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/suitesparse_test.cc b/internal/ceres/suitesparse_test.cc
new file mode 100644
index 0000000..9211788
--- /dev/null
+++ b/internal/ceres/suitesparse_test.cc
@@ -0,0 +1,194 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 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
+// 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)
+
+#include <algorithm>
+#include <glog/logging.h>
+#include "gtest/gtest.h"
+#include "ceres/suitesparse.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/internal/port.h"
+
+namespace ceres {
+namespace internal {
+
+TEST(SuiteSparse, BlockPermutationToScalarPermutation) {
+ vector<int> blocks;
+ // Block structure
+ // 0 --1- ---2--- ---3--- 4
+ // [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+ blocks.push_back(1);
+ blocks.push_back(2);
+ blocks.push_back(3);
+ blocks.push_back(3);
+ blocks.push_back(1);
+
+ // Block ordering
+ // [1, 0, 2, 4, 5]
+ vector<int> block_ordering;
+ block_ordering.push_back(1);
+ block_ordering.push_back(0);
+ block_ordering.push_back(2);
+ block_ordering.push_back(4);
+ block_ordering.push_back(3);
+
+ // Expected ordering
+ // [1, 2, 0, 3, 4, 5, 9, 6, 7, 8]
+ vector<int> expected_scalar_ordering;
+ expected_scalar_ordering.push_back(1);
+ expected_scalar_ordering.push_back(2);
+ expected_scalar_ordering.push_back(0);
+ expected_scalar_ordering.push_back(3);
+ expected_scalar_ordering.push_back(4);
+ expected_scalar_ordering.push_back(5);
+ expected_scalar_ordering.push_back(9);
+ expected_scalar_ordering.push_back(6);
+ expected_scalar_ordering.push_back(7);
+ expected_scalar_ordering.push_back(8);
+
+ vector<int> scalar_ordering;
+ SuiteSparse::BlockOrderingToScalarOrdering(blocks,
+ block_ordering,
+ &scalar_ordering);
+ EXPECT_EQ(scalar_ordering.size(), expected_scalar_ordering.size());
+ for (int i = 0; i < expected_scalar_ordering.size(); ++i) {
+ EXPECT_EQ(scalar_ordering[i], expected_scalar_ordering[i]);
+ }
+}
+
+// Helper function to fill the sparsity pattern of a TripletSparseMatrix.
+int FillBlock(const vector<int>& row_blocks,
+ const vector<int>& col_blocks,
+ const int row_block_id,
+ const int col_block_id,
+ int* rows,
+ int* cols) {
+ int row_pos = 0;
+ for (int i = 0; i < row_block_id; ++i) {
+ row_pos += row_blocks[i];
+ }
+
+ int col_pos = 0;
+ for (int i = 0; i < col_block_id; ++i) {
+ col_pos += col_blocks[i];
+ }
+
+ int offset = 0;
+ for (int r = 0; r < row_blocks[row_block_id]; ++r) {
+ for (int c = 0; c < col_blocks[col_block_id]; ++c, ++offset) {
+ rows[offset] = row_pos + r;
+ cols[offset] = col_pos + c;
+ }
+ }
+ return offset;
+}
+
+TEST(SuiteSparse, ScalarMatrixToBlockMatrix) {
+ // Block sparsity.
+ //
+ // [1 2 3 2]
+ // [1] x x
+ // [2] x x
+ // [1] x x
+ // num_nonzeros = 1 + 3 + 4 + 4 + 1 + 2 = 15
+
+ vector<int> col_blocks;
+ col_blocks.push_back(1);
+ col_blocks.push_back(2);
+ col_blocks.push_back(3);
+ col_blocks.push_back(2);
+
+ vector<int> row_blocks;
+ row_blocks.push_back(1);
+ row_blocks.push_back(2);
+ row_blocks.push_back(1);
+
+ TripletSparseMatrix tsm(4, 8, 15);
+ int* rows = tsm.mutable_rows();
+ int* cols = tsm.mutable_cols();
+ fill(tsm.mutable_values(), tsm.mutable_values() + 15, 1.0);
+ int offset = 0;
+
+#define CERES_TEST_FILL_BLOCK(r, c) \
+ offset += FillBlock(row_blocks, col_blocks, \
+ row_block_id, col_block_id, \
+ rows + offset, cols + offset);
+
+ CERES_TEST_FILL_BLOCK(0, 0);
+ CERES_TEST_FILL_BLOCK(2, 0);
+ CERES_TEST_FILL_BLOCK(1, 1);
+ CERES_TEST_FILL_BLOCK(2, 1);
+ CERES_TEST_FILL_BLOCK(0, 2);
+ CERES_TEST_FILL_BLOCK(1, 3);
+#undef CERES_TEST_FILL_BLOCK
+
+ tsm.set_num_nonzeros(offset);
+
+ SuiteSparse ss;
+ scoped_ptr<cholmod_sparse> ccsm(ss.CreateSparseMatrix(&tsm));
+
+ vector<int> expected_block_rows;
+ expected_block_rows.push_back(0);
+ expected_block_rows.push_back(2);
+ expected_block_rows.push_back(1);
+ expected_block_rows.push_back(2);
+ expected_block_rows.push_back(0);
+ expected_block_rows.push_back(1);
+
+ vector<int> expected_block_cols;
+ expected_block_cols.push_back(0);
+ expected_block_cols.push_back(2);
+ expected_block_cols.push_back(4);
+ expected_block_cols.push_back(5);
+ expected_block_cols.push_back(6);
+
+ vector<int> block_rows;
+ vector<int> block_cols;
+ SuiteSparse::ScalarMatrixToBlockMatrix(ccsm.get(),
+ row_blocks,
+ col_blocks,
+ &block_rows,
+ &block_cols);
+
+ EXPECT_EQ(block_cols.size(), expected_block_cols.size());
+ EXPECT_EQ(block_rows.size(), expected_block_rows.size());
+
+ for (int i = 0; i < expected_block_cols.size(); ++i) {
+ EXPECT_EQ(block_cols[i], expected_block_cols[i]);
+ }
+
+ for (int i = 0; i < expected_block_rows.size(); ++i) {
+ EXPECT_EQ(block_rows[i], expected_block_rows[i]);
+ }
+
+ ss.Free(ccsm.release());
+}
+
+} // namespace internal
+} // namespace ceres
