ztbrfs(3P) Sun Performance Library ztbrfs(3P)NAMEztbrfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band coeffi‐
cient matrix
SYNOPSIS
SUBROUTINE ZTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE TBRFS(UPLO, [TRANSA], DIAG, N, KD, NRHS, A, [LDA], B,
[LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
INTEGER :: N, KD, NRHS, LDA, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE TBRFS_64(UPLO, [TRANSA], DIAG, N, KD, NRHS, A, [LDA],
B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B, X
INTEGER(8) :: N, KD, NRHS, LDA, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void ztbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs,
doublecomplex *a, int lda, doublecomplex *b, int ldb, double‐
complex *x, int ldx, double *ferr, double *berr, int *info);
void ztbrfs_64(char uplo, char transa, char diag, long n, long kd, long
nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb,
doublecomplex *x, long ldx, double *ferr, double *berr, long
*info);
PURPOSEztbrfs provides error bounds and backward error estimates for the solu‐
tion to a system of linear equations with a triangular band coefficient
matrix.
The solution matrix X must be computed by ZTBTRS or some other means
before entering this routine. ZTBRFS does not do iterative refinement
because doing so cannot improve the backward error.
ARGUMENTS
UPLO (input)
= 'U': A is upper triangular;
= 'L': A is lower triangular.
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.
DIAG (input)
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of superdiagonals or subdiagonals of the triangu‐
lar band matrix A. KD >= 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 upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array A as follows: if UPLO = 'U',
A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U',
the diagonal elements of A are not referenced and are assumed
to be 1.
LDA (input)
The leading dimension of the array A. LDA >= KD+1.
B (input) The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input) The 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 ztbrfs(3P)
