LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ slaqz2()

subroutine slaqz2 ( logical, intent(in)  ILQ,
logical, intent(in)  ILZ,
integer, intent(in)  K,
integer, intent(in)  ISTARTM,
integer, intent(in)  ISTOPM,
integer, intent(in)  IHI,
real, dimension( lda, * )  A,
integer, intent(in)  LDA,
real, dimension( ldb, * )  B,
integer, intent(in)  LDB,
integer, intent(in)  NQ,
integer, intent(in)  QSTART,
real, dimension( ldq, * )  Q,
integer, intent(in)  LDQ,
integer, intent(in)  NZ,
integer, intent(in)  ZSTART,
real, dimension( ldz, * )  Z,
integer, intent(in)  LDZ 
)

SLAQZ2

Download SLAQZ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
      SLAQZ2 chases a 2x2 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+2,k:k+1),B(k+1:k+2,k:k+1)).
              On exit, the bulge is located in
              (A(k+2:k+3,k+1:k+2),B(k+2:k+3,k+1:k+2)).
[in]ISTARTM
          ISTARTM is INTEGER
[in]ISTOPM
          ISTOPM is INTEGER
              Updates to (A,B) are restricted to
              (istartm:k+3,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 REAL 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 REAL 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+4-qStart of Q.
[in,out]Q
          Q is REAL 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+3-qStart of Z.
[in,out]Z
          Z is REAL 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 slaqz2.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  REAL :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
180 *
181 * Parameters
182  REAL :: ZERO, ONE, HALF
183  parameter( zero = 0.0, one = 1.0, half = 0.5 )
184 *
185 * Local variables
186  REAL :: H( 2, 3 ), C1, S1, C2, S2, TEMP
187 *
188 * External functions
189  EXTERNAL :: slartg, srot
190 *
191  IF( k+2 .EQ. ihi ) THEN
192 * Shift is located on the edge of the matrix, remove it
193  h = b( ihi-1:ihi, ihi-2:ihi )
194 * Make H upper triangular
195  CALL slartg( h( 1, 1 ), h( 2, 1 ), c1, s1, temp )
196  h( 2, 1 ) = zero
197  h( 1, 1 ) = temp
198  CALL srot( 2, h( 1, 2 ), 2, h( 2, 2 ), 2, c1, s1 )
199 *
200  CALL slartg( h( 2, 3 ), h( 2, 2 ), c1, s1, temp )
201  CALL srot( 1, h( 1, 3 ), 1, h( 1, 2 ), 1, c1, s1 )
202  CALL slartg( h( 1, 2 ), h( 1, 1 ), c2, s2, temp )
203 *
204  CALL srot( ihi-istartm+1, b( istartm, ihi ), 1, b( istartm,
205  $ ihi-1 ), 1, c1, s1 )
206  CALL srot( ihi-istartm+1, b( istartm, ihi-1 ), 1, b( istartm,
207  $ ihi-2 ), 1, c2, s2 )
208  b( ihi-1, ihi-2 ) = zero
209  b( ihi, ihi-2 ) = zero
210  CALL srot( ihi-istartm+1, a( istartm, ihi ), 1, a( istartm,
211  $ ihi-1 ), 1, c1, s1 )
212  CALL srot( ihi-istartm+1, a( istartm, ihi-1 ), 1, a( istartm,
213  $ ihi-2 ), 1, c2, s2 )
214  IF ( ilz ) THEN
215  CALL srot( nz, z( 1, ihi-zstart+1 ), 1, z( 1, ihi-1-zstart+
216  $ 1 ), 1, c1, s1 )
217  CALL srot( nz, z( 1, ihi-1-zstart+1 ), 1, z( 1,
218  $ ihi-2-zstart+1 ), 1, c2, s2 )
219  END IF
220 *
221  CALL slartg( a( ihi-1, ihi-2 ), a( ihi, ihi-2 ), c1, s1,
222  $ temp )
223  a( ihi-1, ihi-2 ) = temp
224  a( ihi, ihi-2 ) = zero
225  CALL srot( istopm-ihi+2, a( ihi-1, ihi-1 ), lda, a( ihi,
226  $ ihi-1 ), lda, c1, s1 )
227  CALL srot( istopm-ihi+2, b( ihi-1, ihi-1 ), ldb, b( ihi,
228  $ ihi-1 ), ldb, c1, s1 )
229  IF ( ilq ) THEN
230  CALL srot( nq, q( 1, ihi-1-qstart+1 ), 1, q( 1, ihi-qstart+
231  $ 1 ), 1, c1, s1 )
232  END IF
233 *
234  CALL slartg( b( ihi, ihi ), b( ihi, ihi-1 ), c1, s1, temp )
235  b( ihi, ihi ) = temp
236  b( ihi, ihi-1 ) = zero
237  CALL srot( ihi-istartm, b( istartm, ihi ), 1, b( istartm,
238  $ ihi-1 ), 1, c1, s1 )
239  CALL srot( ihi-istartm+1, a( istartm, ihi ), 1, a( istartm,
240  $ ihi-1 ), 1, c1, s1 )
241  IF ( ilz ) THEN
242  CALL srot( nz, z( 1, ihi-zstart+1 ), 1, z( 1, ihi-1-zstart+
243  $ 1 ), 1, c1, s1 )
244  END IF
245 *
246  ELSE
247 *
248 * Normal operation, move bulge down
249 *
250  h = b( k+1:k+2, k:k+2 )
251 *
252 * Make H upper triangular
253 *
254  CALL slartg( h( 1, 1 ), h( 2, 1 ), c1, s1, temp )
255  h( 2, 1 ) = zero
256  h( 1, 1 ) = temp
257  CALL srot( 2, h( 1, 2 ), 2, h( 2, 2 ), 2, c1, s1 )
258 *
259 * Calculate Z1 and Z2
260 *
261  CALL slartg( h( 2, 3 ), h( 2, 2 ), c1, s1, temp )
262  CALL srot( 1, h( 1, 3 ), 1, h( 1, 2 ), 1, c1, s1 )
263  CALL slartg( h( 1, 2 ), h( 1, 1 ), c2, s2, temp )
264 *
265 * Apply transformations from the right
266 *
267  CALL srot( k+3-istartm+1, a( istartm, k+2 ), 1, a( istartm,
268  $ k+1 ), 1, c1, s1 )
269  CALL srot( k+3-istartm+1, a( istartm, k+1 ), 1, a( istartm,
270  $ k ), 1, c2, s2 )
271  CALL srot( k+2-istartm+1, b( istartm, k+2 ), 1, b( istartm,
272  $ k+1 ), 1, c1, s1 )
273  CALL srot( k+2-istartm+1, b( istartm, k+1 ), 1, b( istartm,
274  $ k ), 1, c2, s2 )
275  IF ( ilz ) THEN
276  CALL srot( nz, z( 1, k+2-zstart+1 ), 1, z( 1, k+1-zstart+
277  $ 1 ), 1, c1, s1 )
278  CALL srot( nz, z( 1, k+1-zstart+1 ), 1, z( 1, k-zstart+1 ),
279  $ 1, c2, s2 )
280  END IF
281  b( k+1, k ) = zero
282  b( k+2, k ) = zero
283 *
284 * Calculate Q1 and Q2
285 *
286  CALL slartg( a( k+2, k ), a( k+3, k ), c1, s1, temp )
287  a( k+2, k ) = temp
288  a( k+3, k ) = zero
289  CALL slartg( a( k+1, k ), a( k+2, k ), c2, s2, temp )
290  a( k+1, k ) = temp
291  a( k+2, k ) = zero
292 *
293 * Apply transformations from the left
294 *
295  CALL srot( istopm-k, a( k+2, k+1 ), lda, a( k+3, k+1 ), lda,
296  $ c1, s1 )
297  CALL srot( istopm-k, a( k+1, k+1 ), lda, a( k+2, k+1 ), lda,
298  $ c2, s2 )
299 *
300  CALL srot( istopm-k, b( k+2, k+1 ), ldb, b( k+3, k+1 ), ldb,
301  $ c1, s1 )
302  CALL srot( istopm-k, b( k+1, k+1 ), ldb, b( k+2, k+1 ), ldb,
303  $ c2, s2 )
304  IF ( ilq ) THEN
305  CALL srot( nq, q( 1, k+2-qstart+1 ), 1, q( 1, k+3-qstart+
306  $ 1 ), 1, c1, s1 )
307  CALL srot( nq, q( 1, k+1-qstart+1 ), 1, q( 1, k+2-qstart+
308  $ 1 ), 1, c2, s2 )
309  END IF
310 *
311  END IF
312 *
313 * End of SLAQZ2
314 *
slartg
subroutine slartg(f, g, c, s, r)
SLARTG generates a plane rotation with real cosine and real sine.
Definition: slartg.f90:113
srot
subroutine srot(N, SX, INCX, SY, INCY, C, S)
SROT
Definition: srot.f:92
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