1: *> \brief \b DGEMLQ
2: *
3: * Definition:
4: * ===========
5: *
6: * SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T,
7: * $ TSIZE, C, LDC, WORK, LWORK, INFO )
8: *
9: *
10: * .. Scalar Arguments ..
11: * CHARACTER SIDE, TRANS
12: * INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
13: * ..
14: * .. Array Arguments ..
15: * DOUBLE PRECISION A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
16: * ..
17: *
18: *> \par Purpose:
19: * =============
20: *>
21: *> \verbatim
22: *>
23: *> DGEMLQ overwrites the general real M-by-N matrix C with
24: *>
25: *> SIDE = 'L' SIDE = 'R'
26: *> TRANS = 'N': Q * C C * Q
27: *> TRANS = 'T': Q**T * C C * Q**T
28: *> where Q is a real orthogonal matrix defined as the product
29: *> of blocked elementary reflectors computed by short wide LQ
30: *> factorization (DGELQ)
31: *>
32: *> \endverbatim
33: *
34: * Arguments:
35: * ==========
36: *
37: *> \param[in] SIDE
38: *> \verbatim
39: *> SIDE is CHARACTER*1
40: *> = 'L': apply Q or Q**T from the Left;
41: *> = 'R': apply Q or Q**T from the Right.
42: *> \endverbatim
43: *>
44: *> \param[in] TRANS
45: *> \verbatim
46: *> TRANS is CHARACTER*1
47: *> = 'N': No transpose, apply Q;
48: *> = 'T': Transpose, apply Q**T.
49: *> \endverbatim
50: *>
51: *> \param[in] M
52: *> \verbatim
53: *> M is INTEGER
54: *> The number of rows of the matrix A. M >=0.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The number of columns of the matrix C. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] K
64: *> \verbatim
65: *> K is INTEGER
66: *> The number of elementary reflectors whose product defines
67: *> the matrix Q.
68: *> If SIDE = 'L', M >= K >= 0;
69: *> if SIDE = 'R', N >= K >= 0.
70: *>
71: *> \endverbatim
72: *>
73: *> \param[in] A
74: *> \verbatim
75: *> A is DOUBLE PRECISION array, dimension
76: *> (LDA,M) if SIDE = 'L',
77: *> (LDA,N) if SIDE = 'R'
78: *> Part of the data structure to represent Q as returned by DGELQ.
79: *> \endverbatim
80: *>
81: *> \param[in] LDA
82: *> \verbatim
83: *> LDA is INTEGER
84: *> The leading dimension of the array A. LDA >= max(1,K).
85: *> \endverbatim
86: *>
87: *> \param[in] T
88: *> \verbatim
89: *> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
90: *> Part of the data structure to represent Q as returned by DGELQ.
91: *> \endverbatim
92: *>
93: *> \param[in] TSIZE
94: *> \verbatim
95: *> TSIZE is INTEGER
96: *> The dimension of the array T. TSIZE >= 5.
97: *> \endverbatim
98: *>
99: *> \param[in,out] C
100: *> \verbatim
101: *> C is DOUBLE PRECISION array, dimension (LDC,N)
102: *> On entry, the M-by-N matrix C.
103: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
104: *> \endverbatim
105: *>
106: *> \param[in] LDC
107: *> \verbatim
108: *> LDC is INTEGER
109: *> The leading dimension of the array C. LDC >= max(1,M).
110: *> \endverbatim
111: *>
112: *> \param[out] WORK
113: *> \verbatim
114: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
115: *> \endverbatim
116: *>
117: *> \param[in] LWORK
118: *> \verbatim
119: *> LWORK is INTEGER
120: *> The dimension of the array WORK.
121: *> If LWORK = -1, then a workspace query is assumed. The routine
122: *> only calculates the size of the WORK array, returns this
123: *> value as WORK(1), and no error message related to WORK
124: *> is issued by XERBLA.
125: *> \endverbatim
126: *>
127: *> \param[out] INFO
128: *> \verbatim
129: *> INFO is INTEGER
130: *> = 0: successful exit
131: *> < 0: if INFO = -i, the i-th argument had an illegal value
132: *> \endverbatim
133: *
134: * Authors:
135: * ========
136: *
137: *> \author Univ. of Tennessee
138: *> \author Univ. of California Berkeley
139: *> \author Univ. of Colorado Denver
140: *> \author NAG Ltd.
141: *
142: *> \par Further Details
143: * ====================
144: *>
145: *> \verbatim
146: *>
147: *> These details are particular for this LAPACK implementation. Users should not
148: *> take them for granted. These details may change in the future, and are not likely
149: *> true for another LAPACK implementation. These details are relevant if one wants
150: *> to try to understand the code. They are not part of the interface.
151: *>
152: *> In this version,
153: *>
154: *> T(2): row block size (MB)
155: *> T(3): column block size (NB)
156: *> T(6:TSIZE): data structure needed for Q, computed by
157: *> DLASWLQ or DGELQT
158: *>
159: *> Depending on the matrix dimensions M and N, and row and column
160: *> block sizes MB and NB returned by ILAENV, DGELQ will use either
161: *> DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
162: *> the LQ factorization.
163: *> This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
164: *> multiply matrix Q by another matrix.
165: *> Further Details in DLAMSWLQ or DGEMLQT.
166: *> \endverbatim
167: *>
168: * =====================================================================
169: SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
170: $ C, LDC, WORK, LWORK, INFO )
171: *
172: * -- LAPACK computational routine --
173: * -- LAPACK is a software package provided by Univ. of Tennessee, --
174: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175: *
176: * .. Scalar Arguments ..
177: CHARACTER SIDE, TRANS
178: INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
179: * ..
180: * .. Array Arguments ..
181: DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
182: * ..
183: *
184: * =====================================================================
185: *
186: * ..
187: * .. Local Scalars ..
188: LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
189: INTEGER MB, NB, LW, NBLCKS, MN
190: * ..
191: * .. External Functions ..
192: LOGICAL LSAME
193: EXTERNAL LSAME
194: * ..
195: * .. External Subroutines ..
196: EXTERNAL DLAMSWLQ, DGEMLQT, XERBLA
197: * ..
198: * .. Intrinsic Functions ..
199: INTRINSIC INT, MAX, MIN, MOD
200: * ..
201: * .. Executable Statements ..
202: *
203: * Test the input arguments
204: *
205: LQUERY = LWORK.EQ.-1
206: NOTRAN = LSAME( TRANS, 'N' )
207: TRAN = LSAME( TRANS, 'T' )
208: LEFT = LSAME( SIDE, 'L' )
209: RIGHT = LSAME( SIDE, 'R' )
210: *
211: MB = INT( T( 2 ) )
212: NB = INT( T( 3 ) )
213: IF( LEFT ) THEN
214: LW = N * MB
215: MN = M
216: ELSE
217: LW = M * MB
218: MN = N
219: END IF
220: *
221: IF( ( NB.GT.K ) .AND. ( MN.GT.K ) ) THEN
222: IF( MOD( MN - K, NB - K ) .EQ. 0 ) THEN
223: NBLCKS = ( MN - K ) / ( NB - K )
224: ELSE
225: NBLCKS = ( MN - K ) / ( NB - K ) + 1
226: END IF
227: ELSE
228: NBLCKS = 1
229: END IF
230: *
231: INFO = 0
232: IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
233: INFO = -1
234: ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
235: INFO = -2
236: ELSE IF( M.LT.0 ) THEN
237: INFO = -3
238: ELSE IF( N.LT.0 ) THEN
239: INFO = -4
240: ELSE IF( K.LT.0 .OR. K.GT.MN ) THEN
241: INFO = -5
242: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
243: INFO = -7
244: ELSE IF( TSIZE.LT.5 ) THEN
245: INFO = -9
246: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
247: INFO = -11
248: ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN
249: INFO = -13
250: END IF
251: *
252: IF( INFO.EQ.0 ) THEN
253: WORK( 1 ) = LW
254: END IF
255: *
256: IF( INFO.NE.0 ) THEN
257: CALL XERBLA( 'DGEMLQ', -INFO )
258: RETURN
259: ELSE IF( LQUERY ) THEN
260: RETURN
261: END IF
262: *
263: * Quick return if possible
264: *
265: IF( MIN( M, N, K ).EQ.0 ) THEN
266: RETURN
267: END IF
268: *
269: IF( ( LEFT .AND. M.LE.K ) .OR. ( RIGHT .AND. N.LE.K )
270: $ .OR. ( NB.LE.K ) .OR. ( NB.GE.MAX( M, N, K ) ) ) THEN
271: CALL DGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
272: $ T( 6 ), MB, C, LDC, WORK, INFO )
273: ELSE
274: CALL DLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T( 6 ),
275: $ MB, C, LDC, WORK, LWORK, INFO )
276: END IF
277: *
278: WORK( 1 ) = LW
279: *
280: RETURN
281: *
282: * End of DGEMLQ
283: *
284: END
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