578 lines
18 KiB
C++
578 lines
18 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#include "ceres/compressed_row_sparse_matrix.h"
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#include <numeric>
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#include "ceres/casts.h"
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#include "ceres/crs_matrix.h"
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#include "ceres/cxsparse.h"
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/linear_least_squares_problems.h"
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#include "ceres/random.h"
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#include "ceres/triplet_sparse_matrix.h"
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#include "glog/logging.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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using std::vector;
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void CompareMatrices(const SparseMatrix* a, const SparseMatrix* b) {
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EXPECT_EQ(a->num_rows(), b->num_rows());
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EXPECT_EQ(a->num_cols(), b->num_cols());
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int num_rows = a->num_rows();
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int num_cols = a->num_cols();
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for (int i = 0; i < num_cols; ++i) {
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Vector x = Vector::Zero(num_cols);
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x(i) = 1.0;
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Vector y_a = Vector::Zero(num_rows);
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Vector y_b = Vector::Zero(num_rows);
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a->RightMultiply(x.data(), y_a.data());
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b->RightMultiply(x.data(), y_b.data());
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EXPECT_EQ((y_a - y_b).norm(), 0);
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}
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}
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class CompressedRowSparseMatrixTest : public ::testing::Test {
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protected :
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virtual void SetUp() {
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scoped_ptr<LinearLeastSquaresProblem> problem(
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CreateLinearLeastSquaresProblemFromId(1));
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CHECK_NOTNULL(problem.get());
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tsm.reset(down_cast<TripletSparseMatrix*>(problem->A.release()));
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crsm.reset(new CompressedRowSparseMatrix(*tsm));
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num_rows = tsm->num_rows();
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num_cols = tsm->num_cols();
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vector<int>* row_blocks = crsm->mutable_row_blocks();
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row_blocks->resize(num_rows);
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std::fill(row_blocks->begin(), row_blocks->end(), 1);
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vector<int>* col_blocks = crsm->mutable_col_blocks();
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col_blocks->resize(num_cols);
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std::fill(col_blocks->begin(), col_blocks->end(), 1);
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}
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int num_rows;
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int num_cols;
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scoped_ptr<TripletSparseMatrix> tsm;
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scoped_ptr<CompressedRowSparseMatrix> crsm;
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};
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TEST_F(CompressedRowSparseMatrixTest, RightMultiply) {
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CompareMatrices(tsm.get(), crsm.get());
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}
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TEST_F(CompressedRowSparseMatrixTest, LeftMultiply) {
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for (int i = 0; i < num_rows; ++i) {
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Vector a = Vector::Zero(num_rows);
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a(i) = 1.0;
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Vector b1 = Vector::Zero(num_cols);
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Vector b2 = Vector::Zero(num_cols);
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tsm->LeftMultiply(a.data(), b1.data());
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crsm->LeftMultiply(a.data(), b2.data());
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EXPECT_EQ((b1 - b2).norm(), 0);
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}
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}
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TEST_F(CompressedRowSparseMatrixTest, ColumnNorm) {
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Vector b1 = Vector::Zero(num_cols);
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Vector b2 = Vector::Zero(num_cols);
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tsm->SquaredColumnNorm(b1.data());
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crsm->SquaredColumnNorm(b2.data());
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EXPECT_EQ((b1 - b2).norm(), 0);
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}
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TEST_F(CompressedRowSparseMatrixTest, Scale) {
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Vector scale(num_cols);
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for (int i = 0; i < num_cols; ++i) {
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scale(i) = i + 1;
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}
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tsm->ScaleColumns(scale.data());
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crsm->ScaleColumns(scale.data());
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CompareMatrices(tsm.get(), crsm.get());
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}
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TEST_F(CompressedRowSparseMatrixTest, DeleteRows) {
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// Clear the row and column blocks as these are purely scalar tests.
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crsm->mutable_row_blocks()->clear();
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crsm->mutable_col_blocks()->clear();
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for (int i = 0; i < num_rows; ++i) {
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tsm->Resize(num_rows - i, num_cols);
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crsm->DeleteRows(crsm->num_rows() - tsm->num_rows());
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CompareMatrices(tsm.get(), crsm.get());
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}
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}
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TEST_F(CompressedRowSparseMatrixTest, AppendRows) {
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// Clear the row and column blocks as these are purely scalar tests.
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crsm->mutable_row_blocks()->clear();
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crsm->mutable_col_blocks()->clear();
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for (int i = 0; i < num_rows; ++i) {
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TripletSparseMatrix tsm_appendage(*tsm);
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tsm_appendage.Resize(i, num_cols);
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tsm->AppendRows(tsm_appendage);
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CompressedRowSparseMatrix crsm_appendage(tsm_appendage);
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crsm->AppendRows(crsm_appendage);
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CompareMatrices(tsm.get(), crsm.get());
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}
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}
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TEST_F(CompressedRowSparseMatrixTest, AppendAndDeleteBlockDiagonalMatrix) {
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int num_diagonal_rows = crsm->num_cols();
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scoped_array<double> diagonal(new double[num_diagonal_rows]);
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for (int i = 0; i < num_diagonal_rows; ++i) {
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diagonal[i] = i;
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}
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vector<int> row_and_column_blocks;
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row_and_column_blocks.push_back(1);
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row_and_column_blocks.push_back(2);
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row_and_column_blocks.push_back(2);
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const vector<int> pre_row_blocks = crsm->row_blocks();
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const vector<int> pre_col_blocks = crsm->col_blocks();
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scoped_ptr<CompressedRowSparseMatrix> appendage(
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CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
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diagonal.get(), row_and_column_blocks));
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LOG(INFO) << appendage->row_blocks().size();
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crsm->AppendRows(*appendage);
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const vector<int> post_row_blocks = crsm->row_blocks();
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const vector<int> post_col_blocks = crsm->col_blocks();
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vector<int> expected_row_blocks = pre_row_blocks;
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expected_row_blocks.insert(expected_row_blocks.end(),
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row_and_column_blocks.begin(),
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row_and_column_blocks.end());
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vector<int> expected_col_blocks = pre_col_blocks;
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EXPECT_EQ(expected_row_blocks, crsm->row_blocks());
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EXPECT_EQ(expected_col_blocks, crsm->col_blocks());
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crsm->DeleteRows(num_diagonal_rows);
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EXPECT_EQ(crsm->row_blocks(), pre_row_blocks);
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EXPECT_EQ(crsm->col_blocks(), pre_col_blocks);
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}
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TEST_F(CompressedRowSparseMatrixTest, ToDenseMatrix) {
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Matrix tsm_dense;
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Matrix crsm_dense;
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tsm->ToDenseMatrix(&tsm_dense);
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crsm->ToDenseMatrix(&crsm_dense);
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EXPECT_EQ((tsm_dense - crsm_dense).norm(), 0.0);
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}
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TEST_F(CompressedRowSparseMatrixTest, ToCRSMatrix) {
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CRSMatrix crs_matrix;
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crsm->ToCRSMatrix(&crs_matrix);
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EXPECT_EQ(crsm->num_rows(), crs_matrix.num_rows);
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EXPECT_EQ(crsm->num_cols(), crs_matrix.num_cols);
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EXPECT_EQ(crsm->num_rows() + 1, crs_matrix.rows.size());
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EXPECT_EQ(crsm->num_nonzeros(), crs_matrix.cols.size());
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EXPECT_EQ(crsm->num_nonzeros(), crs_matrix.values.size());
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for (int i = 0; i < crsm->num_rows() + 1; ++i) {
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EXPECT_EQ(crsm->rows()[i], crs_matrix.rows[i]);
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}
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for (int i = 0; i < crsm->num_nonzeros(); ++i) {
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EXPECT_EQ(crsm->cols()[i], crs_matrix.cols[i]);
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EXPECT_EQ(crsm->values()[i], crs_matrix.values[i]);
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}
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}
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TEST(CompressedRowSparseMatrix, CreateBlockDiagonalMatrix) {
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vector<int> blocks;
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blocks.push_back(1);
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blocks.push_back(2);
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blocks.push_back(2);
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Vector diagonal(5);
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for (int i = 0; i < 5; ++i) {
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diagonal(i) = i + 1;
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}
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scoped_ptr<CompressedRowSparseMatrix> matrix(
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CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
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diagonal.data(), blocks));
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EXPECT_EQ(matrix->num_rows(), 5);
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EXPECT_EQ(matrix->num_cols(), 5);
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EXPECT_EQ(matrix->num_nonzeros(), 9);
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EXPECT_EQ(blocks, matrix->row_blocks());
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EXPECT_EQ(blocks, matrix->col_blocks());
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Vector x(5);
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Vector y(5);
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x.setOnes();
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y.setZero();
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matrix->RightMultiply(x.data(), y.data());
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for (int i = 0; i < diagonal.size(); ++i) {
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EXPECT_EQ(y[i], diagonal[i]);
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}
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y.setZero();
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matrix->LeftMultiply(x.data(), y.data());
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for (int i = 0; i < diagonal.size(); ++i) {
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EXPECT_EQ(y[i], diagonal[i]);
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}
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Matrix dense;
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matrix->ToDenseMatrix(&dense);
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EXPECT_EQ((dense.diagonal() - diagonal).norm(), 0.0);
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}
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class SolveLowerTriangularTest : public ::testing::Test {
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protected:
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void SetUp() {
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matrix_.reset(new CompressedRowSparseMatrix(4, 4, 7));
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int* rows = matrix_->mutable_rows();
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int* cols = matrix_->mutable_cols();
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double* values = matrix_->mutable_values();
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rows[0] = 0;
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cols[0] = 0;
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values[0] = 0.50754;
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rows[1] = 1;
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cols[1] = 1;
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values[1] = 0.80483;
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rows[2] = 2;
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cols[2] = 1;
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values[2] = 0.14120;
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cols[3] = 2;
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values[3] = 0.3;
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rows[3] = 4;
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cols[4] = 0;
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values[4] = 0.77696;
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cols[5] = 1;
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values[5] = 0.41860;
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cols[6] = 3;
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values[6] = 0.88979;
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rows[4] = 7;
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}
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scoped_ptr<CompressedRowSparseMatrix> matrix_;
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};
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TEST_F(SolveLowerTriangularTest, SolveInPlace) {
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double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0};
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double expected[] = {1.970288, 1.242498, 6.081864, -0.057255};
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matrix_->SolveLowerTriangularInPlace(rhs_and_solution);
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for (int i = 0; i < 4; ++i) {
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EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i;
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}
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}
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TEST_F(SolveLowerTriangularTest, TransposeSolveInPlace) {
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double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0};
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const double expected[] = { -1.4706, -1.0962, 6.6667, 2.2477};
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matrix_->SolveLowerTriangularTransposeInPlace(rhs_and_solution);
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for (int i = 0; i < 4; ++i) {
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EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i;
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}
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}
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TEST(CompressedRowSparseMatrix, Transpose) {
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// 0 1 0 2 3 0
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// 4 6 7 0 0 8
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// 9 10 0 11 12 0
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// 13 0 14 15 9 0
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// 0 16 17 0 0 0
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// Block structure:
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// A A A A B B
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// A A A A B B
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// A A A A B B
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// C C C C D D
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// C C C C D D
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// C C C C D D
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CompressedRowSparseMatrix matrix(5, 6, 30);
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int* rows = matrix.mutable_rows();
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int* cols = matrix.mutable_cols();
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double* values = matrix.mutable_values();
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matrix.mutable_row_blocks()->push_back(3);
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matrix.mutable_row_blocks()->push_back(3);
|
||
|
|
matrix.mutable_col_blocks()->push_back(4);
|
||
|
|
matrix.mutable_col_blocks()->push_back(2);
|
||
|
|
|
||
|
|
rows[0] = 0;
|
||
|
|
cols[0] = 1;
|
||
|
|
cols[1] = 3;
|
||
|
|
cols[2] = 4;
|
||
|
|
|
||
|
|
rows[1] = 3;
|
||
|
|
cols[3] = 0;
|
||
|
|
cols[4] = 1;
|
||
|
|
cols[5] = 2;
|
||
|
|
cols[6] = 5;
|
||
|
|
|
||
|
|
|
||
|
|
rows[2] = 7;
|
||
|
|
cols[7] = 0;
|
||
|
|
cols[8] = 1;
|
||
|
|
cols[9] = 3;
|
||
|
|
cols[10] = 4;
|
||
|
|
|
||
|
|
rows[3] = 11;
|
||
|
|
cols[11] = 0;
|
||
|
|
cols[12] = 2;
|
||
|
|
cols[13] = 3;
|
||
|
|
cols[14] = 4;
|
||
|
|
|
||
|
|
rows[4] = 15;
|
||
|
|
cols[15] = 1;
|
||
|
|
cols[16] = 2;
|
||
|
|
rows[5] = 17;
|
||
|
|
|
||
|
|
std::copy(values, values + 17, cols);
|
||
|
|
|
||
|
|
scoped_ptr<CompressedRowSparseMatrix> transpose(matrix.Transpose());
|
||
|
|
|
||
|
|
ASSERT_EQ(transpose->row_blocks().size(), matrix.col_blocks().size());
|
||
|
|
for (int i = 0; i < transpose->row_blocks().size(); ++i) {
|
||
|
|
EXPECT_EQ(transpose->row_blocks()[i], matrix.col_blocks()[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
ASSERT_EQ(transpose->col_blocks().size(), matrix.row_blocks().size());
|
||
|
|
for (int i = 0; i < transpose->col_blocks().size(); ++i) {
|
||
|
|
EXPECT_EQ(transpose->col_blocks()[i], matrix.row_blocks()[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
Matrix dense_matrix;
|
||
|
|
matrix.ToDenseMatrix(&dense_matrix);
|
||
|
|
|
||
|
|
Matrix dense_transpose;
|
||
|
|
transpose->ToDenseMatrix(&dense_transpose);
|
||
|
|
EXPECT_NEAR((dense_matrix - dense_transpose.transpose()).norm(), 0.0, 1e-14);
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifndef CERES_NO_CXSPARSE
|
||
|
|
|
||
|
|
struct RandomMatrixOptions {
|
||
|
|
int num_row_blocks;
|
||
|
|
int min_row_block_size;
|
||
|
|
int max_row_block_size;
|
||
|
|
int num_col_blocks;
|
||
|
|
int min_col_block_size;
|
||
|
|
int max_col_block_size;
|
||
|
|
double block_density;
|
||
|
|
};
|
||
|
|
|
||
|
|
CompressedRowSparseMatrix* CreateRandomCompressedRowSparseMatrix(
|
||
|
|
const RandomMatrixOptions& options) {
|
||
|
|
vector<int> row_blocks;
|
||
|
|
for (int i = 0; i < options.num_row_blocks; ++i) {
|
||
|
|
const int delta_block_size =
|
||
|
|
Uniform(options.max_row_block_size - options.min_row_block_size);
|
||
|
|
row_blocks.push_back(options.min_row_block_size + delta_block_size);
|
||
|
|
}
|
||
|
|
|
||
|
|
vector<int> col_blocks;
|
||
|
|
for (int i = 0; i < options.num_col_blocks; ++i) {
|
||
|
|
const int delta_block_size =
|
||
|
|
Uniform(options.max_col_block_size - options.min_col_block_size);
|
||
|
|
col_blocks.push_back(options.min_col_block_size + delta_block_size);
|
||
|
|
}
|
||
|
|
|
||
|
|
vector<int> rows;
|
||
|
|
vector<int> cols;
|
||
|
|
vector<double> values;
|
||
|
|
|
||
|
|
while (values.size() == 0) {
|
||
|
|
int row_block_begin = 0;
|
||
|
|
for (int r = 0; r < options.num_row_blocks; ++r) {
|
||
|
|
int col_block_begin = 0;
|
||
|
|
for (int c = 0; c < options.num_col_blocks; ++c) {
|
||
|
|
if (RandDouble() <= options.block_density) {
|
||
|
|
for (int i = 0; i < row_blocks[r]; ++i) {
|
||
|
|
for (int j = 0; j < col_blocks[c]; ++j) {
|
||
|
|
rows.push_back(row_block_begin + i);
|
||
|
|
cols.push_back(col_block_begin + j);
|
||
|
|
values.push_back(RandNormal());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
col_block_begin += col_blocks[c];
|
||
|
|
}
|
||
|
|
row_block_begin += row_blocks[r];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
const int num_rows = std::accumulate(row_blocks.begin(), row_blocks.end(), 0);
|
||
|
|
const int num_cols = std::accumulate(col_blocks.begin(), col_blocks.end(), 0);
|
||
|
|
const int num_nonzeros = values.size();
|
||
|
|
|
||
|
|
TripletSparseMatrix tsm(num_rows, num_cols, num_nonzeros);
|
||
|
|
std::copy(rows.begin(), rows.end(), tsm.mutable_rows());
|
||
|
|
std::copy(cols.begin(), cols.end(), tsm.mutable_cols());
|
||
|
|
std::copy(values.begin(), values.end(), tsm.mutable_values());
|
||
|
|
tsm.set_num_nonzeros(num_nonzeros);
|
||
|
|
CompressedRowSparseMatrix* matrix = new CompressedRowSparseMatrix(tsm);
|
||
|
|
(*matrix->mutable_row_blocks()) = row_blocks;
|
||
|
|
(*matrix->mutable_col_blocks()) = col_blocks;
|
||
|
|
return matrix;
|
||
|
|
}
|
||
|
|
|
||
|
|
void ToDenseMatrix(const cs_di* matrix, Matrix* dense_matrix) {
|
||
|
|
dense_matrix->resize(matrix->m, matrix->n);
|
||
|
|
dense_matrix->setZero();
|
||
|
|
|
||
|
|
for (int c = 0; c < matrix->n; ++c) {
|
||
|
|
for (int idx = matrix->p[c]; idx < matrix->p[c + 1]; ++idx) {
|
||
|
|
const int r = matrix->i[idx];
|
||
|
|
(*dense_matrix)(r, c) = matrix->x[idx];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
TEST(CompressedRowSparseMatrix, ComputeOuterProduct) {
|
||
|
|
// "Randomly generated seed."
|
||
|
|
SetRandomState(29823);
|
||
|
|
int kMaxNumRowBlocks = 10;
|
||
|
|
int kMaxNumColBlocks = 10;
|
||
|
|
int kNumTrials = 10;
|
||
|
|
|
||
|
|
CXSparse cxsparse;
|
||
|
|
const double kTolerance = 1e-18;
|
||
|
|
|
||
|
|
// Create a random matrix, compute its outer product using CXSParse
|
||
|
|
// and ComputeOuterProduct. Convert both matrices to dense matrices
|
||
|
|
// and compare their upper triangular parts. They should be within
|
||
|
|
// kTolerance of each other.
|
||
|
|
for (int num_row_blocks = 1;
|
||
|
|
num_row_blocks < kMaxNumRowBlocks;
|
||
|
|
++num_row_blocks) {
|
||
|
|
for (int num_col_blocks = 1;
|
||
|
|
num_col_blocks < kMaxNumColBlocks;
|
||
|
|
++num_col_blocks) {
|
||
|
|
for (int trial = 0; trial < kNumTrials; ++trial) {
|
||
|
|
RandomMatrixOptions options;
|
||
|
|
options.num_row_blocks = num_row_blocks;
|
||
|
|
options.num_col_blocks = num_col_blocks;
|
||
|
|
options.min_row_block_size = 1;
|
||
|
|
options.max_row_block_size = 5;
|
||
|
|
options.min_col_block_size = 1;
|
||
|
|
options.max_col_block_size = 10;
|
||
|
|
options.block_density = std::max(0.1, RandDouble());
|
||
|
|
|
||
|
|
VLOG(2) << "num row blocks: " << options.num_row_blocks;
|
||
|
|
VLOG(2) << "num col blocks: " << options.num_col_blocks;
|
||
|
|
VLOG(2) << "min row block size: " << options.min_row_block_size;
|
||
|
|
VLOG(2) << "max row block size: " << options.max_row_block_size;
|
||
|
|
VLOG(2) << "min col block size: " << options.min_col_block_size;
|
||
|
|
VLOG(2) << "max col block size: " << options.max_col_block_size;
|
||
|
|
VLOG(2) << "block density: " << options.block_density;
|
||
|
|
|
||
|
|
scoped_ptr<CompressedRowSparseMatrix> matrix(
|
||
|
|
CreateRandomCompressedRowSparseMatrix(options));
|
||
|
|
|
||
|
|
cs_di cs_matrix_transpose =
|
||
|
|
cxsparse.CreateSparseMatrixTransposeView(matrix.get());
|
||
|
|
cs_di* cs_matrix = cxsparse.TransposeMatrix(&cs_matrix_transpose);
|
||
|
|
cs_di* expected_outer_product =
|
||
|
|
cxsparse.MatrixMatrixMultiply(&cs_matrix_transpose, cs_matrix);
|
||
|
|
|
||
|
|
vector<int> program;
|
||
|
|
scoped_ptr<CompressedRowSparseMatrix> outer_product(
|
||
|
|
CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram(
|
||
|
|
*matrix, &program));
|
||
|
|
CompressedRowSparseMatrix::ComputeOuterProduct(*matrix,
|
||
|
|
program,
|
||
|
|
outer_product.get());
|
||
|
|
|
||
|
|
cs_di actual_outer_product =
|
||
|
|
cxsparse.CreateSparseMatrixTransposeView(outer_product.get());
|
||
|
|
|
||
|
|
ASSERT_EQ(actual_outer_product.m, actual_outer_product.n);
|
||
|
|
ASSERT_EQ(expected_outer_product->m, expected_outer_product->n);
|
||
|
|
ASSERT_EQ(actual_outer_product.m, expected_outer_product->m);
|
||
|
|
|
||
|
|
Matrix actual_matrix;
|
||
|
|
Matrix expected_matrix;
|
||
|
|
|
||
|
|
ToDenseMatrix(expected_outer_product, &expected_matrix);
|
||
|
|
expected_matrix.triangularView<Eigen::StrictlyLower>().setZero();
|
||
|
|
|
||
|
|
ToDenseMatrix(&actual_outer_product, &actual_matrix);
|
||
|
|
const double diff_norm =
|
||
|
|
(actual_matrix - expected_matrix).norm() / expected_matrix.norm();
|
||
|
|
ASSERT_NEAR(diff_norm, 0.0, kTolerance)
|
||
|
|
<< "expected: \n"
|
||
|
|
<< expected_matrix
|
||
|
|
<< "\nactual: \n"
|
||
|
|
<< actual_matrix;
|
||
|
|
|
||
|
|
cxsparse.Free(cs_matrix);
|
||
|
|
cxsparse.Free(expected_outer_product);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif // CERES_NO_CXSPARSE
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
} // namespace ceres
|