// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 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
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// 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
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// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/reorder_program.h"
#include <algorithm>
#include <numeric>
#include <vector>
#include "ceres/cxsparse.h"
#include "ceres/internal/port.h"
#include "ceres/ordered_groups.h"
#include "ceres/parameter_block.h"
#include "ceres/parameter_block_ordering.h"
#include "ceres/problem_impl.h"
#include "ceres/program.h"
#include "ceres/residual_block.h"
#include "ceres/solver.h"
#include "ceres/suitesparse.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "Eigen/SparseCore"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/OrderingMethods"
#endif
#include "glog/logging.h"
namespace ceres {
namespace internal {
using std::map;
using std::set;
using std::string;
using std::vector;
namespace {
// Find the minimum index of any parameter block to the given
// residual. Parameter blocks that have indices greater than
// size_of_first_elimination_group are considered to have an index
// equal to size_of_first_elimination_group.
static int MinParameterBlock(const ResidualBlock* residual_block,
int size_of_first_elimination_group) {
int min_parameter_block_position = size_of_first_elimination_group;
for (int i = 0; i < residual_block->NumParameterBlocks(); ++i) {
ParameterBlock* parameter_block = residual_block->parameter_blocks()[i];
if (!parameter_block->IsConstant()) {
CHECK_NE(parameter_block->index(), -1)
<< "Did you forget to call Program::SetParameterOffsetsAndIndex()? "
<< "This is a Ceres bug; please contact the developers!";
min_parameter_block_position = std::min(parameter_block->index(),
min_parameter_block_position);
}
}
return min_parameter_block_position;
}
#if EIGEN_VERSION_AT_LEAST(3, 2, 2) && defined(CERES_USE_EIGEN_SPARSE)
Eigen::SparseMatrix<int> CreateBlockJacobian(
const TripletSparseMatrix& block_jacobian_transpose) {
typedef Eigen::SparseMatrix<int> SparseMatrix;
typedef Eigen::Triplet<int> Triplet;
const int* rows = block_jacobian_transpose.rows();
const int* cols = block_jacobian_transpose.cols();
int num_nonzeros = block_jacobian_transpose.num_nonzeros();
vector<Triplet> triplets;
triplets.reserve(num_nonzeros);
for (int i = 0; i < num_nonzeros; ++i) {
triplets.push_back(Triplet(cols[i], rows[i], 1));
}
SparseMatrix block_jacobian(block_jacobian_transpose.num_cols(),
block_jacobian_transpose.num_rows());
block_jacobian.setFromTriplets(triplets.begin(), triplets.end());
return block_jacobian;
}
#endif
void OrderingForSparseNormalCholeskyUsingSuiteSparse(
const TripletSparseMatrix& tsm_block_jacobian_transpose,
const vector<ParameterBlock*>& parameter_blocks,
const ParameterBlockOrdering& parameter_block_ordering,
int* ordering) {
#ifdef CERES_NO_SUITESPARSE
LOG(FATAL) << "Congratulations, you found a Ceres bug! "
<< "Please report this error to the developers.";
#else
SuiteSparse ss;
cholmod_sparse* block_jacobian_transpose =
ss.CreateSparseMatrix(
const_cast<TripletSparseMatrix*>(&tsm_block_jacobian_transpose));
// No CAMD or the user did not supply a useful ordering, then just
// use regular AMD.
if (parameter_block_ordering.NumGroups() <= 1 ||
!SuiteSparse::IsConstrainedApproximateMinimumDegreeOrderingAvailable()) {
ss.ApproximateMinimumDegreeOrdering(block_jacobian_transpose, &ordering[0]);
} else {
vector<int> constraints;
for (int i = 0; i < parameter_blocks.size(); ++i) {
constraints.push_back(
parameter_block_ordering.GroupId(
parameter_blocks[i]->mutable_user_state()));
}
// Renumber the entries of constraints to be contiguous integers
// as CAMD requires that the group ids be in the range [0,
// parameter_blocks.size() - 1].
MapValuesToContiguousRange(constraints.size(), &constraints[0]);
ss.ConstrainedApproximateMinimumDegreeOrdering(block_jacobian_transpose,
&constraints[0],
ordering);
}
VLOG(2) << "Block ordering stats: "
<< " flops: " << ss.mutable_cc()->fl
<< " lnz : " << ss.mutable_cc()->lnz
<< " anz : " << ss.mutable_cc()->anz;
ss.Free(block_jacobian_transpose);
#endif // CERES_NO_SUITESPARSE
}
void OrderingForSparseNormalCholeskyUsingCXSparse(
const TripletSparseMatrix& tsm_block_jacobian_transpose,
int* ordering) {
#ifdef CERES_NO_CXSPARSE
LOG(FATAL) << "Congratulations, you found a Ceres bug! "
<< "Please report this error to the developers.";
#else // CERES_NO_CXSPARSE
// CXSparse works with J'J instead of J'. So compute the block
// sparsity for J'J and compute an approximate minimum degree
// ordering.
CXSparse cxsparse;
cs_di* block_jacobian_transpose;
block_jacobian_transpose =
cxsparse.CreateSparseMatrix(
const_cast<TripletSparseMatrix*>(&tsm_block_jacobian_transpose));
cs_di* block_jacobian = cxsparse.TransposeMatrix(block_jacobian_transpose);
cs_di* block_hessian =
cxsparse.MatrixMatrixMultiply(block_jacobian_transpose, block_jacobian);
cxsparse.Free(block_jacobian);
cxsparse.Free(block_jacobian_transpose);
cxsparse.ApproximateMinimumDegreeOrdering(block_hessian, ordering);
cxsparse.Free(block_hessian);
#endif // CERES_NO_CXSPARSE
}
#if EIGEN_VERSION_AT_LEAST(3, 2, 2)
void OrderingForSparseNormalCholeskyUsingEigenSparse(
const TripletSparseMatrix& tsm_block_jacobian_transpose,
int* ordering) {
#ifndef CERES_USE_EIGEN_SPARSE
LOG(FATAL) <<
"SPARSE_NORMAL_CHOLESKY cannot be used with EIGEN_SPARSE "
"because Ceres was not built with support for "
"Eigen's SimplicialLDLT decomposition. "
"This requires enabling building with -DEIGENSPARSE=ON.";
#else
// This conversion from a TripletSparseMatrix to a Eigen::Triplet
// matrix is unfortunate, but unavoidable for now. It is not a
// significant performance penalty in the grand scheme of
// things. The right thing to do here would be to get a compressed
// row sparse matrix representation of the jacobian and go from
// there. But that is a project for another day.
typedef Eigen::SparseMatrix<int> SparseMatrix;
const SparseMatrix block_jacobian =
CreateBlockJacobian(tsm_block_jacobian_transpose);
const SparseMatrix block_hessian =
block_jacobian.transpose() * block_jacobian;
Eigen::AMDOrdering<int> amd_ordering;
Eigen::PermutationMatrix<Eigen::Dynamic, Eigen::Dynamic, int> perm;
amd_ordering(block_hessian, perm);
for (int i = 0; i < block_hessian.rows(); ++i) {
ordering[i] = perm.indices()[i];
}
#endif // CERES_USE_EIGEN_SPARSE
}
#endif
} // namespace
bool ApplyOrdering(const ProblemImpl::ParameterMap& parameter_map,
const ParameterBlockOrdering& ordering,
Program* program,
string* error) {
const int num_parameter_blocks = program->NumParameterBlocks();
if (ordering.NumElements() != num_parameter_blocks) {
*error = StringPrintf("User specified ordering does not have the same "
"number of parameters as the problem. The problem"
"has %d blocks while the ordering has %d blocks.",
num_parameter_blocks,
ordering.NumElements());
return false;
}
vector<ParameterBlock*>* parameter_blocks =
program->mutable_parameter_blocks();
parameter_blocks->clear();
const map<int, set<double*> >& groups = ordering.group_to_elements();
for (map<int, set<double*> >::const_iterator group_it = groups.begin();
group_it != groups.end();
++group_it) {
const set<double*>& group = group_it->second;
for (set<double*>::const_iterator parameter_block_ptr_it = group.begin();
parameter_block_ptr_it != group.end();
++parameter_block_ptr_it) {
ProblemImpl::ParameterMap::const_iterator parameter_block_it =
parameter_map.find(*parameter_block_ptr_it);
if (parameter_block_it == parameter_map.end()) {
*error = StringPrintf("User specified ordering contains a pointer "
"to a double that is not a parameter block in "
"the problem. The invalid double is in group: %d",
group_it->first);
return false;
}
parameter_blocks->push_back(parameter_block_it->second);
}
}
return true;
}
bool LexicographicallyOrderResidualBlocks(
const int size_of_first_elimination_group,
Program* program,
string* error) {
CHECK_GE(size_of_first_elimination_group, 1)
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
// Create a histogram of the number of residuals for each E block. There is an
// extra bucket at the end to catch all non-eliminated F blocks.
vector<int> residual_blocks_per_e_block(size_of_first_elimination_group + 1);
vector<ResidualBlock*>* residual_blocks = program->mutable_residual_blocks();
vector<int> min_position_per_residual(residual_blocks->size());
for (int i = 0; i < residual_blocks->size(); ++i) {
ResidualBlock* residual_block = (*residual_blocks)[i];
int position = MinParameterBlock(residual_block,
size_of_first_elimination_group);
min_position_per_residual[i] = position;
DCHECK_LE(position, size_of_first_elimination_group);
residual_blocks_per_e_block[position]++;
}
// Run a cumulative sum on the histogram, to obtain offsets to the start of
// each histogram bucket (where each bucket is for the residuals for that
// E-block).
vector<int> offsets(size_of_first_elimination_group + 1);
std::partial_sum(residual_blocks_per_e_block.begin(),
residual_blocks_per_e_block.end(),
offsets.begin());
CHECK_EQ(offsets.back(), residual_blocks->size())
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
CHECK(find(residual_blocks_per_e_block.begin(),
residual_blocks_per_e_block.end() - 1, 0) !=
residual_blocks_per_e_block.end())
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
// Fill in each bucket with the residual blocks for its corresponding E block.
// Each bucket is individually filled from the back of the bucket to the front
// of the bucket. The filling order among the buckets is dictated by the
// residual blocks. This loop uses the offsets as counters; subtracting one
// from each offset as a residual block is placed in the bucket. When the
// filling is finished, the offset pointerts should have shifted down one
// entry (this is verified below).
vector<ResidualBlock*> reordered_residual_blocks(
(*residual_blocks).size(), static_cast<ResidualBlock*>(NULL));
for (int i = 0; i < residual_blocks->size(); ++i) {
int bucket = min_position_per_residual[i];
// Decrement the cursor, which should now point at the next empty position.
offsets[bucket]--;
// Sanity.
CHECK(reordered_residual_blocks[offsets[bucket]] == NULL)
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
reordered_residual_blocks[offsets[bucket]] = (*residual_blocks)[i];
}
// Sanity check #1: The difference in bucket offsets should match the
// histogram sizes.
for (int i = 0; i < size_of_first_elimination_group; ++i) {
CHECK_EQ(residual_blocks_per_e_block[i], offsets[i + 1] - offsets[i])
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
}
// Sanity check #2: No NULL's left behind.
for (int i = 0; i < reordered_residual_blocks.size(); ++i) {
CHECK(reordered_residual_blocks[i] != NULL)
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
}
// Now that the residuals are collected by E block, swap them in place.
swap(*program->mutable_residual_blocks(), reordered_residual_blocks);
return true;
}
// Pre-order the columns corresponding to the schur complement if
// possible.
void MaybeReorderSchurComplementColumnsUsingSuiteSparse(
const ParameterBlockOrdering& parameter_block_ordering,
Program* program) {
#ifndef CERES_NO_SUITESPARSE
SuiteSparse ss;
if (!SuiteSparse::IsConstrainedApproximateMinimumDegreeOrderingAvailable()) {
return;
}
vector<int> constraints;
vector<ParameterBlock*>& parameter_blocks =
*(program->mutable_parameter_blocks());
for (int i = 0; i < parameter_blocks.size(); ++i) {
constraints.push_back(
parameter_block_ordering.GroupId(
parameter_blocks[i]->mutable_user_state()));
}
// Renumber the entries of constraints to be contiguous integers as
// CAMD requires that the group ids be in the range [0,
// parameter_blocks.size() - 1].
MapValuesToContiguousRange(constraints.size(), &constraints[0]);
// Compute a block sparse presentation of J'.
scoped_ptr<TripletSparseMatrix> tsm_block_jacobian_transpose(
program->CreateJacobianBlockSparsityTranspose());
cholmod_sparse* block_jacobian_transpose =
ss.CreateSparseMatrix(tsm_block_jacobian_transpose.get());
vector<int> ordering(parameter_blocks.size(), 0);
ss.ConstrainedApproximateMinimumDegreeOrdering(block_jacobian_transpose,
&constraints[0],
&ordering[0]);
ss.Free(block_jacobian_transpose);
const vector<ParameterBlock*> parameter_blocks_copy(parameter_blocks);
for (int i = 0; i < program->NumParameterBlocks(); ++i) {
parameter_blocks[i] = parameter_blocks_copy[ordering[i]];
}
program->SetParameterOffsetsAndIndex();
#endif
}
void MaybeReorderSchurComplementColumnsUsingEigen(
const int size_of_first_elimination_group,
const ProblemImpl::ParameterMap& parameter_map,
Program* program) {
#if !EIGEN_VERSION_AT_LEAST(3, 2, 2) || !defined(CERES_USE_EIGEN_SPARSE)
return;
#else
scoped_ptr<TripletSparseMatrix> tsm_block_jacobian_transpose(
program->CreateJacobianBlockSparsityTranspose());
typedef Eigen::SparseMatrix<int> SparseMatrix;
const SparseMatrix block_jacobian =
CreateBlockJacobian(*tsm_block_jacobian_transpose);
const int num_rows = block_jacobian.rows();
const int num_cols = block_jacobian.cols();
// Vertically partition the jacobian in parameter blocks of type E
// and F.
const SparseMatrix E =
block_jacobian.block(0,
0,
num_rows,
size_of_first_elimination_group);
const SparseMatrix F =
block_jacobian.block(0,
size_of_first_elimination_group,
num_rows,
num_cols - size_of_first_elimination_group);
// Block sparsity pattern of the schur complement.
const SparseMatrix block_schur_complement =
F.transpose() * F - F.transpose() * E * E.transpose() * F;
Eigen::AMDOrdering<int> amd_ordering;
Eigen::PermutationMatrix<Eigen::Dynamic, Eigen::Dynamic, int> perm;
amd_ordering(block_schur_complement, perm);
const vector<ParameterBlock*>& parameter_blocks = program->parameter_blocks();
vector<ParameterBlock*> ordering(num_cols);
// The ordering of the first size_of_first_elimination_group does
// not matter, so we preserve the existing ordering.
for (int i = 0; i < size_of_first_elimination_group; ++i) {
ordering[i] = parameter_blocks[i];
}
// For the rest of the blocks, use the ordering computed using AMD.
for (int i = 0; i < block_schur_complement.cols(); ++i) {
ordering[size_of_first_elimination_group + i] =
parameter_blocks[size_of_first_elimination_group + perm.indices()[i]];
}
swap(*program->mutable_parameter_blocks(), ordering);
program->SetParameterOffsetsAndIndex();
#endif
}
bool ReorderProgramForSchurTypeLinearSolver(
const LinearSolverType linear_solver_type,
const SparseLinearAlgebraLibraryType sparse_linear_algebra_library_type,
const ProblemImpl::ParameterMap& parameter_map,
ParameterBlockOrdering* parameter_block_ordering,
Program* program,
string* error) {
if (parameter_block_ordering->NumElements() !=
program->NumParameterBlocks()) {
*error = StringPrintf(
"The program has %d parameter blocks, but the parameter block "
"ordering has %d parameter blocks.",
program->NumParameterBlocks(),
parameter_block_ordering->NumElements());
return false;
}
if (parameter_block_ordering->NumGroups() == 1) {
// If the user supplied an parameter_block_ordering with just one
// group, it is equivalent to the user supplying NULL as an
// parameter_block_ordering. Ceres is completely free to choose the
// parameter block ordering as it sees fit. For Schur type solvers,
// this means that the user wishes for Ceres to identify the
// e_blocks, which we do by computing a maximal independent set.
vector<ParameterBlock*> schur_ordering;
const int size_of_first_elimination_group =
ComputeStableSchurOrdering(*program, &schur_ordering);
CHECK_EQ(schur_ordering.size(), program->NumParameterBlocks())
<< "Congratulations, you found a Ceres bug! Please report this error "
<< "to the developers.";
// Update the parameter_block_ordering object.
for (int i = 0; i < schur_ordering.size(); ++i) {
double* parameter_block = schur_ordering[i]->mutable_user_state();
const int group_id = (i < size_of_first_elimination_group) ? 0 : 1;
parameter_block_ordering->AddElementToGroup(parameter_block, group_id);
}
// We could call ApplyOrdering but this is cheaper and
// simpler.
swap(*program->mutable_parameter_blocks(), schur_ordering);
} else {
// The user provided an ordering with more than one elimination
// group.
// Verify that the first elimination group is an independent set.
const set<double*>& first_elimination_group =
parameter_block_ordering
->group_to_elements()
.begin()
->second;
if (!program->IsParameterBlockSetIndependent(first_elimination_group)) {
*error =
StringPrintf("The first elimination group in the parameter block "
"ordering of size %zd is not an independent set",
first_elimination_group.size());
return false;
}
if (!ApplyOrdering(parameter_map,
*parameter_block_ordering,
program,
error)) {
return false;
}
}
program->SetParameterOffsetsAndIndex();
const int size_of_first_elimination_group =
parameter_block_ordering->group_to_elements().begin()->second.size();
if (linear_solver_type == SPARSE_SCHUR) {
if (sparse_linear_algebra_library_type == SUITE_SPARSE) {
MaybeReorderSchurComplementColumnsUsingSuiteSparse(
*parameter_block_ordering,
program);
} else if (sparse_linear_algebra_library_type == EIGEN_SPARSE) {
MaybeReorderSchurComplementColumnsUsingEigen(
size_of_first_elimination_group,
parameter_map,
program);
}
}
// Schur type solvers also require that their residual blocks be
// lexicographically ordered.
if (!LexicographicallyOrderResidualBlocks(size_of_first_elimination_group,
program,
error)) {
return false;
}
return true;
}
bool ReorderProgramForSparseNormalCholesky(
const SparseLinearAlgebraLibraryType sparse_linear_algebra_library_type,
const ParameterBlockOrdering& parameter_block_ordering,
Program* program,
string* error) {
if (parameter_block_ordering.NumElements() != program->NumParameterBlocks()) {
*error = StringPrintf(
"The program has %d parameter blocks, but the parameter block "
"ordering has %d parameter blocks.",
program->NumParameterBlocks(),
parameter_block_ordering.NumElements());
return false;
}
// Compute a block sparse presentation of J'.
scoped_ptr<TripletSparseMatrix> tsm_block_jacobian_transpose(
program->CreateJacobianBlockSparsityTranspose());
vector<int> ordering(program->NumParameterBlocks(), 0);
vector<ParameterBlock*>& parameter_blocks =
*(program->mutable_parameter_blocks());
if (sparse_linear_algebra_library_type == SUITE_SPARSE) {
OrderingForSparseNormalCholeskyUsingSuiteSparse(
*tsm_block_jacobian_transpose,
parameter_blocks,
parameter_block_ordering,
&ordering[0]);
} else if (sparse_linear_algebra_library_type == CX_SPARSE) {
OrderingForSparseNormalCholeskyUsingCXSparse(
*tsm_block_jacobian_transpose,
&ordering[0]);
} else if (sparse_linear_algebra_library_type == EIGEN_SPARSE) {
#if EIGEN_VERSION_AT_LEAST(3, 2, 2)
OrderingForSparseNormalCholeskyUsingEigenSparse(
*tsm_block_jacobian_transpose,
&ordering[0]);
#else
// For Eigen versions less than 3.2.2, there is nothing to do as
// older versions of Eigen do not expose a method for doing
// symbolic analysis on pre-ordered matrices, so a block
// pre-ordering is a bit pointless.
return true;
#endif
}
// Apply ordering.
const vector<ParameterBlock*> parameter_blocks_copy(parameter_blocks);
for (int i = 0; i < program->NumParameterBlocks(); ++i) {
parameter_blocks[i] = parameter_blocks_copy[ordering[i]];
}
program->SetParameterOffsetsAndIndex();
return true;
}
} // namespace internal
} // namespace ceres