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/*
Copyright 2018 Google Inc. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS-IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
#include "utils/pseudoinverse.h"
#include "third_party/googletest/googletest/include/gtest/gtest.h"
#include "base/constants_and_types.h"
namespace vraudio {
namespace {
// Tests that the pseudoinverse of an invertible square matrix is equal to the
// inverse of that matrix.
TEST(PseudoinverseTest, SquareInverse) {
Eigen::Matrix<double, 5, 5> invertible_matrix;
invertible_matrix << 0.8478, 0.1676, 0.1961, 0.2654, 0.7662, 0.0279, 0.5309,
0.2043, 0.4947, 0.0918, 0.1367, 0.4714, 0.7113, 0.246, 0.8048, 0.9617,
0.4378, 0.0259, 0.536, 0.9565, 0.1541, 0.6275, 0.8471, 0.1133, 0.8074;
ASSERT_NE(0.0, invertible_matrix.determinant());
auto pseudoinverse = Pseudoinverse(invertible_matrix);
auto inverse = invertible_matrix.inverse();
EXPECT_TRUE(pseudoinverse.isApprox(inverse, kEpsilonDouble))
<< "Pseudoinverse: \n"
<< pseudoinverse << " should be within " << kEpsilonDouble
<< " of inverse: \n"
<< inverse;
}
// Tests that the pseudoinverse of a full-rank matrix with more rows than
// columns works successfully.
TEST(PseudoinverseTest, PseudoinverseMoreRows) {
Eigen::Matrix<double, 5, 4> invertible_matrix;
invertible_matrix << 0.8478, 0.1676, 0.1961, 0.2654, 0.0279, 0.5309, 0.2043,
0.4947, 0.1367, 0.4714, 0.7113, 0.246, 0.9617, 0.4378, 0.0259, 0.536,
0.1541, 0.6275, 0.8471, 0.1133;
auto pseudoinverse = Pseudoinverse(invertible_matrix);
auto should_be_identity = pseudoinverse * invertible_matrix;
EXPECT_TRUE(should_be_identity.isApprox(
decltype(should_be_identity)::Identity(should_be_identity.rows(),
should_be_identity.cols()),
kEpsilonDouble))
<< "Matrix should be within " << kEpsilonDouble
<< " of an identity matrix: \n"
<< should_be_identity;
}
// Tests that the pseudoinverse of a full-rank matrix with more columns than
// rows works successfully.
TEST(PseudoinverseTest, PseudoinverseMoreColumns) {
Eigen::Matrix<double, 4, 5> invertible_matrix;
invertible_matrix << 0.8478, 0.1676, 0.1961, 0.2654, 0.7662, 0.0279, 0.5309,
0.2043, 0.4947, 0.0918, 0.1367, 0.4714, 0.7113, 0.246, 0.8048, 0.9617,
0.4378, 0.0259, 0.536, 0.9565;
auto pseudoinverse = Pseudoinverse(invertible_matrix);
auto should_be_identity = invertible_matrix * pseudoinverse;
EXPECT_TRUE(should_be_identity.isApprox(
decltype(should_be_identity)::Identity(should_be_identity.rows(),
should_be_identity.cols()),
kEpsilonDouble))
<< "Matrix should be within " << kEpsilonDouble
<< " of an identity matrix: \n"
<< should_be_identity;
}
} // namespace
} // namespace vraudio
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