Annotation of rpl/lapack/lapack/zunmbr.f, revision 1.16
1.8 bertrand 1: *> \brief \b ZUNMBR
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download ZUNMBR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmbr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunmbr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunmbr.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
22: * LDC, WORK, LWORK, INFO )
1.14 bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER SIDE, TRANS, VECT
26: * INTEGER INFO, K, LDA, LDC, LWORK, M, N
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30: * ..
1.14 bertrand 31: *
1.8 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
39: *> with
40: *> SIDE = 'L' SIDE = 'R'
41: *> TRANS = 'N': Q * C C * Q
42: *> TRANS = 'C': Q**H * C C * Q**H
43: *>
44: *> If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
45: *> with
46: *> SIDE = 'L' SIDE = 'R'
47: *> TRANS = 'N': P * C C * P
48: *> TRANS = 'C': P**H * C C * P**H
49: *>
50: *> Here Q and P**H are the unitary matrices determined by ZGEBRD when
51: *> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
52: *> and P**H are defined as products of elementary reflectors H(i) and
53: *> G(i) respectively.
54: *>
55: *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
56: *> order of the unitary matrix Q or P**H that is applied.
57: *>
58: *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
59: *> if nq >= k, Q = H(1) H(2) . . . H(k);
60: *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
61: *>
62: *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
63: *> if k < nq, P = G(1) G(2) . . . G(k);
64: *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
65: *> \endverbatim
66: *
67: * Arguments:
68: * ==========
69: *
70: *> \param[in] VECT
71: *> \verbatim
72: *> VECT is CHARACTER*1
73: *> = 'Q': apply Q or Q**H;
74: *> = 'P': apply P or P**H.
75: *> \endverbatim
76: *>
77: *> \param[in] SIDE
78: *> \verbatim
79: *> SIDE is CHARACTER*1
80: *> = 'L': apply Q, Q**H, P or P**H from the Left;
81: *> = 'R': apply Q, Q**H, P or P**H from the Right.
82: *> \endverbatim
83: *>
84: *> \param[in] TRANS
85: *> \verbatim
86: *> TRANS is CHARACTER*1
87: *> = 'N': No transpose, apply Q or P;
88: *> = 'C': Conjugate transpose, apply Q**H or P**H.
89: *> \endverbatim
90: *>
91: *> \param[in] M
92: *> \verbatim
93: *> M is INTEGER
94: *> The number of rows of the matrix C. M >= 0.
95: *> \endverbatim
96: *>
97: *> \param[in] N
98: *> \verbatim
99: *> N is INTEGER
100: *> The number of columns of the matrix C. N >= 0.
101: *> \endverbatim
102: *>
103: *> \param[in] K
104: *> \verbatim
105: *> K is INTEGER
106: *> If VECT = 'Q', the number of columns in the original
107: *> matrix reduced by ZGEBRD.
108: *> If VECT = 'P', the number of rows in the original
109: *> matrix reduced by ZGEBRD.
110: *> K >= 0.
111: *> \endverbatim
112: *>
113: *> \param[in] A
114: *> \verbatim
115: *> A is COMPLEX*16 array, dimension
116: *> (LDA,min(nq,K)) if VECT = 'Q'
117: *> (LDA,nq) if VECT = 'P'
118: *> The vectors which define the elementary reflectors H(i) and
119: *> G(i), whose products determine the matrices Q and P, as
120: *> returned by ZGEBRD.
121: *> \endverbatim
122: *>
123: *> \param[in] LDA
124: *> \verbatim
125: *> LDA is INTEGER
126: *> The leading dimension of the array A.
127: *> If VECT = 'Q', LDA >= max(1,nq);
128: *> if VECT = 'P', LDA >= max(1,min(nq,K)).
129: *> \endverbatim
130: *>
131: *> \param[in] TAU
132: *> \verbatim
133: *> TAU is COMPLEX*16 array, dimension (min(nq,K))
134: *> TAU(i) must contain the scalar factor of the elementary
135: *> reflector H(i) or G(i) which determines Q or P, as returned
136: *> by ZGEBRD in the array argument TAUQ or TAUP.
137: *> \endverbatim
138: *>
139: *> \param[in,out] C
140: *> \verbatim
141: *> C is COMPLEX*16 array, dimension (LDC,N)
142: *> On entry, the M-by-N matrix C.
143: *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
144: *> or P*C or P**H*C or C*P or C*P**H.
145: *> \endverbatim
146: *>
147: *> \param[in] LDC
148: *> \verbatim
149: *> LDC is INTEGER
150: *> The leading dimension of the array C. LDC >= max(1,M).
151: *> \endverbatim
152: *>
153: *> \param[out] WORK
154: *> \verbatim
155: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
156: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
157: *> \endverbatim
158: *>
159: *> \param[in] LWORK
160: *> \verbatim
161: *> LWORK is INTEGER
162: *> The dimension of the array WORK.
163: *> If SIDE = 'L', LWORK >= max(1,N);
164: *> if SIDE = 'R', LWORK >= max(1,M);
165: *> if N = 0 or M = 0, LWORK >= 1.
166: *> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
167: *> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
168: *> optimal blocksize. (NB = 0 if M = 0 or N = 0.)
169: *>
170: *> If LWORK = -1, then a workspace query is assumed; the routine
171: *> only calculates the optimal size of the WORK array, returns
172: *> this value as the first entry of the WORK array, and no error
173: *> message related to LWORK is issued by XERBLA.
174: *> \endverbatim
175: *>
176: *> \param[out] INFO
177: *> \verbatim
178: *> INFO is INTEGER
179: *> = 0: successful exit
180: *> < 0: if INFO = -i, the i-th argument had an illegal value
181: *> \endverbatim
182: *
183: * Authors:
184: * ========
185: *
1.14 bertrand 186: *> \author Univ. of Tennessee
187: *> \author Univ. of California Berkeley
188: *> \author Univ. of Colorado Denver
189: *> \author NAG Ltd.
1.8 bertrand 190: *
1.14 bertrand 191: *> \date December 2016
1.8 bertrand 192: *
193: *> \ingroup complex16OTHERcomputational
194: *
195: * =====================================================================
1.1 bertrand 196: SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
197: $ LDC, WORK, LWORK, INFO )
198: *
1.14 bertrand 199: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 200: * -- LAPACK is a software package provided by Univ. of Tennessee, --
201: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 bertrand 202: * December 2016
1.1 bertrand 203: *
204: * .. Scalar Arguments ..
205: CHARACTER SIDE, TRANS, VECT
206: INTEGER INFO, K, LDA, LDC, LWORK, M, N
207: * ..
208: * .. Array Arguments ..
209: COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
210: * ..
211: *
212: * =====================================================================
213: *
214: * .. Local Scalars ..
215: LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
216: CHARACTER TRANST
217: INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
218: * ..
219: * .. External Functions ..
220: LOGICAL LSAME
221: INTEGER ILAENV
222: EXTERNAL LSAME, ILAENV
223: * ..
224: * .. External Subroutines ..
225: EXTERNAL XERBLA, ZUNMLQ, ZUNMQR
226: * ..
227: * .. Intrinsic Functions ..
228: INTRINSIC MAX, MIN
229: * ..
230: * .. Executable Statements ..
231: *
232: * Test the input arguments
233: *
234: INFO = 0
235: APPLYQ = LSAME( VECT, 'Q' )
236: LEFT = LSAME( SIDE, 'L' )
237: NOTRAN = LSAME( TRANS, 'N' )
238: LQUERY = ( LWORK.EQ.-1 )
239: *
240: * NQ is the order of Q or P and NW is the minimum dimension of WORK
241: *
242: IF( LEFT ) THEN
243: NQ = M
244: NW = N
245: ELSE
246: NQ = N
247: NW = M
248: END IF
249: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
250: NW = 0
251: END IF
252: IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
253: INFO = -1
254: ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
255: INFO = -2
256: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
257: INFO = -3
258: ELSE IF( M.LT.0 ) THEN
259: INFO = -4
260: ELSE IF( N.LT.0 ) THEN
261: INFO = -5
262: ELSE IF( K.LT.0 ) THEN
263: INFO = -6
264: ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
265: $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
266: $ THEN
267: INFO = -8
268: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
269: INFO = -11
270: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
271: INFO = -13
272: END IF
273: *
274: IF( INFO.EQ.0 ) THEN
275: IF( NW.GT.0 ) THEN
276: IF( APPLYQ ) THEN
277: IF( LEFT ) THEN
278: NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1,
279: $ -1 )
280: ELSE
281: NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1,
282: $ -1 )
283: END IF
284: ELSE
285: IF( LEFT ) THEN
286: NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1,
287: $ -1 )
288: ELSE
289: NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1,
290: $ -1 )
291: END IF
292: END IF
293: LWKOPT = MAX( 1, NW*NB )
294: ELSE
295: LWKOPT = 1
296: END IF
297: WORK( 1 ) = LWKOPT
298: END IF
299: *
300: IF( INFO.NE.0 ) THEN
301: CALL XERBLA( 'ZUNMBR', -INFO )
302: RETURN
303: ELSE IF( LQUERY ) THEN
304: RETURN
305: END IF
306: *
307: * Quick return if possible
308: *
309: IF( M.EQ.0 .OR. N.EQ.0 )
310: $ RETURN
311: *
312: IF( APPLYQ ) THEN
313: *
314: * Apply Q
315: *
316: IF( NQ.GE.K ) THEN
317: *
318: * Q was determined by a call to ZGEBRD with nq >= k
319: *
320: CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
321: $ WORK, LWORK, IINFO )
322: ELSE IF( NQ.GT.1 ) THEN
323: *
324: * Q was determined by a call to ZGEBRD with nq < k
325: *
326: IF( LEFT ) THEN
327: MI = M - 1
328: NI = N
329: I1 = 2
330: I2 = 1
331: ELSE
332: MI = M
333: NI = N - 1
334: I1 = 1
335: I2 = 2
336: END IF
337: CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
338: $ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
339: END IF
340: ELSE
341: *
342: * Apply P
343: *
344: IF( NOTRAN ) THEN
345: TRANST = 'C'
346: ELSE
347: TRANST = 'N'
348: END IF
349: IF( NQ.GT.K ) THEN
350: *
351: * P was determined by a call to ZGEBRD with nq > k
352: *
353: CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
354: $ WORK, LWORK, IINFO )
355: ELSE IF( NQ.GT.1 ) THEN
356: *
357: * P was determined by a call to ZGEBRD with nq <= k
358: *
359: IF( LEFT ) THEN
360: MI = M - 1
361: NI = N
362: I1 = 2
363: I2 = 1
364: ELSE
365: MI = M
366: NI = N - 1
367: I1 = 1
368: I2 = 2
369: END IF
370: CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
371: $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
372: END IF
373: END IF
374: WORK( 1 ) = LWKOPT
375: RETURN
376: *
377: * End of ZUNMBR
378: *
379: END
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