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/**
*/
/*
*
* Template Numerical Toolkit (TNT): Linear Algebra Module
*
* Mathematical and Computational Sciences Division
* National Institute of Technology,
* Gaithersburg, MD USA
*
*
* This software was developed at the National Institute of Standards and
* Technology (NIST) by employees of the Federal Government in the course
* of their official duties. Pursuant to title 17 Section 105 of the
* United States Code, this software is not subject to copyright protection
* and is in the public domain. The Template Numerical Toolkit (TNT) is
* an experimental system. NIST assumes no responsibility whatsoever for
* its use by other parties, and makes no guarantees, expressed or implied,
* about its quality, reliability, or any other characteristic.
*
* BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
* see http://math.nist.gov/tnt for latest updates.
*
*/
// Triangular Solves
#ifndef TRISLV_H
#define TRISLV_H
#include "triang.h"
namespace TNT
{
template <class MaTriX, class VecToR>
VecToR Lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
{
Subscript N = A.num_rows();
// make sure matrix sizes agree; A must be square
assert(A.num_cols() == N);
assert(b.dim() == N);
VecToR x(N);
Subscript i;
for (i=1; i<=N; i++)
{
typename MaTriX::element_type tmp=0;
for (Subscript j=1; j<i; j++)
tmp = tmp + A(i,j)*x(j);
x(i) = (b(i) - tmp)/ A(i,i);
}
return x;
}
template <class MaTriX, class VecToR>
VecToR Unit_lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
{
Subscript N = A.num_rows();
// make sure matrix sizes agree; A must be square
assert(A.num_cols() == N);
assert(b.dim() == N);
VecToR x(N);
Subscript i;
for (i=1; i<=N; i++)
{
typename MaTriX::element_type tmp=0;
for (Subscript j=1; j<i; j++)
tmp = tmp + A(i,j)*x(j);
x(i) = b(i) - tmp;
}
return x;
}
template <class MaTriX, class VecToR>
VecToR linear_solve(/*const*/ LowerTriangularView<MaTriX> &A,
/*const*/ VecToR &b)
{
return Lower_triangular_solve(A, b);
}
template <class MaTriX, class VecToR>
VecToR linear_solve(/*const*/ UnitLowerTriangularView<MaTriX> &A,
/*const*/ VecToR &b)
{
return Unit_lower_triangular_solve(A, b);
}
//********************** Upper triangular section ****************
template <class MaTriX, class VecToR>
VecToR Upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
{
Subscript N = A.num_rows();
// make sure matrix sizes agree; A must be square
assert(A.num_cols() == N);
assert(b.dim() == N);
VecToR x(N);
Subscript i;
for (i=N; i>=1; i--)
{
typename MaTriX::element_type tmp=0;
for (Subscript j=i+1; j<=N; j++)
tmp = tmp + A(i,j)*x(j);
x(i) = (b(i) - tmp)/ A(i,i);
}
return x;
}
template <class MaTriX, class VecToR>
VecToR Unit_upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
{
Subscript N = A.num_rows();
// make sure matrix sizes agree; A must be square
assert(A.num_cols() == N);
assert(b.dim() == N);
VecToR x(N);
Subscript i;
for (i=N; i>=1; i--)
{
typename MaTriX::element_type tmp=0;
for (Subscript j=i+1; j<i; j++)
tmp = tmp + A(i,j)*x(j);
x(i) = b(i) - tmp;
}
return x;
}
template <class MaTriX, class VecToR>
VecToR linear_solve(/*const*/ UpperTriangularView<MaTriX> &A,
/*const*/ VecToR &b)
{
return Upper_triangular_solve(A, b);
}
template <class MaTriX, class VecToR>
VecToR linear_solve(/*const*/ UnitUpperTriangularView<MaTriX> &A,
/*const*/ VecToR &b)
{
return Unit_upper_triangular_solve(A, b);
}
} // namespace TNT
#endif // TRISLV_H
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