Caching the symbolic Cholesky factorization when using CXSparse

Average factorization times for bundle adjustment test problem:
SuiteSparse: 0.2794 s.
CXSparse: 0.4039 s.
CXSparse cached: 0.2399 s.

CXSparse will still be slower, though, because it has to compute
the transpose and J^T * J.

Change-Id: If9cdaa3dd520bee84b56e5fd4953b56a93db6bde

internal/ceres/cxsparse.cc

@@ -0,0 +1,127 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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: strandmark@google.com (Petter Strandmark)
+
+#ifndef CERES_NO_CXSPARSE
+
+#include "ceres/cxsparse.h"
+
+#include "ceres/compressed_row_sparse_matrix.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "glog/logging.h"
+
+namespace ceres {
+namespace internal {
+
+CXSparse::CXSparse() : scratch_size_(0), scratch_(NULL) {
+}
+
+CXSparse::~CXSparse() {
+  if (scratch_size_ > 0) {
+    cs_free(scratch_);
+  }
+}
+
+bool CXSparse::SolveCholesky(cs_di* A, cs_dis* factor, double* b) {
+  // Make sure we have enough scratch space available.
+  if (scratch_size_ < A->n) {
+    if (scratch_size_ > 0) {
+      cs_free(scratch_);
+    }
+    scratch_ = reinterpret_cast<CS_ENTRY*>(cs_malloc(A->n, sizeof(CS_ENTRY)));
+  }
+
+  // Solve using Cholesky factorization
+  csn* N = cs_chol(A, factor);
+  if (N == NULL) {
+    LOG(WARNING) << "Cholesky factorization failed.";
+    return false;
+  }
+
+  // When the Cholesky factorization succeeded, these methods are guaranteed to
+  // succeed as well. In the comments below, "x" refers to the scratch space.
+  // Set x = P * b.
+  cs_ipvec(factor->pinv, b, scratch_, A->n);
+
+  // Set x = L \ x.
+  cs_lsolve(N->L, scratch_);
+
+  // Set x = L' \ x.
+  cs_ltsolve(N->L, scratch_);
+
+  // Set b = P' * x.
+  cs_pvec(factor->pinv, scratch_, b, A->n);
+
+  // Free Cholesky factorization.
+  cs_nfree(N);
+  return true;
+}
+
+cs_dis* CXSparse::AnalyzeCholesky(cs_di* A) {
+  // order = 1 for Cholesky factorization.
+  return cs_schol(1, A);
+}
+
+cs_di CXSparse::CreateSparseMatrixTransposeView(CompressedRowSparseMatrix* A) {
+  cs_di At;
+  At.m = A->num_cols();
+  At.n = A->num_rows();
+  At.nz = -1;
+  At.nzmax = A->num_nonzeros();
+  At.p = A->mutable_rows();
+  At.i = A->mutable_cols();
+  At.x = A->mutable_values();
+  return At;
+}
+
+cs_di* CXSparse::CreateSparseMatrix(TripletSparseMatrix* tsm) {
+  cs_di_sparse tsm_wrapper;
+  tsm_wrapper.nzmax = tsm->num_nonzeros();;
+  tsm_wrapper.nz = tsm->num_nonzeros();;
+  tsm_wrapper.m = tsm->num_rows();
+  tsm_wrapper.n = tsm->num_cols();
+  tsm_wrapper.p = tsm->mutable_cols();
+  tsm_wrapper.i = tsm->mutable_rows();
+  tsm_wrapper.x = tsm->mutable_values();
+
+  return cs_compress(&tsm_wrapper);
+}
+
+void CXSparse::Free(cs_di* factor) {
+  cs_free(factor);
+}
+
+void CXSparse::Free(cs_dis* factor) {
+  cs_sfree(factor);
+}
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_NO_CXSPARSE