..34c93e7 100644
--- a/tests/test_norm_peak.py
+++ b/tests/test_norm_peak.py
@@ -5,7 +5,6 @@
 from pyamapping.mappings import norm_peak
 
 
-
 class TestNormPeakDefaultPeak:
     """Test peak normalization with default peak=1.0."""
 
@@ -42,7 +41,7 @@ def test_custom_peak_known_array(self):
     def test_scaling_is_linear(self):
         x = np.array([1.0, 2.0, 3.0])
         result = norm_peak(x, peak=2.0)
-        assert_allclose(result, [2/3, 4/3, 2.0])
+        assert_allclose(result, [2 / 3, 4 / 3, 2.0])
 
     def test_ratios_between_elements_preserved(self):
         x = np.array([1.0, 2.0, 4.0])
@@ -76,4 +75,4 @@ def test_single_element_array(self):
         assert norm_peak(np.array([5.0])) == pytest.approx(1.0)
 
     def test_single_negative_element(self):
-        assert norm_peak(np.array([-5.0])) == pytest.approx(-1.0)
\ No newline at end of file
+        assert norm_peak(np.array([-5.0])) == pytest.approx(-1.0)
diff --git a/tests/test_normalize.py b/tests/test_normalize.py
index e5d5c64..c6a5e14 100644
--- a/tests/test_normalize.py
+++ b/tests/test_normalize.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import normalize
@@ -83,4 +83,4 @@ def test_linear_mapping_preserves_order(self):
 
     def test_already_normalized_input(self):
         x = np.array([-1.0, 0.0, 1.0])
-        assert_allclose(normalize(x), x)
\ No newline at end of file
+        assert_allclose(normalize(x), x)
diff --git a/tests/test_remove_dc.py b/tests/test_remove_dc.py
index 4c1b222..87c2483 100644
--- a/tests/test_remove_dc.py
+++ b/tests/test_remove_dc.py
@@ -67,4 +67,4 @@ def test_idempotent(self):
     def test_variance_preserved(self):
         # DC removal does not change variance
         x = np.array([1.0, 2.0, 3.0, 4.0])
-        assert np.var(remove_dc(x)) == pytest.approx(np.var(x))
\ No newline at end of file
+        assert np.var(remove_dc(x)) == pytest.approx(np.var(x))
diff --git a/tests/test_scurve.py b/tests/test_scurve.py
index 86713ca..4f58194 100644
--- a/tests/test_scurve.py
+++ b/tests/test_scurve.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import scurve
@@ -72,4 +72,4 @@ def test_scalar_input_returns_float(self):
         assert isinstance(scurve(0.5), float)
 
     def test_array_input_returns_ndarray(self):
-        assert isinstance(scurve(np.array([0.25, 0.75])), np.ndarray)
\ No newline at end of file
+        assert isinstance(scurve(np.array([0.25, 0.75])), np.ndarray)
diff --git a/tests/test_softclip.py b/tests/test_softclip.py
index a1a897e..ac70aa6 100644
--- a/tests/test_softclip.py
+++ b/tests/test_softclip.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import softclip
@@ -77,4 +77,4 @@ def test_scalar_input_returns_float(self):
         assert isinstance(softclip(1.0), float)
 
     def test_array_input_returns_ndarray(self):
-        assert isinstance(softclip(np.array([0.3, 1.0])), np.ndarray)
\ No newline at end of file
+        assert isinstance(softclip(np.array([0.3, 1.0])), np.ndarray)
diff --git a/tests/test_wrap.py b/tests/test_wrap.py
index 039085b..3425074 100644
--- a/tests/test_wrap.py
+++ b/tests/test_wrap.py
@@ -1,5 +1,5 @@
-import pytest
 import numpy as np
+import pytest
 from numpy.testing import assert_allclose
 
 from pyamapping.mappings import wrap
@@ -62,9 +62,8 @@ def test_periodic_with_period_equal_to_range(self):
         x = np.linspace(-5, 5, 50)
         assert_allclose(wrap(x, 0, period), wrap(x + period, 0, period))
 
-
     def test_array_input_returns_ndarray(self):
         assert isinstance(wrap(np.array([0.0, 1.0])), np.ndarray)
 
     def test_scalar_input_returns_scalar(self):
-        assert isinstance(float(wrap(0.5)), float)
\ No newline at end of file
+        assert isinstance(float(wrap(0.5)), float)

From 5a69e557a33177e4ed54e44afdde9f20e9040651 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 12:00:26 +0200
Subject: [PATCH 83/87] corrected indentation of conftest

---
 tests/conftest.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/tests/conftest.py b/tests/conftest.py
index 8800d29..7c034fa 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -1,10 +1,10 @@
 """
-    Dummy conftest.py for pyamapping.
+Dummy conftest.py for pyamapping.
 
-    If you don't know what this is for, just leave it empty.
-    Read more about conftest.py under:
-    - https://docs.pytest.org/en/stable/fixture.html
-    - https://docs.pytest.org/en/stable/writing_plugins.html
+If you don't know what this is for, just leave it empty.
+Read more about conftest.py under:
+- https://docs.pytest.org/en/stable/fixture.html
+- https://docs.pytest.org/en/stable/writing_plugins.html
 """
 
 # import pytest

From acfe10c4d8e49ed160bc797eb9a461ad882baee5 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Tue, 28 Apr 2026 14:53:37 +0200
Subject: [PATCH 84/87] Switched to manual versioning

---
 .pre-commit-config.yaml             |   2 +-
 notebooks/pyamapping-examples.ipynb | 991 ++++++++++++----------------
 pyproject.toml                      |  13 +-
 uv.lock                             | 142 ++--
 4 files changed, 497 insertions(+), 651 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index c7c5a42..76d97eb 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -1,4 +1,4 @@
-exclude: '^docs/conf.py'
+exclude: '^docs/conf.py|^uv\.lock$'
 
 repos:
 - repo: https://github.com/pre-commit/pre-commit-hooks
diff --git a/notebooks/pyamapping-examples.ipynb b/notebooks/pyamapping-examples.ipynb
index e4934fb..fa0f611 100644
--- a/notebooks/pyamapping-examples.ipynb
+++ b/notebooks/pyamapping-examples.ipynb
@@ -67,19 +67,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "2",
    "metadata": {},
    "outputs": [],
    "source": [
-    "import numpy as np\n",
+    "from pprint import pprint\n",
+    "\n",
     "import matplotlib as mpl\n",
     "import matplotlib.pyplot as plt\n",
-    "from pprint import pprint\n",
+    "import numpy as np\n",
+    "\n",
     "import pyamapping as pam\n",
     "from pyamapping import chain\n",
     "\n",
-    "mpl.rcParams['figure.figsize'] = (9, 2.5)"
+    "mpl.rcParams[\"figure.figsize\"] = (9, 2.5)"
    ]
   },
   {
@@ -96,49 +98,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "id": "4",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "=== numpy functions with 1 argument ===\n",
-      "['absolute', 'absolute', 'arccos', 'arccosh', 'arccos', 'arccosh', 'arcsin',\n",
-      " 'arcsinh', 'arctan', 'arctanh', 'arcsin', 'arcsinh', 'arctan', 'arctanh',\n",
-      " 'bitwise_count', 'invert', 'invert', 'cbrt', 'ceil', 'conjugate', 'conjugate',\n",
-      " 'cos', 'cosh', 'deg2rad', 'degrees', 'exp', 'exp2', 'expm1', 'fabs', 'floor',\n",
-      " 'frexp', 'invert', 'isfinite', 'isinf', 'isnan', 'isnat', 'log', 'log10',\n",
-      " 'log1p', 'log2', 'logical_not', 'modf', 'negative', 'positive', 'rad2deg',\n",
-      " 'radians', 'reciprocal', 'rint', 'sign', 'signbit', 'sin', 'sinh', 'spacing',\n",
-      " 'sqrt', 'square', 'tan', 'tanh', 'trunc']\n",
-      "\n",
-      "=== numpy functions with 2 argument ===\n",
-      "['add', 'arctan2', 'arctan2', 'bitwise_and', 'left_shift', 'bitwise_or',\n",
-      " 'right_shift', 'bitwise_xor', 'copysign', 'divide', 'divmod', 'equal',\n",
-      " 'float_power', 'floor_divide', 'fmax', 'fmin', 'fmod', 'gcd', 'greater',\n",
-      " 'greater_equal', 'heaviside', 'hypot', 'lcm', 'ldexp', 'left_shift', 'less',\n",
-      " 'less_equal', 'logaddexp', 'logaddexp2', 'logical_and', 'logical_or',\n",
-      " 'logical_xor', 'matmul', 'matvec', 'maximum', 'minimum', 'remainder',\n",
-      " 'multiply', 'nextafter', 'not_equal', 'power', 'power', 'remainder',\n",
-      " 'right_shift', 'subtract', 'divide', 'vecdot', 'vecmat']\n",
-      "\n",
-      "=== pyamapping functions: ===\n",
-      "['amp_to_db', 'bilin', 'clip', 'cps_to_midi', 'cps_to_octave', 'curvelin',\n",
-      " 'db_to_amp', 'distort', 'ecdf_to_lin', 'ecdf', 'explin', 'fermi', 'fold',\n",
-      " 'gain', 'hz_to_mel', 'interp_spline', 'interp', 'lcurve', 'lin_to_ecdf',\n",
-      " 'lincurve', 'linexp', 'linlin', 'linpoly', 'mel_to_hz', 'midi_to_cps',\n",
-      " 'midi_to_ratio', 'norm_peak', 'norm_rms', 'normalize', 'octave_to_cps',\n",
-      " 'ratio_to_midi', 'remove_dc', 'scurve', 'softclip', 'wrap']\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from pyamapping import _list_numpy_ufuncs, pyamapping_functions\n",
     "\n",
-    "# print (i) a compact list of all unary and binary numpy functions \n",
+    "# print (i) a compact list of all unary and binary numpy functions\n",
     "# and (ii) all pyamapping functions\n",
     "u_lists = [[], []]\n",
     "\n",
@@ -147,12 +114,12 @@
     "\n",
     "# compact list numpy functions\n",
     "for i, li in enumerate(u_lists):\n",
-    "    print(f\"\\n=== numpy functions with {i+1} argument ===\")\n",
+    "    print(f\"\\n=== numpy functions with {i + 1} argument ===\")\n",
     "    pprint(li, compact=True, width=80)\n",
     "\n",
     "# compact list of pyamapping functions\n",
     "li = [el.__name__ for el in pyamapping_functions]\n",
-    "print(f\"\\n=== pyamapping functions: ===\")\n",
+    "print(\"\\n=== pyamapping functions: ===\")\n",
     "pprint(li, compact=True, width=80)"
    ]
   },
@@ -188,7 +155,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from pyamapping import ChainableArray, chain\n",
+    "from pyamapping import ChainableArray\n",
     "\n",
     "# some data\n",
     "data = np.random.random(100)\n",
@@ -234,7 +201,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "dch2 = dch.map(lambda x: (5*x)**2+0.1).plot(sr=100, color=\"r\").mapvec(pam.amp_to_db)\n",
+    "dch2 = (\n",
+    "    dch.map(lambda x: (5 * x) ** 2 + 0.1).plot(sr=100, color=\"r\").mapvec(pam.amp_to_db)\n",
+    ")\n",
     "a1 = dch2.to_asig(sr=100).plot(color=\"c\", lw=0.8)\n",
     "\n",
     "# conversion back to numpy array is rarely needed but if...\n",
@@ -294,7 +263,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.linlin(7, 0, 5, 100, 300, \"max\") # clip result to maximum input range"
+    "pam.linlin(7, 0, 5, 100, 300, \"max\")  # clip result to maximum input range"
    ]
   },
   {
@@ -313,11 +282,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs = chain(np.linspace(0, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\")  # plot input data\n",
     "xs.linlin(0, 1, 1, 3).plot(\"r-\", label=\"linlin\")\n",
     "xs.linlin(0.2, 0.7, -2, 2, \"minmax\").plot(\"g-\", label=\"linlin with clip\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
@@ -328,8 +298,9 @@
    "outputs": [],
    "source": [
     "# plot mapping function (output vs input)\n",
-    "plt.figure(figsize=(3, 1.5)); plt.grid();\n",
-    "xs.linlin(0.25, 0.75, -1, 1, \"minmax\").plot(xs=xs);  "
+    "plt.figure(figsize=(3, 1.5))\n",
+    "plt.grid()\n",
+    "xs.linlin(0.25, 0.75, -1, 1, \"minmax\").plot(xs=xs);"
    ]
   },
   {
@@ -349,44 +320,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "20",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "np.float64(32.0)"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "pam.linexp(5, 1, 8, 2, 256)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "21",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "np.float64(300.0)"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "pam.linexp(7, 0, 5, 100, 300, \"max\") # clip result to maximum input range"
+    "pam.linexp(7, 0, 5, 100, 300, \"max\")  # clip result to maximum input range"
    ]
   },
   {
@@ -400,46 +349,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "23",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\")  # plot input data\n",
     "xs.linexp(0, 1, 0.01, 1).plot(\"r-\", label=\"linexp\")\n",
     "xs.linexp(0.2, 0.7, 2, 0.2, \"minmix\").plot(\"g-\", label=\"linexp with clip\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "id": "24",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# plot linexp mapping function (output vs input)\n",
     "ys = xs.linexp(0.25, 0.85, 0.2, 2).plot(xs=xs)"
@@ -464,47 +392,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "26",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "np.float64(-5.0)"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# example: unmap a frequency to MIDI note with explin\n",
-    "f = 220 * 2**(-5/12) # 5 semitones higher than 220 Hz\n",
-    "pam.explin(f, 220, 440, 0, 12)\n"
+    "f = 220 * 2 ** (-5 / 12)  # 5 semitones higher than 220 Hz\n",
+    "pam.explin(f, 220, 440, 0, 12)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "27",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "np.float64(-20.0)"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# example: unmap amplitude to level in decibel\n",
-    "pam.explin(0.01, 0.001, 1.0, -30, 0, \"max\") # clip result to maximum input range"
+    "pam.explin(0.01, 0.001, 1.0, -30, 0, \"max\")  # clip result to maximum input range"
    ]
   },
   {
@@ -523,11 +429,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(0.01, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+    "xs = chain(np.linspace(0.01, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\")  # plot input data\n",
     "xs.explin(0.1, 1, 0, 1).plot(\"r-\", label=\"explin\")\n",
     "xs.explin(0.1, 0.5, 1, 0, \"minmix\").plot(\"g-\", label=\"explin with clip\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
@@ -569,27 +476,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "id": "33",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data\") # plot input data\n",
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data\")  # plot input data\n",
     "xs.lincurve(0, 1, 0, 0.4, 5).plot(\"r-\", label=\"lincurve\")\n",
     "xs.lincurve(0.2, 0.5, 1, 0, 2.5, \"minmax\").plot(\"g-\", label=\"lincurve with clip\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
@@ -602,26 +499,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "35",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "xs = chain(np.linspace(0, 100, 100))\n",
     "for i, curve in enumerate(range(-9, 10, 3)):\n",
-    "    xs.lincurve(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
-    "plt.legend(fontsize=6); plt.grid();"
+    "    xs.lincurve(0, 100, -10, 10, curve).plot(\"-\", label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6)\n",
+    "plt.grid();"
    ]
   },
   {
@@ -653,28 +540,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": null,
    "id": "38",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data for lincurve\") # plot input data\n",
+   "outputs": [],
+   "source": [
+    "xs = chain(np.linspace(0, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data for lincurve\")  # plot input data\n",
     "curve = 10\n",
     "ys = xs.lincurve(0, 1, 0, 0.6, curve).plot(\"r-\", label=\"lincurve output\")\n",
-    "xs = ys.curvelin(0, 0.6, 0, 1, curve).plot(\"b-.\", lw=3, alpha=0.5, label=\"curvelin to undo lincurve\")\n",
-    "plt.legend(); plt.grid()"
+    "xs = ys.curvelin(0, 0.6, 0, 1, curve).plot(\n",
+    "    \"b-.\", lw=3, alpha=0.5, label=\"curvelin to undo lincurve\"\n",
+    ")\n",
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
@@ -687,26 +566,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": null,
    "id": "40",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "xs = chain(np.linspace(0, 100, 500))\n",
     "for i, curve in enumerate(range(-9, 10, 3)):\n",
-    "    xs.curvelin(0, 100, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
-    "plt.legend(fontsize=6); plt.grid();"
+    "    xs.curvelin(0, 100, -10, 10, curve).plot(\"-\", label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6)\n",
+    "plt.grid();"
    ]
   },
   {
@@ -738,54 +607,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": null,
    "id": "43",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 900x250 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "xs = chain(np.arange(0, 100)) # turn data into ChainableArray\n",
-    "xs.bilin(60, 20, 80, 0, -20, 60).plot(\"b.\", ms=1, label='bilin');\n",
-    "for (x, y, t) in [[20, -20, \"(xmin, ymin)\"], [80, 60, \"(xmax, ymax)\"], [60, 0, \"(xcenter, ycenter)\"]]:\n",
+   "outputs": [],
+   "source": [
+    "xs = chain(np.arange(0, 100))  # turn data into ChainableArray\n",
+    "xs.bilin(60, 20, 80, 0, -20, 60).plot(\"b.\", ms=1, label=\"bilin\")\n",
+    "for x, y, t in [\n",
+    "    [20, -20, \"(xmin, ymin)\"],\n",
+    "    [80, 60, \"(xmax, ymax)\"],\n",
+    "    [60, 0, \"(xcenter, ycenter)\"],\n",
+    "]:\n",
     "    plt.plot([x], [y], \"ro\")\n",
-    "    plt.text(x+1, y-5, t, fontsize=6)\n",
-    "plt.legend(); plt.grid()"
+    "    plt.text(x + 1, y - 5, t, fontsize=6)\n",
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
-   "id": "cb3b9473",
+   "execution_count": null,
+   "id": "44",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ChainableArray([-30., -20., -10.,   0.,  60., 120.])"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "pam.bilin(np.array([0, 20, 40, 60, 80, 100]), 60, 20, 80, 0, -20, 60)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "44",
+   "id": "45",
    "metadata": {},
    "source": [
     "### `clip`\n",
@@ -797,7 +649,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45",
+   "id": "46",
    "metadata": {},
    "source": [
     "- ChainableArray.clip uses self as input.\n",
@@ -807,30 +659,32 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46",
+   "id": "47",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(0, 1, 100)) # turn data into ChainableArray\n",
-    "xs.plot(\"k:\", label=\"input data\") # plot input data\n",
+    "xs = chain(np.linspace(0, 1, 100))  # turn data into ChainableArray\n",
+    "xs.plot(\"k:\", label=\"input data\")  # plot input data\n",
     "xs.clip(0.2, 0.7).plot(\"r-\", label=\"linlin with clip\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47",
+   "id": "48",
    "metadata": {},
    "outputs": [],
    "source": [
     "# plot mapping function (output vs input)\n",
-    "ys = xs.clip(0.25, 0.75).plot(xs=xs, label=''); plt.grid(); "
+    "ys = xs.clip(0.25, 0.75).plot(xs=xs, label=\"\")\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "48",
+   "id": "49",
    "metadata": {},
    "source": [
     "### `midi_to_cps`\n",
@@ -846,26 +700,28 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49",
+   "id": "50",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.midi_to_cps(69+12) # should be 880, i.e. one octave above MIDI 69"
+    "pam.midi_to_cps(69 + 12)  # should be 880, i.e. one octave above MIDI 69"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "50",
+   "id": "51",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(60, 74, 2)).midicps().round(1) # rounded frequencies of whole-tone scale ('c-d-e-f#-g#-a#-c')"
+    "chain(np.arange(60, 74, 2)).midicps().round(\n",
+    "    1\n",
+    ")  # rounded frequencies of whole-tone scale ('c-d-e-f#-g#-a#-c')"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "51",
+   "id": "52",
    "metadata": {},
    "source": [
     "- ChainableArray.midi_to_cps uses self as input.\n",
@@ -875,19 +731,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "52",
+   "id": "53",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(21, 109)) # the standard MIDI range\n",
-    "xs.plot(\"k-\", label=\"input data (MIDI notes)\") # plot input data\n",
+    "xs = chain(np.arange(21, 109))  # the standard MIDI range\n",
+    "xs.plot(\"k-\", label=\"input data (MIDI notes)\")  # plot input data\n",
     "xs.midi_to_cps().plot(\"r-\", label=\"midi_to_cps result [in Hz]\")\n",
-    "plt.legend(); plt.grid();"
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "53",
+   "id": "54",
    "metadata": {},
    "source": [
     "### `cps_to_midi`\n",
@@ -903,26 +760,28 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "54",
+   "id": "55",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.cps_to_midi(440*2) # should be 81=69+12"
+    "pam.cps_to_midi(440 * 2)  # should be 81=69+12"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55",
+   "id": "56",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain([110, 220, 330, 440, 550, 660, 770, 880]).cpsmidi().round(2) # rounded MIDI notes for the harmonics series over low A"
+    "chain([110, 220, 330, 440, 550, 660, 770, 880]).cpsmidi().round(\n",
+    "    2\n",
+    ")  # rounded MIDI notes for the harmonics series over low A"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "56",
+   "id": "57",
    "metadata": {},
    "source": [
     "- ChainableArray.cps_to_midi uses self as input.\n",
@@ -932,21 +791,23 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57",
+   "id": "58",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(100, 1000, 100)) # frequencies with 50 Hz spacing\n",
-    "ys = xs.cps_to_midi() \n",
+    "xs = chain(np.arange(100, 1000, 100))  # frequencies with 50 Hz spacing\n",
+    "ys = xs.cps_to_midi()\n",
     "\n",
-    "plt.plot(xs, ys, \"o-\", label=\"MIDI note for harmonics series\"); \n",
-    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"MIDI note\"); \n",
-    "plt.legend(); plt.grid();"
+    "plt.plot(xs, ys, \"o-\", label=\"MIDI note for harmonics series\")\n",
+    "plt.xlabel(\"frequency [Hz]\")\n",
+    "plt.ylabel(\"MIDI note\")\n",
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "58",
+   "id": "59",
    "metadata": {},
    "source": [
     "### `midi_to_ratio`\n",
@@ -960,38 +821,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
-   "id": "59",
+   "execution_count": null,
+   "id": "60",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.4983070768766815"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "pam.midi_to_ratio(7) # a fifth is ~3/2 (in equal tuning)"
+    "pam.midi_to_ratio(7)  # a fifth is ~3/2 (in equal tuning)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "60",
+   "id": "61",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(0, 12, 2)).midi_to_ratio().round(2) # ratio of tones in the whole-tone scale ('c-d-e-f#-g#-a#-c')"
+    "chain(np.arange(0, 12, 2)).midi_to_ratio().round(\n",
+    "    2\n",
+    ")  # ratio of tones in the whole-tone scale ('c-d-e-f#-g#-a#-c')"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "61",
+   "id": "62",
    "metadata": {},
    "source": [
     "- ChainableArray.midi_to_cps uses self as input.\n",
@@ -1001,19 +853,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62",
+   "id": "63",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(-12, 13)) # one octave around any note\n",
+    "xs = chain(np.arange(-12, 13))  # one octave around any note\n",
     "ys = xs.midi_to_ratio().plot(xs=xs, c=\"r\", ls=\"-\", label=\"midi_to_ratio result\")\n",
     "plt.plot(0, 1, \"ro\", label=\"midi_ratio of 0\")\n",
-    "plt.legend(); plt.grid();"
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "63",
+   "id": "64",
    "metadata": {},
    "source": [
     "### `ratio_to_midi`\n",
@@ -1027,38 +880,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
-   "id": "64",
+   "execution_count": null,
+   "id": "65",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "np.float64(12.0)"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "pam.ratio_to_midi(2) # should be 12 for ratio=2 (i.e. an octave)"
+    "pam.ratio_to_midi(2)  # should be 12 for ratio=2 (i.e. an octave)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65",
+   "id": "66",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(1, 10)).ratio_to_midi().round(2) # rounded MIDI offsets for the harmonics series"
+    "chain(np.arange(1, 10)).ratio_to_midi().round(\n",
+    "    2\n",
+    ")  # rounded MIDI offsets for the harmonics series"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "66",
+   "id": "67",
    "metadata": {},
    "source": [
     "- ChainableArray.ratio_to_midi uses self as input.\n",
@@ -1068,21 +912,23 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67",
+   "id": "68",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(1, 10)) # integer frequency ratios / harmonics\n",
+    "xs = chain(np.arange(1, 10))  # integer frequency ratios / harmonics\n",
     "ys = xs.ratio_to_midi()  # likewise ratiomidi()\n",
     "\n",
-    "plt.plot(xs, ys, \"o-\", label=\"MIDI offsets for harmonics series\"); \n",
-    "plt.xlabel(\"ratio to fundamental frequency\"); plt.ylabel(\"MIDI offset\"); \n",
-    "plt.legend(); plt.grid();"
+    "plt.plot(xs, ys, \"o-\", label=\"MIDI offsets for harmonics series\")\n",
+    "plt.xlabel(\"ratio to fundamental frequency\")\n",
+    "plt.ylabel(\"MIDI offset\")\n",
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "68",
+   "id": "69",
    "metadata": {},
    "source": [
     "### `octave_to_cps`\n",
@@ -1097,26 +943,26 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69",
+   "id": "70",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.octave_to_cps(3.75) # one octave below 440"
+    "pam.octave_to_cps(3.75)  # one octave below 440"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70",
+   "id": "71",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(2, 9)).octcps().round(1) # rounded frequencies of c-tones"
+    "chain(np.arange(2, 9)).octcps().round(1)  # rounded frequencies of c-tones"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "71",
+   "id": "72",
    "metadata": {},
    "source": [
     "- ChainableArray.octave_to_cps uses self as input.\n",
@@ -1126,19 +972,21 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "72",
+   "id": "73",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(0, 8, 1/4)) # 8 octaves in minor thirds (3 semitone steps)\n",
+    "xs = chain(np.arange(0, 8, 1 / 4))  # 8 octaves in minor thirds (3 semitone steps)\n",
     "ys = xs.octave_to_cps()\n",
-    "plt.plot(xs, ys, \"ro-\", ms=2,label=\"octave_to_cps result [in Hz]\")\n",
-    "plt.legend(); plt.grid(); plt.semilogy()"
+    "plt.plot(xs, ys, \"ro-\", ms=2, label=\"octave_to_cps result [in Hz]\")\n",
+    "plt.legend()\n",
+    "plt.grid()\n",
+    "plt.semilogy()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "73",
+   "id": "74",
    "metadata": {},
    "source": [
     "### `cps_to_octave`\n",
@@ -1153,26 +1001,28 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "74",
+   "id": "75",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.cps_to_octave(440*2) # one octave above reference"
+    "pam.cps_to_octave(440 * 2)  # one octave above reference"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "75",
+   "id": "76",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(pam.midicps(12) * np.arange(1, 10)).cpsoct().round(2) # harmonics series over low C in octaves"
+    "chain(pam.midicps(12) * np.arange(1, 10)).cpsoct().round(\n",
+    "    2\n",
+    ")  # harmonics series over low C in octaves"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "76",
+   "id": "77",
    "metadata": {},
    "source": [
     "- ChainableArray.cps_to_octave uses self as input.\n",
@@ -1182,21 +1032,23 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "77",
+   "id": "78",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(100, 1000, 100)) # frequencies with 50 Hz spacing\n",
-    "ys = xs.cps_to_octave() \n",
+    "xs = chain(np.arange(100, 1000, 100))  # frequencies with 50 Hz spacing\n",
+    "ys = xs.cps_to_octave()\n",
     "\n",
-    "plt.plot(xs, ys, \"o-\", label=\"octaves for harmonics series\"); \n",
-    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"octave\"); \n",
-    "plt.legend(); plt.grid();"
+    "plt.plot(xs, ys, \"o-\", label=\"octaves for harmonics series\")\n",
+    "plt.xlabel(\"frequency [Hz]\")\n",
+    "plt.ylabel(\"octave\")\n",
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78",
+   "id": "79",
    "metadata": {},
    "source": [
     "### `db_to_amp`\n",
@@ -1211,7 +1063,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "79",
+   "id": "80",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1220,7 +1072,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80",
+   "id": "81",
    "metadata": {},
    "source": [
     "- ChainableArray.db_to_amp uses self as input.\n",
@@ -1230,18 +1082,19 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "81",
+   "id": "82",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(-60, 0, 6)) # some 6 dB steps\n",
+    "xs = chain(np.arange(-60, 0, 6))  # some 6 dB steps\n",
     "ys = xs.dbamp().plot(xs=xs, marker=\"o\", ms=2, label=\"db_to_amp result [arb. unit]\")\n",
-    "plt.legend(); plt.grid();"
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "82",
+   "id": "83",
    "metadata": {},
    "source": [
     "### `amp_to_db`\n",
@@ -1256,26 +1109,26 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83",
+   "id": "84",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.amp_to_db(0.01) # 10^(-2) will be 10^(-4) for energy, aka -40 dB"
+    "pam.amp_to_db(0.01)  # 10^(-2) will be 10^(-4) for energy, aka -40 dB"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "84",
+   "id": "85",
    "metadata": {},
    "outputs": [],
    "source": [
-    "chain(np.arange(0.1, 1, 0.1)).ampdb().round(2) # harmonics series over low C in octaves"
+    "chain(np.arange(0.1, 1, 0.1)).ampdb().round(2)  # harmonics series over low C in octaves"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "85",
+   "id": "86",
    "metadata": {},
    "source": [
     "- ChainableArray.amp_to_db uses self as input.\n",
@@ -1285,20 +1138,22 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "86",
+   "id": "87",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(0.1, 2.1, 0.1)) # ampltitudes from 0.1 to 2.0\n",
-    "ys = xs.ampdb() # likewise amp_to_db()\n",
-    "plt.plot(xs, ys, \"o-\", label=\"decibel\"); \n",
-    "plt.xlabel(\"amplitudes\"); plt.ylabel(\"dB\"); \n",
-    "plt.legend(); plt.grid();"
+    "xs = chain(np.arange(0.1, 2.1, 0.1))  # ampltitudes from 0.1 to 2.0\n",
+    "ys = xs.ampdb()  # likewise amp_to_db()\n",
+    "plt.plot(xs, ys, \"o-\", label=\"decibel\")\n",
+    "plt.xlabel(\"amplitudes\")\n",
+    "plt.ylabel(\"dB\")\n",
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "87",
+   "id": "88",
    "metadata": {},
    "source": [
     "### `mel_to_hz`\n",
@@ -1319,26 +1174,26 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "88",
+   "id": "89",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.mel_to_hz(1000, htk=True) # using the O'Shaughnessy (1987) formula"
+    "pam.mel_to_hz(1000, htk=True)  # using the O'Shaughnessy (1987) formula"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89",
+   "id": "90",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.mel_to_hz(15) # using the Slaney formula"
+    "pam.mel_to_hz(15)  # using the Slaney formula"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "90",
+   "id": "91",
    "metadata": {},
    "source": [
     "- ChainableArray.mel_to_hz uses self as input.\n",
@@ -1348,32 +1203,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "91",
+   "id": "92",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(0, 2500, 100)) \n",
+    "xs = chain(np.arange(0, 2500, 100))\n",
     "ys = xs.mel_to_hz(htk=True)\n",
     "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz (O'Shaughnessy)\")\n",
-    "plt.legend(); plt.grid();"
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "92",
+   "id": "93",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(0, 40, 1)) \n",
-    "ys = xs.mel_to_hz() # i.e. Slaney\n",
+    "xs = chain(np.arange(0, 40, 1))\n",
+    "ys = xs.mel_to_hz()  # i.e. Slaney\n",
     "plt.plot(xs, ys, \"r-\", label=\"mel_to_hz (Slaney)\")\n",
-    "plt.legend(); plt.grid();"
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "93",
+   "id": "94",
    "metadata": {},
    "source": [
     "### `hz_to_mel`\n",
@@ -1391,18 +1248,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94",
+   "id": "95",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(1, 10000))\n",
     "xs.hz_to_mel().plot(xs=xs)\n",
-    "plt.xlabel('frequencies [Hz]'); plt.ylabel('mel scale (Slaney)'); plt.grid();"
+    "plt.xlabel(\"frequencies [Hz]\")\n",
+    "plt.ylabel(\"mel scale (Slaney)\")\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "95",
+   "id": "96",
    "metadata": {},
    "source": [
     "- ChainableArray.hz_to_mel uses self as input.\n",
@@ -1412,20 +1271,23 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96",
+   "id": "97",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(21, 120, 7)).midicps() # frequencies of fifth series\n",
-    "xs.hz_to_mel(htk=True).plot(xs=xs, marker=\"o\", label=\"mel values for frequencies\"); \n",
-    "plt.xlabel(\"frequency [Hz]\"); plt.ylabel(\"mel scale\"); \n",
-    "plt.legend(); plt.grid(); plt.loglog()\n",
+    "xs = chain(np.arange(21, 120, 7)).midicps()  # frequencies of fifth series\n",
+    "xs.hz_to_mel(htk=True).plot(xs=xs, marker=\"o\", label=\"mel values for frequencies\")\n",
+    "plt.xlabel(\"frequency [Hz]\")\n",
+    "plt.ylabel(\"mel scale\")\n",
+    "plt.legend()\n",
+    "plt.grid()\n",
+    "plt.loglog()\n",
     "plt.plot([1000], [1000], \"ro-\", label=\"a reference point\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "97",
+   "id": "98",
    "metadata": {},
    "source": [
     "### `distort`\n",
@@ -1441,7 +1303,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98",
+   "id": "99",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1450,7 +1312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99",
+   "id": "100",
    "metadata": {},
    "source": [
     "- ChainableArray.distort uses self as input.\n",
@@ -1460,32 +1322,35 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "100",
+   "id": "101",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-3, 3, 0.01))\n",
     "for theta in [0.1, 0.5, 1, 3]:\n",
     "    xs.distort(theta).plot(xs=xs, label=f\"threshold = {theta}\")\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(); plt.title(\"distort mapping function\");"
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
+    "plt.legend()\n",
+    "plt.title(\"distort mapping function\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "101",
+   "id": "102",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "np.sin(2*np.pi*50*ts).plot(label='sine').distort(0.3).plot(label='distorted');\n",
-    "plt.legend(loc='upper right');"
+    "np.sin(2 * np.pi * 50 * ts).plot(label=\"sine\").distort(0.3).plot(label=\"distorted\")\n",
+    "plt.legend(loc=\"upper right\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "102",
+   "id": "103",
    "metadata": {},
    "source": [
     "### `softclip`\n",
@@ -1503,7 +1368,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "103",
+   "id": "104",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1512,7 +1377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "104",
+   "id": "105",
    "metadata": {},
    "source": [
     "- ChainableArray.softclip uses self as input.\n",
@@ -1522,32 +1387,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "105",
+   "id": "106",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-3, 3, 0.01))\n",
     "xs.softclip().plot(xs=xs)\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
     "plt.title(\"softclip mapping function\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "106",
+   "id": "107",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').softclip().plot(label='softclip distorted');\n",
-    "plt.legend(loc='upper right');"
+    "xs = np.sin(2 * np.pi * 50 * ts)\n",
+    "xs.plot(label=\"sine\").softclip().plot(label=\"softclip distorted\")\n",
+    "plt.legend(loc=\"upper right\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "107",
+   "id": "108",
    "metadata": {},
    "source": [
     "### `scurve`\n",
@@ -1562,7 +1429,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "108",
+   "id": "109",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1571,7 +1438,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "109",
+   "id": "110",
    "metadata": {},
    "source": [
     "- ChainableArray.scurve uses self as input.\n",
@@ -1581,32 +1448,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "110",
+   "id": "111",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(0, 1, 0.01))\n",
     "xs.scurve().plot(xs=xs)\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
     "plt.title(\"scurve mapping function\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "111",
+   "id": "112",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = (2*np.pi*50*ts).sin().linlin(-1, 1, 0, 1)\n",
-    "xs.plot(label='sine with offset').scurve().plot(label='scurve distorted');\n",
-    "plt.legend(loc='upper right');"
+    "xs = (2 * np.pi * 50 * ts).sin().linlin(-1, 1, 0, 1)\n",
+    "xs.plot(label=\"sine with offset\").scurve().plot(label=\"scurve distorted\")\n",
+    "plt.legend(loc=\"upper right\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "112",
+   "id": "113",
    "metadata": {},
    "source": [
     "### `lcurve`\n",
@@ -1622,7 +1491,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "113",
+   "id": "114",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1631,7 +1500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "114",
+   "id": "115",
    "metadata": {},
    "source": [
     "- ChainableArray.lcurve uses self as input.\n",
@@ -1641,33 +1510,36 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "115",
+   "id": "116",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-10, 10, 0.005))\n",
     "for tau in [0.2, 0.5, 1, 2]:\n",
-    "    xs.lcurve(tau=tau).plot(xs=xs, label=f'lcurve for tau={tau}')\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(); plt.title(\"lcurve mapping function\");"
+    "    xs.lcurve(tau=tau).plot(xs=xs, label=f\"lcurve for tau={tau}\")\n",
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
+    "plt.legend()\n",
+    "plt.title(\"lcurve mapping function\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "116",
+   "id": "117",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').lcurve(tau=0.25).plot(label='lcurve distorted');\n",
-    "plt.legend(loc='upper right');"
+    "xs = np.sin(2 * np.pi * 50 * ts)\n",
+    "xs.plot(label=\"sine\").lcurve(tau=0.25).plot(label=\"lcurve distorted\")\n",
+    "plt.legend(loc=\"upper right\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "117",
+   "id": "118",
    "metadata": {},
    "source": [
     "### `wrap`\n",
@@ -1684,7 +1556,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "118",
+   "id": "119",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1693,7 +1565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "119",
+   "id": "120",
    "metadata": {},
    "source": [
     "- ChainableArray.wrap uses self as input.\n",
@@ -1703,32 +1575,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "120",
+   "id": "121",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-5, 5, 0.01))\n",
     "xs.wrap(y1=-1, y2=1).plot(xs=xs)\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
     "plt.title(\"wrap mapping function\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "121",
+   "id": "122",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*30*ts)\n",
-    "xs.plot(label='sine').wrap(-0.8, 0.5).plot(label='wrapped sine');\n",
-    "plt.legend(loc='upper right');"
+    "xs = np.sin(2 * np.pi * 30 * ts)\n",
+    "xs.plot(label=\"sine\").wrap(-0.8, 0.5).plot(label=\"wrapped sine\")\n",
+    "plt.legend(loc=\"upper right\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "122",
+   "id": "123",
    "metadata": {},
    "source": [
     "### `fold`\n",
@@ -1744,7 +1618,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "123",
+   "id": "124",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1753,7 +1627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "124",
+   "id": "125",
    "metadata": {},
    "source": [
     "- ChainableArray.wrap uses self as input.\n",
@@ -1763,31 +1637,34 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "125",
+   "id": "126",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-5, 5, 0.01))\n",
     "xs.fold(y1=-1, y2=1).plot(xs=xs)\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); "
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "126",
+   "id": "127",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*30*ts)\n",
-    "xs.plot(label='sine').fold(-0.75, 0.5).plot(label='folded sine');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 30 * ts)\n",
+    "xs.plot(label=\"sine\").fold(-0.75, 0.5).plot(label=\"folded sine\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "127",
+   "id": "128",
    "metadata": {},
    "source": [
     "## Tour of Mapping Functions: additional/novel mapping functions\n",
@@ -1798,7 +1675,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "128",
+   "id": "129",
    "metadata": {},
    "source": [
     "### `linpoly`\n",
@@ -1821,7 +1698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "129",
+   "id": "130",
    "metadata": {},
    "source": [
     "- ChainableArray.linpoly uses self as input.\n",
@@ -1831,20 +1708,21 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "130",
+   "id": "131",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(-3, 3, 200)) # turn data into ChainableArray\n",
-    "xs.plot(\"k-\", label=\"input data for linpoly\") # plot input data\n",
+    "xs = chain(np.linspace(-3, 3, 200))  # turn data into ChainableArray\n",
+    "xs.plot(\"k-\", label=\"input data for linpoly\")  # plot input data\n",
     "xs.linpoly(3, 0, 20, curve=1).plot(\"r-\", label=\"linpoly output\")\n",
     "xs.linpoly(3, 0, 20, curve=-1).plot(\"b-\", label=\"linpoly output\")\n",
-    "plt.legend(); plt.grid()"
+    "plt.legend()\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "131",
+   "id": "132",
    "metadata": {},
    "source": [
     "the following plot shows how the curve parameter influences the mapping function"
@@ -1853,19 +1731,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "132",
+   "id": "133",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.linspace(-1, 1, 200))\n",
     "for i, curve in enumerate(range(-3, 3, 1)):\n",
-    "    xs.linpoly(1, -10, 10, curve).plot('-', label=f\"curve={curve}\")\n",
-    "plt.legend(fontsize=6); plt.grid();"
+    "    xs.linpoly(1, -10, 10, curve).plot(\"-\", label=f\"curve={curve}\")\n",
+    "plt.legend(fontsize=6)\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "133",
+   "id": "134",
    "metadata": {},
    "source": [
     "### `interp_spline`\n",
@@ -1882,23 +1761,24 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "134",
+   "id": "135",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(0, 8.2, 1000)) # turn data into ChainableArray\n",
+    "xs = chain(np.linspace(0, 8.2, 1000))  # turn data into ChainableArray\n",
     "xc = [1, 2, 5, 7, 8]\n",
     "yc = [3, 1, 2, 9, 1]\n",
     "plt.plot(xc, yc, \"ro\", label=\"given points\")\n",
     "for k in [0, 1, 2]:\n",
     "    ys = xs.interp_spline(xc, yc, k=k)\n",
-    "    plt.plot(xs,ys, label=f\"spline with k={k}\")\n",
-    "plt.legend(fontsize=7); plt.grid()"
+    "    plt.plot(xs, ys, label=f\"spline with k={k}\")\n",
+    "plt.legend(fontsize=7)\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "135",
+   "id": "136",
    "metadata": {},
    "source": [
     "### `interp`\n",
@@ -1915,36 +1795,38 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "136",
+   "id": "137",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.linspace(0, 8.2, 1000)) # turn data into ChainableArray\n",
+    "xs = chain(np.linspace(0, 8.2, 1000))  # turn data into ChainableArray\n",
     "xc = [1, 2, 5, 7, 8]\n",
     "yc = [7, 1, 2, 9, 1]\n",
     "plt.plot(xc, yc, \"ro\", ms=3, label=\"given points\")\n",
     "ys = xs.interp(xc, yc)\n",
-    "plt.plot(xs, ys, \"b,\", label=f\"interp\")\n",
-    "plt.legend(fontsize=7); plt.grid()"
+    "plt.plot(xs, ys, \"b,\", label=\"interp\")\n",
+    "plt.legend(fontsize=7)\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "137",
+   "id": "138",
    "metadata": {},
    "outputs": [],
    "source": [
-    "xs = chain(np.arange(-100, 150)) # turn data into ChainableArray\n",
+    "xs = chain(np.arange(-100, 150))  # turn data into ChainableArray\n",
     "# use interp if clipping is wanted (faster for small datasets)\n",
-    "xs.interp([-50, 50, 100],[0, 0.4, 1]).plot(\"r-.\", label=\"interp with clipping\"); \n",
-    "xs.bilin(50, -50, 100, 0.4, 0, 1).plot(\"b:\", label='bilin with extrapolation');\n",
-    "plt.legend();plt.grid();"
+    "xs.interp([-50, 50, 100], [0, 0.4, 1]).plot(\"r-.\", label=\"interp with clipping\")\n",
+    "xs.bilin(50, -50, 100, 0.4, 0, 1).plot(\"b:\", label=\"bilin with extrapolation\")\n",
+    "plt.legend()\n",
+    "plt.grid();"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "138",
+   "id": "139",
    "metadata": {},
    "source": [
     "### `fermi`\n",
@@ -1960,7 +1842,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "139",
+   "id": "140",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1969,7 +1851,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "140",
+   "id": "141",
    "metadata": {},
    "source": [
     "- ChainableArray.fermi uses self as input.\n",
@@ -1979,35 +1861,40 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "141",
+   "id": "142",
    "metadata": {},
    "outputs": [],
    "source": [
     "xs = chain(np.arange(-10, 10, 0.005))\n",
     "for i, mu in enumerate([-2, 0, 2]):\n",
     "    for j, tau in enumerate([0.2, 0.5, 1]):\n",
-    "        xs.fermi(tau, mu).plot(xs=xs, color=['r','g','b'][i], \n",
-    "                 lw=j+1, label=f'lcurve for tau={tau}')\n",
-    "plt.xlabel('input'); plt.ylabel('output'); plt.grid(); \n",
-    "plt.legend(fontsize=8); plt.title(\"fermi curve mapping functions\");"
+    "        xs.fermi(tau, mu).plot(\n",
+    "            xs=xs, color=[\"r\", \"g\", \"b\"][i], lw=j + 1, label=f\"lcurve for tau={tau}\"\n",
+    "        )\n",
+    "plt.xlabel(\"input\")\n",
+    "plt.ylabel(\"output\")\n",
+    "plt.grid()\n",
+    "plt.legend(fontsize=8)\n",
+    "plt.title(\"fermi curve mapping functions\");"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "142",
+   "id": "143",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').fermi(tau=0.25, mu=1).plot(label='fermi distorted');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 50 * ts)\n",
+    "xs.plot(label=\"sine\").fermi(tau=0.25, mu=1).plot(label=\"fermi distorted\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "143",
+   "id": "144",
    "metadata": {},
    "source": [
     "### `normalize`\n",
@@ -2025,16 +1912,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "144",
+   "id": "145",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.normalize(np.random.rand(10)) # you'll find a 1 and a -1"
+    "pam.normalize(np.random.rand(10))  # you'll find a 1 and a -1"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "145",
+   "id": "146",
    "metadata": {},
    "source": [
     "- ChainableArray.normalize uses self as input.\n",
@@ -2044,19 +1931,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "146",
+   "id": "147",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = (2*np.pi*50*ts).sin()\n",
-    "xs.plot(label='sine').normalize(0.5,1).plot(label='normalized to [0.5, 1]');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = (2 * np.pi * 50 * ts).sin()\n",
+    "xs.plot(label=\"sine\").normalize(0.5, 1).plot(label=\"normalized to [0.5, 1]\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "147",
+   "id": "148",
    "metadata": {},
    "source": [
     "### `norm_peak`\n",
@@ -2073,16 +1961,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "148",
+   "id": "149",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.norm_peak(np.random.rand(10), 5) # you'll find a 5 (not not a -5)"
+    "pam.norm_peak(np.random.rand(10), 5)  # you'll find a 5 (not not a -5)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "149",
+   "id": "150",
    "metadata": {},
    "source": [
     "- ChainableArray.norm_peak uses self as input.\n",
@@ -2092,19 +1980,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "150",
+   "id": "151",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').norm_peak(0.5).plot(label='norm_peak to 0.5');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 50 * ts)\n",
+    "xs.plot(label=\"sine\").norm_peak(0.5).plot(label=\"norm_peak to 0.5\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "151",
+   "id": "152",
    "metadata": {},
    "source": [
     "### `norm_rms`\n",
@@ -2121,16 +2010,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "152",
+   "id": "153",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.norm_rms(np.array([1,0,0,-1]), 1) # scale by sqrt(2) to magnify RMS"
+    "pam.norm_rms(np.array([1, 0, 0, -1]), 1)  # scale by sqrt(2) to magnify RMS"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "153",
+   "id": "154",
    "metadata": {},
    "source": [
     "- ChainableArray.norm_rms uses self as input.\n",
@@ -2140,19 +2029,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "154",
+   "id": "155",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*50*ts)\n",
-    "xs.plot(label='sine').norm_rms(0.5).plot(label='norm_rms to 0.5');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 50 * ts)\n",
+    "xs.plot(label=\"sine\").norm_rms(0.5).plot(label=\"norm_rms to 0.5\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "155",
+   "id": "156",
    "metadata": {},
    "source": [
     "### `remove_dc`\n",
@@ -2167,16 +2057,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "156",
+   "id": "157",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.remove_dc(np.array([1,2,3,4]))"
+    "pam.remove_dc(np.array([1, 2, 3, 4]))"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "157",
+   "id": "158",
    "metadata": {},
    "source": [
     "- ChainableArray.remove_dc uses self as input.\n",
@@ -2186,19 +2076,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "158",
+   "id": "159",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*25*ts)**2\n",
-    "xs.plot(label='sine').remove_dc().plot(label='remove_dc output');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 25 * ts) ** 2\n",
+    "xs.plot(label=\"sine\").remove_dc().plot(label=\"remove_dc output\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "159",
+   "id": "160",
    "metadata": {},
    "source": [
     "### `gain`\n",
@@ -2215,16 +2106,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "160",
+   "id": "161",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pam.gain(np.array([1,2,3,4]), amp=2)"
+    "pam.gain(np.array([1, 2, 3, 4]), amp=2)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "161",
+   "id": "162",
    "metadata": {},
    "source": [
     "- ChainableArray.gain uses self as input.\n",
@@ -2234,19 +2125,20 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "162",
+   "id": "163",
    "metadata": {},
    "outputs": [],
    "source": [
     "ts = chain(np.linspace(0, 0.1, 500))\n",
-    "xs = np.sin(2*np.pi*25*ts)\n",
-    "xs.plot(label='sine').gain(db=-6).plot(label='-6 dB gain');\n",
-    "plt.legend(loc='upper right'); plt.grid()"
+    "xs = np.sin(2 * np.pi * 25 * ts)\n",
+    "xs.plot(label=\"sine\").gain(db=-6).plot(label=\"-6 dB gain\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "163",
+   "id": "164",
    "metadata": {},
    "source": [
     "### `ecdf`\n",
@@ -2271,7 +2163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "164",
+   "id": "165",
    "metadata": {},
    "source": [
     "**Example 1**: (compute once - use many)\n"
@@ -2280,29 +2172,29 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "165",
+   "id": "166",
    "metadata": {},
    "outputs": [],
    "source": [
     "from pyamapping import ecdf\n",
     "\n",
     "data = np.array([1, 3, 1.5, 3.5, 2, 5, 8, 9, 16])  # your data, unsorted\n",
-    "myecdf = ecdf(data) # compute the (xc, yc) for interp()\n",
+    "myecdf = ecdf(data)  # compute the (xc, yc) for interp()\n",
     "\n",
     "# now myecdf may be used many times\n",
-    "xn = chain(np.linspace(0, 20, 50)) # your custom x (at which you need ecdf)\n",
-    "yn = xn.interp(*myecdf, left=0) # extra argument to specify left extrapolation\n",
+    "xn = chain(np.linspace(0, 20, 50))  # your custom x (at which you need ecdf)\n",
+    "yn = xn.interp(*myecdf, left=0)  # extra argument to specify left extrapolation\n",
     "\n",
     "# plot data, ecdf and results of interp\n",
     "plt.plot(data, np.zeros_like(data), \"bx\", label=\"data\")\n",
     "plt.plot(*myecdf, \"ro\", ms=5, label=\"ecdf for data\")\n",
     "plt.plot(xn, yn, \"ko-\", lw=0.5, ms=2, label=\"your applied ecdf to custom data\")\n",
-    "plt.grid()\n"
+    "plt.grid()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "166",
+   "id": "167",
    "metadata": {},
    "source": [
     "**Example 2:** (compute and map in one go)\n",
@@ -2313,17 +2205,17 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "167",
+   "id": "168",
    "metadata": {},
    "outputs": [],
    "source": [
     "newdata = chain(np.array([0.5, 3.25, 20]))\n",
-    "newdata.interp(*ecdf(data), left=0) # turn newdata into ecdfs of data "
+    "newdata.interp(*ecdf(data), left=0)  # turn newdata into ecdfs of data"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "168",
+   "id": "169",
    "metadata": {},
    "source": [
     "### `lin_to_ecdf`\n",
@@ -2338,18 +2230,18 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "169",
+   "id": "170",
    "metadata": {},
    "outputs": [],
    "source": [
-    "data_feat = np.random.randn(200) # data used for crafting the mapping\n",
-    "test_data = np.linspace(-3, 3, 200) # data to apply mapping to\n",
+    "data_feat = np.random.randn(200)  # data used for crafting the mapping\n",
+    "test_data = np.linspace(-3, 3, 200)  # data to apply mapping to\n",
     "chain(test_data).lin_to_ecdf(data_feat, sorted=False).plot(xs=test_data);"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "170",
+   "id": "171",
    "metadata": {},
    "source": [
     "### `ecdf_to_lin`\n",
@@ -2363,23 +2255,24 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "171",
+   "id": "172",
    "metadata": {},
    "outputs": [],
    "source": [
     "# ecdf_to_lin\n",
-    "data = chain(np.random.randn(500)).normalize(0,10) # some quantiles, i.e. in [0,1]\n",
-    "test_data = np.linspace(0, 1, 100) # data to apply mapping to\n",
+    "data = chain(np.random.randn(500)).normalize(0, 10)  # some quantiles, i.e. in [0,1]\n",
+    "test_data = np.linspace(0, 1, 100)  # data to apply mapping to\n",
     "chain(test_data).ecdf_to_lin(data).plot(xs=test_data)\n",
     "\n",
-    "plt.axvline(0.5, ls=\":\", color='k'); \n",
-    "plt.xlabel('test data, resp. quantile'); plt.ylabel('feature values')\n",
-    "plt.axhline(np.median(data), ls=\":\", color='k');"
+    "plt.axvline(0.5, ls=\":\", color=\"k\")\n",
+    "plt.xlabel(\"test data, resp. quantile\")\n",
+    "plt.ylabel(\"feature values\")\n",
+    "plt.axhline(np.median(data), ls=\":\", color=\"k\");"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "172",
+   "id": "173",
    "metadata": {},
    "source": [
     "- quantiles mapping should pass a cdf array \n",
@@ -2389,37 +2282,21 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "173",
+   "id": "174",
    "metadata": {},
    "outputs": [],
    "source": [
-    "data = chain(np.random.randn(200)) # data used for crafting the mapping\n",
-    "test_data = np.linspace(-3, 3, 200) # data to apply mapping to\n",
+    "data = chain(np.random.randn(200))  # data used for crafting the mapping\n",
+    "test_data = np.linspace(-3, 3, 200)  # data to apply mapping to\n",
     "\n",
-    "chain(test_data).interp(*ecdf(data)).plot(xs=test_data, label='full data ecdf');\n",
-    "chain(test_data).interp(*ecdf(data, np.s_[20:-15:10])).plot(\"r-\", xs=test_data, ms=1, label='ecdf sliced');"
+    "chain(test_data).interp(*ecdf(data)).plot(xs=test_data, label=\"full data ecdf\")\n",
+    "chain(test_data).interp(*ecdf(data, np.s_[20:-15:10])).plot(\n",
+    "    \"r-\", xs=test_data, ms=1, label=\"ecdf sliced\"\n",
+    ");"
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "pyamapping (3.12.8)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.8"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/pyproject.toml b/pyproject.toml
index 0e97942..8a52045 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,7 @@
 [project]
 name = "pyamapping"
 description = "A Python package containing audio related functions and mappings"
+version = "0.1.0"
 authors = [
     { name = "Thomas Hermann", email = "thermann@techfak.uni-bielefeld.de"},
     { name = "Dennis Reinsch", email = "dreinsch@techfak.uni-bielefeld.de"}
@@ -9,7 +10,6 @@ maintainers = [
     {name = "Fabian Hommel", email = "fhommel@techfa.uni-bielefeld.de"}
 ]
 readme = "README.rst"
-dynamic = ["version"]
 requires-python = ">=3.9"
 dependencies = [
     "numpy",
@@ -26,20 +26,12 @@ classifiers = [
 github = "https://github.com/interactive-sonification/pyamapping"
 
 [build-system]
-requires = ["hatchling", "hatch-vcs"]
+requires = ["hatchling"]
 build-backend = "hatchling.build"
 
-[tool.hatch.version]
-source = "vcs"
-
 [tool.hatch.build.targets.wheel]
 packages = ["pyamapping"]
 
-[tool.setuptools_scm]
-# For smarter version schemes and other configuration options,
-# check out https://github.com/pypa/setuptools_scm
-version_scheme = "no-guess-dev"
-
 [project.optional-dependencies]
 example-notebooks = ["notebook"]
 
@@ -51,6 +43,7 @@ line-length = 88
 
 [tool.ruff.lint]
 select = ["E", "F", "I", "T10"]  # E/F = flake8, I = isort
+ignore = ["E702"]
 
 [tool.ruff.lint.isort]
 known-first-party = ["pyamapping"]
diff --git a/uv.lock b/uv.lock
index cc10495..18547d4 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,5 +1,4 @@
 version = 1
-revision = 1
 requires-python = ">=3.9"
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -273,7 +272,7 @@ wheels = [
 
 [[package]]
 name = "cachetools"
-version = "7.0.5"
+version = "7.0.6"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -281,18 +280,18 @@ resolution-markers = [
     "python_full_version == '3.11.*'",
     "python_full_version == '3.10.*'",
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/af/dd/57fe3fdb6e65b25a5987fd2cdc7e22db0aef508b91634d2e57d22928d41b/cachetools-7.0.5.tar.gz", hash = "sha256:0cd042c24377200c1dcd225f8b7b12b0ca53cc2c961b43757e774ebe190fd990", size = 37367 }
+sdist = { url = "https://files.pythonhosted.org/packages/76/7b/1755ed2c6bfabd1d98b37ae73152f8dcf94aa40fee119d163c19ed484704/cachetools-7.0.6.tar.gz", hash = "sha256:e5d524d36d65703a87243a26ff08ad84f73352adbeafb1cde81e207b456aaf24", size = 37526 }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/06/f3/39cf3367b8107baa44f861dc802cbf16263c945b62d8265d36034fc07bea/cachetools-7.0.5-py3-none-any.whl", hash = "sha256:46bc8ebefbe485407621d0a4264b23c080cedd913921bad7ac3ed2f26c183114", size = 13918 },
+    { url = "https://files.pythonhosted.org/packages/fe/c4/cf76242a5da1410917107ff14551764aa405a5fd10cd10cf9a5ca8fa77f4/cachetools-7.0.6-py3-none-any.whl", hash = "sha256:4e94956cfdd3086f12042cdd29318f5ced3893014f7d0d059bf3ead3f85b7f8b", size = 13976 },
 ]
 
 [[package]]
 name = "certifi"
-version = "2026.2.25"
+version = "2026.4.22"
 source = { registry = "https://pypi.org/simple" }
-sdist = { url = "https://files.pythonhosted.org/packages/af/2d/7bf41579a8986e348fa033a31cdd0e4121114f6bce2457e8876010b092dd/certifi-2026.2.25.tar.gz", hash = "sha256:e887ab5cee78ea814d3472169153c2d12cd43b14bd03329a39a9c6e2e80bfba7", size = 155029 }
+sdist = { url = "https://files.pythonhosted.org/packages/25/ee/6caf7a40c36a1220410afe15a1cc64993a1f864871f698c0f93acb72842a/certifi-2026.4.22.tar.gz", hash = "sha256:8d455352a37b71bf76a79caa83a3d6c25afee4a385d632127b6afb3963f1c580", size = 137077 }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/9a/3c/c17fb3ca2d9c3acff52e30b309f538586f9f5b9c9cf454f3845fc9af4881/certifi-2026.2.25-py3-none-any.whl", hash = "sha256:027692e4402ad994f1c42e52a4997a9763c646b73e4096e4d5d6db8af1d6f0fa", size = 153684 },
+    { url = "https://files.pythonhosted.org/packages/22/30/7cd8fdcdfbc5b869528b079bfb76dcdf6056b1a2097a662e5e8c04f42965/certifi-2026.4.22-py3-none-any.whl", hash = "sha256:3cb2210c8f88ba2318d29b0388d1023c8492ff72ecdde4ebdaddbb13a31b1c4a", size = 135707 },
 ]
 
 [[package]]
@@ -900,7 +899,7 @@ name = "exceptiongroup"
 version = "1.3.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "typing-extensions", marker = "python_full_version < '3.11'" },
+    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/50/79/66800aadf48771f6b62f7eb014e352e5d06856655206165d775e675a02c9/exceptiongroup-1.3.1.tar.gz", hash = "sha256:8b412432c6055b0b7d14c310000ae93352ed6754f70fa8f7c34141f91c4e3219", size = 30371 }
 wheels = [
@@ -939,7 +938,7 @@ wheels = [
 
 [[package]]
 name = "filelock"
-version = "3.25.2"
+version = "3.29.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -947,9 +946,9 @@ resolution-markers = [
     "python_full_version == '3.11.*'",
     "python_full_version == '3.10.*'",
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/94/b8/00651a0f559862f3bb7d6f7477b192afe3f583cc5e26403b44e59a55ab34/filelock-3.25.2.tar.gz", hash = "sha256:b64ece2b38f4ca29dd3e810287aa8c48182bbecd1ae6e9ae126c9b35f1382694", size = 40480 }
+sdist = { url = "https://files.pythonhosted.org/packages/b5/fe/997687a931ab51049acce6fa1f23e8f01216374ea81374ddee763c493db5/filelock-3.29.0.tar.gz", hash = "sha256:69974355e960702e789734cb4871f884ea6fe50bd8404051a3530bc07809cf90", size = 57571 }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/a4/a5/842ae8f0c08b61d6484b52f99a03510a3a72d23141942d216ebe81fefbce/filelock-3.25.2-py3-none-any.whl", hash = "sha256:ca8afb0da15f229774c9ad1b455ed96e85a81373065fb10446672f64444ddf70", size = 26759 },
+    { url = "https://files.pythonhosted.org/packages/81/47/dd9a212ef6e343a6857485ffe25bba537304f1913bdbed446a23f7f592e1/filelock-3.29.0-py3-none-any.whl", hash = "sha256:96f5f6344709aa1572bbf631c640e4ebeeb519e08da902c39a001882f30ac258", size = 39812 },
 ]
 
 [[package]]
@@ -1013,7 +1012,7 @@ wheels = [
 
 [[package]]
 name = "identify"
-version = "2.6.18"
+version = "2.6.19"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -1021,18 +1020,18 @@ resolution-markers = [
     "python_full_version == '3.11.*'",
     "python_full_version == '3.10.*'",
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/46/c4/7fb4db12296cdb11893d61c92048fe617ee853f8523b9b296ac03b43757e/identify-2.6.18.tar.gz", hash = "sha256:873ac56a5e3fd63e7438a7ecbc4d91aca692eb3fefa4534db2b7913f3fc352fd", size = 99580 }
+sdist = { url = "https://files.pythonhosted.org/packages/52/63/51723b5f116cc04b061cb6f5a561790abf249d25931d515cd375e063e0f4/identify-2.6.19.tar.gz", hash = "sha256:6be5020c38fcb07da56c53733538a3081ea5aa70d36a156f83044bfbf9173842", size = 99567 }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/46/33/92ef41c6fad0233e41d3d84ba8e8ad18d1780f1e5d99b3c683e6d7f98b63/identify-2.6.18-py2.py3-none-any.whl", hash = "sha256:8db9d3c8ea9079db92cafb0ebf97abdc09d52e97f4dcf773a2e694048b7cd737", size = 99394 },
+    { url = "https://files.pythonhosted.org/packages/94/84/d9273cd09688070a6523c4aee4663a8538721b2b755c4962aafae0011e72/identify-2.6.19-py2.py3-none-any.whl", hash = "sha256:20e6a87f786f768c092a721ad107fc9df0eb89347be9396cadf3f4abbd1fb78a", size = 99397 },
 ]
 
 [[package]]
 name = "idna"
-version = "3.11"
+version = "3.13"
 source = { registry = "https://pypi.org/simple" }
-sdist = { url = "https://files.pythonhosted.org/packages/6f/6d/0703ccc57f3a7233505399edb88de3cbd678da106337b9fcde432b65ed60/idna-3.11.tar.gz", hash = "sha256:795dafcc9c04ed0c1fb032c2aa73654d8e8c5023a7df64a53f39190ada629902", size = 194582 }
+sdist = { url = "https://files.pythonhosted.org/packages/ce/cc/762dfb036166873f0059f3b7de4565e1b5bc3d6f28a414c13da27e442f99/idna-3.13.tar.gz", hash = "sha256:585ea8fe5d69b9181ec1afba340451fba6ba764af97026f92a91d4eef164a242", size = 194210 }
 wheels = [
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+    { url = "https://files.pythonhosted.org/packages/5d/13/ad7d7ca3808a898b4612b6fe93cde56b53f3034dcde235acb1f0e1df24c6/idna-3.13-py3-none-any.whl", hash = "sha256:892ea0cde124a99ce773decba204c5552b69c3c67ffd5f232eb7696135bc8bb3", size = 68629 },
 ]
 
 [[package]]
@@ -1143,8 +1142,7 @@ dependencies = [
     { name = "comm", marker = "python_full_version >= '3.10'" },
     { name = "debugpy", marker = "python_full_version >= '3.10'" },
     { name = "ipython", version = "8.39.0", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version == '3.10.*'" },
-    { name = "ipython", version = "9.10.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version == '3.11.*'" },
-    { name = "ipython", version = "9.12.0", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.12'" },
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 [[package]]
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 [[package]]
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 source = { editable = "." }
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 [[package]]

From 1e3948d787fc282053d061709d39e100a011b1fc Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Wed, 29 Apr 2026 11:42:15 +0200
Subject: [PATCH 85/87] incremented version to 1.0.0

---
 pyproject.toml | 2 +-
 uv.lock        | 6 ++++--
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 8a52045..3111a42 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,7 +1,7 @@
 [project]
 name = "pyamapping"
 description = "A Python package containing audio related functions and mappings"
-version = "0.1.0"
+version = "1.0.0"
 authors = [
     { name = "Thomas Hermann", email = "thermann@techfak.uni-bielefeld.de"},
     { name = "Dennis Reinsch", email = "dreinsch@techfak.uni-bielefeld.de"}
diff --git a/uv.lock b/uv.lock
index 18547d4..fb37578 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,4 +1,5 @@
 version = 1
+revision = 1
 requires-python = ">=3.9"
 resolution-markers = [
     "python_full_version >= '3.14'",
@@ -899,7 +900,7 @@ name = "exceptiongroup"
 version = "1.3.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
+    { name = "typing-extensions", marker = "python_full_version < '3.11'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/50/79/66800aadf48771f6b62f7eb014e352e5d06856655206165d775e675a02c9/exceptiongroup-1.3.1.tar.gz", hash = "sha256:8b412432c6055b0b7d14c310000ae93352ed6754f70fa8f7c34141f91c4e3219", size = 30371 }
 wheels = [
@@ -2274,7 +2275,7 @@ wheels = [
 
 [[package]]
 name = "pyamapping"
-version = "0.1.0"
+version = "1.0.0"
 source = { editable = "." }
 dependencies = [
     { name = "numpy", version = "2.0.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.10'" },
@@ -2311,6 +2312,7 @@ requires-dist = [
     { name = "numpy" },
     { name = "scipy" },
 ]
+provides-extras = ["example-notebooks"]
 
 [package.metadata.requires-dev]
 dev = [

From 70816eefc0e0ee9d4d01a7c07831b2db95451db8 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Thu, 30 Apr 2026 14:01:55 +0200
Subject: [PATCH 86/87] Added manual dispatch to publish step in github
 workflow

---
 .github/workflows/ci.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index ef2fd2e..b70a480 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -98,7 +98,7 @@ jobs:
 
   publish:
     needs: finalize
-    if: ${{ github.event_name == 'push' && contains(github.ref, 'refs/tags/') }}
+    if: ${{ (github.event_name == 'push' || github.event_name == 'workflow_dispatch') && contains(github.ref, 'refs/tags/') }}
     runs-on: ubuntu-latest
     permissions:
       contents: write

From 4d9b770a1f7da19cf2e51b48d6a6a96e3e8612f7 Mon Sep 17 00:00:00 2001
From: Fabian Hommel <fhommel2@gmail.com>
Date: Thu, 30 Apr 2026 14:08:17 +0200
Subject: [PATCH 87/87] added debug step to finalize

---
 .github/workflows/ci.yml | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index b70a480..ffde73f 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -95,6 +95,10 @@ jobs:
         with:
           github-token: ${{ secrets.GITHUB_TOKEN }}
           parallel-finished: true
+      - name: debug
+        run: echo "ref=${{ github.ref }} event=${{ github.event_name }}"
+    
+  
 
   publish:
     needs: finalize