ZGERFS - improve the computed solution to a system of lin
ear equations and provides error bounds and backward error
estimates for the solution
SYNOPSIS
SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
B, LDB, X, LDX, FERR, BERR, WORK,
RWORK, INFO )
CHARACTER TRANS
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
ZGERFS improves the computed solution to a system of lin
ear equations and provides error bounds and backward error
estimates for the solution.
ARGUMENTS
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
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 original N-by-N matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF (input) COMPLEX*16 array, dimension (LDAF,N)
The factors L and U from the factorization A =
P*L*U as computed by ZGETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >=
IPIV (input) INTEGER array, dimension (N)
The pivot indices from ZGETRF; for 1<=i<=N, row i
of the matrix was interchanged with row IPIV(i).
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
ZGETRS. 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
< 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.
Man(1) output converted with
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