#include "blaswrap.h"
/* sgbt01.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static real c_b12 = -1.f;
/* Subroutine */ int sgbt01_(integer *m, integer *n, integer *kl, integer *ku,
real *a, integer *lda, real *afac, integer *ldafac, integer *ipiv,
real *work, real *resid)
{
/* System generated locals */
integer a_dim1, a_offset, afac_dim1, afac_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
/* Local variables */
static integer i__, j;
static real t;
static integer i1, i2, kd, il, jl, ip, ju, iw, jua;
static real eps;
static integer lenj;
static real anorm;
extern doublereal sasum_(integer *, real *, integer *);
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), saxpy_(integer *, real *, real *, integer *, real *,
integer *);
extern doublereal slamch_(char *);
/* -- LAPACK test routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
SGBT01 reconstructs a band matrix A from its L*U factorization and
computes the residual:
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
The expression L*U - A is computed one column at a time, so A and
AFAC are not modified.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
A (input/output) REAL array, dimension (LDA,N)
The original matrix A in band storage, stored in rows 1 to
KL+KU+1.
LDA (input) INTEGER.
The leading dimension of the array A. LDA >= max(1,KL+KU+1).
AFAC (input) REAL array, dimension (LDAFAC,N)
The factored form of the matrix A. AFAC contains the banded
factors L and U from the L*U factorization, as computed by
SGBTRF. U is stored as an upper triangular band matrix with
KL+KU superdiagonals in rows 1 to KL+KU+1, and the
multipliers used during the factorization are stored in rows
KL+KU+2 to 2*KL+KU+1. See SGBTRF for further details.
LDAFAC (input) INTEGER
The leading dimension of the array AFAC.
LDAFAC >= max(1,2*KL*KU+1).
IPIV (input) INTEGER array, dimension (min(M,N))
The pivot indices from SGBTRF.
WORK (workspace) REAL array, dimension (2*KL+KU+1)
RESID (output) REAL
norm(L*U - A) / ( N * norm(A) * EPS )
=====================================================================
Quick exit if M = 0 or N = 0.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
afac_dim1 = *ldafac;
afac_offset = 1 + afac_dim1;
afac -= afac_offset;
--ipiv;
--work;
/* Function Body */
*resid = 0.f;
if (*m <= 0 || *n <= 0) {
return 0;
}
/* Determine EPS and the norm of A. */
eps = slamch_("Epsilon");
kd = *ku + 1;
anorm = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = kd + 1 - j;
i1 = max(i__2,1);
/* Computing MIN */
i__2 = kd + *m - j, i__3 = *kl + kd;
i2 = min(i__2,i__3);
if (i2 >= i1) {
/* Computing MAX */
i__2 = i2 - i1 + 1;
r__1 = anorm, r__2 = sasum_(&i__2, &a[i1 + j * a_dim1], &c__1);
anorm = dmax(r__1,r__2);
}
/* L10: */
}
/* Compute one column at a time of L*U - A. */
kd = *kl + *ku + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Copy the J-th column of U to WORK.
Computing MIN */
i__2 = *kl + *ku, i__3 = j - 1;
ju = min(i__2,i__3);
/* Computing MIN */
i__2 = *kl, i__3 = *m - j;
jl = min(i__2,i__3);
lenj = min(*m,j) - j + ju + 1;
if (lenj > 0) {
scopy_(&lenj, &afac[kd - ju + j * afac_dim1], &c__1, &work[1], &
c__1);
i__2 = ju + jl + 1;
for (i__ = lenj + 1; i__ <= i__2; ++i__) {
work[i__] = 0.f;
/* L20: */
}
/* Multiply by the unit lower triangular matrix L. Note that L
is stored as a product of transformations and permutations.
Computing MIN */
i__2 = *m - 1;
i__3 = j - ju;
for (i__ = min(i__2,j); i__ >= i__3; --i__) {
/* Computing MIN */
i__2 = *kl, i__4 = *m - i__;
il = min(i__2,i__4);
if (il > 0) {
iw = i__ - j + ju + 1;
t = work[iw];
saxpy_(&il, &t, &afac[kd + 1 + i__ * afac_dim1], &c__1, &
work[iw + 1], &c__1);
ip = ipiv[i__];
if (i__ != ip) {
ip = ip - j + ju + 1;
work[iw] = work[ip];
work[ip] = t;
}
}
/* L30: */
}
/* Subtract the corresponding column of A. */
jua = min(ju,*ku);
if (jua + jl + 1 > 0) {
i__3 = jua + jl + 1;
saxpy_(&i__3, &c_b12, &a[*ku + 1 - jua + j * a_dim1], &c__1, &
work[ju + 1 - jua], &c__1);
}
/* Compute the 1-norm of the column.
Computing MAX */
i__3 = ju + jl + 1;
r__1 = *resid, r__2 = sasum_(&i__3, &work[1], &c__1);
*resid = dmax(r__1,r__2);
}
/* L40: */
}
/* Compute norm( L*U - A ) / ( N * norm(A) * EPS ) */
if (anorm <= 0.f) {
if (*resid != 0.f) {
*resid = 1.f / eps;
}
} else {
*resid = *resid / (real) (*n) / anorm / eps;
}
return 0;
/* End of SGBT01 */
} /* sgbt01_ */