zgbrfs(3P) Sun Performance Library zgbrfs(3P)NAMEzgbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error bounds and
backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZGBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE GBRFS([TRANSA], [N], KL, KU, [NRHS], A, [LDA], AF,
[LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2],
[INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE GBRFS_64([TRANSA], [N], KL, KU, [NRHS], A, [LDA],
AF, [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zgbrfs(char transa, int n, int kl, int ku, int nrhs, doublecomplex
*a, int lda, doublecomplex *af, int ldaf, int *ipivot, dou‐
blecomplex *b, int ldb, doublecomplex *x, int ldx, double
*ferr, double *berr, int *info);
void zgbrfs_64(char transa, long n, long kl, long ku, long nrhs, dou‐
blecomplex *a, long lda, doublecomplex *af, long ldaf, long
*ipivot, doublecomplex *b, long ldb, doublecomplex *x, long
ldx, double *ferr, double *berr, long *info);
PURPOSEzgbrfs improves the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides error bounds and
backward error estimates for the solution.
ARGUMENTS
TRANSA (input)
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
TRANSA is defaulted to 'N' for F95 INTERFACE.
N (input) The order of the matrix A. N >= 0.
KL (input)
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
The number of superdiagonals within the band of A. KU >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) The original band matrix A, stored in rows 1 to KL+KU+1. The
j-th column of A is stored in the j-th column of the array A
as follows: A(ku+1+i-j,j) = A(i,j) for max(1,j-
ku)<=i<=min(n,j+kl).
LDA (input)
The leading dimension of the array A. LDA >= KL+KU+1.
AF (input)
Details of the LU factorization of the band matrix A, as com‐
puted by ZGBTRF. 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.
LDAF (input)
The leading dimension of the array AF. LDAF >= 2*KL*KU+1.
IPIVOT (input)
The pivot indices from ZGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIVOT(i).
B (input) The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output)
On entry, the solution matrix X, as computed by ZGBTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X). If XTRUE is
the true solution corresponding to X(j), FERR(j) is an esti‐
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele‐
ment in X(j). The estimate is as reliable as the estimate
for RCOND, and is almost always a slight overestimate of the
true error.
BERR (output)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any ele‐
ment of A or B that makes X(j) an exact solution).
WORK (workspace)
dimension(2*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zgbrfs(3P)
