// 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);
// 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 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 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 SuiteSparseCholesky* Create(const 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
// accidently 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_