1 // Copyright (c) 2013 The Chromium Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style license that can be 3 // found in the LICENSE file. 4 5 #include <cmath> 6 #include <limits> 7 8 #include "base/basictypes.h" 9 #include "testing/gtest/include/gtest/gtest.h" 10 #include "ui/gfx/geometry/matrix3_f.h" 11 12 namespace gfx { 13 namespace { 14 15 TEST(Matrix3fTest, Constructors) { 16 Matrix3F zeros = Matrix3F::Zeros(); 17 Matrix3F ones = Matrix3F::Ones(); 18 Matrix3F identity = Matrix3F::Identity(); 19 20 Matrix3F product_ones = Matrix3F::FromOuterProduct( 21 Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(1.0f, 1.0f, 1.0f)); 22 Matrix3F product_zeros = Matrix3F::FromOuterProduct( 23 Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(0.0f, 0.0f, 0.0f)); 24 EXPECT_EQ(ones, product_ones); 25 EXPECT_EQ(zeros, product_zeros); 26 27 for (int i = 0; i < 3; ++i) { 28 for (int j = 0; j < 3; ++j) 29 EXPECT_EQ(i == j ? 1.0f : 0.0f, identity.get(i, j)); 30 } 31 } 32 33 TEST(Matrix3fTest, DataAccess) { 34 Matrix3F matrix = Matrix3F::Ones(); 35 Matrix3F identity = Matrix3F::Identity(); 36 37 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), identity.get_column(1)); 38 matrix.set(0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f); 39 EXPECT_EQ(Vector3dF(2.0f, 5.0f, 8.0f), matrix.get_column(2)); 40 matrix.set_column(0, Vector3dF(0.1f, 0.2f, 0.3f)); 41 EXPECT_EQ(Vector3dF(0.1f, 0.2f, 0.3f), matrix.get_column(0)); 42 43 EXPECT_EQ(0.1f, matrix.get(0, 0)); 44 EXPECT_EQ(5.0f, matrix.get(1, 2)); 45 } 46 47 TEST(Matrix3fTest, Determinant) { 48 EXPECT_EQ(1.0f, Matrix3F::Identity().Determinant()); 49 EXPECT_EQ(0.0f, Matrix3F::Zeros().Determinant()); 50 EXPECT_EQ(0.0f, Matrix3F::Ones().Determinant()); 51 52 // Now for something non-trivial... 53 Matrix3F matrix = Matrix3F::Zeros(); 54 matrix.set(0, 5, 6, 8, 7, 0, 1, 9, 0); 55 EXPECT_EQ(390.0f, matrix.Determinant()); 56 matrix.set(2, 0, 3 * matrix.get(0, 0)); 57 matrix.set(2, 1, 3 * matrix.get(0, 1)); 58 matrix.set(2, 2, 3 * matrix.get(0, 2)); 59 EXPECT_EQ(0, matrix.Determinant()); 60 61 matrix.set(0.57f, 0.205f, 0.942f, 62 0.314f, 0.845f, 0.826f, 63 0.131f, 0.025f, 0.962f); 64 EXPECT_NEAR(0.3149f, matrix.Determinant(), 0.0001f); 65 } 66 67 TEST(Matrix3fTest, Inverse) { 68 Matrix3F identity = Matrix3F::Identity(); 69 Matrix3F inv_identity = identity.Inverse(); 70 EXPECT_EQ(identity, inv_identity); 71 72 Matrix3F singular = Matrix3F::Zeros(); 73 singular.set(1.0f, 3.0f, 4.0f, 74 2.0f, 11.0f, 5.0f, 75 0.5f, 1.5f, 2.0f); 76 EXPECT_EQ(0, singular.Determinant()); 77 EXPECT_EQ(Matrix3F::Zeros(), singular.Inverse()); 78 79 Matrix3F regular = Matrix3F::Zeros(); 80 regular.set(0.57f, 0.205f, 0.942f, 81 0.314f, 0.845f, 0.826f, 82 0.131f, 0.025f, 0.962f); 83 Matrix3F inv_regular = regular.Inverse(); 84 regular.set(2.51540616f, -0.55138018f, -1.98968043f, 85 -0.61552266f, 1.34920184f, -0.55573636f, 86 -0.32653861f, 0.04002158f, 1.32488726f); 87 EXPECT_TRUE(regular.IsNear(inv_regular, 0.00001f)); 88 } 89 90 TEST(Matrix3fTest, EigenvectorsIdentity) { 91 // This block tests the trivial case of eigenvalues of the identity matrix. 92 Matrix3F identity = Matrix3F::Identity(); 93 Vector3dF eigenvals = identity.SolveEigenproblem(NULL); 94 EXPECT_EQ(Vector3dF(1.0f, 1.0f, 1.0f), eigenvals); 95 } 96 97 TEST(Matrix3fTest, EigenvectorsDiagonal) { 98 // This block tests the another trivial case of eigenvalues of a diagonal 99 // matrix. Here we expect values to be sorted. 100 Matrix3F matrix = Matrix3F::Zeros(); 101 matrix.set(0, 0, 1.0f); 102 matrix.set(1, 1, -2.5f); 103 matrix.set(2, 2, 3.14f); 104 Matrix3F eigenvectors = Matrix3F::Zeros(); 105 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors); 106 EXPECT_EQ(Vector3dF(3.14f, 1.0f, -2.5f), eigenvals); 107 108 EXPECT_EQ(Vector3dF(0.0f, 0.0f, 1.0f), eigenvectors.get_column(0)); 109 EXPECT_EQ(Vector3dF(1.0f, 0.0f, 0.0f), eigenvectors.get_column(1)); 110 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), eigenvectors.get_column(2)); 111 } 112 113 TEST(Matrix3fTest, EigenvectorsNiceNotPositive) { 114 // This block tests computation of eigenvectors of a matrix where nice 115 // round values are expected. 116 Matrix3F matrix = Matrix3F::Zeros(); 117 // This is not a positive-definite matrix but eigenvalues and the first 118 // eigenvector should nonetheless be computed correctly. 119 matrix.set(3, 2, 4, 2, 0, 2, 4, 2, 3); 120 Matrix3F eigenvectors = Matrix3F::Zeros(); 121 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors); 122 EXPECT_EQ(Vector3dF(8.0f, -1.0f, -1.0f), eigenvals); 123 124 Vector3dF expected_principal(0.66666667f, 0.33333333f, 0.66666667f); 125 EXPECT_NEAR(0.0f, 126 (expected_principal - eigenvectors.get_column(0)).Length(), 127 0.000001f); 128 } 129 130 TEST(Matrix3fTest, EigenvectorsPositiveDefinite) { 131 // This block tests computation of eigenvectors of a matrix where output 132 // is not as nice as above, but it actually meets the definition. 133 Matrix3F matrix = Matrix3F::Zeros(); 134 Matrix3F eigenvectors = Matrix3F::Zeros(); 135 Matrix3F expected_eigenvectors = Matrix3F::Zeros(); 136 matrix.set(1, -1, 2, -1, 4, 5, 2, 5, 0); 137 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors); 138 Vector3dF expected_eigv(7.3996266f, 1.91197255f, -4.31159915f); 139 expected_eigv -= eigenvals; 140 EXPECT_NEAR(0, expected_eigv.LengthSquared(), 0.00001f); 141 expected_eigenvectors.set(0.04926317f, -0.92135662f, -0.38558414f, 142 0.82134249f, 0.25703273f, -0.50924521f, 143 0.56830419f, -0.2916096f, 0.76941158f); 144 EXPECT_TRUE(expected_eigenvectors.IsNear(eigenvectors, 0.00001f)); 145 } 146 147 } 148 } 149
