Annotation of rpl/lapack/lapack/dormql.f, revision 1.11
1.9 bertrand 1: *> \brief \b DORMQL
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORMQL + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormql.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22: * WORK, LWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER SIDE, TRANS
26: * INTEGER INFO, K, LDA, LDC, LWORK, M, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DORMQL overwrites the general real M-by-N matrix C with
39: *>
40: *> SIDE = 'L' SIDE = 'R'
41: *> TRANS = 'N': Q * C C * Q
42: *> TRANS = 'T': Q**T * C C * Q**T
43: *>
44: *> where Q is a real orthogonal matrix defined as the product of k
45: *> elementary reflectors
46: *>
47: *> Q = H(k) . . . H(2) H(1)
48: *>
49: *> as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N
50: *> if SIDE = 'R'.
51: *> \endverbatim
52: *
53: * Arguments:
54: * ==========
55: *
56: *> \param[in] SIDE
57: *> \verbatim
58: *> SIDE is CHARACTER*1
59: *> = 'L': apply Q or Q**T from the Left;
60: *> = 'R': apply Q or Q**T from the Right.
61: *> \endverbatim
62: *>
63: *> \param[in] TRANS
64: *> \verbatim
65: *> TRANS is CHARACTER*1
66: *> = 'N': No transpose, apply Q;
67: *> = 'T': Transpose, apply Q**T.
68: *> \endverbatim
69: *>
70: *> \param[in] M
71: *> \verbatim
72: *> M is INTEGER
73: *> The number of rows of the matrix C. M >= 0.
74: *> \endverbatim
75: *>
76: *> \param[in] N
77: *> \verbatim
78: *> N is INTEGER
79: *> The number of columns of the matrix C. N >= 0.
80: *> \endverbatim
81: *>
82: *> \param[in] K
83: *> \verbatim
84: *> K is INTEGER
85: *> The number of elementary reflectors whose product defines
86: *> the matrix Q.
87: *> If SIDE = 'L', M >= K >= 0;
88: *> if SIDE = 'R', N >= K >= 0.
89: *> \endverbatim
90: *>
91: *> \param[in] A
92: *> \verbatim
93: *> A is DOUBLE PRECISION array, dimension (LDA,K)
94: *> The i-th column must contain the vector which defines the
95: *> elementary reflector H(i), for i = 1,2,...,k, as returned by
96: *> DGEQLF in the last k columns of its array argument A.
97: *> \endverbatim
98: *>
99: *> \param[in] LDA
100: *> \verbatim
101: *> LDA is INTEGER
102: *> The leading dimension of the array A.
103: *> If SIDE = 'L', LDA >= max(1,M);
104: *> if SIDE = 'R', LDA >= max(1,N).
105: *> \endverbatim
106: *>
107: *> \param[in] TAU
108: *> \verbatim
109: *> TAU is DOUBLE PRECISION array, dimension (K)
110: *> TAU(i) must contain the scalar factor of the elementary
111: *> reflector H(i), as returned by DGEQLF.
112: *> \endverbatim
113: *>
114: *> \param[in,out] C
115: *> \verbatim
116: *> C is DOUBLE PRECISION array, dimension (LDC,N)
117: *> On entry, the M-by-N matrix C.
118: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
119: *> \endverbatim
120: *>
121: *> \param[in] LDC
122: *> \verbatim
123: *> LDC is INTEGER
124: *> The leading dimension of the array C. LDC >= max(1,M).
125: *> \endverbatim
126: *>
127: *> \param[out] WORK
128: *> \verbatim
129: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
130: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
131: *> \endverbatim
132: *>
133: *> \param[in] LWORK
134: *> \verbatim
135: *> LWORK is INTEGER
136: *> The dimension of the array WORK.
137: *> If SIDE = 'L', LWORK >= max(1,N);
138: *> if SIDE = 'R', LWORK >= max(1,M).
139: *> For optimum performance LWORK >= N*NB if SIDE = 'L', and
140: *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
141: *> blocksize.
142: *>
143: *> If LWORK = -1, then a workspace query is assumed; the routine
144: *> only calculates the optimal size of the WORK array, returns
145: *> this value as the first entry of the WORK array, and no error
146: *> message related to LWORK is issued by XERBLA.
147: *> \endverbatim
148: *>
149: *> \param[out] INFO
150: *> \verbatim
151: *> INFO is INTEGER
152: *> = 0: successful exit
153: *> < 0: if INFO = -i, the i-th argument had an illegal value
154: *> \endverbatim
155: *
156: * Authors:
157: * ========
158: *
159: *> \author Univ. of Tennessee
160: *> \author Univ. of California Berkeley
161: *> \author Univ. of Colorado Denver
162: *> \author NAG Ltd.
163: *
164: *> \date November 2011
165: *
166: *> \ingroup doubleOTHERcomputational
167: *
168: * =====================================================================
1.1 bertrand 169: SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
170: $ WORK, LWORK, INFO )
171: *
1.9 bertrand 172: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 173: * -- LAPACK is a software package provided by Univ. of Tennessee, --
174: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 175: * November 2011
1.1 bertrand 176: *
177: * .. Scalar Arguments ..
178: CHARACTER SIDE, TRANS
179: INTEGER INFO, K, LDA, LDC, LWORK, M, N
180: * ..
181: * .. Array Arguments ..
182: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
183: * ..
184: *
185: * =====================================================================
186: *
187: * .. Parameters ..
188: INTEGER NBMAX, LDT
189: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
190: * ..
191: * .. Local Scalars ..
192: LOGICAL LEFT, LQUERY, NOTRAN
193: INTEGER I, I1, I2, I3, IB, IINFO, IWS, LDWORK, LWKOPT,
194: $ MI, NB, NBMIN, NI, NQ, NW
195: * ..
196: * .. Local Arrays ..
197: DOUBLE PRECISION T( LDT, NBMAX )
198: * ..
199: * .. External Functions ..
200: LOGICAL LSAME
201: INTEGER ILAENV
202: EXTERNAL LSAME, ILAENV
203: * ..
204: * .. External Subroutines ..
205: EXTERNAL DLARFB, DLARFT, DORM2L, XERBLA
206: * ..
207: * .. Intrinsic Functions ..
208: INTRINSIC MAX, MIN
209: * ..
210: * .. Executable Statements ..
211: *
212: * Test the input arguments
213: *
214: INFO = 0
215: LEFT = LSAME( SIDE, 'L' )
216: NOTRAN = LSAME( TRANS, 'N' )
217: LQUERY = ( LWORK.EQ.-1 )
218: *
219: * NQ is the order of Q and NW is the minimum dimension of WORK
220: *
221: IF( LEFT ) THEN
222: NQ = M
223: NW = MAX( 1, N )
224: ELSE
225: NQ = N
226: NW = MAX( 1, M )
227: END IF
228: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
229: INFO = -1
230: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
231: INFO = -2
232: ELSE IF( M.LT.0 ) THEN
233: INFO = -3
234: ELSE IF( N.LT.0 ) THEN
235: INFO = -4
236: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
237: INFO = -5
238: ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
239: INFO = -7
240: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
241: INFO = -10
242: END IF
243: *
244: IF( INFO.EQ.0 ) THEN
245: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
246: LWKOPT = 1
247: ELSE
248: *
249: * Determine the block size. NB may be at most NBMAX, where
250: * NBMAX is used to define the local array T.
251: *
252: NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N,
253: $ K, -1 ) )
254: LWKOPT = NW*NB
255: END IF
256: WORK( 1 ) = LWKOPT
257: *
258: IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
259: INFO = -12
260: END IF
261: END IF
262: *
263: IF( INFO.NE.0 ) THEN
264: CALL XERBLA( 'DORMQL', -INFO )
265: RETURN
266: ELSE IF( LQUERY ) THEN
267: RETURN
268: END IF
269: *
270: * Quick return if possible
271: *
272: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
273: RETURN
274: END IF
275: *
276: NBMIN = 2
277: LDWORK = NW
278: IF( NB.GT.1 .AND. NB.LT.K ) THEN
279: IWS = NW*NB
280: IF( LWORK.LT.IWS ) THEN
281: NB = LWORK / LDWORK
282: NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K,
283: $ -1 ) )
284: END IF
285: ELSE
286: IWS = NW
287: END IF
288: *
289: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
290: *
291: * Use unblocked code
292: *
293: CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
294: $ IINFO )
295: ELSE
296: *
297: * Use blocked code
298: *
299: IF( ( LEFT .AND. NOTRAN ) .OR.
300: $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
301: I1 = 1
302: I2 = K
303: I3 = NB
304: ELSE
305: I1 = ( ( K-1 ) / NB )*NB + 1
306: I2 = 1
307: I3 = -NB
308: END IF
309: *
310: IF( LEFT ) THEN
311: NI = N
312: ELSE
313: MI = M
314: END IF
315: *
316: DO 10 I = I1, I2, I3
317: IB = MIN( NB, K-I+1 )
318: *
319: * Form the triangular factor of the block reflector
320: * H = H(i+ib-1) . . . H(i+1) H(i)
321: *
322: CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
323: $ A( 1, I ), LDA, TAU( I ), T, LDT )
324: IF( LEFT ) THEN
325: *
1.8 bertrand 326: * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
1.1 bertrand 327: *
328: MI = M - K + I + IB - 1
329: ELSE
330: *
1.8 bertrand 331: * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
1.1 bertrand 332: *
333: NI = N - K + I + IB - 1
334: END IF
335: *
1.8 bertrand 336: * Apply H or H**T
1.1 bertrand 337: *
338: CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
339: $ IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
340: $ LDWORK )
341: 10 CONTINUE
342: END IF
343: WORK( 1 ) = LWKOPT
344: RETURN
345: *
346: * End of DORMQL
347: *
348: END
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