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Fixes for control systems AND SVD and QR decomposition (#9)

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Reviewed-on: #9
Co-authored-by: Cynopolis <quinn.henthorne@gmail.com>
This commit was merged in pull request #9.
This commit is contained in:
Cynopolis
2026-08-26 13:08:21 -04:00
committed by Cynopolis
parent 48b016d8b7
commit f0035ab67f
16 changed files with 6471 additions and 67 deletions
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unit-tests/svd-integration-test.cpp
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#include "Matrix.hpp"
#include "SVD.hpp"
#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include <iostream>
// Generic helper functions for any matrix size
template <uint8_t rows, uint8_t columns>
static float frobeniusNorm(const Matrix<rows, columns> &M) {
float sum = 0.0f;
for (int i = 0; i < rows; i++)
for (int j = 0; j < columns; j++) {
float v = M.Get(i, j);
sum += v * v;
}
return sqrtf(sum);
}
template <uint8_t n>
static bool isOrthogonal(const Matrix<n, n> &M, float tol = 1e-4f) {
Matrix<n, n> Mt = M.Transpose();
Matrix<n, n> MtM{0};
Mt.Mult(M, MtM);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
float expected = (i == j) ? 1.0f : 0.0f;
if (fabsf(MtM.Get(i, j) - expected) > tol)
return false;
}
return true;
}
TEST_CASE("SVD Integration: 2x2 [[1,2],[3,4]]", "[Matrix][SVD][Integration]") {
Matrix<2, 2> A{1, 2, 3, 4};
Matrix<2, 2> U{0};
Matrix<2, 1> sigma{0};
Matrix<2, 2> Vt{0};
SVD::SVD(A, U, sigma, Vt);
// Reference singular values from scipy: [5.464985704219, 0.365966190626]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(5.4649857f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(0.3659662f, 1e-3f));
// Check orthogonality of U and Vt (first 2x2 blocks)
REQUIRE(isOrthogonal<2>(U));
REQUIRE(isOrthogonal<2>(Vt));
// Check reconstruction: A ≈ U · diag(sigma) · Vt
Matrix<2, 2> recon{0};
Matrix<2, 2> Usig{0};
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++)
Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
Usig.Mult(Vt, recon);
float err = 0.0f;
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++) {
float diff = recon.Get(i, j) - A.Get(i, j);
err += diff * diff;
}
err = sqrtf(err);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-3f));
std::cout << "SVD 2x2 [[1,2],[3,4]]:\n";
std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0)
<< "]\n";
}
TEST_CASE("SVD Integration: 3x3 diagonal [10,5,2]",
"[Matrix][SVD][Integration]") {
Matrix<3, 3> A{10, 0, 0, 0, 5, 0, 0, 0, 2};
Matrix<3, 3> U{0};
Matrix<3, 1> sigma{0};
Matrix<3, 3> Vt{0};
SVD::SVD(A, U, sigma, Vt);
// Singular values should be [10, 5, 2] (already diagonal)
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(10.0f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(5.0f, 1e-3f));
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinRel(2.0f, 1e-3f));
// U and Vt should be identity (or close) for diagonal matrix
float uErr = frobeniusNorm(U - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
float vtErr = frobeniusNorm(Vt - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
REQUIRE_THAT(uErr, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
REQUIRE_THAT(vtErr, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
}
TEST_CASE("SVD Integration: 3x3 rank-deficient [[1,2,3],[4,5,6],[7,8,9]]",
"[Matrix][SVD][Integration]") {
Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
Matrix<3, 3> U{0};
Matrix<3, 1> sigma{0};
Matrix<3, 3> Vt{0};
SVD::SVD(A, U, sigma, Vt);
// Reference: [16.848103352614, 1.068369514555, 0.0]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(16.8481f, 1e-2f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.06837f, 1e-2f));
// Third singular value should be ~0 (rank-deficient)
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
// Check reconstruction
Matrix<3, 3> recon{0};
Matrix<3, 3> Usig{0};
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
Usig.Mult(Vt, recon);
float err = 0.0f;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) {
float diff = recon.Get(i, j) - A.Get(i, j);
err += diff * diff;
}
err = sqrtf(err);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
std::cout << "SVD 3x3 rank-deficient:\n";
std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
<< sigma.Get(2, 0) << "]\n";
}
TEST_CASE("SVD Integration: tall 4x3 matrix", "[Matrix][SVD][Integration]") {
Matrix<4, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
Matrix<4, 3> U{0};
Matrix<3, 1> sigma{0};
Matrix<3, 3> Vt{0};
SVD::SVD(A, U, sigma, Vt);
// Reference: [25.462407436036, 1.290661675761, 0.0]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(25.4624f, 1e-2f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.29066f, 1e-2f));
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
// Check reconstruction
Matrix<4, 3> recon{0};
Matrix<4, 3> Usig{0};
for (int i = 0; i < 4; i++)
for (int j = 0; j < 3; j++)
Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
Usig.Mult(Vt, recon);
float err = 0.0f;
for (int i = 0; i < 4; i++)
for (int j = 0; j < 3; j++) {
float diff = recon.Get(i, j) - A.Get(i, j);
err += diff * diff;
}
err = sqrtf(err);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
std::cout << "SVD tall 4x3:\n";
std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
<< sigma.Get(2, 0) << "]\n";
}
TEST_CASE("SVD Integration: wide 3x5 matrix", "[Matrix][SVD][Integration]") {
Matrix<3, 5> A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
Matrix<3, 5> U{0};
Matrix<5, 1> sigma{0}; // sigma is columns x 1 = 5x1 for wide matrix
Matrix<5, 5> Vt{0}; // Vt is columns x columns = 5x5
SVD::SVD(A, U, sigma, Vt);
// Reference: [35.127223333575, 2.465396696917, 0.0]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(35.1272f, 1e-2f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(2.46540f, 1e-2f));
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
// Check reconstruction: A (3x5) = U * Sigma * Vt, where U (3x5) has
// its meaningful part in the first 3 columns, sigma (5x1) in the
// first 3 entries, and Vt (5x5) in its first 3 rows (right
// singular vectors as rows). So:
// A[i][j] = sum_k U[i][k] * sigma[k] * Vt[k][j]
float err2 = 0.0f;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 5; j++) {
float recon_val = 0.0f;
for (int k = 0; k < 3; k++) {
recon_val += U.Get(i, k) * sigma.Get(k, 0) * Vt.Get(k, j);
}
float diff = recon_val - A.Get(i, j);
err2 += diff * diff;
}
}
err2 = sqrtf(err2);
REQUIRE_THAT(err2, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
std::cout << "SVD wide 3x5:\n";
std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
<< sigma.Get(2, 0) << "]\n";
}
TEST_CASE("SVD Integration: identity 3x3", "[Matrix][SVD][Integration]") {
Matrix<3, 3> A{1, 0, 0, 0, 1, 0, 0, 0, 1};
Matrix<3, 3> U{0};
Matrix<3, 1> sigma{0};
Matrix<3, 3> Vt{0};
SVD::SVD(A, U, sigma, Vt);
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
float err = frobeniusNorm(U - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-2f));
}
TEST_CASE("SVD Integration: symmetric positive definite 2x2 [[5,3],[3,5]]",
"[Matrix][SVD][Integration]") {
Matrix<2, 2> A{5, 3, 3, 5};
Matrix<2, 2> U{0};
Matrix<2, 1> sigma{0};
Matrix<2, 2> Vt{0};
SVD::SVD(A, U, sigma, Vt);
// For SPD matrix, singular values = eigenvalues: [8, 2]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(8.0f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(2.0f, 1e-3f));
// Check reconstruction
Matrix<2, 2> recon{0};
Matrix<2, 2> Usig{0};
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++)
Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
Usig.Mult(Vt, recon);
float err = 0.0f;
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++) {
float diff = recon.Get(i, j) - A.Get(i, j);
err += diff * diff;
}
err = sqrtf(err);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-3f));
std::cout << "SVD SPD 2x2 [[5,3],[3,5]]:\n";
std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0)
<< "]\n";
}
// ----------------------------------------------------------------------------
// Matrix::SVD member wrapper (delegates to SVD::SVD)
// ----------------------------------------------------------------------------
/**
* Reconstruction error ‖U·diag(sigma)·Vᵀ − A‖_F. Zero-padded entries of
* U/sigma/Vt (wide/tall cases) are zero by the output conventions, so the
* full product equals U[:, :k]·diag(sigma[:k])·Vt[:k, :].
*/
template <uint8_t rows, uint8_t columns>
static float svdReconstructionError(const Matrix<rows, columns> &A,
const Matrix<rows, columns> &U,
const Matrix<columns, 1> &sigma,
const Matrix<columns, columns> &Vt) {
Matrix<rows, columns> recon{0};
Matrix<rows, columns> Usig{0};
for (int i = 0; i < rows; i++)
for (int j = 0; j < columns; j++)
Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
Usig.Mult(Vt, recon);
float err = 0.0f;
for (int i = 0; i < rows; i++)
for (int j = 0; j < columns; j++) {
float diff = recon.Get(i, j) - A.Get(i, j);
err += diff * diff;
}
return sqrtf(err);
}
/**
* Orthonormality of the first k columns of M: the k×k leading block of
* MᵀM must equal I_k. (For a tall SVD, U has k = min(rows, cols)
* meaningful columns and this is the full UᵀU.)
*/
template <uint8_t r, uint8_t c>
static bool leadingColumnsOrthonormal(const Matrix<r, c> &M, uint8_t k,
float tol = 1e-4f) {
Matrix<c, r> Mt = M.Transpose();
Matrix<c, c> MtM{0};
Mt.Mult(M, MtM);
for (int i = 0; i < k; i++)
for (int j = 0; j < k; j++) {
float expected = (i == j) ? 1.0f : 0.0f;
if (fabsf(MtM.Get(i, j) - expected) > tol)
return false;
}
return true;
}
/**
* Orthonormality of the first k rows of M: the k×k leading block of
* M·Mᵀ must equal I_k. (Vᵀ may have zero-padded trailing rows in the
* wide case, so check only the meaningful leading block.)
*/
template <uint8_t r, uint8_t c>
static bool leadingRowsOrthonormal(const Matrix<r, c> &M, uint8_t k,
float tol = 1e-4f) {
Matrix<c, r> Mt = M.Transpose();
Matrix<r, r> MMt{0};
M.Mult(Mt, MMt);
for (int i = 0; i < k; i++)
for (int j = 0; j < k; j++) {
float expected = (i == j) ? 1.0f : 0.0f;
if (fabsf(MMt.Get(i, j) - expected) > tol)
return false;
}
return true;
}
TEST_CASE("Matrix::SVD wrapper: 3x2 tall [[1,2],[3,4],[5,6]]",
"[Matrix][SVD][Wrapper]") {
Matrix<3, 2> A{1, 2, 3, 4, 5, 6};
Matrix<3, 2> U{0};
Matrix<2, 1> sigma{0};
Matrix<2, 2> Vt{0};
A.SVD(U, sigma, Vt);
// Reference singular values from numpy: [9.52552, 0.514301]
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(9.52552f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(0.514301f, 1e-3f));
REQUIRE(leadingColumnsOrthonormal(U, 2));
REQUIRE(leadingRowsOrthonormal(Vt, 2));
float err = svdReconstructionError(A, U, sigma, Vt);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-3f));
}
TEST_CASE("Matrix::SVD wrapper: 2x3 wide [[1,2,3],[4,5,6]]",
"[Matrix][SVD][Wrapper]") {
Matrix<2, 3> A{1, 2, 3, 4, 5, 6};
Matrix<2, 3> U{0};
Matrix<3, 1> sigma{0};
Matrix<3, 3> Vt{0};
A.SVD(U, sigma, Vt);
// Reference singular values from numpy: [9.50803, 0.77287]; the third
// entry (wide-matrix padding) must be zero.
REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(9.50803f, 1e-3f));
REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(0.77287f, 1e-3f));
REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-6f));
REQUIRE(leadingColumnsOrthonormal(U, 2));
REQUIRE(leadingRowsOrthonormal(Vt, 2));
float err = svdReconstructionError(A, U, sigma, Vt);
REQUIRE_THAT(err, Catch::Matchers::WithinAbs(0.0f, 1e-3f));
}