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// 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
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// 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)
//
// TODO(sameeragarwal): row_block_counter can perhaps be replaced by
// Chunk::start ?
#ifndef CERES_INTERNAL_SCHUR_ELIMINATOR_IMPL_H_
#define CERES_INTERNAL_SCHUR_ELIMINATOR_IMPL_H_
// Eigen has an internal threshold switching between different matrix
// multiplication algorithms. In particular for matrices larger than
// EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD it uses a cache friendly
// matrix matrix product algorithm that has a higher setup cost. For
// matrix sizes close to this threshold, especially when the matrices
// are thin and long, the default choice may not be optimal. This is
// the case for us, as the default choice causes a 30% performance
// regression when we moved from Eigen2 to Eigen3.
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 10
#ifdef CERES_USE_OPENMP
#include <omp.h>
#endif
#include <algorithm>
#include <map>
#include "ceres/blas.h"
#include "ceres/block_random_access_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/fixed_array.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/map_util.h"
#include "ceres/schur_eliminator.h"
#include "ceres/stl_util.h"
#include "Eigen/Dense"
#include "glog/logging.h"
namespace ceres {
namespace internal {
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::~SchurEliminator() {
STLDeleteElements(&rhs_locks_);
}
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
Init(int num_eliminate_blocks, const CompressedRowBlockStructure* bs) {
CHECK_GT(num_eliminate_blocks, 0)
<< "SchurComplementSolver cannot be initialized with "
<< "num_eliminate_blocks = 0.";
num_eliminate_blocks_ = num_eliminate_blocks;
const int num_col_blocks = bs->cols.size();
const int num_row_blocks = bs->rows.size();
buffer_size_ = 1;
chunks_.clear();
lhs_row_layout_.clear();
int lhs_num_rows = 0;
// Add a map object for each block in the reduced linear system
// and build the row/column block structure of the reduced linear
// system.
lhs_row_layout_.resize(num_col_blocks - num_eliminate_blocks_);
for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {
lhs_row_layout_[i - num_eliminate_blocks_] = lhs_num_rows;
lhs_num_rows += bs->cols[i].size;
}
int r = 0;
// Iterate over the row blocks of A, and detect the chunks. The
// matrix should already have been ordered so that all rows
// containing the same y block are vertically contiguous. Along
// the way also compute the amount of space each chunk will need
// to perform the elimination.
while (r < num_row_blocks) {
const int chunk_block_id = bs->rows[r].cells.front().block_id;
if (chunk_block_id >= num_eliminate_blocks_) {
break;
}
chunks_.push_back(Chunk());
Chunk& chunk = chunks_.back();
chunk.size = 0;
chunk.start = r;
int buffer_size = 0;
const int e_block_size = bs->cols[chunk_block_id].size;
// Add to the chunk until the first block in the row is
// different than the one in the first row for the chunk.
while (r + chunk.size < num_row_blocks) {
const CompressedRow& row = bs->rows[r + chunk.size];
if (row.cells.front().block_id != chunk_block_id) {
break;
}
// Iterate over the blocks in the row, ignoring the first
// block since it is the one to be eliminated.
for (int c = 1; c < row.cells.size(); ++c) {
const Cell& cell = row.cells[c];
if (InsertIfNotPresent(
&(chunk.buffer_layout), cell.block_id, buffer_size)) {
buffer_size += e_block_size * bs->cols[cell.block_id].size;
}
}
buffer_size_ = max(buffer_size, buffer_size_);
++chunk.size;
}
CHECK_GT(chunk.size, 0);
r += chunk.size;
}
const Chunk& chunk = chunks_.back();
uneliminated_row_begins_ = chunk.start + chunk.size;
if (num_threads_ > 1) {
random_shuffle(chunks_.begin(), chunks_.end());
}
buffer_.reset(new double[buffer_size_ * num_threads_]);
// chunk_outer_product_buffer_ only needs to store e_block_size *
// f_block_size, which is always less than buffer_size_, so we just
// allocate buffer_size_ per thread.
chunk_outer_product_buffer_.reset(new double[buffer_size_ * num_threads_]);
STLDeleteElements(&rhs_locks_);
rhs_locks_.resize(num_col_blocks - num_eliminate_blocks_);
for (int i = 0; i < num_col_blocks - num_eliminate_blocks_; ++i) {
rhs_locks_[i] = new Mutex;
}
}
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
Eliminate(const BlockSparseMatrix* A,
const double* b,
const double* D,
BlockRandomAccessMatrix* lhs,
double* rhs) {
if (lhs->num_rows() > 0) {
lhs->SetZero();
VectorRef(rhs, lhs->num_rows()).setZero();
}
const CompressedRowBlockStructure* bs = A->block_structure();
const int num_col_blocks = bs->cols.size();
// Add the diagonal to the schur complement.
if (D != NULL) {
#pragma omp parallel for num_threads(num_threads_) schedule(dynamic)
for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {
const int block_id = i - num_eliminate_blocks_;
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block_id, block_id,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
const int block_size = bs->cols[i].size;
typename EigenTypes<kFBlockSize>::ConstVectorRef
diag(D + bs->cols[i].position, block_size);
CeresMutexLock l(&cell_info->m);
MatrixRef m(cell_info->values, row_stride, col_stride);
m.block(r, c, block_size, block_size).diagonal()
+= diag.array().square().matrix();
}
}
}
// Eliminate y blocks one chunk at a time. For each chunk,x3
// compute the entries of the normal equations and the gradient
// vector block corresponding to the y block and then apply
// Gaussian elimination to them. The matrix ete stores the normal
// matrix corresponding to the block being eliminated and array
// buffer_ contains the non-zero blocks in the row corresponding
// to this y block in the normal equations. This computation is
// done in ChunkDiagonalBlockAndGradient. UpdateRhs then applies
// gaussian elimination to the rhs of the normal equations,
// updating the rhs of the reduced linear system by modifying rhs
// blocks for all the z blocks that share a row block/residual
// term with the y block. EliminateRowOuterProduct does the
// corresponding operation for the lhs of the reduced linear
// system.
#pragma omp parallel for num_threads(num_threads_) schedule(dynamic)
for (int i = 0; i < chunks_.size(); ++i) {
#ifdef CERES_USE_OPENMP
int thread_id = omp_get_thread_num();
#else
int thread_id = 0;
#endif
double* buffer = buffer_.get() + thread_id * buffer_size_;
const Chunk& chunk = chunks_[i];
const int e_block_id = bs->rows[chunk.start].cells.front().block_id;
const int e_block_size = bs->cols[e_block_id].size;
VectorRef(buffer, buffer_size_).setZero();
typename EigenTypes<kEBlockSize, kEBlockSize>::Matrix
ete(e_block_size, e_block_size);
if (D != NULL) {
const typename EigenTypes<kEBlockSize>::ConstVectorRef
diag(D + bs->cols[e_block_id].position, e_block_size);
ete = diag.array().square().matrix().asDiagonal();
} else {
ete.setZero();
}
FixedArray<double, 8> g(e_block_size);
typename EigenTypes<kEBlockSize>::VectorRef gref(g.get(), e_block_size);
gref.setZero();
// We are going to be computing
//
// S += F'F - F'E(E'E)^{-1}E'F
//
// for each Chunk. The computation is broken down into a number of
// function calls as below.
// Compute the outer product of the e_blocks with themselves (ete
// = E'E). Compute the product of the e_blocks with the
// corresonding f_blocks (buffer = E'F), the gradient of the terms
// in this chunk (g) and add the outer product of the f_blocks to
// Schur complement (S += F'F).
ChunkDiagonalBlockAndGradient(
chunk, A, b, chunk.start, &ete, g.get(), buffer, lhs);
// Normally one wouldn't compute the inverse explicitly, but
// e_block_size will typically be a small number like 3, in
// which case its much faster to compute the inverse once and
// use it to multiply other matrices/vectors instead of doing a
// Solve call over and over again.
typename EigenTypes<kEBlockSize, kEBlockSize>::Matrix inverse_ete =
ete
.template selfadjointView<Eigen::Upper>()
.llt()
.solve(Matrix::Identity(e_block_size, e_block_size));
// For the current chunk compute and update the rhs of the reduced
// linear system.
//
// rhs = F'b - F'E(E'E)^(-1) E'b
FixedArray<double, 8> inverse_ete_g(e_block_size);
MatrixVectorMultiply<kEBlockSize, kEBlockSize, 0>(
inverse_ete.data(),
e_block_size,
e_block_size,
g.get(),
inverse_ete_g.get());
UpdateRhs(chunk, A, b, chunk.start, inverse_ete_g.get(), rhs);
// S -= F'E(E'E)^{-1}E'F
ChunkOuterProduct(bs, inverse_ete, buffer, chunk.buffer_layout, lhs);
}
// For rows with no e_blocks, the schur complement update reduces to
// S += F'F.
NoEBlockRowsUpdate(A, b, uneliminated_row_begins_, lhs, rhs);
}
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
BackSubstitute(const BlockSparseMatrix* A,
const double* b,
const double* D,
const double* z,
double* y) {
const CompressedRowBlockStructure* bs = A->block_structure();
#pragma omp parallel for num_threads(num_threads_) schedule(dynamic)
for (int i = 0; i < chunks_.size(); ++i) {
const Chunk& chunk = chunks_[i];
const int e_block_id = bs->rows[chunk.start].cells.front().block_id;
const int e_block_size = bs->cols[e_block_id].size;
double* y_ptr = y + bs->cols[e_block_id].position;
typename EigenTypes<kEBlockSize>::VectorRef y_block(y_ptr, e_block_size);
typename EigenTypes<kEBlockSize, kEBlockSize>::Matrix
ete(e_block_size, e_block_size);
if (D != NULL) {
const typename EigenTypes<kEBlockSize>::ConstVectorRef
diag(D + bs->cols[e_block_id].position, e_block_size);
ete = diag.array().square().matrix().asDiagonal();
} else {
ete.setZero();
}
const double* values = A->values();
for (int j = 0; j < chunk.size; ++j) {
const CompressedRow& row = bs->rows[chunk.start + j];
const Cell& e_cell = row.cells.front();
DCHECK_EQ(e_block_id, e_cell.block_id);
FixedArray<double, 8> sj(row.block.size);
typename EigenTypes<kRowBlockSize>::VectorRef(sj.get(), row.block.size) =
typename EigenTypes<kRowBlockSize>::ConstVectorRef
(b + bs->rows[chunk.start + j].block.position, row.block.size);
for (int c = 1; c < row.cells.size(); ++c) {
const int f_block_id = row.cells[c].block_id;
const int f_block_size = bs->cols[f_block_id].size;
const int r_block = f_block_id - num_eliminate_blocks_;
MatrixVectorMultiply<kRowBlockSize, kFBlockSize, -1>(
values + row.cells[c].position, row.block.size, f_block_size,
z + lhs_row_layout_[r_block],
sj.get());
}
MatrixTransposeVectorMultiply<kRowBlockSize, kEBlockSize, 1>(
values + e_cell.position, row.block.size, e_block_size,
sj.get(),
y_ptr);
MatrixTransposeMatrixMultiply
<kRowBlockSize, kEBlockSize, kRowBlockSize, kEBlockSize, 1>(
values + e_cell.position, row.block.size, e_block_size,
values + e_cell.position, row.block.size, e_block_size,
ete.data(), 0, 0, e_block_size, e_block_size);
}
ete.llt().solveInPlace(y_block);
}
}
// Update the rhs of the reduced linear system. Compute
//
// F'b - F'E(E'E)^(-1) E'b
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
UpdateRhs(const Chunk& chunk,
const BlockSparseMatrix* A,
const double* b,
int row_block_counter,
const double* inverse_ete_g,
double* rhs) {
const CompressedRowBlockStructure* bs = A->block_structure();
const int e_block_id = bs->rows[chunk.start].cells.front().block_id;
const int e_block_size = bs->cols[e_block_id].size;
int b_pos = bs->rows[row_block_counter].block.position;
const double* values = A->values();
for (int j = 0; j < chunk.size; ++j) {
const CompressedRow& row = bs->rows[row_block_counter + j];
const Cell& e_cell = row.cells.front();
typename EigenTypes<kRowBlockSize>::Vector sj =
typename EigenTypes<kRowBlockSize>::ConstVectorRef
(b + b_pos, row.block.size);
MatrixVectorMultiply<kRowBlockSize, kEBlockSize, -1>(
values + e_cell.position, row.block.size, e_block_size,
inverse_ete_g, sj.data());
for (int c = 1; c < row.cells.size(); ++c) {
const int block_id = row.cells[c].block_id;
const int block_size = bs->cols[block_id].size;
const int block = block_id - num_eliminate_blocks_;
CeresMutexLock l(rhs_locks_[block]);
MatrixTransposeVectorMultiply<kRowBlockSize, kFBlockSize, 1>(
values + row.cells[c].position,
row.block.size, block_size,
sj.data(), rhs + lhs_row_layout_[block]);
}
b_pos += row.block.size;
}
}
// Given a Chunk - set of rows with the same e_block, e.g. in the
// following Chunk with two rows.
//
// E F
// [ y11 0 0 0 | z11 0 0 0 z51]
// [ y12 0 0 0 | z12 z22 0 0 0]
//
// this function computes twp matrices. The diagonal block matrix
//
// ete = y11 * y11' + y12 * y12'
//
// and the off diagonal blocks in the Guass Newton Hessian.
//
// buffer = [y11'(z11 + z12), y12' * z22, y11' * z51]
//
// which are zero compressed versions of the block sparse matrices E'E
// and E'F.
//
// and the gradient of the e_block, E'b.
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
ChunkDiagonalBlockAndGradient(
const Chunk& chunk,
const BlockSparseMatrix* A,
const double* b,
int row_block_counter,
typename EigenTypes<kEBlockSize, kEBlockSize>::Matrix* ete,
double* g,
double* buffer,
BlockRandomAccessMatrix* lhs) {
const CompressedRowBlockStructure* bs = A->block_structure();
int b_pos = bs->rows[row_block_counter].block.position;
const int e_block_size = ete->rows();
// Iterate over the rows in this chunk, for each row, compute the
// contribution of its F blocks to the Schur complement, the
// contribution of its E block to the matrix EE' (ete), and the
// corresponding block in the gradient vector.
const double* values = A->values();
for (int j = 0; j < chunk.size; ++j) {
const CompressedRow& row = bs->rows[row_block_counter + j];
if (row.cells.size() > 1) {
EBlockRowOuterProduct(A, row_block_counter + j, lhs);
}
// Extract the e_block, ETE += E_i' E_i
const Cell& e_cell = row.cells.front();
MatrixTransposeMatrixMultiply
<kRowBlockSize, kEBlockSize, kRowBlockSize, kEBlockSize, 1>(
values + e_cell.position, row.block.size, e_block_size,
values + e_cell.position, row.block.size, e_block_size,
ete->data(), 0, 0, e_block_size, e_block_size);
// g += E_i' b_i
MatrixTransposeVectorMultiply<kRowBlockSize, kEBlockSize, 1>(
values + e_cell.position, row.block.size, e_block_size,
b + b_pos,
g);
// buffer = E'F. This computation is done by iterating over the
// f_blocks for each row in the chunk.
for (int c = 1; c < row.cells.size(); ++c) {
const int f_block_id = row.cells[c].block_id;
const int f_block_size = bs->cols[f_block_id].size;
double* buffer_ptr =
buffer + FindOrDie(chunk.buffer_layout, f_block_id);
MatrixTransposeMatrixMultiply
<kRowBlockSize, kEBlockSize, kRowBlockSize, kFBlockSize, 1>(
values + e_cell.position, row.block.size, e_block_size,
values + row.cells[c].position, row.block.size, f_block_size,
buffer_ptr, 0, 0, e_block_size, f_block_size);
}
b_pos += row.block.size;
}
}
// Compute the outer product F'E(E'E)^{-1}E'F and subtract it from the
// Schur complement matrix, i.e
//
// S -= F'E(E'E)^{-1}E'F.
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
ChunkOuterProduct(const CompressedRowBlockStructure* bs,
const Matrix& inverse_ete,
const double* buffer,
const BufferLayoutType& buffer_layout,
BlockRandomAccessMatrix* lhs) {
// This is the most computationally expensive part of this
// code. Profiling experiments reveal that the bottleneck is not the
// computation of the right-hand matrix product, but memory
// references to the left hand side.
const int e_block_size = inverse_ete.rows();
BufferLayoutType::const_iterator it1 = buffer_layout.begin();
#ifdef CERES_USE_OPENMP
int thread_id = omp_get_thread_num();
#else
int thread_id = 0;
#endif
double* b1_transpose_inverse_ete =
chunk_outer_product_buffer_.get() + thread_id * buffer_size_;
// S(i,j) -= bi' * ete^{-1} b_j
for (; it1 != buffer_layout.end(); ++it1) {
const int block1 = it1->first - num_eliminate_blocks_;
const int block1_size = bs->cols[it1->first].size;
MatrixTransposeMatrixMultiply
<kEBlockSize, kFBlockSize, kEBlockSize, kEBlockSize, 0>(
buffer + it1->second, e_block_size, block1_size,
inverse_ete.data(), e_block_size, e_block_size,
b1_transpose_inverse_ete, 0, 0, block1_size, e_block_size);
BufferLayoutType::const_iterator it2 = it1;
for (; it2 != buffer_layout.end(); ++it2) {
const int block2 = it2->first - num_eliminate_blocks_;
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block1, block2,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
const int block2_size = bs->cols[it2->first].size;
CeresMutexLock l(&cell_info->m);
MatrixMatrixMultiply
<kFBlockSize, kEBlockSize, kEBlockSize, kFBlockSize, -1>(
b1_transpose_inverse_ete, block1_size, e_block_size,
buffer + it2->second, e_block_size, block2_size,
cell_info->values, r, c, row_stride, col_stride);
}
}
}
}
// For rows with no e_blocks, the schur complement update reduces to S
// += F'F. This function iterates over the rows of A with no e_block,
// and calls NoEBlockRowOuterProduct on each row.
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
NoEBlockRowsUpdate(const BlockSparseMatrix* A,
const double* b,
int row_block_counter,
BlockRandomAccessMatrix* lhs,
double* rhs) {
const CompressedRowBlockStructure* bs = A->block_structure();
const double* values = A->values();
for (; row_block_counter < bs->rows.size(); ++row_block_counter) {
const CompressedRow& row = bs->rows[row_block_counter];
for (int c = 0; c < row.cells.size(); ++c) {
const int block_id = row.cells[c].block_id;
const int block_size = bs->cols[block_id].size;
const int block = block_id - num_eliminate_blocks_;
MatrixTransposeVectorMultiply<Eigen::Dynamic, Eigen::Dynamic, 1>(
values + row.cells[c].position, row.block.size, block_size,
b + row.block.position,
rhs + lhs_row_layout_[block]);
}
NoEBlockRowOuterProduct(A, row_block_counter, lhs);
}
}
// A row r of A, which has no e_blocks gets added to the Schur
// Complement as S += r r'. This function is responsible for computing
// the contribution of a single row r to the Schur complement. It is
// very similar in structure to EBlockRowOuterProduct except for
// one difference. It does not use any of the template
// parameters. This is because the algorithm used for detecting the
// static structure of the matrix A only pays attention to rows with
// e_blocks. This is becase rows without e_blocks are rare and
// typically arise from regularization terms in the original
// optimization problem, and have a very different structure than the
// rows with e_blocks. Including them in the static structure
// detection will lead to most template parameters being set to
// dynamic. Since the number of rows without e_blocks is small, the
// lack of templating is not an issue.
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
NoEBlockRowOuterProduct(const BlockSparseMatrix* A,
int row_block_index,
BlockRandomAccessMatrix* lhs) {
const CompressedRowBlockStructure* bs = A->block_structure();
const CompressedRow& row = bs->rows[row_block_index];
const double* values = A->values();
for (int i = 0; i < row.cells.size(); ++i) {
const int block1 = row.cells[i].block_id - num_eliminate_blocks_;
DCHECK_GE(block1, 0);
const int block1_size = bs->cols[row.cells[i].block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block1, block1,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
CeresMutexLock l(&cell_info->m);
// This multiply currently ignores the fact that this is a
// symmetric outer product.
MatrixTransposeMatrixMultiply
<Eigen::Dynamic, Eigen::Dynamic, Eigen::Dynamic, Eigen::Dynamic, 1>(
values + row.cells[i].position, row.block.size, block1_size,
values + row.cells[i].position, row.block.size, block1_size,
cell_info->values, r, c, row_stride, col_stride);
}
for (int j = i + 1; j < row.cells.size(); ++j) {
const int block2 = row.cells[j].block_id - num_eliminate_blocks_;
DCHECK_GE(block2, 0);
DCHECK_LT(block1, block2);
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block1, block2,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
const int block2_size = bs->cols[row.cells[j].block_id].size;
CeresMutexLock l(&cell_info->m);
MatrixTransposeMatrixMultiply
<Eigen::Dynamic, Eigen::Dynamic, Eigen::Dynamic, Eigen::Dynamic, 1>(
values + row.cells[i].position, row.block.size, block1_size,
values + row.cells[j].position, row.block.size, block2_size,
cell_info->values, r, c, row_stride, col_stride);
}
}
}
}
// For a row with an e_block, compute the contribition S += F'F. This
// function has the same structure as NoEBlockRowOuterProduct, except
// that this function uses the template parameters.
template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
void
SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
EBlockRowOuterProduct(const BlockSparseMatrix* A,
int row_block_index,
BlockRandomAccessMatrix* lhs) {
const CompressedRowBlockStructure* bs = A->block_structure();
const CompressedRow& row = bs->rows[row_block_index];
const double* values = A->values();
for (int i = 1; i < row.cells.size(); ++i) {
const int block1 = row.cells[i].block_id - num_eliminate_blocks_;
DCHECK_GE(block1, 0);
const int block1_size = bs->cols[row.cells[i].block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block1, block1,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
CeresMutexLock l(&cell_info->m);
// block += b1.transpose() * b1;
MatrixTransposeMatrixMultiply
<kRowBlockSize, kFBlockSize, kRowBlockSize, kFBlockSize, 1>(
values + row.cells[i].position, row.block.size, block1_size,
values + row.cells[i].position, row.block.size, block1_size,
cell_info->values, r, c, row_stride, col_stride);
}
for (int j = i + 1; j < row.cells.size(); ++j) {
const int block2 = row.cells[j].block_id - num_eliminate_blocks_;
DCHECK_GE(block2, 0);
DCHECK_LT(block1, block2);
const int block2_size = bs->cols[row.cells[j].block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = lhs->GetCell(block1, block2,
&r, &c,
&row_stride, &col_stride);
if (cell_info != NULL) {
// block += b1.transpose() * b2;
CeresMutexLock l(&cell_info->m);
MatrixTransposeMatrixMultiply
<kRowBlockSize, kFBlockSize, kRowBlockSize, kFBlockSize, 1>(
values + row.cells[i].position, row.block.size, block1_size,
values + row.cells[j].position, row.block.size, block2_size,
cell_info->values, r, c, row_stride, col_stride);
}
}
}
}
} // namespace internal
} // namespace ceres
#endif // CERES_INTERNAL_SCHUR_ELIMINATOR_IMPL_H_