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zherfs.f(3) | LAPACK | zherfs.f(3) |
NAME¶
zherfs.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine zherfs (UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
Function/Subroutine Documentation¶
subroutine zherfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldaf, * )AF, integerLDAF, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)¶
ZHERFS Purpose:ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution.
UPLO
N
NRHS
A
LDA
AF
LDAF
IPIV
B
LDB
X
LDX
FERR
BERR
WORK
RWORK
INFO
Internal Parameters:
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N is INTEGER The order of the matrix A. N >= 0.
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
A is COMPLEX*16 array, dimension (LDA,N) The Hermitian 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 is INTEGER The leading dimension of the array A. LDA >= max(1,N).
AF is COMPLEX*16 array, dimension (LDAF,N) 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**H or A = L*D*L**H as computed by ZHETRF.
LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF.
B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B.
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
X is COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZHETRS. On exit, the improved solution matrix X.
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERR is 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 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 is 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 is COMPLEX*16 array, dimension (2*N)
RWORK is DOUBLE PRECISION array, dimension (N)
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Author¶
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