## MB02SZ

### LU factorization of a complex upper Hessenberg matrix H

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

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

Specification

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

Arguments

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).

Error Indicator

      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.

Method

      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).

References

      -

Numerical Aspects

                                 2
      The algorithm requires 0( N ) complex operations.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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