LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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

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.```
Date
May 2020

Definition at line 171 of file zlaqz1.f.

173 IMPLICIT NONE
174*
175* Arguments
176 LOGICAL, INTENT( IN ) :: ILQ, ILZ
177 INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
178 \$ NQ, NZ, QSTART, ZSTART, IHI
179 COMPLEX*16 :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
180*
181* Parameters
182 COMPLEX*16 CZERO, CONE
183 parameter( czero = ( 0.0d+0, 0.0d+0 ), cone = ( 1.0d+0,
184 \$ 0.0d+0 ) )
185 DOUBLE PRECISION :: ZERO, ONE, HALF
186 parameter( zero = 0.0d0, one = 1.0d0, half = 0.5d0 )
187*
188* Local variables
189 DOUBLE PRECISION :: C
190 COMPLEX*16 :: S, TEMP
191*
192* External Functions
193 EXTERNAL :: zlartg, zrot
194*
195 IF( k+1 .EQ. ihi ) THEN
196*
197* Shift is located on the edge of the matrix, remove it
198*
199 CALL zlartg( b( ihi, ihi ), b( ihi, ihi-1 ), c, s, temp )
200 b( ihi, ihi ) = temp
201 b( ihi, ihi-1 ) = czero
202 CALL zrot( ihi-istartm, b( istartm, ihi ), 1, b( istartm,
203 \$ ihi-1 ), 1, c, s )
204 CALL zrot( ihi-istartm+1, a( istartm, ihi ), 1, a( istartm,
205 \$ ihi-1 ), 1, c, s )
206 IF ( ilz ) THEN
207 CALL zrot( nz, z( 1, ihi-zstart+1 ), 1, z( 1, ihi-1-zstart+
208 \$ 1 ), 1, c, s )
209 END IF
210*
211 ELSE
212*
213* Normal operation, move bulge down
214*
215*
216* Apply transformation from the right
217*
218 CALL zlartg( b( k+1, k+1 ), b( k+1, k ), c, s, temp )
219 b( k+1, k+1 ) = temp
220 b( k+1, k ) = czero
221 CALL zrot( k+2-istartm+1, a( istartm, k+1 ), 1, a( istartm,
222 \$ k ), 1, c, s )
223 CALL zrot( k-istartm+1, b( istartm, k+1 ), 1, b( istartm, k ),
224 \$ 1, c, s )
225 IF ( ilz ) THEN
226 CALL zrot( nz, z( 1, k+1-zstart+1 ), 1, z( 1, k-zstart+1 ),
227 \$ 1, c, s )
228 END IF
229*
230* Apply transformation from the left
231*
232 CALL zlartg( a( k+1, k ), a( k+2, k ), c, s, temp )
233 a( k+1, k ) = temp
234 a( k+2, k ) = czero
235 CALL zrot( istopm-k, a( k+1, k+1 ), lda, a( k+2, k+1 ), lda, c,
236 \$ s )
237 CALL zrot( istopm-k, b( k+1, k+1 ), ldb, b( k+2, k+1 ), ldb, c,
238 \$ s )
239 IF ( ilq ) THEN
240 CALL zrot( nq, q( 1, k+1-qstart+1 ), 1, q( 1, k+2-qstart+
241 \$ 1 ), 1, c, dconjg( s ) )
242 END IF
243*
244 END IF
245*
246* End of ZLAQZ1
247*
subroutine zlartg(f, g, c, s, r)
ZLARTG generates a plane rotation with real cosine and complex sine.
Definition: zlartg.f90:116
subroutine zrot(N, CX, INCX, CY, INCY, C, S)
ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.
Definition: zrot.f:103
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