Working on an SVD implimentation
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#include "Matrix.hpp"
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#include "SVD.hpp"
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/matchers/catch_matchers_floating_point.hpp>
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#include <iostream>
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// Generic helper functions for any matrix size
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template <uint8_t rows, uint8_t columns>
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static float frobeniusNorm(const Matrix<rows, columns> &M) {
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float sum = 0.0f;
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < columns; j++) {
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float v = M.Get(i, j);
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sum += v * v;
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}
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return sqrtf(sum);
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}
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template <uint8_t n>
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static bool isOrthogonal(const Matrix<n, n> &M, float tol = 1e-4f) {
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Matrix<n, n> Mt = M.Transpose();
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Matrix<n, n> MtM{0};
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Mt.Mult(M, MtM);
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++) {
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float expected = (i == j) ? 1.0f : 0.0f;
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if (fabsf(MtM.Get(i, j) - expected) > tol)
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return false;
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}
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return true;
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}
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TEST_CASE("SVD Integration: 2x2 [[1,2],[3,4]]", "[Matrix][SVD][Integration]") {
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Matrix<2, 2> A{1, 2, 3, 4};
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Matrix<2, 2> U{0};
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Matrix<2, 1> sigma{0};
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Matrix<2, 2> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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// Reference singular values from scipy: [5.464985704219, 0.365966190626]
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(5.4649857f, 1e-3f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(0.3659662f, 1e-3f));
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// Check orthogonality of U and Vt (first 2x2 blocks)
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REQUIRE(isOrthogonal<2>(U));
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REQUIRE(isOrthogonal<2>(Vt));
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// Check reconstruction: A ≈ U · diag(sigma) · Vt
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Matrix<2, 2> recon{0};
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Matrix<2, 2> Usig{0};
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for (int i = 0; i < 2; i++)
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for (int j = 0; j < 2; j++)
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Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
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Usig.Mult(Vt, recon);
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float err = 0.0f;
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for (int i = 0; i < 2; i++)
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for (int j = 0; j < 2; j++) {
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float diff = recon.Get(i, j) - A.Get(i, j);
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err += diff * diff;
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}
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err = sqrtf(err);
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REQUIRE_THAT(err, Catch::Matchers::WithinRel(0.0f, 1e-3f));
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std::cout << "SVD 2x2 [[1,2],[3,4]]:\n";
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std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0)
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<< "]\n";
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}
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TEST_CASE("SVD Integration: 3x3 diagonal [10,5,2]",
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"[Matrix][SVD][Integration]") {
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Matrix<3, 3> A{10, 0, 0, 0, 5, 0, 0, 0, 2};
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Matrix<3, 3> U{0};
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Matrix<3, 1> sigma{0};
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Matrix<3, 3> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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// Singular values should be [10, 5, 2] (already diagonal)
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(10.0f, 1e-3f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(5.0f, 1e-3f));
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REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinRel(2.0f, 1e-3f));
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// U and Vt should be identity (or close) for diagonal matrix
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float uErr = frobeniusNorm(U - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
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float vtErr = frobeniusNorm(Vt - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
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REQUIRE_THAT(uErr, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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REQUIRE_THAT(vtErr, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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}
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TEST_CASE("SVD Integration: 3x3 rank-deficient [[1,2,3],[4,5,6],[7,8,9]]",
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"[Matrix][SVD][Integration]") {
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Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<3, 3> U{0};
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Matrix<3, 1> sigma{0};
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Matrix<3, 3> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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// Reference: [16.848103352614, 1.068369514555, 0.0]
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(16.8481f, 1e-2f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.06837f, 1e-2f));
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// Third singular value should be ~0 (rank-deficient)
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REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
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// Check reconstruction
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Matrix<3, 3> recon{0};
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Matrix<3, 3> Usig{0};
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for (int i = 0; i < 3; i++)
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for (int j = 0; j < 3; j++)
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Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
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Usig.Mult(Vt, recon);
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float err = 0.0f;
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for (int i = 0; i < 3; i++)
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for (int j = 0; j < 3; j++) {
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float diff = recon.Get(i, j) - A.Get(i, j);
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err += diff * diff;
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}
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err = sqrtf(err);
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REQUIRE_THAT(err, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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std::cout << "SVD 3x3 rank-deficient:\n";
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std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
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<< sigma.Get(2, 0) << "]\n";
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}
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TEST_CASE("SVD Integration: tall 4x3 matrix", "[Matrix][SVD][Integration]") {
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Matrix<4, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
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Matrix<4, 3> U{0};
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Matrix<3, 1> sigma{0};
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Matrix<3, 3> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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// Reference: [25.462407436036, 1.290661675761, 0.0]
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(25.4624f, 1e-2f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.29066f, 1e-2f));
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REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
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// Check reconstruction
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Matrix<4, 3> recon{0};
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Matrix<4, 3> Usig{0};
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for (int i = 0; i < 4; i++)
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for (int j = 0; j < 3; j++)
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Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
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Usig.Mult(Vt, recon);
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float err = 0.0f;
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for (int i = 0; i < 4; i++)
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for (int j = 0; j < 3; j++) {
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float diff = recon.Get(i, j) - A.Get(i, j);
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err += diff * diff;
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}
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err = sqrtf(err);
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REQUIRE_THAT(err, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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std::cout << "SVD tall 4x3:\n";
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std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
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<< sigma.Get(2, 0) << "]\n";
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}
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TEST_CASE("SVD Integration: wide 3x5 matrix", "[Matrix][SVD][Integration]") {
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Matrix<3, 5> A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
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Matrix<3, 5> U{0};
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Matrix<5, 1> sigma{0}; // sigma is columns x 1 = 5x1 for wide matrix
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Matrix<5, 5> Vt{0}; // Vt is columns x columns = 5x5
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SVD::SVD(A, U, sigma, Vt);
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// Reference: [35.127223333575, 2.465396696917, 0.0]
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(35.1272f, 1e-2f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(2.46540f, 1e-2f));
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REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinAbs(0.0f, 1e-2f));
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// Check reconstruction: U (3x5) * diag(sigma) (5x3) = 3x3, then * Vt (3x5) =
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// 3x5
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Matrix<3, 5> recon{0};
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Matrix<3, 5> Usig{0};
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for (int i = 0; i < 3; i++)
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for (int j = 0; j < 5; j++)
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Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
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// For wide matrix: A = U * Sigma * Vt where U is 3x5, Sigma is 5x5
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// (diagonal), Vt is 5x5 But our implementation returns sigma as 3x1 and Vt as
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// 3x5 So we need: recon = Usig (3x5) * Vt (3x5)^T ... no that doesn't work
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// either The SVD for wide matrices is: A = U * Sigma * Vt where:
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// U is m×m (3×3), Sigma is m×n (3×5), Vt is n×n (5×5)
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// But our API returns U as m×n (3×5), sigma as n×1 (3×1), Vt as n×n (3×5)
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// So: recon = U (3x5) * diag(sigma) (5x5) * Vt (5x5)^T ...
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// Actually, looking at the implementation, for wide matrices we swap roles.
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// Let me just check reconstruction using the actual dimensions returned.
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// For wide matrix: A (3x5) = U (3x5) * diag(sigma) (5x5 padded) * Vt (5x5)
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// But our API returns Vt as 3x5, not 5x5
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// The implementation stores: U = QR[:,0:p]^T (3x5), sigma (3x1), Vt =
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// QL[:,0:p]^T (3x5) Reconstruction: A[i][j] = sum_k U[i][k]*sigma[k]*Vt[j][k]
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float err2 = 0.0f;
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 5; j++) {
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float recon_val = 0.0f;
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for (int k = 0; k < 3; k++) {
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recon_val += U.Get(i, k) * sigma.Get(k, 0) * Vt.Get(j, k);
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}
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float diff = recon_val - A.Get(i, j);
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err2 += diff * diff;
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}
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}
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err2 = sqrtf(err2);
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REQUIRE_THAT(err2, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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std::cout << "SVD wide 3x5:\n";
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std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0) << ", "
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<< sigma.Get(2, 0) << "]\n";
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}
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TEST_CASE("SVD Integration: identity 3x3", "[Matrix][SVD][Integration]") {
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Matrix<3, 3> A{1, 0, 0, 0, 1, 0, 0, 0, 1};
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Matrix<3, 3> U{0};
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Matrix<3, 1> sigma{0};
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Matrix<3, 3> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
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REQUIRE_THAT(sigma.Get(2, 0), Catch::Matchers::WithinRel(1.0f, 1e-3f));
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float err = frobeniusNorm(U - Matrix<3, 3>{1, 0, 0, 0, 1, 0, 0, 0, 1});
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REQUIRE_THAT(err, Catch::Matchers::WithinRel(0.0f, 1e-2f));
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}
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TEST_CASE("SVD Integration: symmetric positive definite 2x2 [[5,3],[3,5]]",
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"[Matrix][SVD][Integration]") {
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Matrix<2, 2> A{5, 3, 3, 5};
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Matrix<2, 2> U{0};
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Matrix<2, 1> sigma{0};
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Matrix<2, 2> Vt{0};
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SVD::SVD(A, U, sigma, Vt);
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// For SPD matrix, singular values = eigenvalues: [8, 2]
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REQUIRE_THAT(sigma.Get(0, 0), Catch::Matchers::WithinRel(8.0f, 1e-3f));
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REQUIRE_THAT(sigma.Get(1, 0), Catch::Matchers::WithinRel(2.0f, 1e-3f));
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// Check reconstruction
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Matrix<2, 2> recon{0};
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Matrix<2, 2> Usig{0};
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for (int i = 0; i < 2; i++)
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for (int j = 0; j < 2; j++)
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Usig[i][j] = U.Get(i, j) * sigma.Get(j, 0);
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Usig.Mult(Vt, recon);
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float err = 0.0f;
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for (int i = 0; i < 2; i++)
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for (int j = 0; j < 2; j++) {
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float diff = recon.Get(i, j) - A.Get(i, j);
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err += diff * diff;
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}
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err = sqrtf(err);
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REQUIRE_THAT(err, Catch::Matchers::WithinRel(0.0f, 1e-3f));
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std::cout << "SVD SPD 2x2 [[5,3],[3,5]]:\n";
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std::cout << "Sigma: [" << sigma.Get(0, 0) << ", " << sigma.Get(1, 0)
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<< "]\n";
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}
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