internal/ceres/sparse_normal_cholesky_solver.cc

// 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)

#include "ceres/sparse_normal_cholesky_solver.h"

#include <algorithm>
#include <cstring>
#include <ctime>

#ifndef CERES_NO_CXSPARSE
#include "cs.h"
#endif

#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/linear_solver.h"
#include "ceres/suitesparse.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"

namespace ceres {
namespace internal {

SparseNormalCholeskySolver::SparseNormalCholeskySolver(
    const LinearSolver::Options& options)
    : options_(options) {
#ifndef CERES_NO_SUITESPARSE
  factor_ = NULL;
#endif
}

SparseNormalCholeskySolver::~SparseNormalCholeskySolver() {
#ifndef CERES_NO_SUITESPARSE
  if (factor_ != NULL) {
    ss_.Free(factor_);
    factor_ = NULL;
  }
#endif
}

LinearSolver::Summary SparseNormalCholeskySolver::SolveImpl(
    CompressedRowSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double * x) {
  switch (options_.sparse_linear_algebra_library) {
    case SUITE_SPARSE:
      return SolveImplUsingSuiteSparse(A, b, per_solve_options, x);
    case CX_SPARSE:
      return SolveImplUsingCXSparse(A, b, per_solve_options, x);
    default:
      LOG(FATAL) << "Unknown sparse linear algebra library : "
                 << options_.sparse_linear_algebra_library;
  }

  LOG(FATAL) << "Unknown sparse linear algebra library : "
             << options_.sparse_linear_algebra_library;
  return LinearSolver::Summary();
}

#ifndef CERES_NO_CXSPARSE
LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingCXSparse(
    CompressedRowSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double * x) {
  LinearSolver::Summary summary;
  summary.num_iterations = 1;
  const int num_cols = A->num_cols();
  Vector Atb = Vector::Zero(num_cols);
  A->LeftMultiply(b, Atb.data());

  if (per_solve_options.D != NULL) {
    // Temporarily append a diagonal block to the A matrix, but undo
    // it before returning the matrix to the user.
    CompressedRowSparseMatrix D(per_solve_options.D, num_cols);
    A->AppendRows(D);
  }

  VectorRef(x, num_cols).setZero();

  // Wrap the augmented Jacobian in a compressed sparse column matrix.
  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();

  // Compute the normal equations. J'J delta = J'f and solve them
  // using a sparse Cholesky factorization. Notice that when compared
  // to SuiteSparse we have to explicitly compute the transpose of Jt,
  // and then the normal equations before they can be
  // factorized. CHOLMOD/SuiteSparse on the other hand can just work
  // off of Jt to compute the Cholesky factorization of the normal
  // equations.
  cs_di* A2 = cs_transpose(&At, 1);
  cs_di* AtA = cs_multiply(&At,A2);

  cs_free(A2);
  if (per_solve_options.D != NULL) {
    A->DeleteRows(num_cols);
  }

  // This recomputes the symbolic factorization every time it is
  // invoked. It will perhaps be worth it to cache the symbolic
  // factorization the way we do for SuiteSparse.
  if (cs_cholsol(1, AtA, Atb.data())) {
    VectorRef(x, Atb.rows()) = Atb;
    summary.termination_type = TOLERANCE;
  }

  cs_free(AtA);
  return summary;
}
#else
LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingCXSparse(
    CompressedRowSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double * x) {
  LOG(FATAL) << "No CXSparse support in Ceres.";

  // Unreachable but MSVC does not know this.
  return LinearSolver::Summary();
}
#endif

#ifndef CERES_NO_SUITESPARSE
LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
    CompressedRowSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double * x) {
  const time_t start_time = time(NULL);
  const int num_cols = A->num_cols();

  LinearSolver::Summary summary;
  Vector Atb = Vector::Zero(num_cols);
  A->LeftMultiply(b, Atb.data());

  if (per_solve_options.D != NULL) {
    // Temporarily append a diagonal block to the A matrix, but undo it before
    // returning the matrix to the user.
    CompressedRowSparseMatrix D(per_solve_options.D, num_cols);
    A->AppendRows(D);
  }

  VectorRef(x, num_cols).setZero();

  scoped_ptr<cholmod_sparse> lhs(ss_.CreateSparseMatrixTransposeView(A));
  CHECK_NOTNULL(lhs.get());

  cholmod_dense* rhs = ss_.CreateDenseVector(Atb.data(), num_cols, num_cols);
  const time_t init_time = time(NULL);

  if (factor_ == NULL) {
    if (options_.use_block_amd) {
      factor_ = ss_.BlockAnalyzeCholesky(lhs.get(),
                                         A->col_blocks(),
                                         A->row_blocks());
    } else {
      factor_ = ss_.AnalyzeCholesky(lhs.get());
    }

    if (VLOG_IS_ON(2)) {
      cholmod_print_common("Symbolic Analysis", ss_.mutable_cc());
    }
  }

  CHECK_NOTNULL(factor_);

  const time_t symbolic_time = time(NULL);

  cholmod_dense* sol = ss_.SolveCholesky(lhs.get(), factor_, rhs);
  const time_t solve_time = time(NULL);

  ss_.Free(rhs);
  rhs = NULL;

  if (per_solve_options.D != NULL) {
    A->DeleteRows(num_cols);
  }

  summary.num_iterations = 1;
  if (sol != NULL) {
    memcpy(x, sol->x, num_cols * sizeof(*x));

    ss_.Free(sol);
    sol = NULL;
    summary.termination_type = TOLERANCE;
  }

  const time_t cleanup_time = time(NULL);
  VLOG(2) << "time (sec) total: " << (cleanup_time - start_time)
          << " init: " << (init_time - start_time)
          << " symbolic: " << (symbolic_time - init_time)
          << " solve: " << (solve_time - symbolic_time)
          << " cleanup: " << (cleanup_time - solve_time);
  return summary;
}
#else
LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
    CompressedRowSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double * x) {
  LOG(FATAL) << "No SuiteSparse support in Ceres.";

  // Unreachable but MSVC does not know this.
  return LinearSolver::Summary();
}
#endif

}   // namespace internal
}   // namespace ceres