zhprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provide error bounds and backward error estimates for the solution
SUBROUTINE ZHPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZHPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE HPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A, AF, WORK COMPLEX(8), DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE HPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A, 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 zhprfs(char uplo, int n, int nrhs, doublecomplex *a, doublecomplex *af, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zhprfs_64(char uplo, long n, long nrhs, doublecomplex *a, 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 zhprfs(3P)
NAME
zhprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian indefinite and packed, and
provide error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZHPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZHPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE HPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A, 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 zhprfs(char uplo, int n, int nrhs, doublecomplex *a, doublecomplex
*af, int *ipivot, doublecomplex *b, int ldb, doublecomplex
*x, int ldx, double *ferr, double *berr, int *info);
void zhprfs_64(char uplo, long n, long nrhs, doublecomplex *a, double-
complex *af, long *ipivot, doublecomplex *b, long ldb, dou-
blecomplex *x, long ldx, double *ferr, double *berr, long
*info);
PURPOSE
zhprfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian 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.
A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) =
A(i,j) for j<=i<=n.
AF (input) COMPLEX*16 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 fac-
tor U or L from the factorization A = U*D*U**H or A =
L*D*L**H as computed by ZHPTRF, 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 ZHPTRF.
B (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZHPTRS. 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 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) DOUBLE PRECISION array, dimension (NRHS)
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)
COMPLEX*16 array, dimension(2*N)
WORK2 (workspace)
DOUBLE PRECISION array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
7 Nov 2015 zhprfs(3P)