Delete Incomplete LQ Factorization. This code never got expanded into a full preconditioner. No point keeping dead code around. Change-Id: I45badcd9e5f7eb39e8d288a96c65a02f325d76bd
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt index 1472e65..f9bb9d0 100644 --- a/internal/ceres/CMakeLists.txt +++ b/internal/ceres/CMakeLists.txt
@@ -67,7 +67,6 @@ gradient_problem.cc gradient_problem_solver.cc implicit_schur_complement.cc - incomplete_lq_factorization.cc iterative_schur_complement_solver.cc levenberg_marquardt_strategy.cc lapack.cc @@ -261,7 +260,6 @@ CERES_TEST(graph) CERES_TEST(graph_algorithms) CERES_TEST(implicit_schur_complement) - CERES_TEST(incomplete_lq_factorization) CERES_TEST(iterative_schur_complement_solver) CERES_TEST(jet) CERES_TEST(levenberg_marquardt_strategy)
diff --git a/internal/ceres/incomplete_lq_factorization.cc b/internal/ceres/incomplete_lq_factorization.cc deleted file mode 100644 index 6ba38ec..0000000 --- a/internal/ceres/incomplete_lq_factorization.cc +++ /dev/null
@@ -1,239 +0,0 @@ -// Ceres Solver - A fast non-linear least squares minimizer -// Copyright 2013 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 "ceres/incomplete_lq_factorization.h" - -#include <vector> -#include <utility> -#include <cmath> -#include "ceres/compressed_row_sparse_matrix.h" -#include "ceres/internal/eigen.h" -#include "ceres/internal/port.h" -#include "glog/logging.h" - -namespace ceres { -namespace internal { - -// Normalize a row and return it's norm. -inline double NormalizeRow(const int row, CompressedRowSparseMatrix* matrix) { - const int row_begin = matrix->rows()[row]; - const int row_end = matrix->rows()[row + 1]; - - double* values = matrix->mutable_values(); - double norm = 0.0; - for (int i = row_begin; i < row_end; ++i) { - norm += values[i] * values[i]; - } - - norm = sqrt(norm); - const double inverse_norm = 1.0 / norm; - for (int i = row_begin; i < row_end; ++i) { - values[i] *= inverse_norm; - } - - return norm; -} - -// Compute a(row_a,:) * b(row_b, :)' -inline double RowDotProduct(const CompressedRowSparseMatrix& a, - const int row_a, - const CompressedRowSparseMatrix& b, - const int row_b) { - const int* a_rows = a.rows(); - const int* a_cols = a.cols(); - const double* a_values = a.values(); - - const int* b_rows = b.rows(); - const int* b_cols = b.cols(); - const double* b_values = b.values(); - - const int row_a_end = a_rows[row_a + 1]; - const int row_b_end = b_rows[row_b + 1]; - - int idx_a = a_rows[row_a]; - int idx_b = b_rows[row_b]; - double dot_product = 0.0; - while (idx_a < row_a_end && idx_b < row_b_end) { - if (a_cols[idx_a] == b_cols[idx_b]) { - dot_product += a_values[idx_a++] * b_values[idx_b++]; - } - - while (a_cols[idx_a] < b_cols[idx_b] && idx_a < row_a_end) { - ++idx_a; - } - - while (a_cols[idx_a] > b_cols[idx_b] && idx_b < row_b_end) { - ++idx_b; - } - } - - return dot_product; -} - -struct SecondGreaterThan { - public: - bool operator()(const pair<int, double>& lhs, - const pair<int, double>& rhs) const { - return (fabs(lhs.second) > fabs(rhs.second)); - } -}; - -// In the row vector dense_row(0:num_cols), drop values smaller than -// the max_value * drop_tolerance. Of the remaining non-zero values, -// choose at most level_of_fill values and then add the resulting row -// vector to matrix. - -void DropEntriesAndAddRow(const Vector& dense_row, - const int num_entries, - const int level_of_fill, - const double drop_tolerance, - vector<pair<int, double> >* scratch, - CompressedRowSparseMatrix* matrix) { - int* rows = matrix->mutable_rows(); - int* cols = matrix->mutable_cols(); - double* values = matrix->mutable_values(); - int num_nonzeros = rows[matrix->num_rows()]; - - if (num_entries == 0) { - matrix->set_num_rows(matrix->num_rows() + 1); - rows[matrix->num_rows()] = num_nonzeros; - return; - } - - const double max_value = dense_row.head(num_entries).cwiseAbs().maxCoeff(); - const double threshold = drop_tolerance * max_value; - - int scratch_count = 0; - for (int i = 0; i < num_entries; ++i) { - if (fabs(dense_row[i]) > threshold) { - pair<int, double>& entry = (*scratch)[scratch_count]; - entry.first = i; - entry.second = dense_row[i]; - ++scratch_count; - } - } - - if (scratch_count > level_of_fill) { - nth_element(scratch->begin(), - scratch->begin() + level_of_fill, - scratch->begin() + scratch_count, - SecondGreaterThan()); - scratch_count = level_of_fill; - sort(scratch->begin(), scratch->begin() + scratch_count); - } - - for (int i = 0; i < scratch_count; ++i) { - const pair<int, double>& entry = (*scratch)[i]; - cols[num_nonzeros] = entry.first; - values[num_nonzeros] = entry.second; - ++num_nonzeros; - } - - matrix->set_num_rows(matrix->num_rows() + 1); - rows[matrix->num_rows()] = num_nonzeros; -} - -// Saad's Incomplete LQ factorization algorithm. -CompressedRowSparseMatrix* IncompleteLQFactorization( - const CompressedRowSparseMatrix& matrix, - const int l_level_of_fill, - const double l_drop_tolerance, - const int q_level_of_fill, - const double q_drop_tolerance) { - const int num_rows = matrix.num_rows(); - const int num_cols = matrix.num_cols(); - const int* rows = matrix.rows(); - const int* cols = matrix.cols(); - const double* values = matrix.values(); - - CompressedRowSparseMatrix* l = - new CompressedRowSparseMatrix(num_rows, - num_rows, - l_level_of_fill * num_rows); - l->set_num_rows(0); - - CompressedRowSparseMatrix q(num_rows, num_cols, q_level_of_fill * num_rows); - q.set_num_rows(0); - - int* l_rows = l->mutable_rows(); - int* l_cols = l->mutable_cols(); - double* l_values = l->mutable_values(); - - int* q_rows = q.mutable_rows(); - int* q_cols = q.mutable_cols(); - double* q_values = q.mutable_values(); - - Vector l_i(num_rows); - Vector q_i(num_cols); - vector<pair<int, double> > scratch(num_cols); - for (int i = 0; i < num_rows; ++i) { - // l_i = q * matrix(i,:)'); - l_i.setZero(); - for (int j = 0; j < i; ++j) { - l_i(j) = RowDotProduct(matrix, i, q, j); - } - DropEntriesAndAddRow(l_i, - i, - l_level_of_fill, - l_drop_tolerance, - &scratch, - l); - - // q_i = matrix(i,:) - q(0:i-1,:) * l_i); - q_i.setZero(); - for (int idx = rows[i]; idx < rows[i + 1]; ++idx) { - q_i(cols[idx]) = values[idx]; - } - - for (int j = l_rows[i]; j < l_rows[i + 1]; ++j) { - const int r = l_cols[j]; - const double lij = l_values[j]; - for (int idx = q_rows[r]; idx < q_rows[r + 1]; ++idx) { - q_i(q_cols[idx]) -= lij * q_values[idx]; - } - } - DropEntriesAndAddRow(q_i, - num_cols, - q_level_of_fill, - q_drop_tolerance, - &scratch, - &q); - - // lii = |qi| - l_cols[l->num_nonzeros()] = i; - l_values[l->num_nonzeros()] = NormalizeRow(i, &q); - l_rows[l->num_rows()] += 1; - } - - return l; -} - -} // namespace internal -} // namespace ceres
diff --git a/internal/ceres/incomplete_lq_factorization.h b/internal/ceres/incomplete_lq_factorization.h deleted file mode 100644 index e678463..0000000 --- a/internal/ceres/incomplete_lq_factorization.h +++ /dev/null
@@ -1,90 +0,0 @@ -// Ceres Solver - A fast non-linear least squares minimizer -// Copyright 2013 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) - -#ifndef CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_ -#define CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_ - -#include <vector> -#include <utility> -#include "ceres/compressed_row_sparse_matrix.h" - -namespace ceres { -namespace internal { - -// Incomplete LQ factorization as described in -// -// Preconditioning techniques for indefinite and nonsymmetric linear -// systems. Yousef Saad, Preprint RIACS-ILQ-TR, RIACS, NASA Ames -// Research Center, Moffett Field, CA, 1987. -// -// An incomplete LQ factorization of a matrix A is a decomposition -// -// A = LQ + E -// -// Where L is a lower triangular matrix, and Q is a near orthonormal -// matrix. The extent of orthonormality depends on E. E is the "drop" -// matrix. Each row of L has a maximum of l_level_of_fill entries, and -// all non-zero entries are within l_drop_tolerance of the largest -// entry. Each row of Q has a maximum of q_level_of_fill entries and -// all non-zero entries are within q_drop_tolerance of the largest -// entry. -// -// E is the error of the incomplete factorization. -// -// The purpose of incomplete factorizations is preconditioning and -// there one only needs the L matrix, therefore this function just -// returns L. -// -// Caller owns the result. -CompressedRowSparseMatrix* IncompleteLQFactorization( - const CompressedRowSparseMatrix& matrix, - const int l_level_of_fill, - const double l_drop_tolerance, - const int q_level_of_fill, - const double q_drop_tolerance); - -// In the row vector dense_row(0:num_cols), drop values smaller than -// the max_value * drop_tolerance. Of the remaining non-zero values, -// choose at most level_of_fill values and then add the resulting row -// vector to matrix. -// -// scratch is used to prevent allocations inside this function. It is -// assumed that scratch is of size matrix->num_cols(). -void DropEntriesAndAddRow(const Vector& dense_row, - const int num_entries, - const int level_of_fill, - const double drop_tolerance, - vector<pair<int, double> >* scratch, - CompressedRowSparseMatrix* matrix); - -} // namespace internal -} // namespace ceres - -#endif // CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
diff --git a/internal/ceres/incomplete_lq_factorization_test.cc b/internal/ceres/incomplete_lq_factorization_test.cc deleted file mode 100644 index 1ed181f..0000000 --- a/internal/ceres/incomplete_lq_factorization_test.cc +++ /dev/null
@@ -1,198 +0,0 @@ -// Ceres Solver - A fast non-linear least squares minimizer -// Copyright 2013 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 "ceres/incomplete_lq_factorization.h" - -#include "Eigen/Dense" -#include "ceres/compressed_row_sparse_matrix.h" -#include "ceres/internal/scoped_ptr.h" -#include "glog/logging.h" -#include "gtest/gtest.h" - -namespace ceres { -namespace internal { - -void ExpectMatricesAreEqual(const CompressedRowSparseMatrix& expected, - const CompressedRowSparseMatrix& actual, - const double tolerance) { - EXPECT_EQ(expected.num_rows(), actual.num_rows()); - EXPECT_EQ(expected.num_cols(), actual.num_cols()); - for (int i = 0; i < expected.num_rows(); ++i) { - EXPECT_EQ(expected.rows()[i], actual.rows()[i]); - } - - for (int i = 0; i < actual.num_nonzeros(); ++i) { - EXPECT_EQ(expected.cols()[i], actual.cols()[i]); - EXPECT_NEAR(expected.values()[i], actual.values()[i], tolerance); - } -} - -TEST(IncompleteQRFactorization, OneByOneMatrix) { - CompressedRowSparseMatrix matrix(1, 1, 1); - matrix.mutable_rows()[0] = 0; - matrix.mutable_rows()[1] = 1; - matrix.mutable_cols()[0] = 0; - matrix.mutable_values()[0] = 2; - - scoped_ptr<CompressedRowSparseMatrix> l( - IncompleteLQFactorization(matrix, 1, 0.0, 1, 0.0)); - ExpectMatricesAreEqual(matrix, *l, 1e-16); -} - -TEST(IncompleteLQFactorization, CompleteFactorization) { - double dense_matrix[] = { - 0.00000, 0.00000, 0.20522, 0.00000, 0.49077, 0.92835, 0.00000, 0.83825, 0.00000, 0.00000, // NOLINT - 0.00000, 0.00000, 0.00000, 0.62491, 0.38144, 0.00000, 0.79394, 0.79178, 0.00000, 0.44382, // NOLINT - 0.00000, 0.00000, 0.00000, 0.61517, 0.55941, 0.00000, 0.00000, 0.00000, 0.00000, 0.60664, // NOLINT - 0.00000, 0.00000, 0.00000, 0.00000, 0.45031, 0.00000, 0.64132, 0.00000, 0.38832, 0.00000, // NOLINT - 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.57121, 0.00000, 0.01375, 0.70640, 0.00000, // NOLINT - 0.00000, 0.00000, 0.07451, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, // NOLINT - 0.68095, 0.00000, 0.00000, 0.95473, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, // NOLINT - 0.00000, 0.00000, 0.00000, 0.00000, 0.59374, 0.00000, 0.00000, 0.00000, 0.49139, 0.00000, // NOLINT - 0.91276, 0.96641, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.91797, // NOLINT - 0.96828, 0.00000, 0.00000, 0.72583, 0.00000, 0.00000, 0.81459, 0.00000, 0.04560, 0.00000 // NOLINT - }; - - CompressedRowSparseMatrix matrix(10, 10, 100); - int* rows = matrix.mutable_rows(); - int* cols = matrix.mutable_cols(); - double* values = matrix.mutable_values(); - - int idx = 0; - for (int i = 0; i < 10; ++i) { - rows[i] = idx; - for (int j = 0; j < 10; ++j) { - const double v = dense_matrix[i * 10 + j]; - if (fabs(v) > 1e-6) { - cols[idx] = j; - values[idx] = v; - ++idx; - } - } - } - rows[10] = idx; - - scoped_ptr<CompressedRowSparseMatrix> lmatrix( - IncompleteLQFactorization(matrix, 10, 0.0, 10, 0.0)); - - ConstMatrixRef mref(dense_matrix, 10, 10); - - // Use Cholesky factorization to compute the L matrix. - Matrix expected_l_matrix = (mref * mref.transpose()).llt().matrixL(); - Matrix actual_l_matrix; - lmatrix->ToDenseMatrix(&actual_l_matrix); - - EXPECT_NEAR((expected_l_matrix * expected_l_matrix.transpose() - - actual_l_matrix * actual_l_matrix.transpose()).norm(), - 0.0, - 1e-10) - << "expected: \n" << expected_l_matrix - << "\actual: \n" << actual_l_matrix; -} - -TEST(IncompleteLQFactorization, DropEntriesAndAddRow) { - // Allocate space and then make it a zero sized matrix. - CompressedRowSparseMatrix matrix(10, 10, 100); - matrix.set_num_rows(0); - - vector<pair<int, double> > scratch(10); - - Vector dense_vector(10); - dense_vector(0) = 5; - dense_vector(1) = 1; - dense_vector(2) = 2; - dense_vector(3) = 3; - dense_vector(4) = 1; - dense_vector(5) = 4; - - // Add a row with just one entry. - DropEntriesAndAddRow(dense_vector, 1, 1, 0, &scratch, &matrix); - EXPECT_EQ(matrix.num_rows(), 1); - EXPECT_EQ(matrix.num_cols(), 10); - EXPECT_EQ(matrix.num_nonzeros(), 1); - EXPECT_EQ(matrix.values()[0], 5.0); - EXPECT_EQ(matrix.cols()[0], 0); - - // Add a row with six entries - DropEntriesAndAddRow(dense_vector, 6, 10, 0, &scratch, &matrix); - EXPECT_EQ(matrix.num_rows(), 2); - EXPECT_EQ(matrix.num_cols(), 10); - EXPECT_EQ(matrix.num_nonzeros(), 7); - for (int idx = matrix.rows()[1]; idx < matrix.rows()[2]; ++idx) { - EXPECT_EQ(matrix.cols()[idx], idx - matrix.rows()[1]); - EXPECT_EQ(matrix.values()[idx], dense_vector(idx - matrix.rows()[1])); - } - - // Add the top 3 entries. - DropEntriesAndAddRow(dense_vector, 6, 3, 0, &scratch, &matrix); - EXPECT_EQ(matrix.num_rows(), 3); - EXPECT_EQ(matrix.num_cols(), 10); - EXPECT_EQ(matrix.num_nonzeros(), 10); - - EXPECT_EQ(matrix.cols()[matrix.rows()[2]], 0); - EXPECT_EQ(matrix.cols()[matrix.rows()[2] + 1], 3); - EXPECT_EQ(matrix.cols()[matrix.rows()[2] + 2], 5); - - EXPECT_EQ(matrix.values()[matrix.rows()[2]], 5); - EXPECT_EQ(matrix.values()[matrix.rows()[2] + 1], 3); - EXPECT_EQ(matrix.values()[matrix.rows()[2] + 2], 4); - - // Only keep entries greater than 1.0; - DropEntriesAndAddRow(dense_vector, 6, 6, 0.2, &scratch, &matrix); - EXPECT_EQ(matrix.num_rows(), 4); - EXPECT_EQ(matrix.num_cols(), 10); - EXPECT_EQ(matrix.num_nonzeros(), 14); - - EXPECT_EQ(matrix.cols()[matrix.rows()[3]], 0); - EXPECT_EQ(matrix.cols()[matrix.rows()[3] + 1], 2); - EXPECT_EQ(matrix.cols()[matrix.rows()[3] + 2], 3); - EXPECT_EQ(matrix.cols()[matrix.rows()[3] + 3], 5); - - EXPECT_EQ(matrix.values()[matrix.rows()[3]], 5); - EXPECT_EQ(matrix.values()[matrix.rows()[3] + 1], 2); - EXPECT_EQ(matrix.values()[matrix.rows()[3] + 2], 3); - EXPECT_EQ(matrix.values()[matrix.rows()[3] + 3], 4); - - // Only keep the top 2 entries greater than 1.0 - DropEntriesAndAddRow(dense_vector, 6, 2, 0.2, &scratch, &matrix); - EXPECT_EQ(matrix.num_rows(), 5); - EXPECT_EQ(matrix.num_cols(), 10); - EXPECT_EQ(matrix.num_nonzeros(), 16); - - EXPECT_EQ(matrix.cols()[matrix.rows()[4]], 0); - EXPECT_EQ(matrix.cols()[matrix.rows()[4] + 1], 5); - - EXPECT_EQ(matrix.values()[matrix.rows()[4]], 5); - EXPECT_EQ(matrix.values()[matrix.rows()[4] + 1], 4); -} - - -} // namespace internal -} // namespace ceres