csyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution
SUBROUTINE CSYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CSYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER(8), DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void csyrfs(char uplo, int n, int nrhs, complex *a, int lda, complex *af, int ldaf, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void csyrfs_64(char uplo, long n, long nrhs, complex *a, long lda, com- plex *af, long ldaf, long *ipivot, complex *b, long ldb, com- plex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library csyrfs(3P)
NAME
csyrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, provide error
bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CSYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CSYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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
INTEGER*8 IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE SYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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
INTEGER, DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE SYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT,
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
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void csyrfs(char uplo, int n, int nrhs, complex *a, int lda, complex
*af, int ldaf, int *ipivot, complex *b, int ldb, complex *x,
int ldx, float *ferr, float *berr, int *info);
void csyrfs_64(char uplo, long n, long nrhs, complex *a, long lda, com-
plex *af, long ldaf, long *ipivot, complex *b, long ldb, com-
plex *x, long ldx, float *ferr, float *berr, long *info);
PURPOSE
csyrfs improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite, and provides 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 symmetric 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 factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the fac-
tor U or L from the factorization A = U*D*U**T or A =
L*D*L**T as computed by CSYTRF.
LDAF (input)
The leading dimension of the array AF. LDAF >= max(1,N).
IPIVOT (input)
Details of the interchanges and the block structure of D as
determined by CSYTRF.
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 CSYTRS. 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 csyrfs(3P)