internal/ceres/suitesparse.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

// This include must come before any #ifndef check on Ceres compile options.
#include "ceres/internal/port.h"

#ifndef CERES_NO_SUITESPARSE
#include <vector>

#include "ceres/compressed_col_sparse_matrix_utils.h"
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/linear_solver.h"
#include "ceres/suitesparse.h"
#include "ceres/triplet_sparse_matrix.h"
#include "cholmod.h"

namespace ceres {
namespace internal {

using std::string;
using std::vector;

SuiteSparse::SuiteSparse() { cholmod_start(&cc_); }

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

cholmod_sparse* SuiteSparse::CreateSparseMatrix(TripletSparseMatrix* A) {
  cholmod_triplet triplet;

  triplet.nrow = A->num_rows();
  triplet.ncol = A->num_cols();
  triplet.nzmax = A->max_num_nonzeros();
  triplet.nnz = A->num_nonzeros();
  triplet.i = reinterpret_cast<void*>(A->mutable_rows());
  triplet.j = reinterpret_cast<void*>(A->mutable_cols());
  triplet.x = reinterpret_cast<void*>(A->mutable_values());
  triplet.stype = 0;  // Matrix is not symmetric.
  triplet.itype = CHOLMOD_INT;
  triplet.xtype = CHOLMOD_REAL;
  triplet.dtype = CHOLMOD_DOUBLE;

  return cholmod_triplet_to_sparse(&triplet, triplet.nnz, &cc_);
}

cholmod_sparse* SuiteSparse::CreateSparseMatrixTranspose(
    TripletSparseMatrix* A) {
  cholmod_triplet triplet;

  triplet.ncol = A->num_rows();  // swap row and columns
  triplet.nrow = A->num_cols();
  triplet.nzmax = A->max_num_nonzeros();
  triplet.nnz = A->num_nonzeros();

  // swap rows and columns
  triplet.j = reinterpret_cast<void*>(A->mutable_rows());
  triplet.i = reinterpret_cast<void*>(A->mutable_cols());
  triplet.x = reinterpret_cast<void*>(A->mutable_values());
  triplet.stype = 0;  // Matrix is not symmetric.
  triplet.itype = CHOLMOD_INT;
  triplet.xtype = CHOLMOD_REAL;
  triplet.dtype = CHOLMOD_DOUBLE;

  return cholmod_triplet_to_sparse(&triplet, triplet.nnz, &cc_);
}

cholmod_sparse SuiteSparse::CreateSparseMatrixTransposeView(
    CompressedRowSparseMatrix* A) {
  cholmod_sparse m;
  m.nrow = A->num_cols();
  m.ncol = A->num_rows();
  m.nzmax = A->num_nonzeros();
  m.nz = nullptr;
  m.p = reinterpret_cast<void*>(A->mutable_rows());
  m.i = reinterpret_cast<void*>(A->mutable_cols());
  m.x = reinterpret_cast<void*>(A->mutable_values());
  m.z = nullptr;

  if (A->storage_type() == CompressedRowSparseMatrix::LOWER_TRIANGULAR) {
    m.stype = 1;
  } else if (A->storage_type() == CompressedRowSparseMatrix::UPPER_TRIANGULAR) {
    m.stype = -1;
  } else {
    m.stype = 0;
  }

  m.itype = CHOLMOD_INT;
  m.xtype = CHOLMOD_REAL;
  m.dtype = CHOLMOD_DOUBLE;
  m.sorted = 1;
  m.packed = 1;

  return m;
}

cholmod_dense SuiteSparse::CreateDenseVectorView(const double* x, int size) {
  cholmod_dense v;
  v.nrow = size;
  v.ncol = 1;
  v.nzmax = size;
  v.d = size;
  v.x = const_cast<void*>(reinterpret_cast<const void*>(x));
  v.xtype = CHOLMOD_REAL;
  v.dtype = CHOLMOD_DOUBLE;
  return v;
}

cholmod_dense* SuiteSparse::CreateDenseVector(const double* x,
                                              int in_size,
                                              int out_size) {
  CHECK_LE(in_size, out_size);
  cholmod_dense* v = cholmod_zeros(out_size, 1, CHOLMOD_REAL, &cc_);
  if (x != nullptr) {
    memcpy(v->x, x, in_size * sizeof(*x));
  }
  return v;
}

cholmod_factor* SuiteSparse::AnalyzeCholesky(cholmod_sparse* A,
                                             string* message) {
  // Cholmod can try multiple re-ordering strategies to find a fill
  // reducing ordering. Here we just tell it use AMD with automatic
  // matrix dependence choice of supernodal versus simplicial
  // factorization.
  cc_.nmethods = 1;
  cc_.method[0].ordering = CHOLMOD_AMD;
  cc_.supernodal = CHOLMOD_AUTO;

  cholmod_factor* factor = cholmod_analyze(A, &cc_);
  if (VLOG_IS_ON(2)) {
    cholmod_print_common(const_cast<char*>("Symbolic Analysis"), &cc_);
  }

  if (cc_.status != CHOLMOD_OK) {
    *message =
        StringPrintf("cholmod_analyze failed. error code: %d", cc_.status);
    return nullptr;
  }

  CHECK(factor != nullptr);
  return factor;
}

cholmod_factor* SuiteSparse::BlockAnalyzeCholesky(cholmod_sparse* A,
                                                  const vector<int>& row_blocks,
                                                  const vector<int>& col_blocks,
                                                  string* message) {
  vector<int> ordering;
  if (!BlockAMDOrdering(A, row_blocks, col_blocks, &ordering)) {
    return nullptr;
  }
  return AnalyzeCholeskyWithUserOrdering(A, ordering, message);
}

cholmod_factor* SuiteSparse::AnalyzeCholeskyWithUserOrdering(
    cholmod_sparse* A, const vector<int>& ordering, string* message) {
  CHECK_EQ(ordering.size(), A->nrow);

  cc_.nmethods = 1;
  cc_.method[0].ordering = CHOLMOD_GIVEN;

  cholmod_factor* factor =
      cholmod_analyze_p(A, const_cast<int*>(&ordering[0]), nullptr, 0, &cc_);
  if (VLOG_IS_ON(2)) {
    cholmod_print_common(const_cast<char*>("Symbolic Analysis"), &cc_);
  }
  if (cc_.status != CHOLMOD_OK) {
    *message =
        StringPrintf("cholmod_analyze failed. error code: %d", cc_.status);
    return nullptr;
  }

  CHECK(factor != nullptr);
  return factor;
}

cholmod_factor* SuiteSparse::AnalyzeCholeskyWithNaturalOrdering(
    cholmod_sparse* A, string* message) {
  cc_.nmethods = 1;
  cc_.method[0].ordering = CHOLMOD_NATURAL;
  cc_.postorder = 0;

  cholmod_factor* factor = cholmod_analyze(A, &cc_);
  if (VLOG_IS_ON(2)) {
    cholmod_print_common(const_cast<char*>("Symbolic Analysis"), &cc_);
  }
  if (cc_.status != CHOLMOD_OK) {
    *message =
        StringPrintf("cholmod_analyze failed. error code: %d", cc_.status);
    return nullptr;
  }

  CHECK(factor != nullptr);
  return factor;
}

bool SuiteSparse::BlockAMDOrdering(const cholmod_sparse* A,
                                   const vector<int>& row_blocks,
                                   const vector<int>& col_blocks,
                                   vector<int>* ordering) {
  const int num_row_blocks = row_blocks.size();
  const int num_col_blocks = col_blocks.size();

  // Arrays storing the compressed column structure of the matrix
  // incoding the block sparsity of A.
  vector<int> block_cols;
  vector<int> block_rows;

  CompressedColumnScalarMatrixToBlockMatrix(reinterpret_cast<const int*>(A->i),
                                            reinterpret_cast<const int*>(A->p),
                                            row_blocks,
                                            col_blocks,
                                            &block_rows,
                                            &block_cols);
  cholmod_sparse_struct block_matrix;
  block_matrix.nrow = num_row_blocks;
  block_matrix.ncol = num_col_blocks;
  block_matrix.nzmax = block_rows.size();
  block_matrix.p = reinterpret_cast<void*>(&block_cols[0]);
  block_matrix.i = reinterpret_cast<void*>(&block_rows[0]);
  block_matrix.x = nullptr;
  block_matrix.stype = A->stype;
  block_matrix.itype = CHOLMOD_INT;
  block_matrix.xtype = CHOLMOD_PATTERN;
  block_matrix.dtype = CHOLMOD_DOUBLE;
  block_matrix.sorted = 1;
  block_matrix.packed = 1;

  vector<int> block_ordering(num_row_blocks);
  if (!cholmod_amd(&block_matrix, nullptr, 0, &block_ordering[0], &cc_)) {
    return false;
  }

  BlockOrderingToScalarOrdering(row_blocks, block_ordering, ordering);
  return true;
}

LinearSolverTerminationType SuiteSparse::Cholesky(cholmod_sparse* A,
                                                  cholmod_factor* L,
                                                  string* message) {
  CHECK(A != nullptr);
  CHECK(L != nullptr);

  // Save the current print level and silence CHOLMOD, otherwise
  // CHOLMOD is prone to dumping stuff to stderr, which can be
  // distracting when the error (matrix is indefinite) is not a fatal
  // failure.
  const int old_print_level = cc_.print;
  cc_.print = 0;

  cc_.quick_return_if_not_posdef = 1;
  int cholmod_status = cholmod_factorize(A, L, &cc_);
  cc_.print = old_print_level;

  switch (cc_.status) {
    case CHOLMOD_NOT_INSTALLED:
      *message = "CHOLMOD failure: Method not installed.";
      return LINEAR_SOLVER_FATAL_ERROR;
    case CHOLMOD_OUT_OF_MEMORY:
      *message = "CHOLMOD failure: Out of memory.";
      return LINEAR_SOLVER_FATAL_ERROR;
    case CHOLMOD_TOO_LARGE:
      *message = "CHOLMOD failure: Integer overflow occurred.";
      return LINEAR_SOLVER_FATAL_ERROR;
    case CHOLMOD_INVALID:
      *message = "CHOLMOD failure: Invalid input.";
      return LINEAR_SOLVER_FATAL_ERROR;
    case CHOLMOD_NOT_POSDEF:
      *message = "CHOLMOD warning: Matrix not positive definite.";
      return LINEAR_SOLVER_FAILURE;
    case CHOLMOD_DSMALL:
      *message =
          "CHOLMOD warning: D for LDL' or diag(L) or "
          "LL' has tiny absolute value.";
      return LINEAR_SOLVER_FAILURE;
    case CHOLMOD_OK:
      if (cholmod_status != 0) {
        return LINEAR_SOLVER_SUCCESS;
      }

      *message =
          "CHOLMOD failure: cholmod_factorize returned false "
          "but cholmod_common::status is CHOLMOD_OK."
          "Please report this to ceres-solver@googlegroups.com.";
      return LINEAR_SOLVER_FATAL_ERROR;
    default:
      *message = StringPrintf(
          "Unknown cholmod return code: %d. "
          "Please report this to ceres-solver@googlegroups.com.",
          cc_.status);
      return LINEAR_SOLVER_FATAL_ERROR;
  }

  return LINEAR_SOLVER_FATAL_ERROR;
}

cholmod_dense* SuiteSparse::Solve(cholmod_factor* L,
                                  cholmod_dense* b,
                                  string* message) {
  if (cc_.status != CHOLMOD_OK) {
    *message = "cholmod_solve failed. CHOLMOD status is not CHOLMOD_OK";
    return nullptr;
  }

  return cholmod_solve(CHOLMOD_A, L, b, &cc_);
}

bool SuiteSparse::ApproximateMinimumDegreeOrdering(cholmod_sparse* matrix,
                                                   int* ordering) {
  return cholmod_amd(matrix, nullptr, 0, ordering, &cc_);
}

bool SuiteSparse::ConstrainedApproximateMinimumDegreeOrdering(
    cholmod_sparse* matrix, int* constraints, int* ordering) {
#ifndef CERES_NO_CAMD
  return cholmod_camd(matrix, nullptr, 0, constraints, ordering, &cc_);
#else
  LOG(FATAL) << "Congratulations you have found a bug in Ceres."
             << "Ceres Solver was compiled with SuiteSparse "
             << "version 4.1.0 or less. Calling this function "
             << "in that case is a bug. Please contact the"
             << "the Ceres Solver developers.";
  return false;
#endif
}

std::unique_ptr<SparseCholesky> SuiteSparseCholesky::Create(
    const OrderingType ordering_type) {
  return std::unique_ptr<SparseCholesky>(
      new SuiteSparseCholesky(ordering_type));
}

SuiteSparseCholesky::SuiteSparseCholesky(const OrderingType ordering_type)
    : ordering_type_(ordering_type), factor_(nullptr) {}

SuiteSparseCholesky::~SuiteSparseCholesky() {
  if (factor_ != nullptr) {
    ss_.Free(factor_);
  }
}

LinearSolverTerminationType SuiteSparseCholesky::Factorize(
    CompressedRowSparseMatrix* lhs, string* message) {
  if (lhs == nullptr) {
    *message = "Failure: Input lhs is NULL.";
    return LINEAR_SOLVER_FATAL_ERROR;
  }

  cholmod_sparse cholmod_lhs = ss_.CreateSparseMatrixTransposeView(lhs);

  if (factor_ == nullptr) {
    if (ordering_type_ == NATURAL) {
      factor_ = ss_.AnalyzeCholeskyWithNaturalOrdering(&cholmod_lhs, message);
    } else {
      if (!lhs->col_blocks().empty() && !(lhs->row_blocks().empty())) {
        factor_ = ss_.BlockAnalyzeCholesky(
            &cholmod_lhs, lhs->col_blocks(), lhs->row_blocks(), message);
      } else {
        factor_ = ss_.AnalyzeCholesky(&cholmod_lhs, message);
      }
    }

    if (factor_ == nullptr) {
      return LINEAR_SOLVER_FATAL_ERROR;
    }
  }

  return ss_.Cholesky(&cholmod_lhs, factor_, message);
}

CompressedRowSparseMatrix::StorageType SuiteSparseCholesky::StorageType()
    const {
  return ((ordering_type_ == NATURAL)
              ? CompressedRowSparseMatrix::UPPER_TRIANGULAR
              : CompressedRowSparseMatrix::LOWER_TRIANGULAR);
}

LinearSolverTerminationType SuiteSparseCholesky::Solve(const double* rhs,
                                                       double* solution,
                                                       string* message) {
  // Error checking
  if (factor_ == nullptr) {
    *message = "Solve called without a call to Factorize first.";
    return LINEAR_SOLVER_FATAL_ERROR;
  }

  const int num_cols = factor_->n;
  cholmod_dense cholmod_rhs = ss_.CreateDenseVectorView(rhs, num_cols);
  cholmod_dense* cholmod_dense_solution =
      ss_.Solve(factor_, &cholmod_rhs, message);

  if (cholmod_dense_solution == nullptr) {
    return LINEAR_SOLVER_FAILURE;
  }

  memcpy(solution, cholmod_dense_solution->x, num_cols * sizeof(*solution));
  ss_.Free(cholmod_dense_solution);
  return LINEAR_SOLVER_SUCCESS;
}

}  // namespace internal
}  // namespace ceres

#endif  // CERES_NO_SUITESPARSE