fix: Add reproducible_smatrix()

Some algorithms may not converge when used on completely random values
with the default value of epsilon and unlimited iterations.

`reproducible_dmatrix()` already exist to circumvent this for `DMatrix`,
so I implemented the same for `SMatrix`.

In my tests this problem manifested itself only on
`schur_decompose_4x4`, but I decided to apply similar fix for all
benchmarks that also use `reproducible_dmatrix()` for `DMatrix`.

Author: im-0

benches/lib.rs

@@ -6,14 +6,25 @@ extern crate rand_package as rand;
 #[macro_use]
 extern crate criterion;
 
-use na::DMatrix;
+use na::{DMatrix, SMatrix, Scalar};
 use rand::Rng;
+use rand::distr::{Distribution, StandardUniform};
 use rand_isaac::IsaacRng;
 
 pub mod core;
 pub mod geometry;
 pub mod linalg;
 
+fn reproducible_smatrix<T, const R: usize, const C: usize>() -> SMatrix<T, R, C>
+where
+    T: Scalar,
+    StandardUniform: Distribution<T>,
+{
+    use rand::SeedableRng;
+    let mut rng = IsaacRng::seed_from_u64(0);
+    SMatrix::from_fn(|_, _| rng.random())
+}
+
 fn reproducible_dmatrix(nrows: usize, ncols: usize) -> DMatrix<f64> {
     use rand::SeedableRng;
     let mut rng = IsaacRng::seed_from_u64(0);

benches/linalg/schur.rs

@@ -1,9 +1,9 @@
-use na::{Matrix4, Schur};
+use na::Schur;
 
 fn schur_decompose_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("schur_decompose_4x4", |bh| {
         bh.iter_batched(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| Schur::new(m),
             criterion::BatchSize::SmallInput,
         )
@@ -43,7 +43,7 @@ fn schur_decompose_200x200(bh: &mut criterion::Criterion) {
 fn eigenvalues_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("eigenvalues_4x4", |bh| {
         bh.iter_batched_ref(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| m.complex_eigenvalues(),
             criterion::BatchSize::SmallInput,
         )

benches/linalg/svd.rs

@@ -1,9 +1,9 @@
-use na::{Matrix2, Matrix3, Matrix4, SVD};
+use na::SVD;
 
 fn svd_decompose_2x2_f32(bh: &mut criterion::Criterion) {
     bh.bench_function("svd_decompose_2x2", |bh| {
         bh.iter_batched(
-            || Matrix2::<f32>::new_random(),
+            || crate::reproducible_smatrix::<f32, 2, 2>(),
             |m| SVD::new_unordered(m, true, true),
             criterion::BatchSize::SmallInput,
         )
@@ -13,7 +13,7 @@ fn svd_decompose_2x2_f32(bh: &mut criterion::Criterion) {
 fn svd_decompose_3x3_f32(bh: &mut criterion::Criterion) {
     bh.bench_function("svd_decompose_3x3", |bh| {
         bh.iter_batched(
-            || Matrix3::<f32>::new_random(),
+            || crate::reproducible_smatrix::<f32, 3, 3>(),
             |m| SVD::new_unordered(m, true, true),
             criterion::BatchSize::SmallInput,
         )
@@ -23,7 +23,7 @@ fn svd_decompose_3x3_f32(bh: &mut criterion::Criterion) {
 fn svd_decompose_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("svd_decompose_4x4", |bh| {
         bh.iter_batched(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| SVD::new(m, true, true),
             criterion::BatchSize::SmallInput,
         )
@@ -63,7 +63,7 @@ fn svd_decompose_200x200(bh: &mut criterion::Criterion) {
 fn rank_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("rank_4x4", |bh| {
         bh.iter_batched_ref(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| m.rank(1.0e-10),
             criterion::BatchSize::SmallInput,
         )
@@ -103,7 +103,7 @@ fn rank_200x200(bh: &mut criterion::Criterion) {
 fn singular_values_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("singular_values_4x4", |bh| {
         bh.iter_batched_ref(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| m.singular_values(),
             criterion::BatchSize::SmallInput,
         )
@@ -143,7 +143,7 @@ fn singular_values_200x200(bh: &mut criterion::Criterion) {
 fn pseudo_inverse_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("pseudo_inverse_4x4", |bh| {
         bh.iter_batched(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| m.pseudo_inverse(1.0e-10),
             criterion::BatchSize::SmallInput,
         )

benches/linalg/symmetric_eigen.rs

@@ -1,9 +1,9 @@
-use na::{Matrix4, SymmetricEigen};
+use na::SymmetricEigen;
 
 fn symmetric_eigen_decompose_4x4(bh: &mut criterion::Criterion) {
     bh.bench_function("symmetric_eigen_decompose_4x4", |bh| {
         bh.iter_batched(
-            || Matrix4::<f64>::new_random(),
+            || crate::reproducible_smatrix::<f64, 4, 4>(),
             |m| SymmetricEigen::new(m),
             criterion::BatchSize::SmallInput,
         )