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

// Copyright 2015 Google Inc. All rights reserved.

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

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// Author: keir@google.com (Keir Mierle)

#ifndef CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_

#define CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_

#include <algorithm>

#include "ceres/linear_operator.h"

#include "ceres/internal/scoped_ptr.h"

#include "ceres/internal/eigen.h"

namespace ceres {

namespace internal {

class SparseMatrix;

// A linear operator which takes a matrix A and a diagonal vector D and

// performs products of the form

//

//   (A^T A + D^T D)x

//

// This is used to implement iterative general sparse linear solving with

// conjugate gradients, where A is the Jacobian and D is a regularizing

// parameter. A brief proof that D^T D is the correct regularizer:

//

// Given a regularized least squares problem:

//

//   min  ||Ax - b||^2 + ||Dx||^2

//    x

//

// First expand into matrix notation:

//

//   (Ax - b)^T (Ax - b) + xD^TDx

//

// Then multiply out to get:

//

//   = xA^TAx - 2b^T Ax + b^Tb + xD^TDx

//

// Take the derivative:

//

//   0 = 2A^TAx - 2A^T b + 2 D^TDx

//   0 = A^TAx - A^T b + D^TDx

//   0 = (A^TA + D^TD)x - A^T b

//

// Thus, the symmetric system we need to solve for CGNR is

//

//   Sx = z

//

// with S = A^TA + D^TD

//  and z = A^T b

//

// Note: This class is not thread safe, since it uses some temporary storage.

class CgnrLinearOperator : public LinearOperator {

 public:

  CgnrLinearOperator(const LinearOperator& A, const double *D)

      : A_(A), D_(D), z_(new double[A.num_rows()]) {

  }

  virtual ~CgnrLinearOperator() {}

  virtual void RightMultiply(const double* x, double* y) const {

    std::fill(z_.get(), z_.get() + A_.num_rows(), 0.0);

    // z = Ax

    A_.RightMultiply(x, z_.get());

    // y = y + Atz

    A_.LeftMultiply(z_.get(), y);

    // y = y + DtDx

    if (D_ != NULL) {

      int n = A_.num_cols();

      VectorRef(y, n).array() += ConstVectorRef(D_, n).array().square() *

                                 ConstVectorRef(x, n).array();

    }

  }

  virtual void LeftMultiply(const double* x, double* y) const {

    RightMultiply(x, y);

  }

  virtual int num_rows() const { return A_.num_cols(); }

  virtual int num_cols() const { return A_.num_cols(); }

 private:

  const LinearOperator& A_;

  const double* D_;

  scoped_array<double> z_;

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_CGNR_LINEAR_OPERATOR_H_