1: *> \brief \b DORGLQ
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGLQ + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorglq.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorglq.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorglq.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, K, LDA, LWORK, M, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DORGLQ generates an M-by-N real matrix Q with orthonormal rows,
37: *> which is defined as the first M rows of a product of K elementary
38: *> reflectors of order N
39: *>
40: *> Q = H(k) . . . H(2) H(1)
41: *>
42: *> as returned by DGELQF.
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. N >= M.
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. M >= K >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is DOUBLE PRECISION array, dimension (LDA,N)
70: *> On entry, the i-th row must contain the vector which defines
71: *> the elementary reflector H(i), for i = 1,2,...,k, as returned
72: *> by DGELQF in the first k rows of its array argument A.
73: *> On exit, the M-by-N matrix Q.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The first dimension of the array A. LDA >= max(1,M).
80: *> \endverbatim
81: *>
82: *> \param[in] TAU
83: *> \verbatim
84: *> TAU is DOUBLE PRECISION array, dimension (K)
85: *> TAU(i) must contain the scalar factor of the elementary
86: *> reflector H(i), as returned by DGELQF.
87: *> \endverbatim
88: *>
89: *> \param[out] WORK
90: *> \verbatim
91: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
92: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
93: *> \endverbatim
94: *>
95: *> \param[in] LWORK
96: *> \verbatim
97: *> LWORK is INTEGER
98: *> The dimension of the array WORK. LWORK >= max(1,M).
99: *> For optimum performance LWORK >= M*NB, where NB is
100: *> the optimal blocksize.
101: *>
102: *> If LWORK = -1, then a workspace query is assumed; the routine
103: *> only calculates the optimal size of the WORK array, returns
104: *> this value as the first entry of the WORK array, and no error
105: *> message related to LWORK is issued by XERBLA.
106: *> \endverbatim
107: *>
108: *> \param[out] INFO
109: *> \verbatim
110: *> INFO is INTEGER
111: *> = 0: successful exit
112: *> < 0: if INFO = -i, the i-th argument has an illegal value
113: *> \endverbatim
114: *
115: * Authors:
116: * ========
117: *
118: *> \author Univ. of Tennessee
119: *> \author Univ. of California Berkeley
120: *> \author Univ. of Colorado Denver
121: *> \author NAG Ltd.
122: *
123: *> \ingroup doubleOTHERcomputational
124: *
125: * =====================================================================
126: SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
127: *
128: * -- LAPACK computational routine --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: *
132: * .. Scalar Arguments ..
133: INTEGER INFO, K, LDA, LWORK, M, N
134: * ..
135: * .. Array Arguments ..
136: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ZERO
143: PARAMETER ( ZERO = 0.0D+0 )
144: * ..
145: * .. Local Scalars ..
146: LOGICAL LQUERY
147: INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
148: $ LWKOPT, NB, NBMIN, NX
149: * ..
150: * .. External Subroutines ..
151: EXTERNAL DLARFB, DLARFT, DORGL2, XERBLA
152: * ..
153: * .. Intrinsic Functions ..
154: INTRINSIC MAX, MIN
155: * ..
156: * .. External Functions ..
157: INTEGER ILAENV
158: EXTERNAL ILAENV
159: * ..
160: * .. Executable Statements ..
161: *
162: * Test the input arguments
163: *
164: INFO = 0
165: NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )
166: LWKOPT = MAX( 1, M )*NB
167: WORK( 1 ) = LWKOPT
168: LQUERY = ( LWORK.EQ.-1 )
169: IF( M.LT.0 ) THEN
170: INFO = -1
171: ELSE IF( N.LT.M ) THEN
172: INFO = -2
173: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
174: INFO = -3
175: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
176: INFO = -5
177: ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
178: INFO = -8
179: END IF
180: IF( INFO.NE.0 ) THEN
181: CALL XERBLA( 'DORGLQ', -INFO )
182: RETURN
183: ELSE IF( LQUERY ) THEN
184: RETURN
185: END IF
186: *
187: * Quick return if possible
188: *
189: IF( M.LE.0 ) THEN
190: WORK( 1 ) = 1
191: RETURN
192: END IF
193: *
194: NBMIN = 2
195: NX = 0
196: IWS = M
197: IF( NB.GT.1 .AND. NB.LT.K ) THEN
198: *
199: * Determine when to cross over from blocked to unblocked code.
200: *
201: NX = MAX( 0, ILAENV( 3, 'DORGLQ', ' ', M, N, K, -1 ) )
202: IF( NX.LT.K ) THEN
203: *
204: * Determine if workspace is large enough for blocked code.
205: *
206: LDWORK = M
207: IWS = LDWORK*NB
208: IF( LWORK.LT.IWS ) THEN
209: *
210: * Not enough workspace to use optimal NB: reduce NB and
211: * determine the minimum value of NB.
212: *
213: NB = LWORK / LDWORK
214: NBMIN = MAX( 2, ILAENV( 2, 'DORGLQ', ' ', M, N, K, -1 ) )
215: END IF
216: END IF
217: END IF
218: *
219: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
220: *
221: * Use blocked code after the last block.
222: * The first kk rows are handled by the block method.
223: *
224: KI = ( ( K-NX-1 ) / NB )*NB
225: KK = MIN( K, KI+NB )
226: *
227: * Set A(kk+1:m,1:kk) to zero.
228: *
229: DO 20 J = 1, KK
230: DO 10 I = KK + 1, M
231: A( I, J ) = ZERO
232: 10 CONTINUE
233: 20 CONTINUE
234: ELSE
235: KK = 0
236: END IF
237: *
238: * Use unblocked code for the last or only block.
239: *
240: IF( KK.LT.M )
241: $ CALL DORGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
242: $ TAU( KK+1 ), WORK, IINFO )
243: *
244: IF( KK.GT.0 ) THEN
245: *
246: * Use blocked code
247: *
248: DO 50 I = KI + 1, 1, -NB
249: IB = MIN( NB, K-I+1 )
250: IF( I+IB.LE.M ) THEN
251: *
252: * Form the triangular factor of the block reflector
253: * H = H(i) H(i+1) . . . H(i+ib-1)
254: *
255: CALL DLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
256: $ LDA, TAU( I ), WORK, LDWORK )
257: *
258: * Apply H**T to A(i+ib:m,i:n) from the right
259: *
260: CALL DLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise',
261: $ M-I-IB+1, N-I+1, IB, A( I, I ), LDA, WORK,
262: $ LDWORK, A( I+IB, I ), LDA, WORK( IB+1 ),
263: $ LDWORK )
264: END IF
265: *
266: * Apply H**T to columns i:n of current block
267: *
268: CALL DORGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
269: $ IINFO )
270: *
271: * Set columns 1:i-1 of current block to zero
272: *
273: DO 40 J = 1, I - 1
274: DO 30 L = I, I + IB - 1
275: A( L, J ) = ZERO
276: 30 CONTINUE
277: 40 CONTINUE
278: 50 CONTINUE
279: END IF
280: *
281: WORK( 1 ) = IWS
282: RETURN
283: *
284: * End of DORGLQ
285: *
286: END
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