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NAME
     dgerfs - improve the computed solution to a system of linear
     equations and provides error bounds and backward error esti-
     mates for the solution

SYNOPSIS
     SUBROUTINE DGERFS( TRANS, N, NRHS, A, LDA, AF,  LDAF,  IPIV,
               B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

     CHARACTER TRANS

     INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS

     INTEGER IPIV( * ), IWORK( * )

     DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B(  LDB,  *  ),
               BERR( * ), FERR( * ), WORK( * ), X( LDX, * )



     #include <sunperf.h>

     void dgerfs(char trans, int n, int  nrhs,  double  *da,  int
               lda,  double  *af,  int  ldaf, int *ipivot, double
               *db, int ldb, double *dx, int ldx,  double  *ferr,
               double *berr, int *info) ;

PURPOSE
     DGERFS improves the computed solution to a system of  linear
     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 = Tran-
               spose)

     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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAF,N)
               The factors L and U from  the  factorization  A  =
               P*L*U as computed by DGETRF.

     LDAF      (input) INTEGER
               The leading dimension of the array  AF.   LDAF  >=
               max(1,N).

     IPIV      (input) INTEGER array, dimension (N)
               The pivot indices from DGETRF; for 1<=i<=N, row  i
               of the matrix was interchanged with row IPIV(i).

     B         (input)   DOUBLE   PRECISION   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) DOUBLE PRECISION  array,  dimension
               (LDX,NRHS)
               On entry, the solution matrix X,  as  computed  by
               DGETRS.  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  ele-
               ment 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)  DOUBLE  PRECISION  array,   dimension
               (3*N)

     IWORK     (workspace) INTEGER array, dimension (N)

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value

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