1: SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
2: $ WORK, LWORK, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER SIDE, TRANS
11: INTEGER INFO, K, LDA, LDC, LWORK, M, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DORMQL overwrites the general real M-by-N matrix C with
21: *
22: * SIDE = 'L' SIDE = 'R'
23: * TRANS = 'N': Q * C C * Q
24: * TRANS = 'T': Q**T * C C * Q**T
25: *
26: * where Q is a real orthogonal matrix defined as the product of k
27: * elementary reflectors
28: *
29: * Q = H(k) . . . H(2) H(1)
30: *
31: * as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N
32: * if SIDE = 'R'.
33: *
34: * Arguments
35: * =========
36: *
37: * SIDE (input) CHARACTER*1
38: * = 'L': apply Q or Q**T from the Left;
39: * = 'R': apply Q or Q**T from the Right.
40: *
41: * TRANS (input) CHARACTER*1
42: * = 'N': No transpose, apply Q;
43: * = 'T': Transpose, apply Q**T.
44: *
45: * M (input) INTEGER
46: * The number of rows of the matrix C. M >= 0.
47: *
48: * N (input) INTEGER
49: * The number of columns of the matrix C. N >= 0.
50: *
51: * K (input) INTEGER
52: * The number of elementary reflectors whose product defines
53: * the matrix Q.
54: * If SIDE = 'L', M >= K >= 0;
55: * if SIDE = 'R', N >= K >= 0.
56: *
57: * A (input) DOUBLE PRECISION array, dimension (LDA,K)
58: * The i-th column must contain the vector which defines the
59: * elementary reflector H(i), for i = 1,2,...,k, as returned by
60: * DGEQLF in the last k columns of its array argument A.
61: * A is modified by the routine but restored on exit.
62: *
63: * LDA (input) INTEGER
64: * The leading dimension of the array A.
65: * If SIDE = 'L', LDA >= max(1,M);
66: * if SIDE = 'R', LDA >= max(1,N).
67: *
68: * TAU (input) DOUBLE PRECISION array, dimension (K)
69: * TAU(i) must contain the scalar factor of the elementary
70: * reflector H(i), as returned by DGEQLF.
71: *
72: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
73: * On entry, the M-by-N matrix C.
74: * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
75: *
76: * LDC (input) INTEGER
77: * The leading dimension of the array C. LDC >= max(1,M).
78: *
79: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
80: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
81: *
82: * LWORK (input) INTEGER
83: * The dimension of the array WORK.
84: * If SIDE = 'L', LWORK >= max(1,N);
85: * if SIDE = 'R', LWORK >= max(1,M).
86: * For optimum performance LWORK >= N*NB if SIDE = 'L', and
87: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
88: * blocksize.
89: *
90: * If LWORK = -1, then a workspace query is assumed; the routine
91: * only calculates the optimal size of the WORK array, returns
92: * this value as the first entry of the WORK array, and no error
93: * message related to LWORK is issued by XERBLA.
94: *
95: * INFO (output) INTEGER
96: * = 0: successful exit
97: * < 0: if INFO = -i, the i-th argument had an illegal value
98: *
99: * =====================================================================
100: *
101: * .. Parameters ..
102: INTEGER NBMAX, LDT
103: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
104: * ..
105: * .. Local Scalars ..
106: LOGICAL LEFT, LQUERY, NOTRAN
107: INTEGER I, I1, I2, I3, IB, IINFO, IWS, LDWORK, LWKOPT,
108: $ MI, NB, NBMIN, NI, NQ, NW
109: * ..
110: * .. Local Arrays ..
111: DOUBLE PRECISION T( LDT, NBMAX )
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: INTEGER ILAENV
116: EXTERNAL LSAME, ILAENV
117: * ..
118: * .. External Subroutines ..
119: EXTERNAL DLARFB, DLARFT, DORM2L, XERBLA
120: * ..
121: * .. Intrinsic Functions ..
122: INTRINSIC MAX, MIN
123: * ..
124: * .. Executable Statements ..
125: *
126: * Test the input arguments
127: *
128: INFO = 0
129: LEFT = LSAME( SIDE, 'L' )
130: NOTRAN = LSAME( TRANS, 'N' )
131: LQUERY = ( LWORK.EQ.-1 )
132: *
133: * NQ is the order of Q and NW is the minimum dimension of WORK
134: *
135: IF( LEFT ) THEN
136: NQ = M
137: NW = MAX( 1, N )
138: ELSE
139: NQ = N
140: NW = MAX( 1, M )
141: END IF
142: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
143: INFO = -1
144: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
145: INFO = -2
146: ELSE IF( M.LT.0 ) THEN
147: INFO = -3
148: ELSE IF( N.LT.0 ) THEN
149: INFO = -4
150: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
151: INFO = -5
152: ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
153: INFO = -7
154: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
155: INFO = -10
156: END IF
157: *
158: IF( INFO.EQ.0 ) THEN
159: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
160: LWKOPT = 1
161: ELSE
162: *
163: * Determine the block size. NB may be at most NBMAX, where
164: * NBMAX is used to define the local array T.
165: *
166: NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N,
167: $ K, -1 ) )
168: LWKOPT = NW*NB
169: END IF
170: WORK( 1 ) = LWKOPT
171: *
172: IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
173: INFO = -12
174: END IF
175: END IF
176: *
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'DORMQL', -INFO )
179: RETURN
180: ELSE IF( LQUERY ) THEN
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
186: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
187: RETURN
188: END IF
189: *
190: NBMIN = 2
191: LDWORK = NW
192: IF( NB.GT.1 .AND. NB.LT.K ) THEN
193: IWS = NW*NB
194: IF( LWORK.LT.IWS ) THEN
195: NB = LWORK / LDWORK
196: NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K,
197: $ -1 ) )
198: END IF
199: ELSE
200: IWS = NW
201: END IF
202: *
203: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
204: *
205: * Use unblocked code
206: *
207: CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
208: $ IINFO )
209: ELSE
210: *
211: * Use blocked code
212: *
213: IF( ( LEFT .AND. NOTRAN ) .OR.
214: $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
215: I1 = 1
216: I2 = K
217: I3 = NB
218: ELSE
219: I1 = ( ( K-1 ) / NB )*NB + 1
220: I2 = 1
221: I3 = -NB
222: END IF
223: *
224: IF( LEFT ) THEN
225: NI = N
226: ELSE
227: MI = M
228: END IF
229: *
230: DO 10 I = I1, I2, I3
231: IB = MIN( NB, K-I+1 )
232: *
233: * Form the triangular factor of the block reflector
234: * H = H(i+ib-1) . . . H(i+1) H(i)
235: *
236: CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
237: $ A( 1, I ), LDA, TAU( I ), T, LDT )
238: IF( LEFT ) THEN
239: *
240: * H or H' is applied to C(1:m-k+i+ib-1,1:n)
241: *
242: MI = M - K + I + IB - 1
243: ELSE
244: *
245: * H or H' is applied to C(1:m,1:n-k+i+ib-1)
246: *
247: NI = N - K + I + IB - 1
248: END IF
249: *
250: * Apply H or H'
251: *
252: CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
253: $ IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
254: $ LDWORK )
255: 10 CONTINUE
256: END IF
257: WORK( 1 ) = LWKOPT
258: RETURN
259: *
260: * End of DORMQL
261: *
262: END
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