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


SYNOPSIS

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

           INTEGER       INFO, LDA, LDB, N, NRHS

           INTEGER       IPIV( * )

           COMPLEX       A( LDA, * ), B( LDB, * )


PURPOSE

       CGESV computes the solution to a complex 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) COMPLEX 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) COMPLEX array, dimension (LDB,NRHS)
               On entry, the N-by-NRHS matrix of right hand  side
               matrix  B.   On  exit,  if INFO = 0, the N-by-NRHS
               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
               > 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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