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/* linalg/invtri.c
*
* Copyright (C) 2016 Patrick Alken
*
* This is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation; either version 3, or (at your option) any
* later version.
*
* This source is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* This module contains code to invert triangular matrices
*/
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
static int triangular_inverse(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_matrix * T);
int
gsl_linalg_tri_upper_invert(gsl_matrix * T)
{
int status = triangular_inverse(CblasUpper, CblasNonUnit, T);
return status;
}
int
gsl_linalg_tri_lower_invert(gsl_matrix * T)
{
int status = triangular_inverse(CblasLower, CblasNonUnit, T);
return status;
}
int
gsl_linalg_tri_upper_unit_invert(gsl_matrix * T)
{
int status = triangular_inverse(CblasUpper, CblasUnit, T);
return status;
}
int
gsl_linalg_tri_lower_unit_invert(gsl_matrix * T)
{
int status = triangular_inverse(CblasLower, CblasUnit, T);
return status;
}
/*
triangular_inverse()
Invert a triangular matrix T
Inputs: Uplo - CblasUpper or CblasLower
Diag - unit triangular?
T - on output the upper (or lower) part of T
is replaced by its inverse
Return: success/error
*/
static int
triangular_inverse(CBLAS_UPLO_t Uplo, CBLAS_DIAG_t Diag, gsl_matrix * T)
{
const size_t N = T->size1;
if (N != T->size2)
{
GSL_ERROR ("matrix must be square", GSL_ENOTSQR);
}
else
{
gsl_matrix_view m;
gsl_vector_view v;
size_t i;
if (Uplo == CblasUpper)
{
for (i = 0; i < N; ++i)
{
double aii;
if (Diag == CblasNonUnit)
{
double *Tii = gsl_matrix_ptr(T, i, i);
*Tii = 1.0 / *Tii;
aii = -(*Tii);
}
else
{
aii = -1.0;
}
if (i > 0)
{
m = gsl_matrix_submatrix(T, 0, 0, i, i);
v = gsl_matrix_subcolumn(T, i, 0, i);
gsl_blas_dtrmv(CblasUpper, CblasNoTrans, Diag,
&m.matrix, &v.vector);
gsl_blas_dscal(aii, &v.vector);
}
} /* for (i = 0; i < N; ++i) */
}
else
{
for (i = 0; i < N; ++i)
{
double ajj;
size_t j = N - i - 1;
if (Diag == CblasNonUnit)
{
double *Tjj = gsl_matrix_ptr(T, j, j);
*Tjj = 1.0 / *Tjj;
ajj = -(*Tjj);
}
else
{
ajj = -1.0;
}
if (j < N - 1)
{
m = gsl_matrix_submatrix(T, j + 1, j + 1,
N - j - 1, N - j - 1);
v = gsl_matrix_subcolumn(T, j, j + 1, N - j - 1);
gsl_blas_dtrmv(CblasLower, CblasNoTrans, Diag,
&m.matrix, &v.vector);
gsl_blas_dscal(ajj, &v.vector);
}
} /* for (i = 0; i < N; ++i) */
}
return GSL_SUCCESS;
}
}
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