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/examples/bundle_adjuster.cc b/examples/bundle_adjuster.cc
index 718fde9..1216a82 100644
--- a/examples/bundle_adjuster.cc
+++ b/examples/bundle_adjuster.cc
@@ -70,17 +70,20 @@
DEFINE_string(preconditioner_type, "jacobi", "Options are: "
"identity, jacobi, schur_jacobi, cluster_jacobi, "
"cluster_tridiagonal");
+DEFINE_string(sparse_linear_algebra_library, "suitesparse",
+ "Options are: suitesparse and cxsparse");
DEFINE_int32(num_iterations, 5, "Number of iterations");
DEFINE_int32(num_threads, 1, "Number of threads");
DEFINE_double(eta, 1e-2, "Default value for eta. Eta determines the "
"accuracy of each linear solve of the truncated newton step. "
"Changing this parameter can affect solve performance ");
-DEFINE_bool(use_schur_ordering, false, "Use automatic Schur ordering.");
+DEFINE_string(ordering_type, "schur", "Options are: schur, user, natural");
DEFINE_bool(use_quaternions, false, "If true, uses quaternions to represent "
"rotations. If false, angle axis is used");
DEFINE_bool(use_local_parameterization, false, "For quaternions, use a local "
"parameterization.");
DEFINE_bool(robustify, false, "Use a robust loss function");
+DEFINE_bool(use_block_amd, true, "Use a block oriented fill reducing ordering.");
namespace ceres {
namespace examples {
@@ -138,10 +141,31 @@
}
}
+ if (FLAGS_sparse_linear_algebra_library == "suitesparse") {
+ options->sparse_linear_algebra_library = SUITE_SPARSE;
+ } else if (FLAGS_sparse_linear_algebra_library == "cxsparse") {
+ options->sparse_linear_algebra_library = CX_SPARSE;
+ } else {
+ LOG(FATAL) << "Unknown sparse linear algebra library type.";
+ }
+
options->num_linear_solver_threads = FLAGS_num_threads;
}
void SetOrdering(BALProblem* bal_problem, Solver::Options* options) {
+ options->use_block_amd = FLAGS_use_block_amd;
+
+ // Only non-Schur solvers support the natural ordering for this
+ // problem.
+ if (FLAGS_ordering_type == "natural") {
+ if (options->linear_solver_type == SPARSE_SCHUR ||
+ options->linear_solver_type == DENSE_SCHUR ||
+ options->linear_solver_type == ITERATIVE_SCHUR) {
+ LOG(FATAL) << "Natural ordering with Schur type solver does not work.";
+ }
+ return;
+ }
+
// Bundle adjustment problems have a sparsity structure that makes
// them amenable to more specialized and much more efficient
// solution strategies. The SPARSE_SCHUR, DENSE_SCHUR and
@@ -156,7 +180,7 @@
// the right ParameterBlock ordering, or by manually specifying a
// suitable ordering vector and defining
// Options::num_eliminate_blocks.
- if (FLAGS_use_schur_ordering) {
+ if (FLAGS_ordering_type == "schur") {
options->ordering_type = ceres::SCHUR;
return;
}
@@ -272,7 +296,6 @@
BuildProblem(&bal_problem, &problem);
Solver::Options options;
SetSolverOptionsFromFlags(&bal_problem, &options);
-
Solver::Summary summary;
Solve(options, &problem, &summary);
std::cout << summary.FullReport() << "\n";
