internal/ceres/suitesparse.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// 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_

#ifndef CERES_NO_SUITESPARSE

#include <cstring>
#include <string>
#include <vector>

#include <glog/logging.h>
#include "cholmod.h"
#include "ceres/internal/port.h"

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()  { cholmod_start(&cc_);  }
  ~SuiteSparse() { cholmod_finish(&cc_); }

  // 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, this object
  // should be disposed off with a delete and not a call to Free as is
  // the case for objects returned by CreateSparseMatrixTranspose.
  cholmod_sparse* CreateSparseMatrixTransposeView(CompressedRowSparseMatrix* A);

  // 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.
  //
  // Caller owns the result.
  cholmod_factor* AnalyzeCholesky(cholmod_sparse* A);

  cholmod_factor* BlockAnalyzeCholesky(cholmod_sparse* A,
                                       const vector<int>& row_blocks,
                                       const vector<int>& col_blocks);

  // 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.
  //
  // Caller owns the result.
  cholmod_factor* AnalyzeCholeskyWithUserOrdering(cholmod_sparse* A,
                                                  const vector<int>& ordering);

  // 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.
  bool Cholesky(cholmod_sparse* A, cholmod_factor* L);

  // 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.
  cholmod_dense* Solve(cholmod_factor* L, cholmod_dense* b);

  // Combine the calls to Cholesky and Solve into a single call. If
  // the cholesky factorization or the solve fails, return
  // NULL. Caller owns the result.
  cholmod_dense* SolveCholesky(cholmod_sparse* A,
                               cholmod_factor* L,
                               cholmod_dense* b);

  // 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 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 structre 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 vector<int>& row_blocks,
                        const vector<int>& col_blocks,
                        vector<int>* ordering);

  // Given a set of blocks and a permutation of these blocks, compute
  // the corresponding "scalar" ordering, where the scalar ordering of
  // size sum(blocks).
  static void BlockOrderingToScalarOrdering(const vector<int>& blocks,
                                            const vector<int>& block_ordering,
                                            vector<int>* scalar_ordering);

  // Extract the block sparsity pattern of the scalar sparse matrix
  // A and return it in compressed column form. The compressed column
  // form is stored in two vectors block_rows, and block_cols, which
  // correspond to the row and column arrays in a compressed column sparse
  // matrix.
  //
  // If c_ij is the block in the matrix A corresponding to row block i
  // and column block j, then it is expected that A contains at least
  // one non-zero entry corresponding to the top left entry of c_ij,
  // as that entry is used to detect the presence of a non-zero c_ij.
  static void ScalarMatrixToBlockMatrix(const cholmod_sparse* A,
                                        const vector<int>& row_blocks,
                                        const vector<int>& col_blocks,
                                        vector<int>* block_rows,
                                        vector<int>* block_cols);

  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 string& name) {
    cholmod_print_sparse(m, const_cast<char*>(name.c_str()), &cc_);
  }

  void Print(cholmod_dense* m, const string& name) {
    cholmod_print_dense(m, const_cast<char*>(name.c_str()), &cc_);
  }

  void Print(cholmod_triplet* m, const string& name) {
    cholmod_print_triplet(m, const_cast<char*>(name.c_str()), &cc_);
  }

  cholmod_common* mutable_cc() { return &cc_; }

 private:
  cholmod_common cc_;
};

}  // namespace internal
}  // namespace ceres

#endif  // CERES_NO_SUITESPARSE

#endif  // CERES_INTERNAL_SUITESPARSE_H_