1: SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
2: $ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
3: $ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
4: IMPLICIT NONE
5: *
6: * -- LAPACK routine ((version 3.3.0)) --
7: *
8: * -- Contributed by Brian Sutton of the Randolph-Macon College --
9: * -- November 2010
10: *
11: * -- LAPACK is a software package provided by Univ. of Tennessee, --
12: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
13: *
14: * .. Scalar Arguments ..
15: CHARACTER SIGNS, TRANS
16: INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
17: $ Q
18: * ..
19: * .. Array Arguments ..
20: DOUBLE PRECISION PHI( * ), THETA( * )
21: COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
22: $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
23: $ X21( LDX21, * ), X22( LDX22, * )
24: * ..
25: *
26: * Purpose
27: * =======
28: *
29: * ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
30: * partitioned unitary matrix X:
31: *
32: * [ B11 | B12 0 0 ]
33: * [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
34: * X = [-----------] = [---------] [----------------] [---------] .
35: * [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
36: * [ 0 | 0 0 I ]
37: *
38: * X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
39: * not the case, then X must be transposed and/or permuted. This can be
40: * done in constant time using the TRANS and SIGNS options. See ZUNCSD
41: * for details.)
42: *
43: * The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
44: * (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
45: * represented implicitly by Householder vectors.
46: *
47: * B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
48: * implicitly by angles THETA, PHI.
49: *
50: * Arguments
51: * =========
52: *
53: * TRANS (input) CHARACTER
54: * = 'T': X, U1, U2, V1T, and V2T are stored in row-major
55: * order;
56: * otherwise: X, U1, U2, V1T, and V2T are stored in column-
57: * major order.
58: *
59: * SIGNS (input) CHARACTER
60: * = 'O': The lower-left block is made nonpositive (the
61: * "other" convention);
62: * otherwise: The upper-right block is made nonpositive (the
63: * "default" convention).
64: *
65: * M (input) INTEGER
66: * The number of rows and columns in X.
67: *
68: * P (input) INTEGER
69: * The number of rows in X11 and X12. 0 <= P <= M.
70: *
71: * Q (input) INTEGER
72: * The number of columns in X11 and X21. 0 <= Q <=
73: * MIN(P,M-P,M-Q).
74: *
75: * X11 (input/output) COMPLEX*16 array, dimension (LDX11,Q)
76: * On entry, the top-left block of the unitary matrix to be
77: * reduced. On exit, the form depends on TRANS:
78: * If TRANS = 'N', then
79: * the columns of tril(X11) specify reflectors for P1,
80: * the rows of triu(X11,1) specify reflectors for Q1;
81: * else TRANS = 'T', and
82: * the rows of triu(X11) specify reflectors for P1,
83: * the columns of tril(X11,-1) specify reflectors for Q1.
84: *
85: * LDX11 (input) INTEGER
86: * The leading dimension of X11. If TRANS = 'N', then LDX11 >=
87: * P; else LDX11 >= Q.
88: *
89: * X12 (input/output) COMPLEX*16 array, dimension (LDX12,M-Q)
90: * On entry, the top-right block of the unitary matrix to
91: * be reduced. On exit, the form depends on TRANS:
92: * If TRANS = 'N', then
93: * the rows of triu(X12) specify the first P reflectors for
94: * Q2;
95: * else TRANS = 'T', and
96: * the columns of tril(X12) specify the first P reflectors
97: * for Q2.
98: *
99: * LDX12 (input) INTEGER
100: * The leading dimension of X12. If TRANS = 'N', then LDX12 >=
101: * P; else LDX11 >= M-Q.
102: *
103: * X21 (input/output) COMPLEX*16 array, dimension (LDX21,Q)
104: * On entry, the bottom-left block of the unitary matrix to
105: * be reduced. On exit, the form depends on TRANS:
106: * If TRANS = 'N', then
107: * the columns of tril(X21) specify reflectors for P2;
108: * else TRANS = 'T', and
109: * the rows of triu(X21) specify reflectors for P2.
110: *
111: * LDX21 (input) INTEGER
112: * The leading dimension of X21. If TRANS = 'N', then LDX21 >=
113: * M-P; else LDX21 >= Q.
114: *
115: * X22 (input/output) COMPLEX*16 array, dimension (LDX22,M-Q)
116: * On entry, the bottom-right block of the unitary matrix to
117: * be reduced. On exit, the form depends on TRANS:
118: * If TRANS = 'N', then
119: * the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
120: * M-P-Q reflectors for Q2,
121: * else TRANS = 'T', and
122: * the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
123: * M-P-Q reflectors for P2.
124: *
125: * LDX22 (input) INTEGER
126: * The leading dimension of X22. If TRANS = 'N', then LDX22 >=
127: * M-P; else LDX22 >= M-Q.
128: *
129: * THETA (output) DOUBLE PRECISION array, dimension (Q)
130: * The entries of the bidiagonal blocks B11, B12, B21, B22 can
131: * be computed from the angles THETA and PHI. See Further
132: * Details.
133: *
134: * PHI (output) DOUBLE PRECISION array, dimension (Q-1)
135: * The entries of the bidiagonal blocks B11, B12, B21, B22 can
136: * be computed from the angles THETA and PHI. See Further
137: * Details.
138: *
139: * TAUP1 (output) COMPLEX*16 array, dimension (P)
140: * The scalar factors of the elementary reflectors that define
141: * P1.
142: *
143: * TAUP2 (output) COMPLEX*16 array, dimension (M-P)
144: * The scalar factors of the elementary reflectors that define
145: * P2.
146: *
147: * TAUQ1 (output) COMPLEX*16 array, dimension (Q)
148: * The scalar factors of the elementary reflectors that define
149: * Q1.
150: *
151: * TAUQ2 (output) COMPLEX*16 array, dimension (M-Q)
152: * The scalar factors of the elementary reflectors that define
153: * Q2.
154: *
155: * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
156: *
157: * LWORK (input) INTEGER
158: * The dimension of the array WORK. LWORK >= M-Q.
159: *
160: * If LWORK = -1, then a workspace query is assumed; the routine
161: * only calculates the optimal size of the WORK array, returns
162: * this value as the first entry of the WORK array, and no error
163: * message related to LWORK is issued by XERBLA.
164: *
165: * INFO (output) INTEGER
166: * = 0: successful exit.
167: * < 0: if INFO = -i, the i-th argument had an illegal value.
168: *
169: * Further Details
170: * ===============
171: *
172: * The bidiagonal blocks B11, B12, B21, and B22 are represented
173: * implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
174: * PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
175: * lower bidiagonal. Every entry in each bidiagonal band is a product
176: * of a sine or cosine of a THETA with a sine or cosine of a PHI. See
177: * [1] or ZUNCSD for details.
178: *
179: * P1, P2, Q1, and Q2 are represented as products of elementary
180: * reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
181: * using ZUNGQR and ZUNGLQ.
182: *
183: * Reference
184: * =========
185: *
186: * [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
187: * Algorithms, 50(1):33-65, 2009.
188: *
189: * ====================================================================
190: *
191: * .. Parameters ..
192: DOUBLE PRECISION REALONE
193: PARAMETER ( REALONE = 1.0D0 )
194: COMPLEX*16 NEGONE, ONE
195: PARAMETER ( NEGONE = (-1.0D0,0.0D0),
196: $ ONE = (1.0D0,0.0D0) )
197: * ..
198: * .. Local Scalars ..
199: LOGICAL COLMAJOR, LQUERY
200: INTEGER I, LWORKMIN, LWORKOPT
201: DOUBLE PRECISION Z1, Z2, Z3, Z4
202: * ..
203: * .. External Subroutines ..
204: EXTERNAL ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA
205: EXTERNAL ZLACGV
206: *
207: * ..
208: * .. External Functions ..
209: DOUBLE PRECISION DZNRM2
210: LOGICAL LSAME
211: EXTERNAL DZNRM2, LSAME
212: * ..
213: * .. Intrinsic Functions
214: INTRINSIC ATAN2, COS, MAX, MIN, SIN
215: INTRINSIC DCMPLX, DCONJG
216: * ..
217: * .. Executable Statements ..
218: *
219: * Test input arguments
220: *
221: INFO = 0
222: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
223: IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
224: Z1 = REALONE
225: Z2 = REALONE
226: Z3 = REALONE
227: Z4 = REALONE
228: ELSE
229: Z1 = REALONE
230: Z2 = -REALONE
231: Z3 = REALONE
232: Z4 = -REALONE
233: END IF
234: LQUERY = LWORK .EQ. -1
235: *
236: IF( M .LT. 0 ) THEN
237: INFO = -3
238: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
239: INFO = -4
240: ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
241: $ Q .GT. M-Q ) THEN
242: INFO = -5
243: ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
244: INFO = -7
245: ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
246: INFO = -7
247: ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
248: INFO = -9
249: ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
250: INFO = -9
251: ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
252: INFO = -11
253: ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
254: INFO = -11
255: ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
256: INFO = -13
257: ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
258: INFO = -13
259: END IF
260: *
261: * Compute workspace
262: *
263: IF( INFO .EQ. 0 ) THEN
264: LWORKOPT = M - Q
265: LWORKMIN = M - Q
266: WORK(1) = LWORKOPT
267: IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
268: INFO = -21
269: END IF
270: END IF
271: IF( INFO .NE. 0 ) THEN
272: CALL XERBLA( 'xORBDB', -INFO )
273: RETURN
274: ELSE IF( LQUERY ) THEN
275: RETURN
276: END IF
277: *
278: * Handle column-major and row-major separately
279: *
280: IF( COLMAJOR ) THEN
281: *
282: * Reduce columns 1, ..., Q of X11, X12, X21, and X22
283: *
284: DO I = 1, Q
285: *
286: IF( I .EQ. 1 ) THEN
287: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 1 )
288: ELSE
289: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
290: $ X11(I,I), 1 )
291: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
292: $ 0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 )
293: END IF
294: IF( I .EQ. 1 ) THEN
295: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 1 )
296: ELSE
297: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
298: $ X21(I,I), 1 )
299: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
300: $ 0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 )
301: END IF
302: *
303: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ),
304: $ DZNRM2( P-I+1, X11(I,I), 1 ) )
305: *
306: CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
307: X11(I,I) = ONE
308: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
309: X21(I,I) = ONE
310: *
311: CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1, DCONJG(TAUP1(I)),
312: $ X11(I,I+1), LDX11, WORK )
313: CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
314: $ DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
315: CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
316: $ DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
317: CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
318: $ DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
319: *
320: IF( I .LT. Q ) THEN
321: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
322: $ X11(I,I+1), LDX11 )
323: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
324: $ X21(I,I+1), LDX21, X11(I,I+1), LDX11 )
325: END IF
326: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
327: $ X12(I,I), LDX12 )
328: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
329: $ X22(I,I), LDX22, X12(I,I), LDX12 )
330: *
331: IF( I .LT. Q )
332: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ),
333: $ DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
334: *
335: IF( I .LT. Q ) THEN
336: CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
337: CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
338: $ TAUQ1(I) )
339: X11(I,I+1) = ONE
340: END IF
341: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
342: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
343: $ TAUQ2(I) )
344: X12(I,I) = ONE
345: *
346: IF( I .LT. Q ) THEN
347: CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
348: $ X11(I+1,I+1), LDX11, WORK )
349: CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
350: $ X21(I+1,I+1), LDX21, WORK )
351: END IF
352: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
353: $ X12(I+1,I), LDX12, WORK )
354: CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
355: $ X22(I+1,I), LDX22, WORK )
356: *
357: IF( I .LT. Q )
358: $ CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
359: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
360: *
361: END DO
362: *
363: * Reduce columns Q + 1, ..., P of X12, X22
364: *
365: DO I = Q + 1, P
366: *
367: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I),
368: $ LDX12 )
369: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
370: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
371: $ TAUQ2(I) )
372: X12(I,I) = ONE
373: *
374: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
375: $ X12(I+1,I), LDX12, WORK )
376: IF( M-P-Q .GE. 1 )
377: $ CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
378: $ TAUQ2(I), X22(Q+1,I), LDX22, WORK )
379: *
380: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
381: *
382: END DO
383: *
384: * Reduce columns P + 1, ..., M - Q of X12, X22
385: *
386: DO I = 1, M - P - Q
387: *
388: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
389: $ X22(Q+I,P+I), LDX22 )
390: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
391: CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
392: $ LDX22, TAUQ2(P+I) )
393: X22(Q+I,P+I) = ONE
394: CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
395: $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
396: *
397: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
398: *
399: END DO
400: *
401: ELSE
402: *
403: * Reduce columns 1, ..., Q of X11, X12, X21, X22
404: *
405: DO I = 1, Q
406: *
407: IF( I .EQ. 1 ) THEN
408: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I),
409: $ LDX11 )
410: ELSE
411: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
412: $ X11(I,I), LDX11 )
413: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
414: $ 0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 )
415: END IF
416: IF( I .EQ. 1 ) THEN
417: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I),
418: $ LDX21 )
419: ELSE
420: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
421: $ X21(I,I), LDX21 )
422: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
423: $ 0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 )
424: END IF
425: *
426: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ),
427: $ DZNRM2( P-I+1, X11(I,I), LDX11 ) )
428: *
429: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
430: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
431: *
432: CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
433: X11(I,I) = ONE
434: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
435: $ TAUP2(I) )
436: X21(I,I) = ONE
437: *
438: CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
439: $ X11(I+1,I), LDX11, WORK )
440: CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
441: $ X12(I,I), LDX12, WORK )
442: CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
443: $ X21(I+1,I), LDX21, WORK )
444: CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
445: $ TAUP2(I), X22(I,I), LDX22, WORK )
446: *
447: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
448: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
449: *
450: IF( I .LT. Q ) THEN
451: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
452: $ X11(I+1,I), 1 )
453: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
454: $ X21(I+1,I), 1, X11(I+1,I), 1 )
455: END IF
456: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
457: $ X12(I,I), 1 )
458: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
459: $ X22(I,I), 1, X12(I,I), 1 )
460: *
461: IF( I .LT. Q )
462: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ),
463: $ DZNRM2( M-Q-I+1, X12(I,I), 1 ) )
464: *
465: IF( I .LT. Q ) THEN
466: CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
467: X11(I+1,I) = ONE
468: END IF
469: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
470: X12(I,I) = ONE
471: *
472: IF( I .LT. Q ) THEN
473: CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1,
474: $ DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK )
475: CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1,
476: $ DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK )
477: END IF
478: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
479: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
480: CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
481: $ DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
482: *
483: END DO
484: *
485: * Reduce columns Q + 1, ..., P of X12, X22
486: *
487: DO I = Q + 1, P
488: *
489: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 )
490: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
491: X12(I,I) = ONE
492: *
493: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
494: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
495: IF( M-P-Q .GE. 1 )
496: $ CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
497: $ DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
498: *
499: END DO
500: *
501: * Reduce columns P + 1, ..., M - Q of X12, X22
502: *
503: DO I = 1, M - P - Q
504: *
505: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
506: $ X22(P+I,Q+I), 1 )
507: CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
508: $ TAUQ2(P+I) )
509: X22(P+I,Q+I) = ONE
510: *
511: CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
512: $ DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
513: $ WORK )
514: *
515: END DO
516: *
517: END IF
518: *
519: RETURN
520: *
521: * End of ZUNBDB
522: *
523: END
524:
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