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