Contents
zhprfs - improve the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefin-
ite and packed, and provides 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, doublecomplex *af, long *ipivot, doublecomplex
*b, long ldb, doublecomplex *x, long ldx, double
*ferr, double *berr, long *info);
zhprfs improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefin-
ite and packed, and provides error bounds and backward error
estimates for the solution.
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 factor U or L from the factori-
zation A = U*D*U**H or A = L*D*L**H as computed by
CHPTRF, stored as a packed triangular matrix.
IPIVOT (input) INTEGER array, dimension (N)
Details of the interchanges and the block struc-
ture of D as determined by CHPTRF.
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
CHPTRS. 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 solu-
tion 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 estimated
upper bound for the magnitude of the largest ele-
ment 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)
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 ille-
gal value