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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 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: strandmark@google.com (Petter Strandmark)
+
+#ifndef CERES_INTERNAL_CXSPARSE_H_
+#define CERES_INTERNAL_CXSPARSE_H_
+
+// This include must come before any #ifndef check on Ceres compile options.
+#include "ceres/internal/port.h"
+
+#ifndef CERES_NO_CXSPARSE
+
+#include <memory>
+#include <string>
+#include <vector>
+
+#include "ceres/linear_solver.h"
+#include "ceres/sparse_cholesky.h"
+#include "cs.h"
+
+namespace ceres {
+namespace internal {
+
+class CompressedRowSparseMatrix;
+class TripletSparseMatrix;
+
+// This object provides access to solving linear systems using Cholesky
+// factorization with a known symbolic factorization. This features does not
+// explicitly exist in CXSparse. The methods in the class are nonstatic because
+// the class manages internal scratch space.
+class CXSparse {
+ public:
+ CXSparse();
+ ~CXSparse();
+
+ // Solve the system lhs * solution = rhs in place by using an
+ // approximate minimum degree fill reducing ordering.
+ bool SolveCholesky(cs_di* lhs, double* rhs_and_solution);
+
+ // Solves a linear system given its symbolic and numeric factorization.
+ void Solve(cs_dis* symbolic_factor,
+ csn* numeric_factor,
+ double* rhs_and_solution);
+
+ // Compute the numeric Cholesky factorization of A, given its
+ // symbolic factorization.
+ //
+ // Caller owns the result.
+ csn* Cholesky(cs_di* A, cs_dis* symbolic_factor);
+
+ // Creates a sparse matrix from a compressed-column form. No memory is
+ // allocated or copied; the structure A is filled out with info from the
+ // argument.
+ cs_di CreateSparseMatrixTransposeView(CompressedRowSparseMatrix* A);
+
+ // Creates a new matrix from a triplet form. Deallocate the returned matrix
+ // with Free. May return NULL if the compression or allocation fails.
+ cs_di* CreateSparseMatrix(TripletSparseMatrix* A);
+
+ // B = A'
+ //
+ // The returned matrix should be deallocated with Free when not used
+ // anymore.
+ cs_di* TransposeMatrix(cs_di* A);
+
+ // C = A * B
+ //
+ // The returned matrix should be deallocated with Free when not used
+ // anymore.
+ cs_di* MatrixMatrixMultiply(cs_di* A, cs_di* B);
+
+ // Computes a symbolic factorization of A that can be used in SolveCholesky.
+ //
+ // The returned matrix should be deallocated with Free when not used anymore.
+ cs_dis* AnalyzeCholesky(cs_di* A);
+
+ // Computes a symbolic factorization of A that can be used in
+ // SolveCholesky, but does not compute a fill-reducing ordering.
+ //
+ // The returned matrix should be deallocated with Free when not used anymore.
+ cs_dis* AnalyzeCholeskyWithNaturalOrdering(cs_di* A);
+
+ // Computes a symbolic factorization of A that can be used in
+ // SolveCholesky. The difference from AnalyzeCholesky is that this
+ // function first detects the block sparsity of the matrix using
+ // information about the row and column blocks and uses this block
+ // sparse matrix to find a fill-reducing ordering. This ordering is
+ // then used to find a symbolic factorization. This can result in a
+ // significant performance improvement AnalyzeCholesky on block
+ // sparse matrices.
+ //
+ // The returned matrix should be deallocated with Free when not used
+ // anymore.
+ cs_dis* BlockAnalyzeCholesky(cs_di* A,
+ const std::vector<int>& row_blocks,
+ const std::vector<int>& col_blocks);
+
+ // Compute an fill-reducing approximate minimum degree ordering of
+ // the matrix A. ordering should be non-NULL and should point to
+ // enough memory to hold the ordering for the rows of A.
+ void ApproximateMinimumDegreeOrdering(cs_di* A, int* ordering);
+
+ void Free(cs_di* sparse_matrix);
+ void Free(cs_dis* symbolic_factorization);
+ void Free(csn* numeric_factorization);
+
+ private:
+ // Cached scratch space
+ CS_ENTRY* scratch_;
+ int scratch_size_;
+};
+
+// An implementation of SparseCholesky interface using the CXSparse
+// library.
+class CXSparseCholesky : public SparseCholesky {
+ public:
+ // Factory
+ static std::unique_ptr<SparseCholesky> Create(OrderingType ordering_type);
+
+ // SparseCholesky interface.
+ virtual ~CXSparseCholesky();
+ virtual CompressedRowSparseMatrix::StorageType StorageType() const;
+ virtual LinearSolverTerminationType Factorize(CompressedRowSparseMatrix* lhs,
+ std::string* message);
+ virtual LinearSolverTerminationType Solve(const double* rhs,
+ double* solution,
+ std::string* message);
+
+ private:
+ CXSparseCholesky(const OrderingType ordering_type);
+ void FreeSymbolicFactorization();
+ void FreeNumericFactorization();
+
+ const OrderingType ordering_type_;
+ CXSparse cs_;
+ cs_dis* symbolic_factor_;
+ csn* numeric_factor_;
+};
+
+} // namespace internal
+} // namespace ceres
+
+#else // CERES_NO_CXSPARSE
+
+typedef void cs_dis;
+
+class CXSparse {
+ public:
+ void Free(void* arg) {}
+};
+#endif // CERES_NO_CXSPARSE
+
+#endif // CERES_INTERNAL_CXSPARSE_H_