From 6bec56c4cce9d47d59f895005c28ee6a546dc1e4 Mon Sep 17 00:00:00 2001
From: Ignacia Piccardo <ignacia-fp@Mac.lan>
Date: Fri, 3 Jul 2026 12:40:36 +0100
Subject: [PATCH 1/3] Cap fixed-rank ID after QR/SVD nullification

---
 src/rsrs/rsrs_factors/commutative_factors.rs | 15 +++++++++++----
 src/utils/linear_algebra.rs                  | 19 ++++++++++++++++++-
 2 files changed, 29 insertions(+), 5 deletions(-)

diff --git a/src/rsrs/rsrs_factors/commutative_factors.rs b/src/rsrs/rsrs_factors/commutative_factors.rs
index 595460e..a020196 100644
--- a/src/rsrs/rsrs_factors/commutative_factors.rs
+++ b/src/rsrs/rsrs_factors/commutative_factors.rs
@@ -19,8 +19,8 @@ use crate::utils::{
         row_perm, row_subs,
     },
     linear_algebra::{
-        block_extraction_into, streaming_chunk_rows, BlockExtractionMethod,
-        NormalEquationAccumulator,
+        block_extraction_into, fixed_rank_relative_tol, streaming_chunk_rows,
+        BlockExtractionMethod, NormalEquationAccumulator, NullMethod,
     },
     memory::{matrix_bytes, trace_memory_event, trace_memory_growth},
 };
@@ -536,6 +536,7 @@ where
     where
         StandardNormal: Distribution<Item::Real>,
         Standard: Distribution<Item::Real>,
+        Real<Item>: num::NumCast,
         LuDecomposition<Item, BaseArray<Item, VectorContainer<Item>, 2>>:
             MatrixLuDecomposition<Item = Item>,
         QrDecomposition<Item, BaseArray<Item, VectorContainer<Item>, 2>>:
@@ -582,6 +583,12 @@ where
             };
             return (None, Times::Id(id_times));
         }
+        let fixed_rank_accuracy = |rank: usize| match id_options.null_method {
+            NullMethod::Svd | NullMethod::Qr => {
+                Accuracy::MinRank(fixed_rank_relative_tol::<Item>(), rank)
+            }
+            NullMethod::Projection => Accuracy::FixedRank(rank),
+        };
         let id_sketch = match rank_par {
             BoxType::Full(tol) => {
                 // for a box that hasn't been merged yet it
@@ -605,7 +612,7 @@ where
                         .r_mut()
                         .into_subview([0, 0], null_shape)
                         .into_id_alloc_no_skel(
-                            Accuracy::FixedRank(loc_rank),
+                            fixed_rank_accuracy(loc_rank),
                             id_options.qr_method.clone(),
                             TransMode::Trans,
                         )
@@ -619,7 +626,7 @@ where
                 .r_mut()
                 .into_subview([0, 0], null_shape)
                 .into_id_alloc_no_skel(
-                    Accuracy::FixedRank((*rank).min(max_rank)),
+                    fixed_rank_accuracy((*rank).min(max_rank)),
                     id_options.qr_method.clone(),
                     TransMode::Trans,
                 )
diff --git a/src/utils/linear_algebra.rs b/src/utils/linear_algebra.rs
index e8c0e84..42a4528 100644
--- a/src/utils/linear_algebra.rs
+++ b/src/utils/linear_algebra.rs
@@ -1,4 +1,4 @@
-use num::{Float, One, Zero};
+use num::{Float, NumCast, One, Zero};
 use rlst::dense::linalg::{lu::MatrixLu, null_space::Method};
 pub use rlst::prelude::*;
 use serde::Deserialize;
@@ -93,6 +93,17 @@ pub fn add_diagonal<Item: RlstScalar>(
     }
 }
 
+pub fn fixed_rank_relative_tol<Item: RlstScalar>() -> Real<Item>
+where
+    Real<Item>: NumCast,
+{
+    if std::mem::size_of::<Real<Item>>() <= std::mem::size_of::<f32>() {
+        NumCast::from(1e-5f64).unwrap()
+    } else {
+        NumCast::from(1e-10f64).unwrap()
+    }
+}
+
 fn normal_equation_scale<Item: RlstScalar>(normal: &DynamicArray<Item, 2>) -> Real<Item> {
     let shape = normal.shape();
     let view = normal.r();
@@ -421,4 +432,10 @@ mod tests {
             .iter()
             .all(|entry| Float::abs(*entry) <= f64::EPSILON));
     }
+
+    #[test]
+    fn fixed_rank_relative_tol_depends_on_precision() {
+        assert_eq!(fixed_rank_relative_tol::<f32>(), 1e-5f32);
+        assert_eq!(fixed_rank_relative_tol::<f64>(), 1e-10f64);
+    }
 }

From 0b0b008e01883da9be6b0c4ca666ff22a8af806b Mon Sep 17 00:00:00 2001
From: Ignacia Piccardo <ignacia-fp@Ignacias-MacBook-Air.local>
Date: Fri, 3 Jul 2026 15:12:47 +0100
Subject: [PATCH 2/3] Pin rlst revision with MinRank support

---
 Cargo.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Cargo.toml b/Cargo.toml
index f258460..99ff60f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -26,7 +26,7 @@ itertools = "0.14.*"
 rand = { version = "0.8.5", features = ["alloc"] }
 rand_chacha = "0.3.*"
 num = "0.4.*"
-rlst = { git = "https://github.com/ignacia-fp/rlst.git", branch = "extend_abstract_operator", features = [
+rlst = { git = "https://github.com/ignacia-fp/rlst.git", rev = "90da192c9563edf4b54a3728819f80ad093f4296", features = [
     "enable_tracing",
     "mpi",
 ] }

From 99f621fcf86c2d534cca542861ab923a619e6e12 Mon Sep 17 00:00:00 2001
From: Ignacia Piccardo <ignacia-fp@Ignacias-MacBook-Air.local>
Date: Fri, 3 Jul 2026 16:00:24 +0100
Subject: [PATCH 3/3] Use branch-based rlst dependency

---
 Cargo.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Cargo.toml b/Cargo.toml
index 99ff60f..f258460 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -26,7 +26,7 @@ itertools = "0.14.*"
 rand = { version = "0.8.5", features = ["alloc"] }
 rand_chacha = "0.3.*"
 num = "0.4.*"
-rlst = { git = "https://github.com/ignacia-fp/rlst.git", rev = "90da192c9563edf4b54a3728819f80ad093f4296", features = [
+rlst = { git = "https://github.com/ignacia-fp/rlst.git", branch = "extend_abstract_operator", features = [
     "enable_tracing",
     "mpi",
 ] }