New Matrix3F class added in gfx.

ui/gfx/matrix3_unittest.cc

+// Copyright (c) 2013 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <cmath>
+#include <limits>
+
+#include "base/basictypes.h"
+#include "testing/gtest/include/gtest/gtest.h"
+#include "ui/gfx/matrix3_f.h"
+
+namespace gfx {
+namespace {
+
+TEST(Matrix3fTest, Constructors) {
+  Matrix3F zeros = Matrix3F::Zeros();
+  Matrix3F ones = Matrix3F::Ones();
+  Matrix3F identity = Matrix3F::Identity();
+
+  Matrix3F product_ones = Matrix3F::FromOuterProduct(
+      Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(1.0f, 1.0f, 1.0f));
+  Matrix3F product_zeros = Matrix3F::FromOuterProduct(
+      Vector3dF(1.0f, 1.0f, 1.0f), Vector3dF(0.0f, 0.0f, 0.0f));
+  EXPECT_EQ(ones, product_ones);
+  EXPECT_EQ(zeros, product_zeros);
+
+  for (int i = 0; i < 3; ++i) {
+    for (int j = 0; j < 3; ++j)
+      EXPECT_EQ(i == j ? 1.0f : 0.0f, identity.get(i, j));
+  }
+}
+
+TEST(Matrix3fTest, DataAccess) {
+  Matrix3F matrix = Matrix3F::Ones();
+  Matrix3F identity = Matrix3F::Identity();
+
+  EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), identity.get_column(1));
+  matrix.set(0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f);
+  EXPECT_EQ(Vector3dF(2.0f, 5.0f, 8.0f), matrix.get_column(2));
+  matrix.set_column(0, Vector3dF(0.1f, 0.2f, 0.3f));
+  EXPECT_EQ(Vector3dF(0.1f, 0.2f, 0.3f), matrix.get_column(0));
+
+  EXPECT_EQ(0.1f, matrix.get(0, 0));
+  EXPECT_EQ(5.0f, matrix.get(1, 2));
+}
+
+TEST(Matrix3fTest, Determinant) {
+  EXPECT_EQ(1.0f, Matrix3F::Identity().Determinant());
+  EXPECT_EQ(0.0f, Matrix3F::Zeros().Determinant());
+  EXPECT_EQ(0.0f, Matrix3F::Ones().Determinant());
+
+  // Now for something non-trivial...
+  Matrix3F matrix = Matrix3F::Zeros();
+  matrix.set(0, 5, 6, 8, 7, 0, 1, 9, 0);
+  EXPECT_EQ(390.0f, matrix.Determinant());
+  matrix.set(2, 0, 3 * matrix.get(0, 0));
+  matrix.set(2, 1, 3 * matrix.get(0, 1));
+  matrix.set(2, 2, 3 * matrix.get(0, 2));
+  EXPECT_EQ(0, matrix.Determinant());
+
+  matrix.set(0.57f,  0.205f,  0.942f,
+             0.314f,  0.845f,  0.826f,
+             0.131f,  0.025f,  0.962f);
+  EXPECT_NEAR(0.3149f, matrix.Determinant(), 0.0001f);
+}
+
+TEST(Matrix3fTest, Inverse) {
+  Matrix3F identity = Matrix3F::Identity();
+  Matrix3F inv_identity = identity.Inverse();
+  EXPECT_EQ(identity, inv_identity);
+
+  Matrix3F singular = Matrix3F::Zeros();
+  singular.set(1.0f, 3.0f, 4.0f,
+               2.0f, 11.0f, 5.0f,
+               0.5f, 1.5f, 2.0f);
+  EXPECT_EQ(0, singular.Determinant());
+  EXPECT_EQ(Matrix3F::Zeros(), singular.Inverse());
+
+  Matrix3F regular = Matrix3F::Zeros();
+  regular.set(0.57f,  0.205f,  0.942f,
+              0.314f,  0.845f,  0.826f,
+              0.131f,  0.025f,  0.962f);
+  Matrix3F inv_regular = regular.Inverse();
+  regular.set(2.51540616f, -0.55138018f, -1.98968043f,
+              -0.61552266f,  1.34920184f, -0.55573636f,
+              -0.32653861f,  0.04002158f,  1.32488726f);
+  EXPECT_TRUE(regular.IsNear(inv_regular, 0.00001f));
+}
+
+TEST(Matrix3fTest, EigenvectorsIdentity) {
+  // This block tests the trivial case of eigenvalues of the identity matrix.
+  Matrix3F identity = Matrix3F::Identity();
+  Vector3dF eigenvals = identity.SolveEigenproblem(NULL);
+  EXPECT_EQ(Vector3dF(1.0f, 1.0f, 1.0f), eigenvals);
+}
+
+TEST(Matrix3fTest, EigenvectorsDiagonal)  {
+  // This block tests the another trivial case of eigenvalues of a diagonal
+  // matrix. Here we expect values to be sorted.
+  Matrix3F matrix = Matrix3F::Zeros();
+  matrix.set(0, 0, 1.0f);
+  matrix.set(1, 1, -2.5f);
+  matrix.set(2, 2, 3.14f);
+  Matrix3F eigenvectors = Matrix3F::Zeros();
+  Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors);
+  EXPECT_EQ(Vector3dF(3.14f, 1.0f, -2.5f), eigenvals);
+
+  EXPECT_EQ(Vector3dF(0.0f, 0.0f, 1.0f), eigenvectors.get_column(0));
+  EXPECT_EQ(Vector3dF(1.0f, 0.0f, 0.0f), eigenvectors.get_column(1));
+  EXPECT_EQ(Vector3dF(0.0f, 1.0f, 0.0f), eigenvectors.get_column(2));
+}
+
+TEST(Matrix3fTest, EigenvectorsNiceNotPositive)  {
+  // This block tests computation of eigenvectors of a matrix where nice
+  // round values are expected.
+  Matrix3F matrix = Matrix3F::Zeros();
+  // This is not a positive-definite matrix but eigenvalues and the first
+  // eigenvector should nonetheless be computed correctly.
+  matrix.set(3, 2, 4, 2, 0, 2, 4, 2, 3);
+  Matrix3F eigenvectors = Matrix3F::Zeros();
+  Vector3dF eigenvals = matrix.SolveEigenproblem(&eigenvectors);
+  EXPECT_EQ(Vector3dF(8.0f, -1.0f, -1.0f), eigenvals);
+
+  Vector3dF expected_principal(0.66666667f, 0.33333333f, 0.66666667f);
+  EXPECT_NEAR(0.0f,
+              (expected_principal - eigenvectors.get_column(0)).Length(),
+              0.000001f);
+}
+
+TEST(Matrix3fTest, EigenvectorsPositiveDefinite) {
+  // This block tests computation of eigenvectors of a matrix where output
+  // is not as nice as above, but it actually meets the definition.
+  Matrix3F matrix = Matrix3F::Zeros();
+  Matrix3F eigenvectors = Matrix3F::Zeros();
+  Matrix3F expected_eigenvectors = Matrix3F::Zeros();
+  matrix.set(1, -1,  2, -1,  4,  5, 2,  5,  0);
+  Vector3dF eigenvals =  matrix.SolveEigenproblem(&eigenvectors);
+  Vector3dF expected_eigv(7.3996266f, 1.91197255f, -4.31159915f);
+  expected_eigv -= eigenvals;
+  EXPECT_NEAR(0, expected_eigv.LengthSquared(), 0.00001f);
+  expected_eigenvectors.set(0.04926317f, -0.92135662f, -0.38558414f,
+                            0.82134249f, 0.25703273f, -0.50924521f,
+                            0.56830419f, -0.2916096f, 0.76941158f);
+  EXPECT_TRUE(expected_eigenvectors.IsNear(eigenvectors, 0.00001f));
+}
+
+}
+}