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+// 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)
+//
+// A simple C++ interface to the SuiteSparse and CHOLMOD libraries.
+
+#ifndef CERES_INTERNAL_SUITESPARSE_H_
+#define CERES_INTERNAL_SUITESPARSE_H_
+
+// This include must come before any #ifndef check on Ceres compile options.
+#include "ceres/internal/port.h"
+
+#ifndef CERES_NO_SUITESPARSE
+
+#include <cstring>
+#include <string>
+#include <vector>
+#include "SuiteSparseQR.hpp"
+#include "ceres/linear_solver.h"
+#include "ceres/sparse_cholesky.h"
+#include "cholmod.h"
+#include "glog/logging.h"
+
+// Before SuiteSparse version 4.2.0, cholmod_camd was only enabled
+// if SuiteSparse was compiled with Metis support. This makes
+// calling and linking into cholmod_camd problematic even though it
+// has nothing to do with Metis. This has been fixed reliably in
+// 4.2.0.
+//
+// The fix was actually committed in 4.1.0, but there is
+// some confusion about a silent update to the tar ball, so we are
+// being conservative and choosing the next minor version where
+// things are stable.
+#if (SUITESPARSE_VERSION < 4002)
+#define CERES_NO_CAMD
+#endif
+
+// UF_long is deprecated but SuiteSparse_long is only available in
+// newer versions of SuiteSparse. So for older versions of
+// SuiteSparse, we define SuiteSparse_long to be the same as UF_long,
+// which is what recent versions of SuiteSparse do anyways.
+#ifndef SuiteSparse_long
+#define SuiteSparse_long UF_long
+#endif
+
+namespace ceres {
+namespace internal {
+
+class CompressedRowSparseMatrix;
+class TripletSparseMatrix;
+
+// The raw CHOLMOD and SuiteSparseQR libraries have a slightly
+// cumbersome c like calling format. This object abstracts it away and
+// provides the user with a simpler interface. The methods here cannot
+// be static as a cholmod_common object serves as a global variable
+// for all cholmod function calls.
+class SuiteSparse {
+ public:
+  SuiteSparse();
+  ~SuiteSparse();
+
+  // Functions for building cholmod_sparse objects from sparse
+  // matrices stored in triplet form. The matrix A is not
+  // modifed. Called owns the result.
+  cholmod_sparse* CreateSparseMatrix(TripletSparseMatrix* A);
+
+  // This function works like CreateSparseMatrix, except that the
+  // return value corresponds to A' rather than A.
+  cholmod_sparse* CreateSparseMatrixTranspose(TripletSparseMatrix* A);
+
+  // Create a cholmod_sparse wrapper around the contents of A. This is
+  // a shallow object, which refers to the contents of A and does not
+  // use the SuiteSparse machinery to allocate memory.
+  cholmod_sparse CreateSparseMatrixTransposeView(CompressedRowSparseMatrix* A);
+
+  // Create a cholmod_dense vector around the contents of the array x.
+  // This is a shallow object, which refers to the contents of x and
+  // does not use the SuiteSparse machinery to allocate memory.
+  cholmod_dense CreateDenseVectorView(const double* x, int size);
+
+  // Given a vector x, build a cholmod_dense vector of size out_size
+  // with the first in_size entries copied from x. If x is NULL, then
+  // an all zeros vector is returned. Caller owns the result.
+  cholmod_dense* CreateDenseVector(const double* x, int in_size, int out_size);
+
+  // The matrix A is scaled using the matrix whose diagonal is the
+  // vector scale. mode describes how scaling is applied. Possible
+  // values are CHOLMOD_ROW for row scaling - diag(scale) * A,
+  // CHOLMOD_COL for column scaling - A * diag(scale) and CHOLMOD_SYM
+  // for symmetric scaling which scales both the rows and the columns
+  // - diag(scale) * A * diag(scale).
+  void Scale(cholmod_dense* scale, int mode, cholmod_sparse* A) {
+     cholmod_scale(scale, mode, A, &cc_);
+  }
+
+  // Create and return a matrix m = A * A'. Caller owns the
+  // result. The matrix A is not modified.
+  cholmod_sparse* AATranspose(cholmod_sparse* A) {
+    cholmod_sparse*m =  cholmod_aat(A, NULL, A->nrow, 1, &cc_);
+    m->stype = 1;  // Pay attention to the upper triangular part.
+    return m;
+  }
+
+  // y = alpha * A * x + beta * y. Only y is modified.
+  void SparseDenseMultiply(cholmod_sparse* A, double alpha, double beta,
+                           cholmod_dense* x, cholmod_dense* y) {
+    double alpha_[2] = {alpha, 0};
+    double beta_[2] = {beta, 0};
+    cholmod_sdmult(A, 0, alpha_, beta_, x, y, &cc_);
+  }
+
+  // Find an ordering of A or AA' (if A is unsymmetric) that minimizes
+  // the fill-in in the Cholesky factorization of the corresponding
+  // matrix. This is done by using the AMD algorithm.
+  //
+  // Using this ordering, the symbolic Cholesky factorization of A (or
+  // AA') is computed and returned.
+  //
+  // A is not modified, only the pattern of non-zeros of A is used,
+  // the actual numerical values in A are of no consequence.
+  //
+  // message contains an explanation of the failures if any.
+  //
+  // Caller owns the result.
+  cholmod_factor* AnalyzeCholesky(cholmod_sparse* A, std::string* message);
+
+  cholmod_factor* BlockAnalyzeCholesky(cholmod_sparse* A,
+                                       const std::vector<int>& row_blocks,
+                                       const std::vector<int>& col_blocks,
+                                       std::string* message);
+
+  // If A is symmetric, then compute the symbolic Cholesky
+  // factorization of A(ordering, ordering). If A is unsymmetric, then
+  // compute the symbolic factorization of
+  // A(ordering,:) A(ordering,:)'.
+  //
+  // A is not modified, only the pattern of non-zeros of A is used,
+  // the actual numerical values in A are of no consequence.
+  //
+  // message contains an explanation of the failures if any.
+  //
+  // Caller owns the result.
+  cholmod_factor* AnalyzeCholeskyWithUserOrdering(
+      cholmod_sparse* A,
+      const std::vector<int>& ordering,
+      std::string* message);
+
+  // Perform a symbolic factorization of A without re-ordering A. No
+  // postordering of the elimination tree is performed. This ensures
+  // that the symbolic factor does not introduce an extra permutation
+  // on the matrix. See the documentation for CHOLMOD for more details.
+  //
+  // message contains an explanation of the failures if any.
+  cholmod_factor* AnalyzeCholeskyWithNaturalOrdering(cholmod_sparse* A,
+                                                     std::string* message);
+
+  // Use the symbolic factorization in L, to find the numerical
+  // factorization for the matrix A or AA^T. Return true if
+  // successful, false otherwise. L contains the numeric factorization
+  // on return.
+  //
+  // message contains an explanation of the failures if any.
+  LinearSolverTerminationType Cholesky(cholmod_sparse* A,
+                                       cholmod_factor* L,
+                                       std::string* message);
+
+  // Given a Cholesky factorization of a matrix A = LL^T, solve the
+  // linear system Ax = b, and return the result. If the Solve fails
+  // NULL is returned. Caller owns the result.
+  //
+  // message contains an explanation of the failures if any.
+  cholmod_dense* Solve(cholmod_factor* L, cholmod_dense* b, std::string* message);
+
+  // By virtue of the modeling layer in Ceres being block oriented,
+  // all the matrices used by Ceres are also block oriented. When
+  // doing sparse direct factorization of these matrices the
+  // fill-reducing ordering algorithms (in particular AMD) can either
+  // be run on the block or the scalar form of these matrices. The two
+  // SuiteSparse::AnalyzeCholesky methods allows the client to
+  // compute the symbolic factorization of a matrix by either using
+  // AMD on the matrix or a user provided ordering of the rows.
+  //
+  // But since the underlying matrices are block oriented, it is worth
+  // running AMD on just the block structure of these matrices and then
+  // lifting these block orderings to a full scalar ordering. This
+  // preserves the block structure of the permuted matrix, and exposes
+  // more of the super-nodal structure of the matrix to the numerical
+  // factorization routines.
+  //
+  // Find the block oriented AMD ordering of a matrix A, whose row and
+  // column blocks are given by row_blocks, and col_blocks
+  // respectively. The matrix may or may not be symmetric. The entries
+  // of col_blocks do not need to sum to the number of columns in
+  // A. If this is the case, only the first sum(col_blocks) are used
+  // to compute the ordering.
+  bool BlockAMDOrdering(const cholmod_sparse* A,
+                        const std::vector<int>& row_blocks,
+                        const std::vector<int>& col_blocks,
+                        std::vector<int>* ordering);
+
+  // Find a fill reducing approximate minimum degree
+  // ordering. ordering is expected to be large enough to hold the
+  // ordering.
+  bool ApproximateMinimumDegreeOrdering(cholmod_sparse* matrix, int* ordering);
+
+
+  // Before SuiteSparse version 4.2.0, cholmod_camd was only enabled
+  // if SuiteSparse was compiled with Metis support. This makes
+  // calling and linking into cholmod_camd problematic even though it
+  // has nothing to do with Metis. This has been fixed reliably in
+  // 4.2.0.
+  //
+  // The fix was actually committed in 4.1.0, but there is
+  // some confusion about a silent update to the tar ball, so we are
+  // being conservative and choosing the next minor version where
+  // things are stable.
+  static bool IsConstrainedApproximateMinimumDegreeOrderingAvailable() {
+    return (SUITESPARSE_VERSION > 4001);
+  }
+
+  // Find a fill reducing approximate minimum degree
+  // ordering. constraints is an array which associates with each
+  // column of the matrix an elimination group. i.e., all columns in
+  // group 0 are eliminated first, all columns in group 1 are
+  // eliminated next etc. This function finds a fill reducing ordering
+  // that obeys these constraints.
+  //
+  // Calling ApproximateMinimumDegreeOrdering is equivalent to calling
+  // ConstrainedApproximateMinimumDegreeOrdering with a constraint
+  // array that puts all columns in the same elimination group.
+  //
+  // If CERES_NO_CAMD is defined then calling this function will
+  // result in a crash.
+  bool ConstrainedApproximateMinimumDegreeOrdering(cholmod_sparse* matrix,
+                                                   int* constraints,
+                                                   int* ordering);
+
+  void Free(cholmod_sparse* m) { cholmod_free_sparse(&m, &cc_); }
+  void Free(cholmod_dense* m)  { cholmod_free_dense(&m, &cc_);  }
+  void Free(cholmod_factor* m) { cholmod_free_factor(&m, &cc_); }
+
+  void Print(cholmod_sparse* m, const std::string& name) {
+    cholmod_print_sparse(m, const_cast<char*>(name.c_str()), &cc_);
+  }
+
+  void Print(cholmod_dense* m, const std::string& name) {
+    cholmod_print_dense(m, const_cast<char*>(name.c_str()), &cc_);
+  }
+
+  void Print(cholmod_triplet* m, const std::string& name) {
+    cholmod_print_triplet(m, const_cast<char*>(name.c_str()), &cc_);
+  }
+
+  cholmod_common* mutable_cc() { return &cc_; }
+
+ private:
+  cholmod_common cc_;
+};
+
+class SuiteSparseCholesky : public SparseCholesky {
+ public:
+  static std::unique_ptr<SparseCholesky> Create(
+      OrderingType ordering_type);
+
+  // SparseCholesky interface.
+  virtual ~SuiteSparseCholesky();
+  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:
+  SuiteSparseCholesky(const OrderingType ordering_type);
+
+  const OrderingType ordering_type_;
+  SuiteSparse ss_;
+  cholmod_factor* factor_;
+};
+
+}  // namespace internal
+}  // namespace ceres
+
+#else  // CERES_NO_SUITESPARSE
+
+typedef void cholmod_factor;
+
+namespace ceres {
+namespace internal {
+
+class SuiteSparse {
+ public:
+  // Defining this static function even when SuiteSparse is not
+  // available, allows client code to check for the presence of CAMD
+  // without checking for the absence of the CERES_NO_CAMD symbol.
+  //
+  // This is safer because the symbol maybe missing due to a user
+  // accidentally not including suitesparse.h in their code when
+  // checking for the symbol.
+  static bool IsConstrainedApproximateMinimumDegreeOrderingAvailable() {
+    return false;
+  }
+
+  void Free(void* arg) {}
+};
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_NO_SUITESPARSE
+
+#endif  // CERES_INTERNAL_SUITESPARSE_H_