ZGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

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, * )

ZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.

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 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 (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 illegal value

ITMAX is the maximum number of steps of iterative refinement.