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

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

#ifndef CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_

#define CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_

#include <set>

#include <utility>

#include <vector>

#include "ceres/block_random_access_diagonal_matrix.h"

#include "ceres/block_random_access_matrix.h"

#include "ceres/block_sparse_matrix.h"

#include "ceres/block_structure.h"

#include "ceres/internal/port.h"

#include "ceres/internal/scoped_ptr.h"

#include "ceres/linear_solver.h"

#include "ceres/schur_eliminator.h"

#include "ceres/types.h"

#ifdef CERES_USE_EIGEN_SPARSE

#include "Eigen/SparseCholesky"

#include "Eigen/OrderingMethods"

#endif

namespace ceres {

namespace internal {

class BlockSparseMatrix;

class SparseCholesky;

// Base class for Schur complement based linear least squares

// solvers. It assumes that the input linear system Ax = b can be

// partitioned into

//

//  E y + F z = b

//

// Where x = [y;z] is a partition of the variables.  The paritioning

// of the variables is such that, E'E is a block diagonal

// matrix. Further, the rows of A are ordered so that for every

// variable block in y, all the rows containing that variable block

// occur as a vertically contiguous block. i.e the matrix A looks like

//

//              E                 F

//  A = [ y1   0   0   0 |  z1    0    0   0    z5]

//      [ y1   0   0   0 |  z1   z2    0   0     0]

//      [  0  y2   0   0 |   0    0   z3   0     0]

//      [  0   0  y3   0 |  z1   z2   z3  z4    z5]

//      [  0   0  y3   0 |  z1    0    0   0    z5]

//      [  0   0   0  y4 |   0    0    0   0    z5]

//      [  0   0   0  y4 |   0   z2    0   0     0]

//      [  0   0   0  y4 |   0    0    0   0     0]

//      [  0   0   0   0 |  z1    0    0   0     0]

//      [  0   0   0   0 |   0    0   z3  z4    z5]

//

// This structure should be reflected in the corresponding

// CompressedRowBlockStructure object associated with A. The linear

// system Ax = b should either be well posed or the array D below

// should be non-null and the diagonal matrix corresponding to it

// should be non-singular.

//

// SchurComplementSolver has two sub-classes.

//

// DenseSchurComplementSolver: For problems where the Schur complement

// matrix is small and dense, or if CHOLMOD/SuiteSparse is not

// installed. For structure from motion problems, this is solver can

// be used for problems with upto a few hundred cameras.

//

// SparseSchurComplementSolver: For problems where the Schur

// complement matrix is large and sparse. It requires that Ceres be

// build with at least one sparse linear algebra library, as it

// computes a sparse Cholesky factorization of the Schur complement.

//

// This solver can be used for solving structure from motion problems

// with tens of thousands of cameras, though depending on the exact

// sparsity structure, it maybe better to use an iterative solver.

//

// The two solvers can be instantiated by calling

// LinearSolver::CreateLinearSolver with LinearSolver::Options::type

// set to DENSE_SCHUR and SPARSE_SCHUR

// respectively. LinearSolver::Options::elimination_groups[0] should

// be at least 1.

class SchurComplementSolver : public BlockSparseMatrixSolver {

 public:

  explicit SchurComplementSolver(const LinearSolver::Options& options)

      : options_(options) {

    CHECK_GT(options.elimination_groups.size(), 1);

    CHECK_GT(options.elimination_groups[0], 0);

  }

  // LinearSolver methods

  virtual ~SchurComplementSolver() {}

  virtual LinearSolver::Summary SolveImpl(

      BlockSparseMatrix* A,

      const double* b,

      const LinearSolver::PerSolveOptions& per_solve_options,

      double* x);

 protected:

  const LinearSolver::Options& options() const { return options_; }

  const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); }

  void set_lhs(BlockRandomAccessMatrix* lhs) { lhs_.reset(lhs); }

  const double* rhs() const { return rhs_.get(); }

  void set_rhs(double* rhs) { rhs_.reset(rhs); }

 private:

  virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0;

  virtual LinearSolver::Summary SolveReducedLinearSystem(

      const LinearSolver::PerSolveOptions& per_solve_options,

      double* solution) = 0;

  LinearSolver::Options options_;

  scoped_ptr<SchurEliminatorBase> eliminator_;

  scoped_ptr<BlockRandomAccessMatrix> lhs_;

  scoped_array<double> rhs_;

  CERES_DISALLOW_COPY_AND_ASSIGN(SchurComplementSolver);

};

// Dense Cholesky factorization based solver.

class DenseSchurComplementSolver : public SchurComplementSolver {

 public:

  explicit DenseSchurComplementSolver(const LinearSolver::Options& options)

      : SchurComplementSolver(options) {}

  virtual ~DenseSchurComplementSolver() {}

 private:

  virtual void InitStorage(const CompressedRowBlockStructure* bs);

  virtual LinearSolver::Summary SolveReducedLinearSystem(

      const LinearSolver::PerSolveOptions& per_solve_options,

      double* solution);

  CERES_DISALLOW_COPY_AND_ASSIGN(DenseSchurComplementSolver);

};

// Sparse Cholesky factorization based solver.

class SparseSchurComplementSolver : public SchurComplementSolver {

 public:

  explicit SparseSchurComplementSolver(const LinearSolver::Options& options);

  virtual ~SparseSchurComplementSolver();

 private:

  virtual void InitStorage(const CompressedRowBlockStructure* bs);

  virtual LinearSolver::Summary SolveReducedLinearSystem(

      const LinearSolver::PerSolveOptions& per_solve_options,

      double* solution);

  LinearSolver::Summary SolveReducedLinearSystemUsingConjugateGradients(

      const LinearSolver::PerSolveOptions& per_solve_options,

      double* solution);

  // Size of the blocks in the Schur complement.

  std::vector<int> blocks_;

  scoped_ptr<SparseCholesky> sparse_cholesky_;

  scoped_ptr<BlockRandomAccessDiagonalMatrix> preconditioner_;

  CERES_DISALLOW_COPY_AND_ASSIGN(SparseSchurComplementSolver);

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_