DGESV  -  compute  the solution to a real system of linear
       equations A * X = B,


SYNOPSIS

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

           INTEGER       INFO, LDA, LDB, N, NRHS

           INTEGER       IPIV( * )

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


PURPOSE

       DGESV computes the solution to a  real  system  of  linear
       equations A * X = B, where A is an N-by-N matrix and X and
       B are N-by-NRHS matrices.

       The LU decomposition with partial pivoting and row  inter­
       changes is used to factor A as
          A = P * L * U,
       where  P is a permutation matrix, L is unit lower triangu­
       lar, and U is upper triangular.  The factored form of A is
       then used to solve the system of equations A * X = B.


ARGUMENTS

       N       (input) INTEGER
               The number of linear equations, i.e., 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/output) DOUBLE PRECISION array, dimension
               (LDA,N)
               On entry, the N-by-N  coefficient  matrix  A.   On
               exit, the factors L and U from the factorization A
               = P*L*U; the unit diagonal elements of L  are  not
               stored.

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

       IPIV    (output) INTEGER array, dimension (N)
               The pivot  indices  that  define  the  permutation
               matrix  P;  row  i  of the matrix was interchanged
               with row IPIV(i).

       B        (input/output)   DOUBLE   PRECISION   array,
               dimension (LDB,NRHS)
               On entry, the N-by-NRHS matrix of right hand  side

               solution matrix X.

       LDB     (input) INTEGER
               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
               > 0:  if INFO = i, U(i,i) is  exactly  zero.   The
               factorization has been completed, but the factor U
               is exactly singular, so the solution could not  be
               computed.


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