Annotation of rpl/lapack/lapack/zungql.f, revision 1.15
1.8 bertrand 1: *> \brief \b ZUNGQL
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 ZUNGQL + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungql.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungql.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungql.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
1.14 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, K, LDA, LWORK, M, N
25: * ..
26: * .. Array Arguments ..
27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
28: * ..
1.14 bertrand 29: *
1.8 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
37: *> which is defined as the last N columns of a product of K elementary
38: *> reflectors of order M
39: *>
40: *> Q = H(k) . . . H(2) H(1)
41: *>
42: *> as returned by ZGEQLF.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] M
49: *> \verbatim
50: *> M is INTEGER
51: *> The number of rows of the matrix Q. M >= 0.
52: *> \endverbatim
53: *>
54: *> \param[in] N
55: *> \verbatim
56: *> N is INTEGER
57: *> The number of columns of the matrix Q. M >= N >= 0.
58: *> \endverbatim
59: *>
60: *> \param[in] K
61: *> \verbatim
62: *> K is INTEGER
63: *> The number of elementary reflectors whose product defines the
64: *> matrix Q. N >= K >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is COMPLEX*16 array, dimension (LDA,N)
70: *> On entry, the (n-k+i)-th column must contain the vector which
71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72: *> returned by ZGEQLF in the last k columns of its array
73: *> argument A.
74: *> On exit, the M-by-N matrix Q.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The first dimension of the array A. LDA >= max(1,M).
81: *> \endverbatim
82: *>
83: *> \param[in] TAU
84: *> \verbatim
85: *> TAU is COMPLEX*16 array, dimension (K)
86: *> TAU(i) must contain the scalar factor of the elementary
87: *> reflector H(i), as returned by ZGEQLF.
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
93: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
94: *> \endverbatim
95: *>
96: *> \param[in] LWORK
97: *> \verbatim
98: *> LWORK is INTEGER
99: *> The dimension of the array WORK. LWORK >= max(1,N).
100: *> For optimum performance LWORK >= N*NB, where NB is the
101: *> optimal blocksize.
102: *>
103: *> If LWORK = -1, then a workspace query is assumed; the routine
104: *> only calculates the optimal size of the WORK array, returns
105: *> this value as the first entry of the WORK array, and no error
106: *> message related to LWORK is issued by XERBLA.
107: *> \endverbatim
108: *>
109: *> \param[out] INFO
110: *> \verbatim
111: *> INFO is INTEGER
112: *> = 0: successful exit
113: *> < 0: if INFO = -i, the i-th argument has an illegal value
114: *> \endverbatim
115: *
116: * Authors:
117: * ========
118: *
1.14 bertrand 119: *> \author Univ. of Tennessee
120: *> \author Univ. of California Berkeley
121: *> \author Univ. of Colorado Denver
122: *> \author NAG Ltd.
1.8 bertrand 123: *
1.14 bertrand 124: *> \date December 2016
1.8 bertrand 125: *
126: *> \ingroup complex16OTHERcomputational
127: *
128: * =====================================================================
1.1 bertrand 129: SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
130: *
1.14 bertrand 131: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 bertrand 134: * December 2016
1.1 bertrand 135: *
136: * .. Scalar Arguments ..
137: INTEGER INFO, K, LDA, LWORK, M, N
138: * ..
139: * .. Array Arguments ..
140: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: COMPLEX*16 ZERO
147: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL LQUERY
151: INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
152: $ NB, NBMIN, NX
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC MAX, MIN
159: * ..
160: * .. External Functions ..
161: INTEGER ILAENV
162: EXTERNAL ILAENV
163: * ..
164: * .. Executable Statements ..
165: *
166: * Test the input arguments
167: *
168: INFO = 0
169: LQUERY = ( LWORK.EQ.-1 )
170: IF( M.LT.0 ) THEN
171: INFO = -1
172: ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
173: INFO = -2
174: ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
175: INFO = -3
176: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
177: INFO = -5
178: END IF
179: *
180: IF( INFO.EQ.0 ) THEN
181: IF( N.EQ.0 ) THEN
182: LWKOPT = 1
183: ELSE
184: NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 )
185: LWKOPT = N*NB
186: END IF
187: WORK( 1 ) = LWKOPT
188: *
189: IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
190: INFO = -8
191: END IF
192: END IF
193: *
194: IF( INFO.NE.0 ) THEN
195: CALL XERBLA( 'ZUNGQL', -INFO )
196: RETURN
197: ELSE IF( LQUERY ) THEN
198: RETURN
199: END IF
200: *
201: * Quick return if possible
202: *
203: IF( N.LE.0 ) THEN
204: RETURN
205: END IF
206: *
207: NBMIN = 2
208: NX = 0
209: IWS = N
210: IF( NB.GT.1 .AND. NB.LT.K ) THEN
211: *
212: * Determine when to cross over from blocked to unblocked code.
213: *
214: NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) )
215: IF( NX.LT.K ) THEN
216: *
217: * Determine if workspace is large enough for blocked code.
218: *
219: LDWORK = N
220: IWS = LDWORK*NB
221: IF( LWORK.LT.IWS ) THEN
222: *
223: * Not enough workspace to use optimal NB: reduce NB and
224: * determine the minimum value of NB.
225: *
226: NB = LWORK / LDWORK
227: NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) )
228: END IF
229: END IF
230: END IF
231: *
232: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
233: *
234: * Use blocked code after the first block.
235: * The last kk columns are handled by the block method.
236: *
237: KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
238: *
239: * Set A(m-kk+1:m,1:n-kk) to zero.
240: *
241: DO 20 J = 1, N - KK
242: DO 10 I = M - KK + 1, M
243: A( I, J ) = ZERO
244: 10 CONTINUE
245: 20 CONTINUE
246: ELSE
247: KK = 0
248: END IF
249: *
250: * Use unblocked code for the first or only block.
251: *
252: CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
253: *
254: IF( KK.GT.0 ) THEN
255: *
256: * Use blocked code
257: *
258: DO 50 I = K - KK + 1, K, NB
259: IB = MIN( NB, K-I+1 )
260: IF( N-K+I.GT.1 ) THEN
261: *
262: * Form the triangular factor of the block reflector
263: * H = H(i+ib-1) . . . H(i+1) H(i)
264: *
265: CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
266: $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
267: *
268: * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
269: *
270: CALL ZLARFB( 'Left', 'No transpose', 'Backward',
271: $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
272: $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
273: $ WORK( IB+1 ), LDWORK )
274: END IF
275: *
276: * Apply H to rows 1:m-k+i+ib-1 of current block
277: *
278: CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
279: $ TAU( I ), WORK, IINFO )
280: *
281: * Set rows m-k+i+ib:m of current block to zero
282: *
283: DO 40 J = N - K + I, N - K + I + IB - 1
284: DO 30 L = M - K + I + IB, M
285: A( L, J ) = ZERO
286: 30 CONTINUE
287: 40 CONTINUE
288: 50 CONTINUE
289: END IF
290: *
291: WORK( 1 ) = IWS
292: RETURN
293: *
294: * End of ZUNGQL
295: *
296: END
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