DGETRS  -  solve a system of linear equations A * X = B or
       A' * X = B with a general N-by-N matrix  A  using  the  LU
       factorization computed by DGETRF


SYNOPSIS

       SUBROUTINE DGETRS( TRANS,  N,  NRHS, A, LDA, IPIV, B, LDB,
                          INFO )

           CHARACTER      TRANS

           INTEGER        INFO, LDA, LDB, N, NRHS

           INTEGER        IPIV( * )

           DOUBLE         PRECISION A( LDA, * ), B( LDB, * )


PURPOSE

       DGETRS solves a system of linear equations A * X = B or A'
       *  X  = B with a general N-by-N matrix A using the LU fac­
       torization computed by DGETRF.


ARGUMENTS

       TRANS   (input) CHARACTER*1
               Specifies the form of the system of equations:
               = 'N':  A * X = B  (No transpose)
               = 'T':  A'* X = B  (Transpose)
               = 'C':  A'* X = B  (Conjugate transpose  =  Trans­
               pose)

       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 matrix B.  NRHS >= 0.

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

       LDA     (input) INTEGER
               The  leading  dimension  of  the  array A.  LDA >=
               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/output)   DOUBLE   PRECISION   array,
               dimension (LDB,NRHS)
               On  entry, the right hand side matrix B.  On exit,
               the solution matrix X.

               The leading dimension of  the  array  B.   LDB  >=
               max(1,N).

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


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