Block oriented fill reducing orderings.
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 can either be run on the
block or the scalar form of these matrices. Running it on the
block form exposes more of the super-nodal structure of the
matrix to the Cholesky factorization routines. This leads to
substantial gains in factorization performance.
This changelist adds support for approximate minimium degree
orderings to be computed on the block structure of the
Schur complement matrix. This affects, SchurComplementSolver
and VisibilityBasedPreconditioner and SparseNormalCholesky
when using SuiteSparse.
A bool, use_block_amd has been added to Solver::Options and
bundle_adjuster.cc has been updated to allow testing with it.
When combined with a multithreaded Schur elimination, speed ups
can be seen quite uniformly across the board. For some problems
this can be dramatic, reducing the factorization time from 70
seconds down to 17 seconds.
Change-Id: I15ebb0afcbc85ada032ec8d179ee3a2f7c8d3e46
diff --git a/internal/ceres/sparse_normal_cholesky_solver.cc b/internal/ceres/sparse_normal_cholesky_solver.cc
index 5a082de..4191f3c 100644
--- a/internal/ceres/sparse_normal_cholesky_solver.cc
+++ b/internal/ceres/sparse_normal_cholesky_solver.cc
@@ -46,8 +46,6 @@
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"
-
-
namespace ceres {
namespace internal {
@@ -55,15 +53,15 @@
const LinearSolver::Options& options)
: options_(options) {
#ifndef CERES_NO_SUITESPARSE
- symbolic_factor_ = NULL;
+ factor_ = NULL;
#endif
}
SparseNormalCholeskySolver::~SparseNormalCholeskySolver() {
#ifndef CERES_NO_SUITESPARSE
- if (symbolic_factor_ != NULL) {
- ss_.Free(symbolic_factor_);
- symbolic_factor_ = NULL;
+ if (factor_ != NULL) {
+ ss_.Free(factor_);
+ factor_ = NULL;
}
#endif
}
@@ -183,13 +181,25 @@
cholmod_dense* rhs = ss_.CreateDenseVector(Atb.data(), num_cols, num_cols);
const time_t init_time = time(NULL);
- if (symbolic_factor_ == NULL) {
- symbolic_factor_ = CHECK_NOTNULL(ss_.AnalyzeCholesky(lhs.get()));
+ 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(), symbolic_factor_, rhs);
+ cholmod_dense* sol = ss_.SolveCholesky(lhs.get(), factor_, rhs);
const time_t solve_time = time(NULL);
ss_.Free(rhs);
@@ -209,11 +219,11 @@
}
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;
+ 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
