// 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/
//
// 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
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// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#ifndef CERES_NO_SUITESPARSE
#include "ceres/suitesparse.h"
#include <vector>
#include "cholmod.h"
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/triplet_sparse_matrix.h"
namespace ceres {
namespace internal {
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 = new cholmod_sparse_struct;
m->nrow = A->num_cols();
m->ncol = A->num_rows();
m->nzmax = A->num_nonzeros();
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->stype = 0; // Matrix is not symmetric.
m->itype = CHOLMOD_INT;
m->xtype = CHOLMOD_REAL;
m->dtype = CHOLMOD_DOUBLE;
m->sorted = 1;
m->packed = 1;
return m;
}
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 != NULL) {
memcpy(v->x, x, in_size*sizeof(*x));
}
return v;
}
cholmod_factor* SuiteSparse::AnalyzeCholesky(cholmod_sparse* A) {
// 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_);
CHECK_EQ(cc_.status, CHOLMOD_OK)
<< "Cholmod symbolic analysis failed " << cc_.status;
CHECK_NOTNULL(factor);
return factor;
}
cholmod_factor* SuiteSparse::BlockAnalyzeCholesky(
cholmod_sparse* A,
const vector<int>& row_blocks,
const vector<int>& col_blocks) {
vector<int> ordering;
if (!BlockAMDOrdering(A, row_blocks, col_blocks, &ordering)) {
return NULL;
}
return AnalyzeCholeskyWithUserOrdering(A, ordering);
}
cholmod_factor* SuiteSparse::AnalyzeCholeskyWithUserOrdering(cholmod_sparse* A,
const vector<int>& ordering) {
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]), NULL, 0, &cc_);
CHECK_EQ(cc_.status, CHOLMOD_OK)
<< "Cholmod symbolic analysis failed " << cc_.status;
CHECK_NOTNULL(factor);
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;
ScalarMatrixToBlockMatrix(A,
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 = NULL;
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, NULL, 0, &block_ordering[0], &cc_)) {
return false;
}
BlockOrderingToScalarOrdering(row_blocks, block_ordering, ordering);
return true;
}
void SuiteSparse::ScalarMatrixToBlockMatrix(const cholmod_sparse* A,
const vector<int>& row_blocks,
const vector<int>& col_blocks,
vector<int>* block_rows,
vector<int>* block_cols) {
CHECK_NOTNULL(block_rows)->clear();
CHECK_NOTNULL(block_cols)->clear();
const int num_row_blocks = row_blocks.size();
const int num_col_blocks = col_blocks.size();
vector<int> row_block_starts(num_row_blocks);
for (int i = 0, cursor = 0; i < num_row_blocks; ++i) {
row_block_starts[i] = cursor;
cursor += row_blocks[i];
}
// The reinterpret_cast is needed here because CHOLMOD stores arrays
// as void*.
const int* scalar_cols = reinterpret_cast<const int*>(A->p);
const int* scalar_rows = reinterpret_cast<const int*>(A->i);
// This loop extracts the block sparsity of the scalar sparse matrix
// A. It does so by iterating over the columns, but only considering
// the columns corresponding to the first element of each column
// block. Within each column, the inner loop iterates over the rows,
// and detects the presence of a row block by checking for the
// presence of a non-zero entry corresponding to its first element.
block_cols->push_back(0);
int c = 0;
for (int col_block = 0; col_block < num_col_blocks; ++col_block) {
int column_size = 0;
for (int idx = scalar_cols[c]; idx < scalar_cols[c + 1]; ++idx) {
vector<int>::const_iterator it = lower_bound(row_block_starts.begin(),
row_block_starts.end(),
scalar_rows[idx]);
// Since we are using lower_bound, it will return the row id
// where the row block starts. For everything but the first row
// of the block, where these values will be the same, we can
// skip, as we only need the first row to detect the presence of
// the block.
//
// For rows all but the first row in the last row block,
// lower_bound will return row_block_starts.end(), but those can
// be skipped like the rows in other row blocks too.
if (it == row_block_starts.end() || *it != scalar_rows[idx]) {
continue;
}
block_rows->push_back(it - row_block_starts.begin());
++column_size;
}
block_cols->push_back(block_cols->back() + column_size);
c += col_blocks[col_block];
}
}
void SuiteSparse::BlockOrderingToScalarOrdering(
const vector<int>& blocks,
const vector<int>& block_ordering,
vector<int>* scalar_ordering) {
CHECK_EQ(blocks.size(), block_ordering.size());
const int num_blocks = blocks.size();
// block_starts = [0, block1, block1 + block2 ..]
vector<int> block_starts(num_blocks);
for (int i = 0, cursor = 0; i < num_blocks ; ++i) {
block_starts[i] = cursor;
cursor += blocks[i];
}
scalar_ordering->resize(block_starts.back() + blocks.back());
int cursor = 0;
for (int i = 0; i < num_blocks; ++i) {
const int block_id = block_ordering[i];
const int block_size = blocks[block_id];
int block_position = block_starts[block_id];
for (int j = 0; j < block_size; ++j) {
(*scalar_ordering)[cursor++] = block_position++;
}
}
}
bool SuiteSparse::Cholesky(cholmod_sparse* A, cholmod_factor* L) {
CHECK_NOTNULL(A);
CHECK_NOTNULL(L);
cc_.quick_return_if_not_posdef = 1;
int status = cholmod_factorize(A, L, &cc_);
switch (cc_.status) {
case CHOLMOD_NOT_INSTALLED:
LOG(WARNING) << "Cholmod failure: method not installed.";
return false;
case CHOLMOD_OUT_OF_MEMORY:
LOG(WARNING) << "Cholmod failure: out of memory.";
return false;
case CHOLMOD_TOO_LARGE:
LOG(WARNING) << "Cholmod failure: integer overflow occured.";
return false;
case CHOLMOD_INVALID:
LOG(WARNING) << "Cholmod failure: invalid input.";
return false;
case CHOLMOD_NOT_POSDEF:
// TODO(sameeragarwal): These two warnings require more
// sophisticated handling going forward. For now we will be
// strict and treat them as failures.
LOG(WARNING) << "Cholmod warning: matrix not positive definite.";
return false;
case CHOLMOD_DSMALL:
LOG(WARNING) << "Cholmod warning: D for LDL' or diag(L) or "
<< "LL' has tiny absolute value.";
return false;
case CHOLMOD_OK:
if (status != 0) {
return true;
}
LOG(WARNING) << "Cholmod failure: cholmod_factorize returned zero "
<< "but cholmod_common::status is CHOLMOD_OK."
<< "Please report this to ceres-solver@googlegroups.com.";
return false;
default:
LOG(WARNING) << "Unknown cholmod return code. "
<< "Please report this to ceres-solver@googlegroups.com.";
return false;
}
return false;
}
cholmod_dense* SuiteSparse::Solve(cholmod_factor* L,
cholmod_dense* b) {
if (cc_.status != CHOLMOD_OK) {
LOG(WARNING) << "CHOLMOD status NOT OK";
return NULL;
}
return cholmod_solve(CHOLMOD_A, L, b, &cc_);
}
cholmod_dense* SuiteSparse::SolveCholesky(cholmod_sparse* A,
cholmod_factor* L,
cholmod_dense* b) {
CHECK_NOTNULL(A);
CHECK_NOTNULL(L);
CHECK_NOTNULL(b);
if (Cholesky(A, L)) {
return Solve(L, b);
}
return NULL;
}
} // namespace internal
} // namespace ceres
#endif // CERES_NO_SUITESPARSE