MB02SZ

LU factorization of a complex upper Hessenberg matrix H

Purpose

  To compute an LU factorization of a complex n-by-n upper
  Hessenberg matrix H using partial pivoting with row interchanges.

      SUBROUTINE MB02SZ( N, H, LDH, IPIV, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDH, N
C     .. Array Arguments ..
      INTEGER           IPIV(*)
      COMPLEX*16        H(LDH,*)

Input/Output Parameters

  N       (input) INTEGER
          The order of the matrix H.  N >= 0.

  H       (input/output) COMPLEX*16 array, dimension (LDH,N)
          On entry, the n-by-n upper Hessenberg matrix to be
          factored.
          On exit, the factors L and U from the factorization
          H = P*L*U; the unit diagonal elements of L are not stored,
          and L is lower bidiagonal.

  LDH     INTEGER
          The leading dimension of the array H.  LDH >= max(1,N).

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

  INFO    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
                factorization has been completed, but the factor U
                is exactly singular, and division by zero will occur
                if it is used to solve a system of equations.

  The factorization has the form
     H = P * L * U
  where P is a permutation matrix, L is lower triangular with unit
  diagonal elements (and one nonzero subdiagonal), and U is upper
  triangular.

  This is the right-looking Level 2 BLAS version of the algorithm
  (adapted after ZGETF2).

  -

                             2
  The algorithm requires 0( N ) complex operations.

  None

Program Text

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