zgerfs(3)

NAME

ZGERFS - improve the computed solution to a system of lin

ear equations and provides error bounds and backward error esti

mates 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 esti

mates 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 >=

max(1,N).

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 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

ZGERFS(3)