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-// 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
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