1*> \brief \b ZUNBDB
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunbdb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunbdb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
22*                          X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
23*                          TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
24*
25*       .. Scalar Arguments ..
26*       CHARACTER          SIGNS, TRANS
27*       INTEGER            INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
28*      $                   Q
29*       ..
30*       .. Array Arguments ..
31*       DOUBLE PRECISION   PHI( * ), THETA( * )
32*       COMPLEX*16         TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
33*      $                   WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
34*      $                   X21( LDX21, * ), X22( LDX22, * )
35*       ..
36*
37*
38*> \par Purpose:
39*  =============
40*>
41*> \verbatim
42*>
43*> ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
44*> partitioned unitary matrix X:
45*>
46*>                                 [ B11 | B12 0  0 ]
47*>     [ X11 | X12 ]   [ P1 |    ] [  0  |  0 -I  0 ] [ Q1 |    ]**H
48*> X = [-----------] = [---------] [----------------] [---------]   .
49*>     [ X21 | X22 ]   [    | P2 ] [ B21 | B22 0  0 ] [    | Q2 ]
50*>                                 [  0  |  0  0  I ]
51*>
52*> X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
53*> not the case, then X must be transposed and/or permuted. This can be
54*> done in constant time using the TRANS and SIGNS options. See ZUNCSD
55*> for details.)
56*>
57*> The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
58*> (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
59*> represented implicitly by Householder vectors.
60*>
61*> B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
62*> implicitly by angles THETA, PHI.
63*> \endverbatim
64*
65*  Arguments:
66*  ==========
67*
68*> \param[in] TRANS
69*> \verbatim
70*>          TRANS is CHARACTER
71*>          = 'T':      X, U1, U2, V1T, and V2T are stored in row-major
72*>                      order;
73*>          otherwise:  X, U1, U2, V1T, and V2T are stored in column-
74*>                      major order.
75*> \endverbatim
76*>
77*> \param[in] SIGNS
78*> \verbatim
79*>          SIGNS is CHARACTER
80*>          = 'O':      The lower-left block is made nonpositive (the
81*>                      "other" convention);
82*>          otherwise:  The upper-right block is made nonpositive (the
83*>                      "default" convention).
84*> \endverbatim
85*>
86*> \param[in] M
87*> \verbatim
88*>          M is INTEGER
89*>          The number of rows and columns in X.
90*> \endverbatim
91*>
92*> \param[in] P
93*> \verbatim
94*>          P is INTEGER
95*>          The number of rows in X11 and X12. 0 <= P <= M.
96*> \endverbatim
97*>
98*> \param[in] Q
99*> \verbatim
100*>          Q is INTEGER
101*>          The number of columns in X11 and X21. 0 <= Q <=
102*>          MIN(P,M-P,M-Q).
103*> \endverbatim
104*>
105*> \param[in,out] X11
106*> \verbatim
107*>          X11 is COMPLEX*16 array, dimension (LDX11,Q)
108*>          On entry, the top-left block of the unitary matrix to be
109*>          reduced. On exit, the form depends on TRANS:
110*>          If TRANS = 'N', then
111*>             the columns of tril(X11) specify reflectors for P1,
112*>             the rows of triu(X11,1) specify reflectors for Q1;
113*>          else TRANS = 'T', and
114*>             the rows of triu(X11) specify reflectors for P1,
115*>             the columns of tril(X11,-1) specify reflectors for Q1.
116*> \endverbatim
117*>
118*> \param[in] LDX11
119*> \verbatim
120*>          LDX11 is INTEGER
121*>          The leading dimension of X11. If TRANS = 'N', then LDX11 >=
122*>          P; else LDX11 >= Q.
123*> \endverbatim
124*>
125*> \param[in,out] X12
126*> \verbatim
127*>          X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
128*>          On entry, the top-right block of the unitary matrix to
129*>          be reduced. On exit, the form depends on TRANS:
130*>          If TRANS = 'N', then
131*>             the rows of triu(X12) specify the first P reflectors for
132*>             Q2;
133*>          else TRANS = 'T', and
134*>             the columns of tril(X12) specify the first P reflectors
135*>             for Q2.
136*> \endverbatim
137*>
138*> \param[in] LDX12
139*> \verbatim
140*>          LDX12 is INTEGER
141*>          The leading dimension of X12. If TRANS = 'N', then LDX12 >=
142*>          P; else LDX11 >= M-Q.
143*> \endverbatim
144*>
145*> \param[in,out] X21
146*> \verbatim
147*>          X21 is COMPLEX*16 array, dimension (LDX21,Q)
148*>          On entry, the bottom-left block of the unitary matrix to
149*>          be reduced. On exit, the form depends on TRANS:
150*>          If TRANS = 'N', then
151*>             the columns of tril(X21) specify reflectors for P2;
152*>          else TRANS = 'T', and
153*>             the rows of triu(X21) specify reflectors for P2.
154*> \endverbatim
155*>
156*> \param[in] LDX21
157*> \verbatim
158*>          LDX21 is INTEGER
159*>          The leading dimension of X21. If TRANS = 'N', then LDX21 >=
160*>          M-P; else LDX21 >= Q.
161*> \endverbatim
162*>
163*> \param[in,out] X22
164*> \verbatim
165*>          X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
166*>          On entry, the bottom-right block of the unitary matrix to
167*>          be reduced. On exit, the form depends on TRANS:
168*>          If TRANS = 'N', then
169*>             the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
170*>             M-P-Q reflectors for Q2,
171*>          else TRANS = 'T', and
172*>             the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
173*>             M-P-Q reflectors for P2.
174*> \endverbatim
175*>
176*> \param[in] LDX22
177*> \verbatim
178*>          LDX22 is INTEGER
179*>          The leading dimension of X22. If TRANS = 'N', then LDX22 >=
180*>          M-P; else LDX22 >= M-Q.
181*> \endverbatim
182*>
183*> \param[out] THETA
184*> \verbatim
185*>          THETA is DOUBLE PRECISION array, dimension (Q)
186*>          The entries of the bidiagonal blocks B11, B12, B21, B22 can
187*>          be computed from the angles THETA and PHI. See Further
188*>          Details.
189*> \endverbatim
190*>
191*> \param[out] PHI
192*> \verbatim
193*>          PHI is DOUBLE PRECISION array, dimension (Q-1)
194*>          The entries of the bidiagonal blocks B11, B12, B21, B22 can
195*>          be computed from the angles THETA and PHI. See Further
196*>          Details.
197*> \endverbatim
198*>
199*> \param[out] TAUP1
200*> \verbatim
201*>          TAUP1 is COMPLEX*16 array, dimension (P)
202*>          The scalar factors of the elementary reflectors that define
203*>          P1.
204*> \endverbatim
205*>
206*> \param[out] TAUP2
207*> \verbatim
208*>          TAUP2 is COMPLEX*16 array, dimension (M-P)
209*>          The scalar factors of the elementary reflectors that define
210*>          P2.
211*> \endverbatim
212*>
213*> \param[out] TAUQ1
214*> \verbatim
215*>          TAUQ1 is COMPLEX*16 array, dimension (Q)
216*>          The scalar factors of the elementary reflectors that define
217*>          Q1.
218*> \endverbatim
219*>
220*> \param[out] TAUQ2
221*> \verbatim
222*>          TAUQ2 is COMPLEX*16 array, dimension (M-Q)
223*>          The scalar factors of the elementary reflectors that define
224*>          Q2.
225*> \endverbatim
226*>
227*> \param[out] WORK
228*> \verbatim
229*>          WORK is COMPLEX*16 array, dimension (LWORK)
230*> \endverbatim
231*>
232*> \param[in] LWORK
233*> \verbatim
234*>          LWORK is INTEGER
235*>          The dimension of the array WORK. LWORK >= M-Q.
236*>
237*>          If LWORK = -1, then a workspace query is assumed; the routine
238*>          only calculates the optimal size of the WORK array, returns
239*>          this value as the first entry of the WORK array, and no error
240*>          message related to LWORK is issued by XERBLA.
241*> \endverbatim
242*>
243*> \param[out] INFO
244*> \verbatim
245*>          INFO is INTEGER
246*>          = 0:  successful exit.
247*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
248*> \endverbatim
249*
250*  Authors:
251*  ========
252*
253*> \author Univ. of Tennessee
254*> \author Univ. of California Berkeley
255*> \author Univ. of Colorado Denver
256*> \author NAG Ltd.
257*
258*> \date November 2013
259*
260*> \ingroup complex16OTHERcomputational
261*
262*> \par Further Details:
263*  =====================
264*>
265*> \verbatim
266*>
267*>  The bidiagonal blocks B11, B12, B21, and B22 are represented
268*>  implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
269*>  PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
270*>  lower bidiagonal. Every entry in each bidiagonal band is a product
271*>  of a sine or cosine of a THETA with a sine or cosine of a PHI. See
272*>  [1] or ZUNCSD for details.
273*>
274*>  P1, P2, Q1, and Q2 are represented as products of elementary
275*>  reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
276*>  using ZUNGQR and ZUNGLQ.
277*> \endverbatim
278*
279*> \par References:
280*  ================
281*>
282*>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
283*>      Algorithms, 50(1):33-65, 2009.
284*>
285*  =====================================================================
286      SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
287     $                   X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
288     $                   TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
289*
290*  -- LAPACK computational routine (version 3.5.0) --
291*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
292*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
293*     November 2013
294*
295*     .. Scalar Arguments ..
296      CHARACTER          SIGNS, TRANS
297      INTEGER            INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
298     $                   Q
299*     ..
300*     .. Array Arguments ..
301      DOUBLE PRECISION   PHI( * ), THETA( * )
302      COMPLEX*16         TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
303     $                   WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
304     $                   X21( LDX21, * ), X22( LDX22, * )
305*     ..
306*
307*  ====================================================================
308*
309*     .. Parameters ..
310      DOUBLE PRECISION   REALONE
311      PARAMETER          ( REALONE = 1.0D0 )
312      COMPLEX*16         ONE
313      PARAMETER          ( ONE = (1.0D0,0.0D0) )
314*     ..
315*     .. Local Scalars ..
316      LOGICAL            COLMAJOR, LQUERY
317      INTEGER            I, LWORKMIN, LWORKOPT, PI1, QI1
318      DOUBLE PRECISION   Z1, Z2, Z3, Z4
319*     ..
320*     .. External Subroutines ..
321      EXTERNAL           ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA
322      EXTERNAL           ZLACGV
323*
324*     ..
325*     .. External Functions ..
326      DOUBLE PRECISION   DZNRM2
327      LOGICAL            LSAME
328      EXTERNAL           DZNRM2, LSAME
329*     ..
330*     .. Intrinsic Functions
331      INTRINSIC          ATAN2, COS, MAX, MIN, SIN
332      INTRINSIC          DCMPLX, DCONJG
333*     ..
334*     .. Executable Statements ..
335*
336*     Test input arguments
337*
338      INFO = 0
339      COLMAJOR = .NOT. LSAME( TRANS, 'T' )
340      IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
341         Z1 = REALONE
342         Z2 = REALONE
343         Z3 = REALONE
344         Z4 = REALONE
345      ELSE
346         Z1 = REALONE
347         Z2 = -REALONE
348         Z3 = REALONE
349         Z4 = -REALONE
350      END IF
351      LQUERY = LWORK .EQ. -1
352*
353      IF( M .LT. 0 ) THEN
354         INFO = -3
355      ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
356         INFO = -4
357      ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
358     $         Q .GT. M-Q ) THEN
359         INFO = -5
360      ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
361         INFO = -7
362      ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
363         INFO = -7
364      ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
365         INFO = -9
366      ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
367         INFO = -9
368      ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
369         INFO = -11
370      ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
371         INFO = -11
372      ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
373         INFO = -13
374      ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
375         INFO = -13
376      END IF
377*
378*     Compute workspace
379*
380      IF( INFO .EQ. 0 ) THEN
381         LWORKOPT = M - Q
382         LWORKMIN = M - Q
383         WORK(1) = LWORKOPT
384         IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
385            INFO = -21
386         END IF
387      END IF
388      IF( INFO .NE. 0 ) THEN
389         CALL XERBLA( 'xORBDB', -INFO )
390         RETURN
391      ELSE IF( LQUERY ) THEN
392         RETURN
393      END IF
394*
395*     Handle column-major and row-major separately
396*
397      IF( COLMAJOR ) THEN
398*
399*        Reduce columns 1, ..., Q of X11, X12, X21, and X22
400*
401         DO I = 1, Q
402*
403            IF( I .EQ. 1 ) THEN
404               CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 1 )
405            ELSE
406               CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
407     $                     X11(I,I), 1 )
408               CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
409     $                     0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 )
410            END IF
411            IF( I .EQ. 1 ) THEN
412               CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 1 )
413            ELSE
414               CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
415     $                     X21(I,I), 1 )
416               CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
417     $                     0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 )
418            END IF
419*
420            THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ),
421     $                 DZNRM2( P-I+1, X11(I,I), 1 ) )
422*
423            IF( P .GT. I ) THEN
424               CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
425            ELSE IF ( P .EQ. I ) THEN
426               CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
427            END IF
428            X11(I,I) = ONE
429            IF ( M-P .GT. I ) THEN
430               CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1,
431     $                       TAUP2(I) )
432            ELSE IF ( M-P .EQ. I ) THEN
433               CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1,
434     $                       TAUP2(I) )
435            END IF
436            X21(I,I) = ONE
437*
438            IF ( Q .GT. I ) THEN
439               CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1,
440     $                     DCONJG(TAUP1(I)), X11(I,I+1), LDX11, WORK )
441               CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
442     $                     DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
443            END IF
444            IF ( M-Q+1 .GT. I ) THEN
445               CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
446     $                     DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
447               CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
448     $                     DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
449            END IF
450*
451            IF( I .LT. Q ) THEN
452               CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
453     $                     X11(I,I+1), LDX11 )
454               CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
455     $                     X21(I,I+1), LDX21, X11(I,I+1), LDX11 )
456            END IF
457            CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
458     $                  X12(I,I), LDX12 )
459            CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
460     $                  X22(I,I), LDX22, X12(I,I), LDX12 )
461*
462            IF( I .LT. Q )
463     $         PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ),
464     $                  DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
465*
466            IF( I .LT. Q ) THEN
467               CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
468               IF ( I .EQ. Q-1 ) THEN
469                  CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
470     $                          TAUQ1(I) )
471               ELSE
472                  CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
473     $                          TAUQ1(I) )
474               END IF
475               X11(I,I+1) = ONE
476            END IF
477            IF ( M-Q+1 .GT. I ) THEN
478               CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
479               IF ( M-Q .EQ. I ) THEN
480                  CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
481     $                          TAUQ2(I) )
482               ELSE
483                  CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
484     $                          TAUQ2(I) )
485               END IF
486            END IF
487            X12(I,I) = ONE
488*
489            IF( I .LT. Q ) THEN
490               CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
491     $                     X11(I+1,I+1), LDX11, WORK )
492               CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
493     $                     X21(I+1,I+1), LDX21, WORK )
494            END IF
495            IF ( P .GT. I ) THEN
496               CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
497     $                     X12(I+1,I), LDX12, WORK )
498            END IF
499            IF ( M-P .GT. I ) THEN
500               CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
501     $                     TAUQ2(I), X22(I+1,I), LDX22, WORK )
502            END IF
503*
504            IF( I .LT. Q )
505     $         CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
506            CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
507*
508         END DO
509*
510*        Reduce columns Q + 1, ..., P of X12, X22
511*
512         DO I = Q + 1, P
513*
514            CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I),
515     $                  LDX12 )
516            CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
517            IF ( I .GE. M-Q ) THEN
518               CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
519     $                       TAUQ2(I) )
520            ELSE
521               CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
522     $                       TAUQ2(I) )
523            END IF
524            X12(I,I) = ONE
525*
526            IF ( P .GT. I ) THEN
527               CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
528     $                     X12(I+1,I), LDX12, WORK )
529            END IF
530            IF( M-P-Q .GE. 1 )
531     $         CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
532     $                     TAUQ2(I), X22(Q+1,I), LDX22, WORK )
533*
534            CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
535*
536         END DO
537*
538*        Reduce columns P + 1, ..., M - Q of X12, X22
539*
540         DO I = 1, M - P - Q
541*
542            CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
543     $                  X22(Q+I,P+I), LDX22 )
544            CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
545            CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
546     $                    LDX22, TAUQ2(P+I) )
547            X22(Q+I,P+I) = ONE
548            CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
549     $                  TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
550*
551            CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
552*
553         END DO
554*
555      ELSE
556*
557*        Reduce columns 1, ..., Q of X11, X12, X21, X22
558*
559         DO I = 1, Q
560*
561            IF( I .EQ. 1 ) THEN
562               CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I),
563     $                     LDX11 )
564            ELSE
565               CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
566     $                     X11(I,I), LDX11 )
567               CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
568     $                     0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 )
569            END IF
570            IF( I .EQ. 1 ) THEN
571               CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I),
572     $                     LDX21 )
573            ELSE
574               CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
575     $                     X21(I,I), LDX21 )
576               CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
577     $                     0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 )
578            END IF
579*
580            THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ),
581     $                 DZNRM2( P-I+1, X11(I,I), LDX11 ) )
582*
583            CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
584            CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
585*
586            CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
587            X11(I,I) = ONE
588            IF ( I .EQ. M-P ) THEN
589               CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
590     $                       TAUP2(I) )
591            ELSE
592               CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
593     $                       TAUP2(I) )
594            END IF
595            X21(I,I) = ONE
596*
597            CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
598     $                  X11(I+1,I), LDX11, WORK )
599            CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
600     $                  X12(I,I), LDX12, WORK )
601            CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
602     $                  X21(I+1,I), LDX21, WORK )
603            CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
604     $                  TAUP2(I), X22(I,I), LDX22, WORK )
605*
606            CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
607            CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
608*
609            IF( I .LT. Q ) THEN
610               CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
611     $                     X11(I+1,I), 1 )
612               CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
613     $                     X21(I+1,I), 1, X11(I+1,I), 1 )
614            END IF
615            CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
616     $                  X12(I,I), 1 )
617            CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
618     $                  X22(I,I), 1, X12(I,I), 1 )
619*
620            IF( I .LT. Q )
621     $         PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ),
622     $                  DZNRM2( M-Q-I+1, X12(I,I), 1 ) )
623*
624            IF( I .LT. Q ) THEN
625               CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
626               X11(I+1,I) = ONE
627            END IF
628            CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
629            X12(I,I) = ONE
630*
631            IF( I .LT. Q ) THEN
632               CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1,
633     $                     DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK )
634               CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1,
635     $                     DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK )
636            END IF
637            CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
638     $                  DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
639            IF ( M-P .GT. I ) THEN
640               CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
641     $                     DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
642            END IF
643*
644         END DO
645*
646*        Reduce columns Q + 1, ..., P of X12, X22
647*
648         DO I = Q + 1, P
649*
650            CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 )
651            CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
652            X12(I,I) = ONE
653*
654            IF ( P .GT. I ) THEN
655               CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
656     $                     DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
657            END IF
658            IF( M-P-Q .GE. 1 )
659     $         CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
660     $                     DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
661*
662         END DO
663*
664*        Reduce columns P + 1, ..., M - Q of X12, X22
665*
666         DO I = 1, M - P - Q
667*
668            CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
669     $                  X22(P+I,Q+I), 1 )
670            CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
671     $                    TAUQ2(P+I) )
672            X22(P+I,Q+I) = ONE
673*
674            IF ( M-P-Q .NE. I ) THEN
675               CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
676     $                     DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
677     $                     WORK )
678            END IF
679*
680         END DO
681*
682      END IF
683*
684      RETURN
685*
686*     End of ZUNBDB
687*
688      END
689
690