## MB02RZ

### Solution of a system of linear equations with complex upper Hessenberg matrix

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

Purpose

      To solve a system of linear equations
         H * X = B,  H' * X = B  or  H**H * X = B
      with a complex upper Hessenberg N-by-N matrix H using the LU
      factorization computed by MB02SZ.

Specification

          SUBROUTINE MB02RZ( TRANS, N, NRHS, H, LDH, IPIV, B, LDB, INFO )
    C     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            INFO, LDB, LDH, N, NRHS
    C     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         B( LDB, * ), H( LDH, * )

Arguments

Mode Parameters

      TRANS   CHARACTER*1
              Specifies the form of the system of equations:
              = 'N':  H * X = B  (No transpose)
              = 'T':  H'* X = B  (Transpose)
              = 'C':  H**H * X = B  (Conjugate transpose)

Input/Output Parameters

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

      NRHS    (input) INTEGER
              The number of right hand sides, i.e., the number of
              columns of the matrix B.  NRHS >= 0.

      H       (input) COMPLEX*16 array, dimension (LDH,N)
              The factors L and U from the factorization H = P*L*U
              as computed by MB02SZ.

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

      IPIV    (input) INTEGER array, dimension (N)
              The pivot indices from MB02SZ; for 1<=i<=N, row i of the
              matrix was interchanged with row IPIV(i).

      B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the right hand side matrix B.
              On exit, the solution matrix X.

      LDB     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.

Method

      The routine uses the factorization
         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.

References

      -

Numerical Aspects

                                 2
      The algorithm requires 0( N x NRHS ) complex operations.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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