zsprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution
SUBROUTINE ZSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, AF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, AF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zsprfs(char uplo, int n, int nrhs, doublecomplex *ap, doublecom- plex *af, int *ipivot, doublecomplex *b, int ldb, doublecom- plex *x, int ldx, double *ferr, double *berr, int *info); void zsprfs_64(char uplo, long n, long nrhs, doublecomplex *pa, double- complex *af, long *ipivot, doublecomplex *b, long ldb, dou- blecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zsprfs(3P)
NAME
zsprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and packed, provide
error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: AP, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: AP, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zsprfs(char uplo, int n, int nrhs, doublecomplex *ap, doublecom-
plex *af, int *ipivot, doublecomplex *b, int ldb, doublecom-
plex *x, int ldx, double *ferr, double *berr, int *info);
void zsprfs_64(char uplo, long n, long nrhs, doublecomplex *pa, double-
complex *af, long *ipivot, doublecomplex *b, long ldb, dou-
blecomplex *x, long ldx, double *ferr, double *berr, long
*info);
PURPOSE
zsprfs improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and packed, 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.
AP (input)
Double complex array, dimension (N*(N+1)/2) The upper or
lower triangle of the symmetric matrix A, packed columnwise
in a linear array. The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
A(i,j) for j<=i<=n.
AF (input)
Double complex array, dimension (N*(N+1)/2) The factored form
of the matrix A. AF contains the block diagonal matrix D and
the multipliers used to obtain the factor U or L from the
factorization A = U*D*U**T or A = L*D*L**T as computed by
ZSPTRF, stored as a packed triangular matrix.
IPIVOT (input)
Integer array, dimension (N) Details of the interchanges and
the block structure of D as determined by ZSPTRF.
B (input) Double 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/output)
Double complex array, dimension (LDX,NRHS) On entry, the
solution matrix X, as computed by ZSPTRS. On exit, the
improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
Double precision array, dimension (NRHS) The estimated for-
ward error bound for each solution vector X(j) (the j-th col-
umn 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 element 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)
Double precision array, dimension (NRHS) 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)
Double precision array, dimension(2*N)
WORK2 (workspace)
Integer array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
7 Nov 2015 zsprfs(3P)