Add a general sparse iterative solver: CGNR
This adds a new LinearOperator which implements symmetric
products of a matrix, and a new CGNR solver to leverage
CG to directly solve the normal equations. This also
includes a block diagonal preconditioner. In experiments
on problem-16, the non-preconditioned version is about
1/5 the speed of SPARSE_SCHUR, and the preconditioned
version using block cholesky is about 20% slower than
SPARSE_SCHUR.
diff --git a/internal/ceres/block_diagonal_preconditioner.cc b/internal/ceres/block_diagonal_preconditioner.cc
new file mode 100644
index 0000000..0779a91
--- /dev/null
+++ b/internal/ceres/block_diagonal_preconditioner.cc
@@ -0,0 +1,118 @@
+// 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: keir@google.com (Keir Mierle)
+
+#include "ceres/block_diagonal_preconditioner.h"
+
+#include "Eigen/Cholesky"
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/block_structure.h"
+#include "ceres/casts.h"
+#include "ceres/internal/eigen.h"
+
+namespace ceres {
+namespace internal {
+
+BlockDiagonalPreconditioner::BlockDiagonalPreconditioner(
+ const LinearOperator& A)
+ : block_structure_(
+ *(down_cast<const BlockSparseMatrix*>(&A)->block_structure())) {
+
+ // Calculate the amount of storage needed.
+ int storage_needed = 0;
+ for (int c = 0; c < block_structure_.cols.size(); ++c) {
+ int size = block_structure_.cols[c].size;
+ storage_needed += size * size;
+ }
+
+ // Size the offsets and storage.
+ blocks_.resize(block_structure_.cols.size());
+ block_storage_.resize(storage_needed);
+
+ // Put pointers to the storage in the offsets.
+ double *block_cursor = &block_storage_[0];
+ for (int c = 0; c < block_structure_.cols.size(); ++c) {
+ int size = block_structure_.cols[c].size;
+ blocks_[c] = block_cursor;
+ block_cursor += size * size;
+ }
+}
+
+BlockDiagonalPreconditioner::~BlockDiagonalPreconditioner() {
+}
+
+void BlockDiagonalPreconditioner::Update(const LinearOperator& matrix) {
+ const BlockSparseMatrix& A = *(down_cast<const BlockSparseMatrix*>(&matrix));
+ const CompressedRowBlockStructure* bs = A.block_structure();
+
+ // Compute the diagonal blocks by block inner products.
+ std::fill(block_storage_.begin(), block_storage_.end(), 0.0);
+ for (int r = 0; r < bs->rows.size(); ++r) {
+ const int row_block_size = bs->rows[r].block.size;
+ const vector<Cell>& cells = bs->rows[r].cells;
+ const double* row_values = A.RowBlockValues(r);
+ for (int c = 0; c < cells.size(); ++c) {
+ const int col_block_size = bs->cols[cells[c].block_id].size;
+ ConstMatrixRef m(row_values + cells[c].position,
+ row_block_size,
+ col_block_size);
+
+ MatrixRef(blocks_[cells[c].block_id],
+ col_block_size,
+ col_block_size).noalias() += m.transpose() * m;
+ }
+ }
+
+ // Invert each block.
+ for (int c = 0; c < bs->cols.size(); ++c) {
+ const int size = block_structure_.cols[c].size;
+ MatrixRef D(blocks_[c], size, size);
+ D = D.selfadjointView<Eigen::Upper>()
+ .ldlt()
+ .solve(Matrix::Identity(size, size));
+ }
+}
+
+void BlockDiagonalPreconditioner::RightMultiply(const double* x, double* y) const {
+ for (int c = 0; c < block_structure_.cols.size(); ++c) {
+ const int size = block_structure_.cols[c].size;
+ const int position = block_structure_.cols[c].position;
+ ConstMatrixRef D(blocks_[c], size, size);
+ ConstVectorRef x_block(x + position, size);
+ VectorRef y_block(y + position, size);
+ y_block += D * x_block;
+ }
+}
+
+void BlockDiagonalPreconditioner::LeftMultiply(const double* x, double* y) const {
+ RightMultiply(x, y);
+}
+
+} // namespace internal
+} // namespace ceres
