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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2017 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)
+
+#ifndef CERES_INTERNAL_INNER_PRODUCT_COMPUTER_H_
+#define CERES_INTERNAL_INNER_PRODUCT_COMPUTER_H_
+
+#include <memory>
+#include <vector>
+
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/compressed_row_sparse_matrix.h"
+
+namespace ceres {
+namespace internal {
+
+// This class is used to repeatedly compute the inner product
+//
+// result = m' * m
+//
+// where the sparsity structure of m remains constant across calls.
+//
+// Upon creation, the class computes and caches information needed to
+// compute v, and then uses it to efficiently compute the product
+// every time InnerProductComputer::Compute is called.
+//
+// See sparse_normal_cholesky_solver.cc for example usage.
+//
+// Note that the result matrix is a block upper or lower-triangular
+// matrix, i.e., it will contain entries in the upper or lower
+// triangular part of the matrix corresponding to the block that occur
+// along its diagonal.
+//
+// This is not a problem as sparse linear algebra libraries can ignore
+// these entries with ease and the space used is minimal/linear in the
+// size of the matrices.
+class InnerProductComputer {
+ public:
+ // Factory
+ //
+ // m is the input matrix
+ //
+ // Since m' * m is a symmetric matrix, we only compute half of the
+ // matrix and the value of storage_type which must be
+ // UPPER_TRIANGULAR or LOWER_TRIANGULAR determines which half is
+ // computed.
+ //
+ // The user must ensure that the matrix m is valid for the life time
+ // of this object.
+ static InnerProductComputer* Create(
+ const BlockSparseMatrix& m,
+ CompressedRowSparseMatrix::StorageType storage_type);
+
+ // This factory method allows the user control over range of row
+ // blocks of m that should be used to compute the inner product.
+ //
+ // a = m(start_row_block : end_row_block, :);
+ // result = a' * a;
+ static InnerProductComputer* Create(
+ const BlockSparseMatrix& m,
+ int start_row_block,
+ int end_row_block,
+ CompressedRowSparseMatrix::StorageType storage_type);
+
+ // Update result_ to be numerically equal to m' * m.
+ void Compute();
+
+ // Accessors for the result containing the inner product.
+ //
+ // Compute must be called before accessing this result for
+ // the first time.
+ const CompressedRowSparseMatrix& result() const { return *result_; }
+ CompressedRowSparseMatrix* mutable_result() const { return result_.get(); }
+
+ private:
+ // A ProductTerm is a term in the block inner 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;
+ };
+
+ InnerProductComputer(const BlockSparseMatrix& m,
+ int start_row_block,
+ int end_row_block);
+
+ void Init(CompressedRowSparseMatrix::StorageType storage_type);
+
+ CompressedRowSparseMatrix* CreateResultMatrix(
+ const CompressedRowSparseMatrix::StorageType storage_type,
+ int num_nonzeros);
+
+ int ComputeNonzeros(const std::vector<ProductTerm>& product_terms,
+ std::vector<int>* row_block_nnz);
+
+ void ComputeOffsetsAndCreateResultMatrix(
+ const CompressedRowSparseMatrix::StorageType storage_type,
+ const std::vector<ProductTerm>& product_terms);
+
+ const BlockSparseMatrix& m_;
+ const int start_row_block_;
+ const int end_row_block_;
+ std::unique_ptr<CompressedRowSparseMatrix> result_;
+
+ // For each term in the inner product, result_offsets_ contains the
+ // location in the values array of the result_ matrix where it
+ // should be stored.
+ //
+ // This is the principal look up table that allows this class to
+ // compute the inner product fast.
+ std::vector<int> result_offsets_;
+};
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_INNER_PRODUCT_COMPUTER_H_