ctprfs(3P) Sun Performance Library ctprfs(3P)NAMEctprfs - provide error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed coef‐
ficient matrix
SYNOPSIS
SUBROUTINE CTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
REAL 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, DIMENSION(:) :: A, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL, 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, DIMENSION(:) :: A, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void ctprfs(char uplo, char transa, char diag, int n, int nrhs, complex
*a, complex *b, int ldb, complex *x, int ldx, float *ferr,
float *berr, int *info);
void ctprfs_64(char uplo, char transa, char diag, long n, long nrhs,
complex *a, complex *b, long ldb, complex *x, long ldx, float
*ferr, float *berr, long *info);
PURPOSEctprfs provides error bounds and backward error estimates for the solu‐
tion to a system of linear equations with a triangular packed coeffi‐
cient 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.
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.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) COMPLEX array, dimension (N*(N+1)/2)
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) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input) COMPLEX array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
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) REAL array, dimension (NRHS)
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)
COMPLEX array, dimension(2*N)
WORK2 (workspace)
REAL array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 ctprfs(3P)
