New Matrix3F class added in gfx.

ui/gfx/matrix3_unittest.cc

+// Copyright (c) 2012 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 "base/memory/scoped_ptr.h"
+#include "testing/gtest/include/gtest/gtest.h"
+#include "ui/gfx/matrix3_f.h"
+
+using gfx::Matrix3F;
+
+TEST(Matrix3fTest, Constructors) {
+  Matrix3F zeros = Matrix3F::Zeros();
+  Matrix3F ones = Matrix3F::Ones();
+  Matrix3F identity = Matrix3F::Identity();
+
+  Matrix3F product_ones(Matrix3F::VectorType(1.0f, 1.0f, 1.0f),
+                        Matrix3F::VectorType(1.0f, 1.0f, 1.0f));
+  Matrix3F product_zeros(Matrix3F::VectorType(1.0f, 1.0f, 1.0f),
+                         Matrix3F::VectorType(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 ? 1.0 : 0.0, identity.get(i, j));
+  }
+}
+
+TEST(Matrix3fTest, DataAccess) {
+  Matrix3F matrix = Matrix3F::Ones();
+  Matrix3F identity = Matrix3F::Identity();
+
+  EXPECT_EQ(Matrix3F::VectorType(0.0, 1.0, 0.0), identity.GetColumn(1));
+  matrix.set(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0);
+  EXPECT_EQ(Matrix3F::VectorType(2.0, 5.0, 8.0), matrix.GetColumn(2));
+  matrix.SetColumn(0, Matrix3F::VectorType(0.1, 0.2, 0.3));
+  EXPECT_EQ(Matrix3F::VectorType(0.1, 0.2, 0.3), matrix.GetColumn(0));
+
+  EXPECT_EQ(0.1f, matrix.get(0, 0));
+  EXPECT_EQ(5.0f, matrix.get(1, 2));
+}
+
+TEST(Matrix3fTest, Determinant) {
+  EXPECT_EQ(1.0, Matrix3F::Identity().Determinant());
+  EXPECT_EQ(0.0, Matrix3F::Zeros().Determinant());
+  EXPECT_EQ(0.0, 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(390.0, 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(0.57 ,  0.205,  0.942,
+             0.314,  0.845,  0.826,
+             0.131,  0.025,  0.962);
+  EXPECT_NEAR(0.3149, matrix.Determinant(), 0.0001);
+}
+
+TEST(Matrix3fTest, Inverse) {
+  Matrix3F identity = Matrix3F::Identity();
+  Matrix3F inv_identity = identity.Inverse();
+  EXPECT_EQ(identity, inv_identity);
+
+  Matrix3F singular = Matrix3F::Zeros();
+  singular.set(1.0, 3.0, 4.0,
+               2.0, 11.0, 5.0,
+               0.5, 1.5, 2.0);
+  EXPECT_EQ(0, singular.Determinant());
+  EXPECT_EQ(Matrix3F::Zeros(), singular.Inverse());
+
+  Matrix3F regular = Matrix3F::Zeros();
+  regular.set(0.57 ,  0.205,  0.942,
+              0.314,  0.845,  0.826,
+              0.131,  0.025,  0.962);
+  Matrix3F inv_regular = regular.Inverse();
+  regular.set(2.51540616, -0.55138018, -1.98968043,
+              -0.61552266,  1.34920184, -0.55573636,
+              -0.32653861,  0.04002158,  1.32488726);
+  EXPECT_TRUE(regular.IsNear(inv_regular, 0.0001));
+}
+
+TEST(Matrix3fTest, EigenvectorsIdentity) {
+  // This block tests the trivial case of eigenvalues of the identity matrix.
+  Matrix3F identity = Matrix3F::Identity();
+  Matrix3F::VectorType eigenvals = identity.SolveEigenproblem(NULL);
+  EXPECT_EQ(Matrix3F::VectorType(1.0, 1.0, 1.0), 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, 1.0);
+  matrix.set(1, 1, -2.5);
+  matrix.set(2, 2, 3.14);
+  Matrix3F eigenvectors = Matrix3F::Zeros();
+  Matrix3F::VectorType eigenvals = matrix.SolveEigenproblem(&eigenvectors);
+  EXPECT_EQ(Matrix3F::VectorType(3.14, 1.0, -2.5), eigenvals);
+
+  EXPECT_EQ(Matrix3F::VectorType(0.0, 0.0, 1.0), eigenvectors.GetColumn(0));
+  EXPECT_EQ(Matrix3F::VectorType(1.0, 0.0, 0.0), eigenvectors.GetColumn(1));
+  EXPECT_EQ(Matrix3F::VectorType(0.0, 1.0, 0.0), eigenvectors.GetColumn(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();
+  Matrix3F::VectorType eigenvals = matrix.SolveEigenproblem(&eigenvectors);
+  EXPECT_EQ(Matrix3F::VectorType(8.0, -1.0, -1.0), eigenvals);
+
+  Matrix3F::VectorType expected_principal(0.66666667, 0.33333333, 0.66666667);
+  EXPECT_NEAR(0.0,
+              (expected_principal - eigenvectors.GetColumn(0)).Length(),
+              0.000001);
+}
+
+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);
+  Matrix3F::VectorType eigenvals =  matrix.SolveEigenproblem(&eigenvectors);
+  Matrix3F::VectorType expected_eigv(7.3996266, 1.91197255, -4.31159915);
+  expected_eigv -= eigenvals;
+  EXPECT_NEAR(0.0, expected_eigv.LengthSquared(), 0.00001);
+  expected_eigenvectors.set(0.04926317, -0.92135662, -0.38558414,
+                            0.82134249, 0.25703273, -0.50924521,
+                            0.56830419, -0.2916096, 0.76941158);
+  EXPECT_TRUE(expected_eigenvectors.IsNear(eigenvectors, 0.00001));
+}