Add InvertPSDMatrix.
This helper function lets the user compute the inverse or
the pseudo-inverse of a matrix.
Change-Id: Ia257859ad901debce2ea19f47907faf0b7b94759
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index 7c42442..5b6e99c 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -330,6 +330,7 @@
ceres_test(graph_algorithms)
ceres_test(householder_vector)
ceres_test(is_close)
+ ceres_test(invert_psd_matrix)
ceres_test(implicit_schur_complement)
ceres_test(iterative_schur_complement_solver)
ceres_test(jet)
diff --git a/internal/ceres/invert_psd_matrix.h b/internal/ceres/invert_psd_matrix.h
new file mode 100644
index 0000000..34daf88
--- /dev/null
+++ b/internal/ceres/invert_psd_matrix.h
@@ -0,0 +1,79 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2017 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#ifndef CERES_INTERNAL_INVERT_PSD_MATRIX_H_
+#define CERES_INTERNAL_INVERT_PSD_MATRIX_H_
+
+#include "ceres/internal/eigen.h"
+#include "glog/logging.h"
+#include "Eigen/Dense"
+
+namespace ceres {
+namespace internal {
+
+// Helper routine to compute the inverse or pseudo-inverse of a
+// symmetric positive semi-definite matrix.
+//
+// assume_full_rank controls whether a Cholesky factorization or an
+// Singular Value Decomposition is used to compute the inverse and the
+// pseudo-inverse respectively.
+//
+// The template parameter kSize can either be Eigen::Dynamic or a
+// positive integer equal to the number of rows of m.
+template <int kSize>
+typename EigenTypes<kSize, kSize>::Matrix InvertPSDMatrix(
+ const bool assume_full_rank,
+ const typename EigenTypes<kSize, kSize>::Matrix& m) {
+ const int size = m.rows();
+
+ // If the matrix can be assumed to be full rank, then just use the
+ // Cholesky factorization to invert it.
+ if (assume_full_rank) {
+ return m.template selfadjointView<Eigen::Upper>().llt().solve(
+ Matrix::Identity(size, size));
+ }
+
+ Eigen::JacobiSVD<typename EigenTypes<kSize, kSize>::Matrix> svd(
+ m, Eigen::ComputeThinU | Eigen::ComputeThinV);
+ const double tolerance =
+ std::numeric_limits<double>::epsilon() * size * svd.singularValues()(0);
+
+ return svd.matrixV() *
+ (svd.singularValues().array() > tolerance)
+ .select(svd.singularValues().array().inverse(), 0)
+ .matrix()
+ .asDiagonal() *
+ svd.matrixU().adjoint();
+}
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_INVERT_PSD_MATRIX_H_
diff --git a/internal/ceres/invert_psd_matrix_test.cc b/internal/ceres/invert_psd_matrix_test.cc
new file mode 100644
index 0000000..5da9c11
--- /dev/null
+++ b/internal/ceres/invert_psd_matrix_test.cc
@@ -0,0 +1,86 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2017 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/invert_psd_matrix.h"
+
+#include "ceres/internal/eigen.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+static const bool kFullRank = true;
+static const bool kRankDeficient = false;
+
+template <int kSize>
+typename EigenTypes<kSize, kSize>::Matrix RandomPSDMatrixWithEigenValues(
+ const typename EigenTypes<kSize>::Vector& eigenvalues) {
+ typename EigenTypes<kSize, kSize>::Matrix m;
+ m.setRandom();
+ Eigen::SelfAdjointEigenSolver<typename EigenTypes<kSize, kSize>::Matrix> es(
+ m);
+ return es.eigenvectors() * eigenvalues.asDiagonal() *
+ es.eigenvectors().transpose();
+}
+
+TEST(InvertPSDMatrix, Identity3x3) {
+ const Matrix m = Matrix::Identity(3, 3);
+ const Matrix inverse_m = InvertPSDMatrix<3>(kFullRank, m);
+ EXPECT_NEAR((inverse_m - m).norm() / m.norm(),
+ 0.0,
+ std::numeric_limits<double>::epsilon());
+}
+
+TEST(InvertPSDMatrix, FullRank5x5) {
+ EigenTypes<5>::Vector eigenvalues;
+ eigenvalues.setRandom();
+ eigenvalues = eigenvalues.array().abs().matrix();
+ const Matrix m = RandomPSDMatrixWithEigenValues<5>(eigenvalues);
+ const Matrix inverse_m = InvertPSDMatrix<5>(kFullRank, m);
+ EXPECT_NEAR((m * inverse_m - Matrix::Identity(5,5)).norm() / 5.0, 0.0,
+ std::numeric_limits<double>::epsilon());
+}
+
+TEST(InvertPSDMatrix, RankDeficient5x5) {
+ EigenTypes<5>::Vector eigenvalues;
+ eigenvalues.setRandom();
+ eigenvalues = eigenvalues.array().abs().matrix();
+ eigenvalues(3) = 0.0;
+ const Matrix m = RandomPSDMatrixWithEigenValues<5>(eigenvalues);
+ const Matrix inverse_m = InvertPSDMatrix<5>(kRankDeficient, m);
+ Matrix pseudo_identity = Matrix::Identity(5, 5);
+ pseudo_identity(3, 3) = 0.0;
+ EXPECT_NEAR((m * inverse_m * m - m).norm() / m.norm(),
+ 0.0,
+ 10 * std::numeric_limits<double>::epsilon());
+}
+
+} // namespace internal
+} // namespace ceres
