ctprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coef- ficient matrix
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);
Oracle Solaris Studio Performance Library ctprfs(3P)
NAME
ctprfs - 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);
PURPOSE
ctprfs 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)
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
7 Nov 2015 ctprfs(3P)