Contents
ztprfs - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix
SUBROUTINE ZTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
DOUBLE COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE TPRFS(UPLO, [TRANSA], DIAG, N, NRHS, A, B, [LDB], X, [LDX],
FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: A, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE TPRFS_64(UPLO, [TRANSA], DIAG, N, NRHS, A, B, [LDB], X,
[LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX(8), DIMENSION(:) :: A, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void ztprfs(char uplo, char transa, char diag, int n, int
nrhs, doublecomplex *a, doublecomplex *b, int ldb,
doublecomplex *x, int ldx, double *ferr, double
*berr, int *info);
void ztprfs_64(char uplo, char transa, char diag, long n,
long nrhs, doublecomplex *a, doublecomplex *b,
long ldb, doublecomplex *x, long ldx, double
*ferr, double *berr, long *info);
ztprfs provides error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix.
The solution matrix X must be computed by CTPTRS or some
other means before entering this routine. CTPRFS does not
do iterative refinement because doing so cannot improve the
backward error.
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.
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 matrix A, packed
columnwise in a linear array. The j-th column of
A is stored in the array A as follows: if UPLO =
'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for
j<=i<=n. If DIAG = 'U', the diagonal elements of
A are not referenced and are assumed to be 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 solu-
tion 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 estimated
upper bound for the magnitude of the largest ele-
ment in (X(j) - XTRUE) divided by the magnitude of
the largest element 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 element 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 ille-
gal value