zhprfs(3)

NAME

ZHPRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is Hermitian indefinite

and packed, and provides error bounds and backward error esti

mates for the solution

SYNOPSIS

SUBROUTINE  ZHPRFS(  UPLO, N, NRHS, AP, AFP, IPIV, B, LDB,
X, LDX, FERR, BERR, WORK, RWORK, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, LDB, LDX, N, NRHS
    INTEGER        IPIV( * )
    DOUBLE         PRECISION BERR( * ), FERR( * ),  RWORK(
* )
    COMPLEX*16     AFP( * ), AP( * ), B( LDB, * ), WORK( *
), X( LDX, * )

PURPOSE

ZHPRFS improves the computed solution to a system of lin

ear equations when the coefficient matrix is Hermitian indefinite

and packed, and provides error bounds and backward error esti

mates for the solution.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The order of the matrix A. N >= 0.

NRHS (input) INTEGER

The number of right hand sides, i.e., the number

of columns of the matrices B and X. NRHS >= 0.

AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)

The upper or lower triangle of the Hermitian ma

trix 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.

AFP (input) COMPLEX*16 array, dimension (N*(N+1)/2)

The factored form of the matrix A. AFP contains

the block diagonal matrix D and the multipliers used to obtain

the factor 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 ma

trix.

IPIV (input) INTEGER array, dimension (N)

Details of the interchanges and the block struc

ture of D as determined by ZHPTRF.

B (input) COMPLEX*16 array, dimension (LDB,NRHS)

The right hand side matrix B.

LDB (input) INTEGER

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) INTEGER

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 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) COMPLEX*16 array, dimension (2*N)

RWORK (workspace) DOUBLE PRECISION array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

ZHPRFS(3)