internal/ceres/block_jacobi_preconditioner.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: keir@google.com (Keir Mierle)

#include "ceres/block_jacobi_preconditioner.h"

#include "Eigen/Dense"
#include "ceres/block_random_access_diagonal_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/internal/eigen.h"
#include "ceres/small_blas.h"

namespace ceres::internal {

BlockSparseJacobiPreconditioner::BlockSparseJacobiPreconditioner(
    const BlockSparseMatrix& A) {
  m_ = std::make_unique<BlockRandomAccessDiagonalMatrix>(
      A.block_structure()->cols);
}

BlockSparseJacobiPreconditioner::~BlockSparseJacobiPreconditioner() = default;

bool BlockSparseJacobiPreconditioner::UpdateImpl(const BlockSparseMatrix& A,
                                                 const double* D) {
  const CompressedRowBlockStructure* bs = A.block_structure();
  const double* values = A.values();
  m_->SetZero();
  for (int i = 0; i < bs->rows.size(); ++i) {
    const int row_block_size = bs->rows[i].block.size;
    const std::vector<Cell>& cells = bs->rows[i].cells;
    for (const auto& cell : cells) {
      const int block_id = cell.block_id;
      const int col_block_size = bs->cols[block_id].size;

      int r, c, row_stride, col_stride;
      CellInfo* cell_info =
          m_->GetCell(block_id, block_id, &r, &c, &row_stride, &col_stride);
      MatrixRef m(cell_info->values, row_stride, col_stride);
      ConstMatrixRef b(values + cell.position, row_block_size, col_block_size);
      // clang-format off
      MatrixTransposeMatrixMultiply<Eigen::Dynamic, Eigen::Dynamic,
          Eigen::Dynamic,Eigen::Dynamic, 1>(
          values + cell.position, row_block_size,col_block_size,
          values + cell.position, row_block_size,col_block_size,
          cell_info->values,r, c,row_stride,col_stride);
      // clang-format on
    }
  }

  if (D != nullptr) {
    // Add the diagonal.
    int position = 0;
    for (int i = 0; i < bs->cols.size(); ++i) {
      const int block_size = bs->cols[i].size;
      int r, c, row_stride, col_stride;
      CellInfo* cell_info = m_->GetCell(i, i, &r, &c, &row_stride, &col_stride);
      MatrixRef m(cell_info->values, row_stride, col_stride);
      m.block(r, c, block_size, block_size).diagonal() +=
          ConstVectorRef(D + position, block_size).array().square().matrix();
      position += block_size;
    }
  }

  m_->Invert();
  return true;
}

BlockCRSJacobiPreconditioner::BlockCRSJacobiPreconditioner(
    const CompressedRowSparseMatrix& A) {
  auto& col_blocks = A.col_blocks();

  // Compute the number of non-zeros in the preconditioner. This is needed so
  // that we can construct the CompressedRowSparseMatrix.
  const int m_nnz = SumSquaredSizes(col_blocks);
  m_ = std::make_unique<CompressedRowSparseMatrix>(
      A.num_cols(), A.num_cols(), m_nnz);

  const int num_col_blocks = col_blocks.size();

  // Populate the sparsity structure of the preconditioner matrix.
  int* m_cols = m_->mutable_cols();
  int* m_rows = m_->mutable_rows();
  m_rows[0] = 0;
  for (int i = 0, idx = 0; i < num_col_blocks; ++i) {
    // For each column block populate a diagonal block in the preconditioner.
    // Not that the because of the way the CompressedRowSparseMatrix format
    // works, the entire diagonal block is laid out contiguously in memory as a
    // row-major matrix. We will use this when updating the block.
    auto& block = col_blocks[i];
    for (int j = 0; j < block.size; ++j) {
      for (int k = 0; k < block.size; ++k, ++idx) {
        m_cols[idx] = block.position + k;
      }
      m_rows[block.position + j + 1] = idx;
    }
  }

  CHECK_EQ(m_rows[A.num_cols()], m_nnz);
}

BlockCRSJacobiPreconditioner::~BlockCRSJacobiPreconditioner() = default;

bool BlockCRSJacobiPreconditioner::UpdateImpl(
    const CompressedRowSparseMatrix& A, const double* D) {
  const auto& col_blocks = A.col_blocks();
  const auto& row_blocks = A.row_blocks();
  const int num_col_blocks = col_blocks.size();
  const int num_row_blocks = row_blocks.size();

  const int* a_rows = A.rows();
  const int* a_cols = A.cols();
  const double* a_values = A.values();

  m_->SetZero();
  double* m_values = m_->mutable_values();
  const int* m_rows = m_->rows();

  for (int i = 0; i < num_row_blocks; ++i) {
    const int row = row_blocks[i].position;
    const int row_block_size = row_blocks[i].size;
    const int row_nnz = a_rows[row + 1] - a_rows[row];
    ConstMatrixRef row_block(a_values + a_rows[row], row_block_size, row_nnz);
    int c = 0;
    while (c < row_nnz) {
      const int idx = a_rows[row] + c;
      const int col = a_cols[idx];
      const int col_block_size = m_rows[col + 1] - m_rows[col];

      // We make use of the fact that the entire diagonal block is stored
      // contiguously in memory as a row-major matrix.
      MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);

      // We do not have a row_stride version of MatrixTransposeMatrixMultiply,
      // otherwise we could use it here to further speed up the following
      // expression.
      auto b = row_block.middleCols(c, col_block_size);
      m.noalias() += b.transpose() * b;
      c += col_block_size;
    }
  }

  for (int i = 0; i < num_col_blocks; ++i) {
    const int col = col_blocks[i].position;
    const int col_block_size = col_blocks[i].size;
    MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);

    if (D != nullptr) {
      m.diagonal() +=
          ConstVectorRef(D + col, col_block_size).array().square().matrix();
    }

    // TODO(sameeragarwal): Deal with Cholesky inversion failure here and
    // elsewhere.
    m = m.llt().solve(Matrix::Identity(col_block_size, col_block_size));
  }

  return true;
}

}  // namespace ceres::internal