MB03BF - SLICOT Library Routine Documentation

## MB03BF

### Applying iterations of a real single shifted periodic QZ algorithm to a 2-by-2 matrix product, with Hessenberg factor the last one

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

Purpose

      To apply at most 20 iterations of a real single shifted
      periodic QZ algorithm to the 2-by-2 product of matrices stored
      in the array A. The Hessenberg matrix is the last one of the
      formal matrix product.

Specification

          SUBROUTINE MB03BF( K, AMAP, S, SINV, A, LDA1, LDA2, ULP )
    C     .. Scalar Arguments ..
          INTEGER           K, LDA1, LDA2, SINV
          DOUBLE PRECISION  ULP
    C     .. Array Arguments ..
          INTEGER           AMAP(*), S(*)
          DOUBLE PRECISION  A(LDA1,LDA2,*)

Arguments

Input/Output Parameters

      K       (input)  INTEGER
              The number of factors.  K >= 1.

      AMAP    (input)  INTEGER array, dimension (K)
              The map for accessing the factors, i.e., if AMAP(I) = J,
              then the factor A_I is stored at the J-th position in A.

      S       (input)  INTEGER array, dimension (K)
              The signature array. Each entry of S must be 1 or -1.

      SINV    (input)  INTEGER
              Signature multiplier. Entries of S are virtually
              multiplied by SINV.

      A       (input/output)  DOUBLE PRECISION array, dimension
                              (LDA1,LDA2,K)
              On entry, the leading 2-by-2-by-K part of this array must
              contain a 2-by-2 product (implicitly represented by its K
              factors) in upper Hessenberg form. The Hessenberg matrix
              is the last one of the formal matrix product.
              On exit, the leading 2-by-2-by-K part of this array
              contains the product after at most 20 iterations of a real
              shifted periodic QZ algorithm.

      LDA1    INTEGER
              The first leading dimension of the array A.  LDA1 >= 2.

      LDA2    INTEGER
              The second leading dimension of the array A.  LDA2 >= 2.

      ULP     INTEGER
              The machine relation precision.

Method

      Twenty iterations of a real single shifted periodic QZ algorithm
      are applied to the 2-by-2 matrix product A.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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