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Added main ipynb + modules
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‎cost_function.ipynb‎

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‎deeplearning.mplstyle‎

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# see https://matplotlib.org/stable/tutorials/introductory/customizing.html
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lines.linewidth: 4
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lines.solid_capstyle: butt
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legend.fancybox: true
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# Verdana" for non-math text,
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# Cambria Math
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#Blue (Crayon-Aqua) 0096FF
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#Dark Red C00000
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#Orange (Apple Orange) FF9300
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#Black 000000
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#Magenta FF40FF
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#Purple 7030A0
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axes.prop_cycle: cycler('color', ['0096FF', 'FF9300', 'FF40FF', '7030A0', 'C00000'])
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#axes.facecolor: f0f0f0 # grey
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axes.facecolor: ffffff # white
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axes.labelsize: large
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axes.axisbelow: true
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axes.grid: False
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axes.edgecolor: f0f0f0
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axes.linewidth: 3.0
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axes.titlesize: x-large
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patch.edgecolor: f0f0f0
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patch.linewidth: 0.5
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svg.fonttype: path
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grid.linestyle: -
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grid.linewidth: 1.0
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grid.color: cbcbcb
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xtick.major.size: 0
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xtick.minor.size: 0
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ytick.major.size: 0
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ytick.minor.size: 0
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savefig.edgecolor: f0f0f0
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savefig.facecolor: f0f0f0
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#figure.subplot.left: 0.08
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#figure.subplot.right: 0.95
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#figure.subplot.bottom: 0.07
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#figure.facecolor: f0f0f0 # grey
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figure.facecolor: ffffff # white
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## ***************************************************************************
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## * FONT *
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## ***************************************************************************
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## The font properties used by `text.Text`.
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## See https://matplotlib.org/api/font_manager_api.html for more information
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## on font properties. The 6 font properties used for font matching are
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## given below with their default values.
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##
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## The font.family property can take either a concrete font name (not supported
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## when rendering text with usetex), or one of the following five generic
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## values:
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## - 'serif' (e.g., Times),
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## - 'sans-serif' (e.g., Helvetica),
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## - 'cursive' (e.g., Zapf-Chancery),
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## - 'fantasy' (e.g., Western), and
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## - 'monospace' (e.g., Courier).
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## Each of these values has a corresponding default list of font names
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## (font.serif, etc.); the first available font in the list is used. Note that
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## for font.serif, font.sans-serif, and font.monospace, the first element of
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## the list (a DejaVu font) will always be used because DejaVu is shipped with
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## Matplotlib and is thus guaranteed to be available; the other entries are
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## left as examples of other possible values.
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##
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## The font.style property has three values: normal (or roman), italic
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## or oblique. The oblique style will be used for italic, if it is not
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## present.
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##
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## The font.variant property has two values: normal or small-caps. For
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## TrueType fonts, which are scalable fonts, small-caps is equivalent
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## to using a font size of 'smaller', or about 83%% of the current font
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## size.
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##
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## The font.weight property has effectively 13 values: normal, bold,
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## bolder, lighter, 100, 200, 300, ..., 900. Normal is the same as
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## 400, and bold is 700. bolder and lighter are relative values with
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## respect to the current weight.
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##
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## The font.stretch property has 11 values: ultra-condensed,
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## extra-condensed, condensed, semi-condensed, normal, semi-expanded,
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## expanded, extra-expanded, ultra-expanded, wider, and narrower. This
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## property is not currently implemented.
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##
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## The font.size property is the default font size for text, given in points.
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## 10 pt is the standard value.
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##
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## Note that font.size controls default text sizes. To configure
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## special text sizes tick labels, axes, labels, title, etc., see the rc
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## settings for axes and ticks. Special text sizes can be defined
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## relative to font.size, using the following values: xx-small, x-small,
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## small, medium, large, x-large, xx-large, larger, or smaller
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font.family: sans-serif
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font.style: normal
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font.variant: normal
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font.weight: normal
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font.stretch: normal
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font.size: 8.0
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font.serif: DejaVu Serif, Bitstream Vera Serif, Computer Modern Roman, New Century Schoolbook, Century Schoolbook L, Utopia, ITC Bookman, Bookman, Nimbus Roman No9 L, Times New Roman, Times, Palatino, Charter, serif
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font.sans-serif: Verdana, DejaVu Sans, Bitstream Vera Sans, Computer Modern Sans Serif, Lucida Grande, Geneva, Lucid, Arial, Helvetica, Avant Garde, sans-serif
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font.cursive: Apple Chancery, Textile, Zapf Chancery, Sand, Script MT, Felipa, Comic Neue, Comic Sans MS, cursive
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font.fantasy: Chicago, Charcoal, Impact, Western, Humor Sans, xkcd, fantasy
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font.monospace: DejaVu Sans Mono, Bitstream Vera Sans Mono, Computer Modern Typewriter, Andale Mono, Nimbus Mono L, Courier New, Courier, Fixed, Terminal, monospace
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## ***************************************************************************
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## * TEXT *
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## ***************************************************************************
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## The text properties used by `text.Text`.
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## See https://matplotlib.org/api/artist_api.html#module-matplotlib.text
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## for more information on text properties
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#text.color: black
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‎lab_utils_common.py‎

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"""
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lab_utils_common.py
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functions common to all optional labs, Course 1, Week 2
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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plt.style.use('./deeplearning.mplstyle')
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dlblue = '#0096ff'; dlorange = '#FF9300'; dldarkred='#C00000'; dlmagenta='#FF40FF'; dlpurple='#7030A0';
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dlcolors = [dlblue, dlorange, dldarkred, dlmagenta, dlpurple]
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dlc = dict(dlblue = '#0096ff', dlorange = '#FF9300', dldarkred='#C00000', dlmagenta='#FF40FF', dlpurple='#7030A0')
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##########################################################
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# Regression Routines
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##########################################################
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#Function to calculate the cost
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def compute_cost_matrix(X, y, w, b, verbose=False):
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"""
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Computes the gradient for linear regression
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Args:
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X (ndarray (m,n)): Data, m examples with n features
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y (ndarray (m,)) : target values
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w (ndarray (n,)) : model parameters
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b (scalar) : model parameter
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verbose : (Boolean) If true, print out intermediate value f_wb
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Returns
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cost: (scalar)
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"""
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m = X.shape[0]
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# calculate f_wb for all examples.
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f_wb = X @ w + b
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# calculate cost
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total_cost = (1/(2*m)) * np.sum((f_wb-y)**2)
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if verbose: print("f_wb:")
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if verbose: print(f_wb)
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return total_cost
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def compute_gradient_matrix(X, y, w, b):
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"""
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Computes the gradient for linear regression
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Args:
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X (ndarray (m,n)): Data, m examples with n features
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y (ndarray (m,)) : target values
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w (ndarray (n,)) : model parameters
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b (scalar) : model parameter
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Returns
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dj_dw (ndarray (n,1)): The gradient of the cost w.r.t. the parameters w.
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dj_db (scalar): The gradient of the cost w.r.t. the parameter b.
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"""
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m,n = X.shape
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f_wb = X @ w + b
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e = f_wb - y
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dj_dw = (1/m) * (X.T @ e)
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dj_db = (1/m) * np.sum(e)
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return dj_db,dj_dw
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# Loop version of multi-variable compute_cost
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def compute_cost(X, y, w, b):
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"""
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compute cost
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Args:
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X (ndarray (m,n)): Data, m examples with n features
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y (ndarray (m,)) : target values
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w (ndarray (n,)) : model parameters
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b (scalar) : model parameter
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Returns
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cost (scalar) : cost
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"""
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m = X.shape[0]
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cost = 0.0
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for i in range(m):
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f_wb_i = np.dot(X[i],w) + b #(n,)(n,)=scalar
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cost = cost + (f_wb_i - y[i])**2
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cost = cost/(2*m)
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return cost
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def compute_gradient(X, y, w, b):
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"""
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Computes the gradient for linear regression
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Args:
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X (ndarray (m,n)): Data, m examples with n features
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y (ndarray (m,)) : target values
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w (ndarray (n,)) : model parameters
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b (scalar) : model parameter
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Returns
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dj_dw (ndarray Shape (n,)): The gradient of the cost w.r.t. the parameters w.
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dj_db (scalar): The gradient of the cost w.r.t. the parameter b.
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"""
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m,n = X.shape #(number of examples, number of features)
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dj_dw = np.zeros((n,))
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dj_db = 0.
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for i in range(m):
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err = (np.dot(X[i], w) + b) - y[i]
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for j in range(n):
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dj_dw[j] = dj_dw[j] + err * X[i,j]
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dj_db = dj_db + err
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dj_dw = dj_dw/m
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dj_db = dj_db/m
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return dj_db,dj_dw
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