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
9: *> Download ZUNBDB + dependencies
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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: *> \ingroup complex16OTHERcomputational
259: *
260: *> \par Further Details:
261: * =====================
262: *>
263: *> \verbatim
264: *>
265: *> The bidiagonal blocks B11, B12, B21, and B22 are represented
266: *> implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
267: *> PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
268: *> lower bidiagonal. Every entry in each bidiagonal band is a product
269: *> of a sine or cosine of a THETA with a sine or cosine of a PHI. See
270: *> [1] or ZUNCSD for details.
271: *>
272: *> P1, P2, Q1, and Q2 are represented as products of elementary
273: *> reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
274: *> using ZUNGQR and ZUNGLQ.
275: *> \endverbatim
276: *
277: *> \par References:
278: * ================
279: *>
280: *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
281: *> Algorithms, 50(1):33-65, 2009.
282: *>
283: * =====================================================================
284: SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
285: $ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
286: $ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
287: *
288: * -- LAPACK computational routine --
289: * -- LAPACK is a software package provided by Univ. of Tennessee, --
290: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
291: *
292: * .. Scalar Arguments ..
293: CHARACTER SIGNS, TRANS
294: INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
295: $ Q
296: * ..
297: * .. Array Arguments ..
298: DOUBLE PRECISION PHI( * ), THETA( * )
299: COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
300: $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
301: $ X21( LDX21, * ), X22( LDX22, * )
302: * ..
303: *
304: * ====================================================================
305: *
306: * .. Parameters ..
307: DOUBLE PRECISION REALONE
308: PARAMETER ( REALONE = 1.0D0 )
309: COMPLEX*16 ONE
310: PARAMETER ( ONE = (1.0D0,0.0D0) )
311: * ..
312: * .. Local Scalars ..
313: LOGICAL COLMAJOR, LQUERY
314: INTEGER I, LWORKMIN, LWORKOPT
315: DOUBLE PRECISION Z1, Z2, Z3, Z4
316: * ..
317: * .. External Subroutines ..
318: EXTERNAL ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA
319: EXTERNAL ZLACGV
320: *
321: * ..
322: * .. External Functions ..
323: DOUBLE PRECISION DZNRM2
324: LOGICAL LSAME
325: EXTERNAL DZNRM2, LSAME
326: * ..
327: * .. Intrinsic Functions
328: INTRINSIC ATAN2, COS, MAX, MIN, SIN
329: INTRINSIC DCMPLX, DCONJG
330: * ..
331: * .. Executable Statements ..
332: *
333: * Test input arguments
334: *
335: INFO = 0
336: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
337: IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
338: Z1 = REALONE
339: Z2 = REALONE
340: Z3 = REALONE
341: Z4 = REALONE
342: ELSE
343: Z1 = REALONE
344: Z2 = -REALONE
345: Z3 = REALONE
346: Z4 = -REALONE
347: END IF
348: LQUERY = LWORK .EQ. -1
349: *
350: IF( M .LT. 0 ) THEN
351: INFO = -3
352: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
353: INFO = -4
354: ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
355: $ Q .GT. M-Q ) THEN
356: INFO = -5
357: ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
358: INFO = -7
359: ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
360: INFO = -7
361: ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
362: INFO = -9
363: ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
364: INFO = -9
365: ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
366: INFO = -11
367: ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
368: INFO = -11
369: ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
370: INFO = -13
371: ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
372: INFO = -13
373: END IF
374: *
375: * Compute workspace
376: *
377: IF( INFO .EQ. 0 ) THEN
378: LWORKOPT = M - Q
379: LWORKMIN = M - Q
380: WORK(1) = LWORKOPT
381: IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
382: INFO = -21
383: END IF
384: END IF
385: IF( INFO .NE. 0 ) THEN
386: CALL XERBLA( 'xORBDB', -INFO )
387: RETURN
388: ELSE IF( LQUERY ) THEN
389: RETURN
390: END IF
391: *
392: * Handle column-major and row-major separately
393: *
394: IF( COLMAJOR ) THEN
395: *
396: * Reduce columns 1, ..., Q of X11, X12, X21, and X22
397: *
398: DO I = 1, Q
399: *
400: IF( I .EQ. 1 ) THEN
401: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 1 )
402: ELSE
403: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
404: $ X11(I,I), 1 )
405: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
406: $ 0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 )
407: END IF
408: IF( I .EQ. 1 ) THEN
409: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 1 )
410: ELSE
411: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
412: $ X21(I,I), 1 )
413: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
414: $ 0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 )
415: END IF
416: *
417: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ),
418: $ DZNRM2( P-I+1, X11(I,I), 1 ) )
419: *
420: IF( P .GT. I ) THEN
421: CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
422: ELSE IF ( P .EQ. I ) THEN
423: CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
424: END IF
425: X11(I,I) = ONE
426: IF ( M-P .GT. I ) THEN
427: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1,
428: $ TAUP2(I) )
429: ELSE IF ( M-P .EQ. I ) THEN
430: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1,
431: $ TAUP2(I) )
432: END IF
433: X21(I,I) = ONE
434: *
435: IF ( Q .GT. I ) THEN
436: CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1,
437: $ DCONJG(TAUP1(I)), X11(I,I+1), LDX11, WORK )
438: CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
439: $ DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
440: END IF
441: IF ( M-Q+1 .GT. I ) THEN
442: CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
443: $ DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
444: CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
445: $ DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
446: END IF
447: *
448: IF( I .LT. Q ) THEN
449: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
450: $ X11(I,I+1), LDX11 )
451: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
452: $ X21(I,I+1), LDX21, X11(I,I+1), LDX11 )
453: END IF
454: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
455: $ X12(I,I), LDX12 )
456: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
457: $ X22(I,I), LDX22, X12(I,I), LDX12 )
458: *
459: IF( I .LT. Q )
460: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ),
461: $ DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
462: *
463: IF( I .LT. Q ) THEN
464: CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
465: IF ( I .EQ. Q-1 ) THEN
466: CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
467: $ TAUQ1(I) )
468: ELSE
469: CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
470: $ TAUQ1(I) )
471: END IF
472: X11(I,I+1) = ONE
473: END IF
474: IF ( M-Q+1 .GT. I ) THEN
475: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
476: IF ( M-Q .EQ. I ) THEN
477: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
478: $ TAUQ2(I) )
479: ELSE
480: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
481: $ TAUQ2(I) )
482: END IF
483: END IF
484: X12(I,I) = ONE
485: *
486: IF( I .LT. Q ) THEN
487: CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
488: $ X11(I+1,I+1), LDX11, WORK )
489: CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
490: $ X21(I+1,I+1), LDX21, WORK )
491: END IF
492: IF ( P .GT. I ) THEN
493: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
494: $ X12(I+1,I), LDX12, WORK )
495: END IF
496: IF ( M-P .GT. I ) THEN
497: CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
498: $ TAUQ2(I), X22(I+1,I), LDX22, WORK )
499: END IF
500: *
501: IF( I .LT. Q )
502: $ CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
503: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
504: *
505: END DO
506: *
507: * Reduce columns Q + 1, ..., P of X12, X22
508: *
509: DO I = Q + 1, P
510: *
511: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I),
512: $ LDX12 )
513: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
514: IF ( I .GE. M-Q ) THEN
515: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
516: $ TAUQ2(I) )
517: ELSE
518: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
519: $ TAUQ2(I) )
520: END IF
521: X12(I,I) = ONE
522: *
523: IF ( P .GT. I ) THEN
524: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
525: $ X12(I+1,I), LDX12, WORK )
526: END IF
527: IF( M-P-Q .GE. 1 )
528: $ CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
529: $ TAUQ2(I), X22(Q+1,I), LDX22, WORK )
530: *
531: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
532: *
533: END DO
534: *
535: * Reduce columns P + 1, ..., M - Q of X12, X22
536: *
537: DO I = 1, M - P - Q
538: *
539: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
540: $ X22(Q+I,P+I), LDX22 )
541: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
542: CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
543: $ LDX22, TAUQ2(P+I) )
544: X22(Q+I,P+I) = ONE
545: CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
546: $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
547: *
548: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
549: *
550: END DO
551: *
552: ELSE
553: *
554: * Reduce columns 1, ..., Q of X11, X12, X21, X22
555: *
556: DO I = 1, Q
557: *
558: IF( I .EQ. 1 ) THEN
559: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I),
560: $ LDX11 )
561: ELSE
562: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
563: $ X11(I,I), LDX11 )
564: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
565: $ 0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 )
566: END IF
567: IF( I .EQ. 1 ) THEN
568: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I),
569: $ LDX21 )
570: ELSE
571: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
572: $ X21(I,I), LDX21 )
573: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
574: $ 0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 )
575: END IF
576: *
577: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ),
578: $ DZNRM2( P-I+1, X11(I,I), LDX11 ) )
579: *
580: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
581: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
582: *
583: CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
584: X11(I,I) = ONE
585: IF ( I .EQ. M-P ) THEN
586: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
587: $ TAUP2(I) )
588: ELSE
589: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
590: $ TAUP2(I) )
591: END IF
592: X21(I,I) = ONE
593: *
594: CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
595: $ X11(I+1,I), LDX11, WORK )
596: CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
597: $ X12(I,I), LDX12, WORK )
598: CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
599: $ X21(I+1,I), LDX21, WORK )
600: CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
601: $ TAUP2(I), X22(I,I), LDX22, WORK )
602: *
603: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
604: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
605: *
606: IF( I .LT. Q ) THEN
607: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
608: $ X11(I+1,I), 1 )
609: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
610: $ X21(I+1,I), 1, X11(I+1,I), 1 )
611: END IF
612: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
613: $ X12(I,I), 1 )
614: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
615: $ X22(I,I), 1, X12(I,I), 1 )
616: *
617: IF( I .LT. Q )
618: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ),
619: $ DZNRM2( M-Q-I+1, X12(I,I), 1 ) )
620: *
621: IF( I .LT. Q ) THEN
622: CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
623: X11(I+1,I) = ONE
624: END IF
625: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
626: X12(I,I) = ONE
627: *
628: IF( I .LT. Q ) THEN
629: CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1,
630: $ DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK )
631: CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1,
632: $ DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK )
633: END IF
634: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
635: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
636: IF ( M-P .GT. I ) THEN
637: CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
638: $ DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
639: END IF
640: *
641: END DO
642: *
643: * Reduce columns Q + 1, ..., P of X12, X22
644: *
645: DO I = Q + 1, P
646: *
647: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 )
648: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
649: X12(I,I) = ONE
650: *
651: IF ( P .GT. I ) THEN
652: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
653: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
654: END IF
655: IF( M-P-Q .GE. 1 )
656: $ CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
657: $ DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
658: *
659: END DO
660: *
661: * Reduce columns P + 1, ..., M - Q of X12, X22
662: *
663: DO I = 1, M - P - Q
664: *
665: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
666: $ X22(P+I,Q+I), 1 )
667: CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
668: $ TAUQ2(P+I) )
669: X22(P+I,Q+I) = ONE
670: *
671: IF ( M-P-Q .NE. I ) THEN
672: CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
673: $ DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
674: $ WORK )
675: END IF
676: *
677: END DO
678: *
679: END IF
680: *
681: RETURN
682: *
683: * End of ZUNBDB
684: *
685: END
686:
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