// Ceres Solver - A fast non-linear least squares minimizer

// Copyright 2015 Google Inc. All rights reserved.

// http://ceres-solver.org/

//

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// modification, are permitted provided that the following conditions are met:

//

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//   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

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//   used to endorse or promote products derived from this software without

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//

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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifndef CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_

#define CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_

#include <vector>

#include "ceres/internal/port.h"

namespace ceres {

namespace internal {

// Extract the block sparsity pattern of the scalar compressed columns

// matrix and return it in compressed column form. The compressed

// column form is stored in two vectors block_rows, and block_cols,

// which correspond to the row and column arrays in a compressed

// column sparse matrix.

//

// If c_ij is the block in the matrix A corresponding to row block i

// and column block j, then it is expected that A contains at least

// one non-zero entry corresponding to the top left entry of c_ij,

// as that entry is used to detect the presence of a non-zero c_ij.

void CompressedColumnScalarMatrixToBlockMatrix(

    const int* scalar_rows,

    const int* scalar_cols,

    const std::vector<int>& row_blocks,

    const std::vector<int>& col_blocks,

    std::vector<int>* block_rows,

    std::vector<int>* block_cols);

// Given a set of blocks and a permutation of these blocks, compute

// the corresponding "scalar" ordering, where the scalar ordering of

// size sum(blocks).

void BlockOrderingToScalarOrdering(

    const std::vector<int>& blocks,

    const std::vector<int>& block_ordering,

    std::vector<int>* scalar_ordering);

// Solve the linear system

//

//   R * solution = rhs

//

// Where R is an upper triangular compressed column sparse matrix.

template <typename IntegerType>

void SolveUpperTriangularInPlace(IntegerType num_cols,

                                 const IntegerType* rows,

                                 const IntegerType* cols,

                                 const double* values,

                                 double* rhs_and_solution) {

  for (IntegerType c = num_cols - 1; c >= 0; --c) {

    rhs_and_solution[c] /= values[cols[c + 1] - 1];

    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {

      const IntegerType r = rows[idx];

      const double v = values[idx];

      rhs_and_solution[r] -= v * rhs_and_solution[c];

    }

  }

}

// Solve the linear system

//

//   R' * solution = rhs

//

// Where R is an upper triangular compressed column sparse matrix.

template <typename IntegerType>

void SolveUpperTriangularTransposeInPlace(IntegerType num_cols,

                                          const IntegerType* rows,

                                          const IntegerType* cols,

                                          const double* values,

                                          double* rhs_and_solution) {

  for (IntegerType c = 0; c < num_cols; ++c) {

    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {

      const IntegerType r = rows[idx];

      const double v = values[idx];

      rhs_and_solution[c] -= v * rhs_and_solution[r];

    }

    rhs_and_solution[c] =  rhs_and_solution[c] / values[cols[c + 1] - 1];

  }

}

// Given a upper triangular matrix R in compressed column form, solve

// the linear system,

//

//  R'R x = b

//

// Where b is all zeros except for rhs_nonzero_index, where it is

// equal to one.

//

// The function exploits this knowledge to reduce the number of

// floating point operations.

template <typename IntegerType>

void SolveRTRWithSparseRHS(IntegerType num_cols,

                           const IntegerType* rows,

                           const IntegerType* cols,

                           const double* values,

                           const int rhs_nonzero_index,

                           double* solution) {

  std::fill(solution, solution + num_cols, 0.0);

  solution[rhs_nonzero_index] = 1.0 / values[cols[rhs_nonzero_index + 1] - 1];

  for (IntegerType c = rhs_nonzero_index + 1; c < num_cols; ++c) {

    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {

      const IntegerType r = rows[idx];

      if (r < rhs_nonzero_index) continue;

      const double v = values[idx];

      solution[c] -= v * solution[r];

    }

    solution[c] =  solution[c] / values[cols[c + 1] - 1];

  }

  SolveUpperTriangularInPlace(num_cols, rows, cols, values, solution);

}

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_