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dgesv

 NAME
      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 equa-
      tions
         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 triangular,
      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).

 (LDB,NRHS)

      B       (input/output) DOUBLE PRECISION array, dimension
              On entry, the N-by-NRHS matrix of right hand side
              matrix B.  On exit, if INFO = 0, the N-by-NRHS solu-
              tion 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 illegal
              value
              > 0:  if INFO = i, U(i,i) is exactly zero.  The fac-
              torization has been completed, but the factor U is
              exactly singular, so the solution could not be com-
              puted.