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enc_linalg_test.cc (2519B)

      1 // Copyright (c) the JPEG XL Project Authors. All rights reserved.
      2 //
      3 // Use of this source code is governed by a BSD-style
      4 // license that can be found in the LICENSE file.
      5 
      6 #include "lib/jxl/enc_linalg.h"
      7 
      8 #include <cstddef>
      9 
     10 #include "lib/jxl/base/random.h"
     11 #include "lib/jxl/testing.h"
     12 
     13 namespace jxl {
     14 namespace {
     15 
     16 Matrix2x2 Diagonal(const Vector2& d) { return {{{d[0], 0.0}, {0.0, d[1]}}}; }
     17 
     18 Matrix2x2 Identity() { return Diagonal({1.0, 1.0}); }
     19 
     20 Matrix2x2 MatMul(const Matrix2x2& A, const Matrix2x2& B) {
     21  Matrix2x2 out;
     22  for (size_t y = 0; y < 2; ++y) {
     23    for (size_t x = 0; x < 2; ++x) {
     24      out[y][x] = A[0][x] * B[y][0] + A[1][x] * B[y][1];
     25    }
     26  }
     27  return out;
     28 }
     29 
     30 Matrix2x2 Transpose(const Matrix2x2& A) {
     31  return {{{A[0][0], A[1][0]}, {A[0][1], A[1][1]}}};
     32 }
     33 
     34 Matrix2x2 RandomSymmetricMatrix(Rng& rng, const double vmin,
     35                                const double vmax) {
     36  Matrix2x2 A;
     37  A[0][0] = rng.UniformF(vmin, vmax);
     38  A[0][1] = A[1][0] = rng.UniformF(vmin, vmax);
     39  A[1][1] = rng.UniformF(vmin, vmax);
     40  return A;
     41 }
     42 
     43 void VerifyMatrixEqual(const Matrix2x2& A, const Matrix2x2& B,
     44                       const double eps) {
     45  for (size_t y = 0; y < 2; ++y) {
     46    for (size_t x = 0; x < 2; ++x) {
     47      ASSERT_NEAR(A[y][x], B[y][x], eps);
     48    }
     49  }
     50 }
     51 
     52 void VerifyOrthogonal(const Matrix2x2& A, const double eps) {
     53  VerifyMatrixEqual(Identity(), MatMul(Transpose(A), A), eps);
     54 }
     55 
     56 TEST(LinAlgTest, ConvertToDiagonal) {
     57  {
     58    Matrix2x2 I = Identity();
     59    Matrix2x2 U;
     60    Vector2 d;
     61    ConvertToDiagonal(I, d, U);
     62    VerifyMatrixEqual(I, U, 1e-15);
     63    for (size_t k = 0; k < 2; ++k) {
     64      ASSERT_NEAR(d[k], 1.0, 1e-15);
     65    }
     66  }
     67  {
     68    Matrix2x2 A = Identity();
     69    A[0][1] = A[1][0] = 2.0;
     70    Matrix2x2 U;
     71    Vector2 d;
     72    ConvertToDiagonal(A, d, U);
     73    VerifyOrthogonal(U, 1e-12);
     74    VerifyMatrixEqual(A, MatMul(U, MatMul(Diagonal(d), Transpose(U))), 1e-12);
     75  }
     76  {
     77    Matrix2x2 A;
     78    A[0] = {0.000208649, 1.13687e-12};
     79    A[1] = {1.13687e-12, 0.000208649};
     80    Matrix2x2 U;
     81    Vector2 d;
     82    ConvertToDiagonal(A, d, U);
     83    VerifyOrthogonal(U, 1e-12);
     84    VerifyMatrixEqual(A, MatMul(U, MatMul(Diagonal(d), Transpose(U))), 1e-11);
     85  }
     86  Rng rng(0);
     87  for (size_t i = 0; i < 1000000; ++i) {
     88    Matrix2x2 A = RandomSymmetricMatrix(rng, -1.0, 1.0);
     89    Matrix2x2 U;
     90    Vector2 d;
     91    ConvertToDiagonal(A, d, U);
     92    VerifyOrthogonal(U, 1e-12);
     93    VerifyMatrixEqual(A, MatMul(U, MatMul(Diagonal(d), Transpose(U))), 5e-10);
     94  }
     95 }
     96 
     97 }  // namespace
     98 }  // namespace jxl