## TG01OA

### Orthogonal equivalence transformation of a SISO descriptor system with E upper triangular, so that B becomes parallel to the first unit vector and E keeps its structure

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

Purpose

      To compute for a single-input single-output descriptor system,
      given by the system matrix

         [ D     C    ]
         [ B  A - s*E ],

      with E upper triangular, a transformed system, (Q'*A*Z, Q'*E*Z,
      Q'*B, C*Z), via an orthogonal equivalence transformation, so that
      Q'*B has only the first element nonzero and Q'*E*Z remains upper
      triangular.

Specification

          SUBROUTINE TG01OA( JOBE, N, DCBA, LDDCBA, E, LDE, INFO )
    C     .. Scalar Arguments ..
          CHARACTER         JOBE
          INTEGER           INFO, LDDCBA, LDE, N
    C     .. Array Arguments ..
          DOUBLE PRECISION  DCBA(LDDCBA,*), E(LDE,*)

Arguments

Mode Parameters

      JOBE    CHARACTER*1
              Specifies whether E is an upper triangular or an identity
              matrix, as follows:
              = 'U':  The matrix E is an upper triangular matrix;
              = 'I':  The matrix E is assumed identity and is not given.

Input/Output Parameters

      N       (input) INTEGER
              The dimension of the descriptor state vector; also the
              order of square matrices A and E, the number of rows of
              matrix B, and the number of columns of matrix C.  N >= 0.

      DCBA    (input/output) DOUBLE PRECISION array, dimension
              (LDDCBA,N+1)
              On entry, the leading (N+1)-by-(N+1) part of this array
              must contain the original system matrices A, B, C, and D,
              stored as follows

                 [ D  C ]
                 [ B  A ].

              On exit, the leading (N+1)-by-(N+1) part of this array
              contains the transformed matrices C*Z, Q'*B, and Q'*A*Z,
              replacing C, B, and A. The scalar D is unchanged.

      LDDCBA  INTEGER
              The leading dimension of the array DCBA.
              LDDCBA >= N+1.

      E       (input/output) DOUBLE PRECISION array, dimension (LDE,*)
              On entry, if JOBE = 'U', the leading N-by-N upper
              triangular part of this array must contain the upper
              triangular part of the descriptor matrix E. The lower
              triangular part under the first subdiagonal is not
              referenced.
              On exit, if JOBE = 'U', the leading N-by-N upper
              triangular part of this array contains the upper
              triangular part of the transformed descriptor matrix,
              Q'*E*Z.
              If JOBE = 'I', this array is not referenced.

      LDE     INTEGER
              The leading dimension of the array E.
              LDE >= MAX(1,N), if JOBE = 'U';
              LDE >= 1,        if JOBE = 'I'.

Error Indicator

      INFO    INTEGER
              = 0:  successful exit;
              < 0:  if INFO = -i, the i-th argument had an illegal
                    value.

Method

      Givens rotations are used to annihilate the last N-1 elements of B
      in reverse order, but preserve the form of E.

Numerical Aspects

      The algorithm is numerically backward stable.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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