ZSYRFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
indefinite, and provides error bounds and backward error
estimates for the solution
SYNOPSIS
SUBROUTINE ZSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV,
B, LDB, X, LDX, FERR, BERR, WORK,
RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IPIV( * )
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK(
* )
COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, *
), WORK( * ), X( LDX, * )
PURPOSE
ZSYRFS improves the computed solution to a system of lin
ear equations when the coefficient matrix is symmetric
indefinite, and provides error bounds and backward error
estimates 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.
A (input) COMPLEX*16 array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the lead
ing 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 refer
enced. 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 tri
angular part of A is not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,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 factor
ization A = U*D*U**T or A = L*D*L**T as computed
by ZSYTRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block struc
ture of D as determined by ZSYTRF.
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
ZSYTRS. 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 corre
sponding 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 reli
able 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
gal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refine
ment.
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