Annotation of rpl/lapack/lapack/zgelqf.f, revision 1.14
1.9 bertrand 1: *> \brief \b ZGELQF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGELQF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelqf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelqf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelqf.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, LWORK, M, N
25: * ..
26: * .. Array Arguments ..
27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
37: *> A = L * Q.
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] M
44: *> \verbatim
45: *> M is INTEGER
46: *> The number of rows of the matrix A. M >= 0.
47: *> \endverbatim
48: *>
49: *> \param[in] N
50: *> \verbatim
51: *> N is INTEGER
52: *> The number of columns of the matrix A. N >= 0.
53: *> \endverbatim
54: *>
55: *> \param[in,out] A
56: *> \verbatim
57: *> A is COMPLEX*16 array, dimension (LDA,N)
58: *> On entry, the M-by-N matrix A.
59: *> On exit, the elements on and below the diagonal of the array
60: *> contain the m-by-min(m,n) lower trapezoidal matrix L (L is
61: *> lower triangular if m <= n); the elements above the diagonal,
62: *> with the array TAU, represent the unitary matrix Q as a
63: *> product of elementary reflectors (see Further Details).
64: *> \endverbatim
65: *>
66: *> \param[in] LDA
67: *> \verbatim
68: *> LDA is INTEGER
69: *> The leading dimension of the array A. LDA >= max(1,M).
70: *> \endverbatim
71: *>
72: *> \param[out] TAU
73: *> \verbatim
74: *> TAU is COMPLEX*16 array, dimension (min(M,N))
75: *> The scalar factors of the elementary reflectors (see Further
76: *> Details).
77: *> \endverbatim
78: *>
79: *> \param[out] WORK
80: *> \verbatim
81: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
82: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
83: *> \endverbatim
84: *>
85: *> \param[in] LWORK
86: *> \verbatim
87: *> LWORK is INTEGER
88: *> The dimension of the array WORK. LWORK >= max(1,M).
89: *> For optimum performance LWORK >= M*NB, where NB is the
90: *> optimal blocksize.
91: *>
92: *> If LWORK = -1, then a workspace query is assumed; the routine
93: *> only calculates the optimal size of the WORK array, returns
94: *> this value as the first entry of the WORK array, and no error
95: *> message related to LWORK is issued by XERBLA.
96: *> \endverbatim
97: *>
98: *> \param[out] INFO
99: *> \verbatim
100: *> INFO is INTEGER
101: *> = 0: successful exit
102: *> < 0: if INFO = -i, the i-th argument had an illegal value
103: *> \endverbatim
104: *
105: * Authors:
106: * ========
107: *
108: *> \author Univ. of Tennessee
109: *> \author Univ. of California Berkeley
110: *> \author Univ. of Colorado Denver
111: *> \author NAG Ltd.
112: *
113: *> \date November 2011
114: *
115: *> \ingroup complex16GEcomputational
116: *
117: *> \par Further Details:
118: * =====================
119: *>
120: *> \verbatim
121: *>
122: *> The matrix Q is represented as a product of elementary reflectors
123: *>
124: *> Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
125: *>
126: *> Each H(i) has the form
127: *>
128: *> H(i) = I - tau * v * v**H
129: *>
130: *> where tau is a complex scalar, and v is a complex vector with
131: *> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
132: *> A(i,i+1:n), and tau in TAU(i).
133: *> \endverbatim
134: *>
135: * =====================================================================
1.1 bertrand 136: SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
137: *
1.9 bertrand 138: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 139: * -- LAPACK is a software package provided by Univ. of Tennessee, --
140: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 141: * November 2011
1.1 bertrand 142: *
143: * .. Scalar Arguments ..
144: INTEGER INFO, LDA, LWORK, M, N
145: * ..
146: * .. Array Arguments ..
147: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
148: * ..
149: *
150: * =====================================================================
151: *
152: * .. Local Scalars ..
153: LOGICAL LQUERY
154: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
155: $ NBMIN, NX
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL XERBLA, ZGELQ2, ZLARFB, ZLARFT
159: * ..
160: * .. Intrinsic Functions ..
161: INTRINSIC MAX, MIN
162: * ..
163: * .. External Functions ..
164: INTEGER ILAENV
165: EXTERNAL ILAENV
166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input arguments
170: *
171: INFO = 0
172: NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
173: LWKOPT = M*NB
174: WORK( 1 ) = LWKOPT
175: LQUERY = ( LWORK.EQ.-1 )
176: IF( M.LT.0 ) THEN
177: INFO = -1
178: ELSE IF( N.LT.0 ) THEN
179: INFO = -2
180: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
181: INFO = -4
182: ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
183: INFO = -7
184: END IF
185: IF( INFO.NE.0 ) THEN
186: CALL XERBLA( 'ZGELQF', -INFO )
187: RETURN
188: ELSE IF( LQUERY ) THEN
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: K = MIN( M, N )
195: IF( K.EQ.0 ) THEN
196: WORK( 1 ) = 1
197: RETURN
198: END IF
199: *
200: NBMIN = 2
201: NX = 0
202: IWS = M
203: IF( NB.GT.1 .AND. NB.LT.K ) THEN
204: *
205: * Determine when to cross over from blocked to unblocked code.
206: *
207: NX = MAX( 0, ILAENV( 3, 'ZGELQF', ' ', M, N, -1, -1 ) )
208: IF( NX.LT.K ) THEN
209: *
210: * Determine if workspace is large enough for blocked code.
211: *
212: LDWORK = M
213: IWS = LDWORK*NB
214: IF( LWORK.LT.IWS ) THEN
215: *
216: * Not enough workspace to use optimal NB: reduce NB and
217: * determine the minimum value of NB.
218: *
219: NB = LWORK / LDWORK
220: NBMIN = MAX( 2, ILAENV( 2, 'ZGELQF', ' ', M, N, -1,
221: $ -1 ) )
222: END IF
223: END IF
224: END IF
225: *
226: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
227: *
228: * Use blocked code initially
229: *
230: DO 10 I = 1, K - NX, NB
231: IB = MIN( K-I+1, NB )
232: *
233: * Compute the LQ factorization of the current block
234: * A(i:i+ib-1,i:n)
235: *
236: CALL ZGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
237: $ IINFO )
238: IF( I+IB.LE.M ) THEN
239: *
240: * Form the triangular factor of the block reflector
241: * H = H(i) H(i+1) . . . H(i+ib-1)
242: *
243: CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
244: $ LDA, TAU( I ), WORK, LDWORK )
245: *
246: * Apply H to A(i+ib:m,i:n) from the right
247: *
248: CALL ZLARFB( 'Right', 'No transpose', 'Forward',
249: $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
250: $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
251: $ WORK( IB+1 ), LDWORK )
252: END IF
253: 10 CONTINUE
254: ELSE
255: I = 1
256: END IF
257: *
258: * Use unblocked code to factor the last or only block.
259: *
260: IF( I.LE.K )
261: $ CALL ZGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
262: $ IINFO )
263: *
264: WORK( 1 ) = IWS
265: RETURN
266: *
267: * End of ZGELQF
268: *
269: END
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