text: // Ceres Solver - A fast non-linear least squares minimizer
  // Copyright 2017 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
  //   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
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  //
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  // Author: sameeragarwal@google.com (Sameer Agarwal)
  
  #ifndef CERES_INTERNAL_SUBSET_PRECONDITIONER_H_
  #define CERES_INTERNAL_SUBSET_PRECONDITIONER_H_
  
  #include "ceres/internal/scoped_ptr.h"
  #include "ceres/preconditioner.h"
  
  namespace ceres {
  namespace internal {
  
  class BlockSparseMatrix;
  class SparseCholesky;
  class InnerProductComputer;
  
  // Subset preconditioning, uses a subset of the rows of the Jacobian
  // to construct a preconditioner for the normal equations.
  //
  // To keep the interface simple, we assume that the matrix A has
  // already been re-ordered that the user wishes to some subset of the
  // bottom row blocks of the matrix as the preconditioner. This is
  // controlled by
  // Preconditioner::Options::subset_preconditioner_start_row_block.
  //
  // When using the subset preconditioner, all row blocks starting
  // from this row block are used to construct the preconditioner.
  //
  // More precisely the matrix A is horizontally partitioned as
  //
  // A = [P]
  //     [Q]
  //
  // where P as subset_preconditioner_start_row_block row blocks,
  // and the preconditioner is the inverse of the matrix Q'Q.
  //
  // Obviously, the smaller this number, the more accurate and
  // computationally expensive this preconditioner will be.
  //
  // See the tests for example usage.
  class SubsetPreconditioner : public BlockSparseMatrixPreconditioner {
   public:
    SubsetPreconditioner(const Preconditioner::Options& options,
                         const BlockSparseMatrix& A);
    virtual ~SubsetPreconditioner();
  
    // Preconditioner interface
    virtual void RightMultiply(const double* x, double* y) const;
    virtual int num_rows() const { return num_cols_; }
    virtual int num_cols() const { return num_cols_; }
  
   private:
    virtual bool UpdateImpl(const BlockSparseMatrix& A, const double* D);
  
    const Preconditioner::Options options_;
    const int num_cols_;
    scoped_ptr<SparseCholesky> sparse_cholesky_;
    scoped_ptr<InnerProductComputer> inner_product_computer_;
  };
  
  }  // namespace internal
  }  // namespace ceres
  
  #endif  // CERES_INTERNAL_SUBSET_PRECONDITIONER_H_
  