Contents
cporfs - improve the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive
definite,
SUBROUTINE CPORFS(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CPORFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE PORFS(UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], B, [LDB],
X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE PORFS_64(UPLO, [N], [NRHS], A, [LDA], AF, [LDAF], B, [LDB],
X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void cporfs(char uplo, int n, int nrhs, complex *a, int lda,
complex *af, int ldaf, complex *b, int ldb, com-
plex *x, int ldx, float *ferr, float *berr, int
*info);
void cporfs_64(char uplo, long n, long nrhs, complex *a,
long lda, complex *af, long ldaf, complex *b, long
ldb, complex *x, long ldx, float *ferr, float
*berr, long *info);
cporfs improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive
definite, and provides error bounds and backward error esti-
mates for the solution.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 Hermitian matrix A. If UPLO = 'U', the lead-
ing N-by-N upper triangular part of A contains the
upper triangular part of the matrix A, and the
strictly lower triangular part of A is not refer-
enced. If UPLO = 'L', the leading N-by-N lower
triangular part of A contains the lower triangular
part of the matrix A, and the strictly upper tri-
angular part of A is not referenced.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
AF (input)
The triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, as com-
puted by CPOTRF.
LDAF (input)
The leading dimension of the array AF. LDAF >=
max(1,N).
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
CPOTRS. 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 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