Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  improves  the  computed solution to a system of linear 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 linear 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 >= 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

PARAMETERS

        ITMAX is the maximum number of steps of iterative refinement.

 LAPACK routine (version 3.2)               April 2011                            ZGERFS(3lapack)