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BandTriangularSolver.h
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Tue, Feb 11, 12:03

BandTriangularSolver.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BAND_TRIANGULARSOLVER_H
#define EIGEN_BAND_TRIANGULARSOLVER_H
namespace internal {
/* \internal
* Solve Ax=b with A a band triangular matrix
* TODO: extend it to matrices for x abd b */
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, int StorageOrder>
struct band_solve_triangular_selector;
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,RowMajor>
{
typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
enum { IsLower = (Mode&Lower) ? 1 : 0 };
static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
{
const LhsMap lhs(_lhs,size,k+1,OuterStride<>(lhsStride));
RhsMap other(_other,size,1);
typename internal::conditional<
ConjLhs,
const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
const LhsMap&>
::type cjLhs(lhs);
for(int col=0 ; col<other.cols() ; ++col)
{
for(int ii=0; ii<size; ++ii)
{
int i = IsLower ? ii : size-ii-1;
int actual_k = (std::min)(k,ii);
int actual_start = IsLower ? k-actual_k : 1;
if(actual_k>0)
other.coeffRef(i,col) -= cjLhs.row(i).segment(actual_start,actual_k).transpose()
.cwiseProduct(other.col(col).segment(IsLower ? i-actual_k : i+1,actual_k)).sum();
if((Mode&UnitDiag)==0)
other.coeffRef(i,col) /= cjLhs(i,IsLower ? k : 0);
}
}
}
};
template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ColMajor>
{
typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
enum { IsLower = (Mode&Lower) ? 1 : 0 };
static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
{
const LhsMap lhs(_lhs,k+1,size,OuterStride<>(lhsStride));
RhsMap other(_other,size,1);
typename internal::conditional<
ConjLhs,
const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
const LhsMap&>
::type cjLhs(lhs);
for(int col=0 ; col<other.cols() ; ++col)
{
for(int ii=0; ii<size; ++ii)
{
int i = IsLower ? ii : size-ii-1;
int actual_k = (std::min)(k,size-ii-1);
int actual_start = IsLower ? 1 : k-actual_k;
if((Mode&UnitDiag)==0)
other.coeffRef(i,col) /= cjLhs(IsLower ? 0 : k, i);
if(actual_k>0)
other.col(col).segment(IsLower ? i+1 : i-actual_k, actual_k)
-= other.coeff(i,col) * cjLhs.col(i).segment(actual_start,actual_k);
}
}
}
};
} // end namespace internal
#endif // EIGEN_BAND_TRIANGULARSOLVER_H

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