zsyrfs - 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 ZSYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZSYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER*8 IPIVOT(*) DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zsyrfs(char uplo, int n, int nrhs, doublecomplex *a, int lda, dou- blecomplex *af, int ldaf, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zsyrfs_64(char uplo, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecom- plex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zsyrfs(3P) NAME zsyrfs - 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 ZSYRFS(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZSYRFS_64(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIVOT, 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 INTEGER*8 IPIVOT(*) DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zsyrfs(char uplo, int n, int nrhs, doublecomplex *a, int lda, dou- blecomplex *af, int ldaf, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zsyrfs_64(char uplo, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecom- plex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info); PURPOSE zsyrfs 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 ZSYTRF. 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 ZSYTRF. 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 ZSYTRS. 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 zsyrfs(3P)