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 "testing/gtest/include/gtest/gtest.h"
9 #include "ui/gfx/geometry/matrix3_f.h"
10
11 namespace gfx {
12 namespace {
13
TEST(Matrix3fTest,Constructors)14 TEST(Matrix3fTest, Constructors) {
15 Matrix3F zeros = Matrix3F::Zeros();
16 Matrix3F ones = Matrix3F::Ones();
17 Matrix3F identity = Matrix3F::Identity();
18
19 Matrix3F product_ones = Matrix3F::FromOuterProduct(
20 Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(1.0f, 1.0f, 1.0f));
21 Matrix3F product_zeros = Matrix3F::FromOuterProduct(
22 Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(0.0f, 0.0f, 0.0f));
23 EXPECT_EQ(ones, product_ones);
24 EXPECT_EQ(zeros, product_zeros);
25
26 for (int i = 0; i < 3; ++i) {
27 for (int j = 0; j < 3; ++j)
28 EXPECT_EQ(i == j ? 1.0f : 0.0f, identity.get(i, j));
29 }
30 }
31
TEST(Matrix3fTest,DataAccess)32 TEST(Matrix3fTest, DataAccess) {
33 Matrix3F matrix = Matrix3F::Ones();
34 Matrix3F identity = Matrix3F::Identity();
35
36 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), identity.get_column(1));
37 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), identity.get_row(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 EXPECT_EQ(Vector3dF(6.0f, 7.0f, 8.0f), matrix.get_row(2));
41 matrix.set_column(0, Vector3dF(0.1f, 0.2f, 0.3f));
42 matrix.set_column(0, Vector3dF(0.1f, 0.2f, 0.3f));
43 EXPECT_EQ(Vector3dF(0.1f, 0.2f, 0.3f), matrix.get_column(0));
44 EXPECT_EQ(Vector3dF(0.1f, 1.0f, 2.0f), matrix.get_row(0));
45
46 EXPECT_EQ(0.1f, matrix.get(0, 0));
47 EXPECT_EQ(5.0f, matrix.get(1, 2));
48 }
49
TEST(Matrix3fTest,Determinant)50 TEST(Matrix3fTest, Determinant) {
51 EXPECT_EQ(1.0f, Matrix3F::Identity().Determinant());
52 EXPECT_EQ(0.0f, Matrix3F::Zeros().Determinant());
53 EXPECT_EQ(0.0f, Matrix3F::Ones().Determinant());
54
55 // Now for something non-trivial...
56 Matrix3F matrix = Matrix3F::Zeros();
57 matrix.set(0, 5, 6, 8, 7, 0, 1, 9, 0);
58 EXPECT_EQ(390.0f, matrix.Determinant());
59 matrix.set(2, 0, 3 * matrix.get(0, 0));
60 matrix.set(2, 1, 3 * matrix.get(0, 1));
61 matrix.set(2, 2, 3 * matrix.get(0, 2));
62 EXPECT_EQ(0, matrix.Determinant());
63
64 matrix.set(0.57f, 0.205f, 0.942f,
65 0.314f, 0.845f, 0.826f,
66 0.131f, 0.025f, 0.962f);
67 EXPECT_NEAR(0.3149f, matrix.Determinant(), 0.0001f);
68 }
69
TEST(Matrix3fTest,Inverse)70 TEST(Matrix3fTest, Inverse) {
71 Matrix3F identity = Matrix3F::Identity();
72 Matrix3F inv_identity = identity.Inverse();
73 EXPECT_EQ(identity, inv_identity);
74
75 Matrix3F singular = Matrix3F::Zeros();
76 singular.set(1.0f, 3.0f, 4.0f,
77 2.0f, 11.0f, 5.0f,
78 0.5f, 1.5f, 2.0f);
79 EXPECT_EQ(0, singular.Determinant());
80 EXPECT_EQ(Matrix3F::Zeros(), singular.Inverse());
81
82 Matrix3F regular = Matrix3F::Zeros();
83 regular.set(0.57f, 0.205f, 0.942f,
84 0.314f, 0.845f, 0.826f,
85 0.131f, 0.025f, 0.962f);
86 Matrix3F inv_regular = regular.Inverse();
87 regular.set(2.51540616f, -0.55138018f, -1.98968043f,
88 -0.61552266f, 1.34920184f, -0.55573636f,
89 -0.32653861f, 0.04002158f, 1.32488726f);
90 EXPECT_TRUE(regular.IsNear(inv_regular, 0.00001f));
91 }
92
TEST(Matrix3fTest,Transpose)93 TEST(Matrix3fTest, Transpose) {
94 Matrix3F matrix = Matrix3F::Zeros();
95
96 matrix.set(0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f);
97
98 Matrix3F transpose = matrix.Transpose();
99 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 2.0f), transpose.get_column(0));
100 EXPECT_EQ(Vector3dF(3.0f, 4.0f, 5.0f), transpose.get_column(1));
101 EXPECT_EQ(Vector3dF(6.0f, 7.0f, 8.0f), transpose.get_column(2));
102
103 EXPECT_TRUE(matrix.IsEqual(transpose.Transpose()));
104 }
105
TEST(Matrix3fTest,EigenvectorsIdentity)106 TEST(Matrix3fTest, EigenvectorsIdentity) {
107 // This block tests the trivial case of eigenvalues of the identity matrix.
108 Matrix3F identity = Matrix3F::Identity();
109 Vector3dF eigenvals = identity.SolveEigenproblem(NULL);
110 EXPECT_EQ(Vector3dF(1.0f, 1.0f, 1.0f), eigenvals);
111 }
112
TEST(Matrix3fTest,EigenvectorsDiagonal)113 TEST(Matrix3fTest, EigenvectorsDiagonal) {
114 // This block tests the another trivial case of eigenvalues of a diagonal
115 // matrix. Here we expect values to be sorted.
116 Matrix3F matrix = Matrix3F::Zeros();
117 matrix.set(0, 0, 1.0f);
118 matrix.set(1, 1, -2.5f);
119 matrix.set(2, 2, 3.14f);
120 Matrix3F eigenvectors = Matrix3F::Zeros();
121 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors);
122 EXPECT_EQ(Vector3dF(3.14f, 1.0f, -2.5f), eigenvals);
123
124 EXPECT_EQ(Vector3dF(0.0f, 0.0f, 1.0f), eigenvectors.get_column(0));
125 EXPECT_EQ(Vector3dF(1.0f, 0.0f, 0.0f), eigenvectors.get_column(1));
126 EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), eigenvectors.get_column(2));
127 }
128
TEST(Matrix3fTest,EigenvectorsNiceNotPositive)129 TEST(Matrix3fTest, EigenvectorsNiceNotPositive) {
130 // This block tests computation of eigenvectors of a matrix where nice
131 // round values are expected.
132 Matrix3F matrix = Matrix3F::Zeros();
133 // This is not a positive-definite matrix but eigenvalues and the first
134 // eigenvector should nonetheless be computed correctly.
135 matrix.set(3, 2, 4, 2, 0, 2, 4, 2, 3);
136 Matrix3F eigenvectors = Matrix3F::Zeros();
137 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors);
138 EXPECT_EQ(Vector3dF(8.0f, -1.0f, -1.0f), eigenvals);
139
140 Vector3dF expected_principal(0.66666667f, 0.33333333f, 0.66666667f);
141 EXPECT_NEAR(0.0f,
142 (expected_principal - eigenvectors.get_column(0)).Length(),
143 0.000001f);
144 }
145
TEST(Matrix3fTest,EigenvectorsPositiveDefinite)146 TEST(Matrix3fTest, EigenvectorsPositiveDefinite) {
147 // This block tests computation of eigenvectors of a matrix where output
148 // is not as nice as above, but it actually meets the definition.
149 Matrix3F matrix = Matrix3F::Zeros();
150 Matrix3F eigenvectors = Matrix3F::Zeros();
151 Matrix3F expected_eigenvectors = Matrix3F::Zeros();
152 matrix.set(1, -1, 2, -1, 4, 5, 2, 5, 0);
153 Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors);
154 Vector3dF expected_eigv(7.3996266f, 1.91197255f, -4.31159915f);
155 expected_eigv -= eigenvals;
156 EXPECT_NEAR(0, expected_eigv.LengthSquared(), 0.00001f);
157 expected_eigenvectors.set(0.04926317f, -0.92135662f, -0.38558414f,
158 0.82134249f, 0.25703273f, -0.50924521f,
159 0.56830419f, -0.2916096f, 0.76941158f);
160 EXPECT_TRUE(expected_eigenvectors.IsNear(eigenvectors, 0.00001f));
161 }
162
TEST(Matrix3fTest,Operators)163 TEST(Matrix3fTest, Operators) {
164 Matrix3F matrix1 = Matrix3F::Zeros();
165 matrix1.set(1, 2, 3, 4, 5, 6, 7, 8, 9);
166 EXPECT_EQ(matrix1 + Matrix3F::Zeros(), matrix1);
167
168 Matrix3F matrix2 = Matrix3F::Zeros();
169 matrix2.set(-1, -2, -3, -4, -5, -6, -7, -8, -9);
170 EXPECT_EQ(matrix1 + matrix2, Matrix3F::Zeros());
171
172 EXPECT_EQ(Matrix3F::Zeros() - matrix1, matrix2);
173
174 Matrix3F result = Matrix3F::Zeros();
175 result.set(2, 4, 6, 8, 10, 12, 14, 16, 18);
176 EXPECT_EQ(matrix1 - matrix2, result);
177 result.set(-2, -4, -6, -8, -10, -12, -14, -16, -18);
178 EXPECT_EQ(matrix2 - matrix1, result);
179 }
180
181 } // namespace
182 } // namespace gfx
183