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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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/compressed_row_sparse_matrix.h"
+
+#include <algorithm>
+#include <numeric>
+#include <vector>
+#include "ceres/crs_matrix.h"
+#include "ceres/internal/port.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "glog/logging.h"
+
+namespace ceres {
+namespace internal {
+
+using std::vector;
+
+namespace {
+
+// Helper functor used by the constructor for reordering the contents
+// of a TripletSparseMatrix. This comparator assumes thay there are no
+// duplicates in the pair of arrays rows and cols, i.e., there is no
+// indices i and j (not equal to each other) s.t.
+//
+// rows[i] == rows[j] && cols[i] == cols[j]
+//
+// If this is the case, this functor will not be a StrictWeakOrdering.
+struct RowColLessThan {
+ RowColLessThan(const int* rows, const int* cols)
+ : rows(rows), cols(cols) {
+ }
+
+ bool operator()(const int x, const int y) const {
+ if (rows[x] == rows[y]) {
+ return (cols[x] < cols[y]);
+ }
+ return (rows[x] < rows[y]);
+ }
+
+ const int* rows;
+ const int* cols;
+};
+
+} // namespace
+
+// This constructor gives you a semi-initialized CompressedRowSparseMatrix.
+CompressedRowSparseMatrix::CompressedRowSparseMatrix(int num_rows,
+ int num_cols,
+ int max_num_nonzeros) {
+ num_rows_ = num_rows;
+ num_cols_ = num_cols;
+ rows_.resize(num_rows + 1, 0);
+ cols_.resize(max_num_nonzeros, 0);
+ values_.resize(max_num_nonzeros, 0.0);
+
+
+ VLOG(1) << "# of rows: " << num_rows_
+ << " # of columns: " << num_cols_
+ << " max_num_nonzeros: " << cols_.size()
+ << ". Allocating " << (num_rows_ + 1) * sizeof(int) + // NOLINT
+ cols_.size() * sizeof(int) + // NOLINT
+ cols_.size() * sizeof(double); // NOLINT
+}
+
+CompressedRowSparseMatrix::CompressedRowSparseMatrix(
+ const TripletSparseMatrix& m) {
+ num_rows_ = m.num_rows();
+ num_cols_ = m.num_cols();
+
+ rows_.resize(num_rows_ + 1, 0);
+ cols_.resize(m.num_nonzeros(), 0);
+ values_.resize(m.max_num_nonzeros(), 0.0);
+
+ // index is the list of indices into the TripletSparseMatrix m.
+ vector<int> index(m.num_nonzeros(), 0);
+ for (int i = 0; i < m.num_nonzeros(); ++i) {
+ index[i] = i;
+ }
+
+ // Sort index such that the entries of m are ordered by row and ties
+ // are broken by column.
+ sort(index.begin(), index.end(), RowColLessThan(m.rows(), m.cols()));
+
+ VLOG(1) << "# of rows: " << num_rows_
+ << " # of columns: " << num_cols_
+ << " max_num_nonzeros: " << cols_.size()
+ << ". Allocating "
+ << ((num_rows_ + 1) * sizeof(int) + // NOLINT
+ cols_.size() * sizeof(int) + // NOLINT
+ cols_.size() * sizeof(double)); // NOLINT
+
+ // Copy the contents of the cols and values array in the order given
+ // by index and count the number of entries in each row.
+ for (int i = 0; i < m.num_nonzeros(); ++i) {
+ const int idx = index[i];
+ ++rows_[m.rows()[idx] + 1];
+ cols_[i] = m.cols()[idx];
+ values_[i] = m.values()[idx];
+ }
+
+ // Find the cumulative sum of the row counts.
+ for (int i = 1; i < num_rows_ + 1; ++i) {
+ rows_[i] += rows_[i - 1];
+ }
+
+ CHECK_EQ(num_nonzeros(), m.num_nonzeros());
+}
+
+CompressedRowSparseMatrix::CompressedRowSparseMatrix(const double* diagonal,
+ int num_rows) {
+ CHECK_NOTNULL(diagonal);
+
+ num_rows_ = num_rows;
+ num_cols_ = num_rows;
+ rows_.resize(num_rows + 1);
+ cols_.resize(num_rows);
+ values_.resize(num_rows);
+
+ rows_[0] = 0;
+ for (int i = 0; i < num_rows_; ++i) {
+ cols_[i] = i;
+ values_[i] = diagonal[i];
+ rows_[i + 1] = i + 1;
+ }
+
+ CHECK_EQ(num_nonzeros(), num_rows);
+}
+
+CompressedRowSparseMatrix::~CompressedRowSparseMatrix() {
+}
+
+void CompressedRowSparseMatrix::SetZero() {
+ std::fill(values_.begin(), values_.end(), 0);
+}
+
+void CompressedRowSparseMatrix::RightMultiply(const double* x,
+ double* y) const {
+ CHECK_NOTNULL(x);
+ CHECK_NOTNULL(y);
+
+ for (int r = 0; r < num_rows_; ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1]; ++idx) {
+ y[r] += values_[idx] * x[cols_[idx]];
+ }
+ }
+}
+
+void CompressedRowSparseMatrix::LeftMultiply(const double* x, double* y) const {
+ CHECK_NOTNULL(x);
+ CHECK_NOTNULL(y);
+
+ for (int r = 0; r < num_rows_; ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1]; ++idx) {
+ y[cols_[idx]] += values_[idx] * x[r];
+ }
+ }
+}
+
+void CompressedRowSparseMatrix::SquaredColumnNorm(double* x) const {
+ CHECK_NOTNULL(x);
+
+ std::fill(x, x + num_cols_, 0.0);
+ for (int idx = 0; idx < rows_[num_rows_]; ++idx) {
+ x[cols_[idx]] += values_[idx] * values_[idx];
+ }
+}
+
+void CompressedRowSparseMatrix::ScaleColumns(const double* scale) {
+ CHECK_NOTNULL(scale);
+
+ for (int idx = 0; idx < rows_[num_rows_]; ++idx) {
+ values_[idx] *= scale[cols_[idx]];
+ }
+}
+
+void CompressedRowSparseMatrix::ToDenseMatrix(Matrix* dense_matrix) const {
+ CHECK_NOTNULL(dense_matrix);
+ dense_matrix->resize(num_rows_, num_cols_);
+ dense_matrix->setZero();
+
+ for (int r = 0; r < num_rows_; ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1]; ++idx) {
+ (*dense_matrix)(r, cols_[idx]) = values_[idx];
+ }
+ }
+}
+
+void CompressedRowSparseMatrix::DeleteRows(int delta_rows) {
+ CHECK_GE(delta_rows, 0);
+ CHECK_LE(delta_rows, num_rows_);
+
+ num_rows_ -= delta_rows;
+ rows_.resize(num_rows_ + 1);
+
+ // Walk the list of row blocks until we reach the new number of rows
+ // and the drop the rest of the row blocks.
+ int num_row_blocks = 0;
+ int num_rows = 0;
+ while (num_row_blocks < row_blocks_.size() && num_rows < num_rows_) {
+ num_rows += row_blocks_[num_row_blocks];
+ ++num_row_blocks;
+ }
+
+ row_blocks_.resize(num_row_blocks);
+}
+
+void CompressedRowSparseMatrix::AppendRows(const CompressedRowSparseMatrix& m) {
+ CHECK_EQ(m.num_cols(), num_cols_);
+
+ CHECK(row_blocks_.size() == 0 || m.row_blocks().size() !=0)
+ << "Cannot append a matrix with row blocks to one without and vice versa."
+ << "This matrix has : " << row_blocks_.size() << " row blocks."
+ << "The matrix being appended has: " << m.row_blocks().size()
+ << " row blocks.";
+
+ if (m.num_rows() == 0) {
+ return;
+ }
+
+ if (cols_.size() < num_nonzeros() + m.num_nonzeros()) {
+ cols_.resize(num_nonzeros() + m.num_nonzeros());
+ values_.resize(num_nonzeros() + m.num_nonzeros());
+ }
+
+ // Copy the contents of m into this matrix.
+ DCHECK_LT(num_nonzeros(), cols_.size());
+ if (m.num_nonzeros() > 0) {
+ std::copy(m.cols(), m.cols() + m.num_nonzeros(), &cols_[num_nonzeros()]);
+ std::copy(m.values(),
+ m.values() + m.num_nonzeros(),
+ &values_[num_nonzeros()]);
+ }
+
+ rows_.resize(num_rows_ + m.num_rows() + 1);
+ // new_rows = [rows_, m.row() + rows_[num_rows_]]
+ std::fill(rows_.begin() + num_rows_,
+ rows_.begin() + num_rows_ + m.num_rows() + 1,
+ rows_[num_rows_]);
+
+ for (int r = 0; r < m.num_rows() + 1; ++r) {
+ rows_[num_rows_ + r] += m.rows()[r];
+ }
+
+ num_rows_ += m.num_rows();
+ row_blocks_.insert(row_blocks_.end(),
+ m.row_blocks().begin(),
+ m.row_blocks().end());
+}
+
+void CompressedRowSparseMatrix::ToTextFile(FILE* file) const {
+ CHECK_NOTNULL(file);
+ for (int r = 0; r < num_rows_; ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1]; ++idx) {
+ fprintf(file,
+ "% 10d % 10d %17f\n",
+ r,
+ cols_[idx],
+ values_[idx]);
+ }
+ }
+}
+
+void CompressedRowSparseMatrix::ToCRSMatrix(CRSMatrix* matrix) const {
+ matrix->num_rows = num_rows_;
+ matrix->num_cols = num_cols_;
+ matrix->rows = rows_;
+ matrix->cols = cols_;
+ matrix->values = values_;
+
+ // Trim.
+ matrix->rows.resize(matrix->num_rows + 1);
+ matrix->cols.resize(matrix->rows[matrix->num_rows]);
+ matrix->values.resize(matrix->rows[matrix->num_rows]);
+}
+
+void CompressedRowSparseMatrix::SetMaxNumNonZeros(int num_nonzeros) {
+ CHECK_GE(num_nonzeros, 0);
+
+ cols_.resize(num_nonzeros);
+ values_.resize(num_nonzeros);
+}
+
+void CompressedRowSparseMatrix::SolveLowerTriangularInPlace(
+ double* solution) const {
+ for (int r = 0; r < num_rows_; ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1] - 1; ++idx) {
+ solution[r] -= values_[idx] * solution[cols_[idx]];
+ }
+ solution[r] /= values_[rows_[r + 1] - 1];
+ }
+}
+
+void CompressedRowSparseMatrix::SolveLowerTriangularTransposeInPlace(
+ double* solution) const {
+ for (int r = num_rows_ - 1; r >= 0; --r) {
+ solution[r] /= values_[rows_[r + 1] - 1];
+ for (int idx = rows_[r + 1] - 2; idx >= rows_[r]; --idx) {
+ solution[cols_[idx]] -= values_[idx] * solution[r];
+ }
+ }
+}
+
+CompressedRowSparseMatrix* CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
+ const double* diagonal,
+ const vector<int>& blocks) {
+ int num_rows = 0;
+ int num_nonzeros = 0;
+ for (int i = 0; i < blocks.size(); ++i) {
+ num_rows += blocks[i];
+ num_nonzeros += blocks[i] * blocks[i];
+ }
+
+ CompressedRowSparseMatrix* matrix =
+ new CompressedRowSparseMatrix(num_rows, num_rows, num_nonzeros);
+
+ int* rows = matrix->mutable_rows();
+ int* cols = matrix->mutable_cols();
+ double* values = matrix->mutable_values();
+ std::fill(values, values + num_nonzeros, 0.0);
+
+ int idx_cursor = 0;
+ int col_cursor = 0;
+ for (int i = 0; i < blocks.size(); ++i) {
+ const int block_size = blocks[i];
+ for (int r = 0; r < block_size; ++r) {
+ *(rows++) = idx_cursor;
+ values[idx_cursor + r] = diagonal[col_cursor + r];
+ for (int c = 0; c < block_size; ++c, ++idx_cursor) {
+ *(cols++) = col_cursor + c;
+ }
+ }
+ col_cursor += block_size;
+ }
+ *rows = idx_cursor;
+
+ *matrix->mutable_row_blocks() = blocks;
+ *matrix->mutable_col_blocks() = blocks;
+
+ CHECK_EQ(idx_cursor, num_nonzeros);
+ CHECK_EQ(col_cursor, num_rows);
+ return matrix;
+}
+
+CompressedRowSparseMatrix* CompressedRowSparseMatrix::Transpose() const {
+ CompressedRowSparseMatrix* transpose =
+ new CompressedRowSparseMatrix(num_cols_, num_rows_, num_nonzeros());
+
+ int* transpose_rows = transpose->mutable_rows();
+ int* transpose_cols = transpose->mutable_cols();
+ double* transpose_values = transpose->mutable_values();
+
+ for (int idx = 0; idx < num_nonzeros(); ++idx) {
+ ++transpose_rows[cols_[idx] + 1];
+ }
+
+ for (int i = 1; i < transpose->num_rows() + 1; ++i) {
+ transpose_rows[i] += transpose_rows[i - 1];
+ }
+
+ for (int r = 0; r < num_rows(); ++r) {
+ for (int idx = rows_[r]; idx < rows_[r + 1]; ++idx) {
+ const int c = cols_[idx];
+ const int transpose_idx = transpose_rows[c]++;
+ transpose_cols[transpose_idx] = r;
+ transpose_values[transpose_idx] = values_[idx];
+ }
+ }
+
+ for (int i = transpose->num_rows() - 1; i > 0 ; --i) {
+ transpose_rows[i] = transpose_rows[i - 1];
+ }
+ transpose_rows[0] = 0;
+
+ *(transpose->mutable_row_blocks()) = col_blocks_;
+ *(transpose->mutable_col_blocks()) = row_blocks_;
+
+ return transpose;
+}
+
+namespace {
+// A ProductTerm is a term in the outer product of a matrix with
+// itself.
+struct ProductTerm {
+ ProductTerm(const int row, const int col, const int index)
+ : row(row), col(col), index(index) {
+ }
+
+ bool operator<(const ProductTerm& right) const {
+ if (row == right.row) {
+ if (col == right.col) {
+ return index < right.index;
+ }
+ return col < right.col;
+ }
+ return row < right.row;
+ }
+
+ int row;
+ int col;
+ int index;
+};
+
+CompressedRowSparseMatrix*
+CompressAndFillProgram(const int num_rows,
+ const int num_cols,
+ const vector<ProductTerm>& product,
+ vector<int>* program) {
+ CHECK_GT(product.size(), 0);
+
+ // Count the number of unique product term, which in turn is the
+ // number of non-zeros in the outer product.
+ int num_nonzeros = 1;
+ for (int i = 1; i < product.size(); ++i) {
+ if (product[i].row != product[i - 1].row ||
+ product[i].col != product[i - 1].col) {
+ ++num_nonzeros;
+ }
+ }
+
+ CompressedRowSparseMatrix* matrix =
+ new CompressedRowSparseMatrix(num_rows, num_cols, num_nonzeros);
+
+ int* crsm_rows = matrix->mutable_rows();
+ std::fill(crsm_rows, crsm_rows + num_rows + 1, 0);
+ int* crsm_cols = matrix->mutable_cols();
+ std::fill(crsm_cols, crsm_cols + num_nonzeros, 0);
+
+ CHECK_NOTNULL(program)->clear();
+ program->resize(product.size());
+
+ // Iterate over the sorted product terms. This means each row is
+ // filled one at a time, and we are able to assign a position in the
+ // values array to each term.
+ //
+ // If terms repeat, i.e., they contribute to the same entry in the
+ // result matrix), then they do not affect the sparsity structure of
+ // the result matrix.
+ int nnz = 0;
+ crsm_cols[0] = product[0].col;
+ crsm_rows[product[0].row + 1]++;
+ (*program)[product[0].index] = nnz;
+ for (int i = 1; i < product.size(); ++i) {
+ const ProductTerm& previous = product[i - 1];
+ const ProductTerm& current = product[i];
+
+ // Sparsity structure is updated only if the term is not a repeat.
+ if (previous.row != current.row || previous.col != current.col) {
+ crsm_cols[++nnz] = current.col;
+ crsm_rows[current.row + 1]++;
+ }
+
+ // All terms get assigned the position in the values array where
+ // their value is accumulated.
+ (*program)[current.index] = nnz;
+ }
+
+ for (int i = 1; i < num_rows + 1; ++i) {
+ crsm_rows[i] += crsm_rows[i - 1];
+ }
+
+ return matrix;
+}
+
+} // namespace
+
+CompressedRowSparseMatrix*
+CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram(
+ const CompressedRowSparseMatrix& m,
+ vector<int>* program) {
+ CHECK_NOTNULL(program)->clear();
+ CHECK_GT(m.num_nonzeros(), 0)
+ << "Congratulations, "
+ << "you found a bug in Ceres. Please report it.";
+
+ vector<ProductTerm> product;
+ const vector<int>& row_blocks = m.row_blocks();
+ int row_block_begin = 0;
+ // Iterate over row blocks
+ for (int row_block = 0; row_block < row_blocks.size(); ++row_block) {
+ const int row_block_end = row_block_begin + row_blocks[row_block];
+ // Compute the outer product terms for just one row per row block.
+ const int r = row_block_begin;
+ // Compute the lower triangular part of the product.
+ for (int idx1 = m.rows()[r]; idx1 < m.rows()[r + 1]; ++idx1) {
+ for (int idx2 = m.rows()[r]; idx2 <= idx1; ++idx2) {
+ product.push_back(ProductTerm(m.cols()[idx1],
+ m.cols()[idx2],
+ product.size()));
+ }
+ }
+ row_block_begin = row_block_end;
+ }
+ CHECK_EQ(row_block_begin, m.num_rows());
+ sort(product.begin(), product.end());
+ return CompressAndFillProgram(m.num_cols(), m.num_cols(), product, program);
+}
+
+void CompressedRowSparseMatrix::ComputeOuterProduct(
+ const CompressedRowSparseMatrix& m,
+ const vector<int>& program,
+ CompressedRowSparseMatrix* result) {
+ result->SetZero();
+ double* values = result->mutable_values();
+ const vector<int>& row_blocks = m.row_blocks();
+
+ int cursor = 0;
+ int row_block_begin = 0;
+ const double* m_values = m.values();
+ const int* m_rows = m.rows();
+ // Iterate over row blocks.
+ for (int row_block = 0; row_block < row_blocks.size(); ++row_block) {
+ const int row_block_end = row_block_begin + row_blocks[row_block];
+ const int saved_cursor = cursor;
+ for (int r = row_block_begin; r < row_block_end; ++r) {
+ // Reuse the program segment for each row in this row block.
+ cursor = saved_cursor;
+ const int row_begin = m_rows[r];
+ const int row_end = m_rows[r + 1];
+ for (int idx1 = row_begin; idx1 < row_end; ++idx1) {
+ const double v1 = m_values[idx1];
+ for (int idx2 = row_begin; idx2 <= idx1; ++idx2, ++cursor) {
+ values[program[cursor]] += v1 * m_values[idx2];
+ }
+ }
+ }
+ row_block_begin = row_block_end;
+ }
+
+ CHECK_EQ(row_block_begin, m.num_rows());
+ CHECK_EQ(cursor, program.size());
+}
+
+} // namespace internal
+} // namespace ceres