zporfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, provide error bounds and backward error estimates for the solution
SUBROUTINE ZPORFS(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZPORFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO REAL(8), 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zporfs(char uplo, int n, int nrhs, doublecomplex *a, int lda, dou- blecomplex *af, int ldaf, doublecomplex *b, int ldb, double- complex *x, int ldx, double *ferr, double *berr, int *info); void zporfs_64(char uplo, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zporfs(3P)
NAME
zporfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite, provide
error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZPORFS(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZPORFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL(8), 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zporfs(char uplo, int n, int nrhs, doublecomplex *a, int lda, dou-
blecomplex *af, int ldaf, doublecomplex *b, int ldb, double-
complex *x, int ldx, double *ferr, double *berr, int *info);
void zporfs_64(char uplo, long n, long nrhs, doublecomplex *a, long
lda, doublecomplex *af, long ldaf, doublecomplex *b, long
ldb, doublecomplex *x, long ldx, double *ferr, double *berr,
long *info);
PURPOSE
zporfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite, and pro-
vides error bounds and backward error estimates for the solution.
ARGUMENTS
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 leading 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 referenced. 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 triangular 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 computed by ZPOTRF.
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 ZPOTRS. 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 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
7 Nov 2015 zporfs(3P)