zlaqz1()

subroutine zlaqz1	(	logical, intent(in)	ilq,
		logical, intent(in)	ilz,
		integer, intent(in)	k,
		integer, intent(in)	istartm,
		integer, intent(in)	istopm,
		integer, intent(in)	ihi,
		complex*16, dimension( lda, * )	a,
		integer, intent(in)	lda,
		complex*16, dimension( ldb, * )	b,
		integer, intent(in)	ldb,
		integer, intent(in)	nq,
		integer, intent(in)	qstart,
		complex*16, dimension( ldq, * )	q,
		integer, intent(in)	ldq,
		integer, intent(in)	nz,
		integer, intent(in)	zstart,
		complex*16, dimension( ldz, * )	z,
		integer, intent(in)	ldz
	)

ZLAQZ1

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Purpose:

      ZLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position

Parameters

[in]	ILQ	ILQ is LOGICAL Determines whether or not to update the matrix Q
[in]	ILZ	ILZ is LOGICAL Determines whether or not to update the matrix Z
[in]	K	K is INTEGER Index indicating the position of the bulge. On entry, the bulge is located in (A(k+1,k),B(k+1,k)). On exit, the bulge is located in (A(k+2,k+1),B(k+2,k+1)).
[in]	ISTARTM	ISTARTM is INTEGER
[in]	ISTOPM	ISTOPM is INTEGER Updates to (A,B) are restricted to (istartm:k+2,k:istopm). It is assumed without checking that istartm <= k+1 and k+2 <= istopm
[in]	IHI	IHI is INTEGER
[in,out]	A	A is COMPLEX*16 array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of A as declared in the calling procedure.
[in,out]	B	B is COMPLEX*16 array, dimension (LDB,N)
[in]	LDB	LDB is INTEGER The leading dimension of B as declared in the calling procedure.
[in]	NQ	NQ is INTEGER The order of the matrix Q
[in]	QSTART	QSTART is INTEGER Start index of the matrix Q. Rotations are applied To columns k+2-qStart:k+3-qStart of Q.
[in,out]	Q	Q is COMPLEX*16 array, dimension (LDQ,NQ)
[in]	LDQ	LDQ is INTEGER The leading dimension of Q as declared in the calling procedure.
[in]	NZ	NZ is INTEGER The order of the matrix Z
[in]	ZSTART	ZSTART is INTEGER Start index of the matrix Z. Rotations are applied To columns k+1-qStart:k+2-qStart of Z.
[in,out]	Z	Z is COMPLEX*16 array, dimension (LDZ,NZ)
[in]	LDZ	LDZ is INTEGER The leading dimension of Q as declared in the calling procedure.

Author

Thijs Steel, KU Leuven

Date

May 2020

Definition at line 171 of file zlaqz1.f.

      IMPLICIT NONE
*
*     Arguments
      LOGICAL, INTENT( IN ) :: ILQ, ILZ
      INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
     $         NQ, NZ, QSTART, ZSTART, IHI
      COMPLEX*16 :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
*
*     Parameters
      COMPLEX*16         CZERO, CONE
      parameter( czero = ( 0.0d+0, 0.0d+0 ), cone = ( 1.0d+0,
     $                     0.0d+0 ) )
      DOUBLE PRECISION :: ZERO, ONE, HALF
      parameter( zero = 0.0d0, one = 1.0d0, half = 0.5d0 )
*
*     Local variables
      DOUBLE PRECISION :: C
      COMPLEX*16 :: S, TEMP
*
*     External Functions
      EXTERNAL :: zlartg, zrot
*
      IF( k+1 .EQ. ihi ) THEN
*
*        Shift is located on the edge of the matrix, remove it
*
         CALL zlartg( b( ihi, ihi ), b( ihi, ihi-1 ), c, s, temp )
         b( ihi, ihi ) = temp
         b( ihi, ihi-1 ) = czero
         CALL zrot( ihi-istartm, b( istartm, ihi ), 1, b( istartm,
     $              ihi-1 ), 1, c, s )
         CALL zrot( ihi-istartm+1, a( istartm, ihi ), 1, a( istartm,
     $              ihi-1 ), 1, c, s )
         IF ( ilz ) THEN
            CALL zrot( nz, z( 1, ihi-zstart+1 ), 1, z( 1, ihi-1-zstart+
     $                 1 ), 1, c, s )
         END IF
*
      ELSE
*
*        Normal operation, move bulge down
*
*
*        Apply transformation from the right
*
         CALL zlartg( b( k+1, k+1 ), b( k+1, k ), c, s, temp )
         b( k+1, k+1 ) = temp
         b( k+1, k ) = czero
         CALL zrot( k+2-istartm+1, a( istartm, k+1 ), 1, a( istartm,
     $              k ), 1, c, s )
         CALL zrot( k-istartm+1, b( istartm, k+1 ), 1, b( istartm, k ),
     $              1, c, s )
         IF ( ilz ) THEN
            CALL zrot( nz, z( 1, k+1-zstart+1 ), 1, z( 1, k-zstart+1 ),
     $                 1, c, s )
         END IF
*
*        Apply transformation from the left
*
         CALL zlartg( a( k+1, k ), a( k+2, k ), c, s, temp )
         a( k+1, k ) = temp
         a( k+2, k ) = czero
         CALL zrot( istopm-k, a( k+1, k+1 ), lda, a( k+2, k+1 ), lda, c,
     $              s )
         CALL zrot( istopm-k, b( k+1, k+1 ), ldb, b( k+2, k+1 ), ldb, c,
     $              s )
         IF ( ilq ) THEN
            CALL zrot( nq, q( 1, k+1-qstart+1 ), 1, q( 1, k+2-qstart+
     $                 1 ), 1, c, dconjg( s ) )
         END IF
*
      END IF
*
*     End of ZLAQZ1
*

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