1 SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
2 $ WORK, LWORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
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 * DORMLQ 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 DGELQF. 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
58 * (LDA,M) if SIDE = 'L',
59 * (LDA,N) if SIDE = 'R'
60 * The i-th row must contain the vector which defines the
61 * elementary reflector H(i), for i = 1,2,...,k, as returned by
62 * DGELQF in the first k rows of its array argument A.
63 * A is modified by the routine but restored on exit.
64 *
65 * LDA (input) INTEGER
66 * The leading dimension of the array A. LDA >= max(1,K).
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 DGELQF.
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 CHARACTER TRANST
108 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
109 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
110 * ..
111 * .. Local Arrays ..
112 DOUBLE PRECISION T( LDT, NBMAX )
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 INTEGER ILAENV
117 EXTERNAL LSAME, ILAENV
118 * ..
119 * .. External Subroutines ..
120 EXTERNAL DLARFB, DLARFT, DORML2, XERBLA
121 * ..
122 * .. Intrinsic Functions ..
123 INTRINSIC MAX, MIN
124 * ..
125 * .. Executable Statements ..
126 *
127 * Test the input arguments
128 *
129 INFO = 0
130 LEFT = LSAME( SIDE, 'L' )
131 NOTRAN = LSAME( TRANS, 'N' )
132 LQUERY = ( LWORK.EQ.-1 )
133 *
134 * NQ is the order of Q and NW is the minimum dimension of WORK
135 *
136 IF( LEFT ) THEN
137 NQ = M
138 NW = N
139 ELSE
140 NQ = N
141 NW = M
142 END IF
143 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
144 INFO = -1
145 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
146 INFO = -2
147 ELSE IF( M.LT.0 ) THEN
148 INFO = -3
149 ELSE IF( N.LT.0 ) THEN
150 INFO = -4
151 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
152 INFO = -5
153 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
154 INFO = -7
155 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
156 INFO = -10
157 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
158 INFO = -12
159 END IF
160 *
161 IF( INFO.EQ.0 ) THEN
162 *
163 * Determine the block size. NB may be at most NBMAX, where NBMAX
164 * is used to define the local array T.
165 *
166 NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K,
167 $ -1 ) )
168 LWKOPT = MAX( 1, NW )*NB
169 WORK( 1 ) = LWKOPT
170 END IF
171 *
172 IF( INFO.NE.0 ) THEN
173 CALL XERBLA( 'DORMLQ', -INFO )
174 RETURN
175 ELSE IF( LQUERY ) THEN
176 RETURN
177 END IF
178 *
179 * Quick return if possible
180 *
181 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
182 WORK( 1 ) = 1
183 RETURN
184 END IF
185 *
186 NBMIN = 2
187 LDWORK = NW
188 IF( NB.GT.1 .AND. NB.LT.K ) THEN
189 IWS = NW*NB
190 IF( LWORK.LT.IWS ) THEN
191 NB = LWORK / LDWORK
192 NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K,
193 $ -1 ) )
194 END IF
195 ELSE
196 IWS = NW
197 END IF
198 *
199 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
200 *
201 * Use unblocked code
202 *
203 CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
204 $ IINFO )
205 ELSE
206 *
207 * Use blocked code
208 *
209 IF( ( LEFT .AND. NOTRAN ) .OR.
210 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
211 I1 = 1
212 I2 = K
213 I3 = NB
214 ELSE
215 I1 = ( ( K-1 ) / NB )*NB + 1
216 I2 = 1
217 I3 = -NB
218 END IF
219 *
220 IF( LEFT ) THEN
221 NI = N
222 JC = 1
223 ELSE
224 MI = M
225 IC = 1
226 END IF
227 *
228 IF( NOTRAN ) THEN
229 TRANST = 'T'
230 ELSE
231 TRANST = 'N'
232 END IF
233 *
234 DO 10 I = I1, I2, I3
235 IB = MIN( NB, K-I+1 )
236 *
237 * Form the triangular factor of the block reflector
238 * H = H(i) H(i+1) . . . H(i+ib-1)
239 *
240 CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
241 $ LDA, TAU( I ), T, LDT )
242 IF( LEFT ) THEN
243 *
244 * H or H**T is applied to C(i:m,1:n)
245 *
246 MI = M - I + 1
247 IC = I
248 ELSE
249 *
250 * H or H**T is applied to C(1:m,i:n)
251 *
252 NI = N - I + 1
253 JC = I
254 END IF
255 *
256 * Apply H or H**T
257 *
258 CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
259 $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
260 $ LDWORK )
261 10 CONTINUE
262 END IF
263 WORK( 1 ) = LWKOPT
264 RETURN
265 *
266 * End of DORMLQ
267 *
268 END
2 $ WORK, LWORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
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 * DORMLQ 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 DGELQF. 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
58 * (LDA,M) if SIDE = 'L',
59 * (LDA,N) if SIDE = 'R'
60 * The i-th row must contain the vector which defines the
61 * elementary reflector H(i), for i = 1,2,...,k, as returned by
62 * DGELQF in the first k rows of its array argument A.
63 * A is modified by the routine but restored on exit.
64 *
65 * LDA (input) INTEGER
66 * The leading dimension of the array A. LDA >= max(1,K).
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 DGELQF.
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 CHARACTER TRANST
108 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
109 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
110 * ..
111 * .. Local Arrays ..
112 DOUBLE PRECISION T( LDT, NBMAX )
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 INTEGER ILAENV
117 EXTERNAL LSAME, ILAENV
118 * ..
119 * .. External Subroutines ..
120 EXTERNAL DLARFB, DLARFT, DORML2, XERBLA
121 * ..
122 * .. Intrinsic Functions ..
123 INTRINSIC MAX, MIN
124 * ..
125 * .. Executable Statements ..
126 *
127 * Test the input arguments
128 *
129 INFO = 0
130 LEFT = LSAME( SIDE, 'L' )
131 NOTRAN = LSAME( TRANS, 'N' )
132 LQUERY = ( LWORK.EQ.-1 )
133 *
134 * NQ is the order of Q and NW is the minimum dimension of WORK
135 *
136 IF( LEFT ) THEN
137 NQ = M
138 NW = N
139 ELSE
140 NQ = N
141 NW = M
142 END IF
143 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
144 INFO = -1
145 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
146 INFO = -2
147 ELSE IF( M.LT.0 ) THEN
148 INFO = -3
149 ELSE IF( N.LT.0 ) THEN
150 INFO = -4
151 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
152 INFO = -5
153 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
154 INFO = -7
155 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
156 INFO = -10
157 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
158 INFO = -12
159 END IF
160 *
161 IF( INFO.EQ.0 ) THEN
162 *
163 * Determine the block size. NB may be at most NBMAX, where NBMAX
164 * is used to define the local array T.
165 *
166 NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K,
167 $ -1 ) )
168 LWKOPT = MAX( 1, NW )*NB
169 WORK( 1 ) = LWKOPT
170 END IF
171 *
172 IF( INFO.NE.0 ) THEN
173 CALL XERBLA( 'DORMLQ', -INFO )
174 RETURN
175 ELSE IF( LQUERY ) THEN
176 RETURN
177 END IF
178 *
179 * Quick return if possible
180 *
181 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
182 WORK( 1 ) = 1
183 RETURN
184 END IF
185 *
186 NBMIN = 2
187 LDWORK = NW
188 IF( NB.GT.1 .AND. NB.LT.K ) THEN
189 IWS = NW*NB
190 IF( LWORK.LT.IWS ) THEN
191 NB = LWORK / LDWORK
192 NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K,
193 $ -1 ) )
194 END IF
195 ELSE
196 IWS = NW
197 END IF
198 *
199 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
200 *
201 * Use unblocked code
202 *
203 CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
204 $ IINFO )
205 ELSE
206 *
207 * Use blocked code
208 *
209 IF( ( LEFT .AND. NOTRAN ) .OR.
210 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
211 I1 = 1
212 I2 = K
213 I3 = NB
214 ELSE
215 I1 = ( ( K-1 ) / NB )*NB + 1
216 I2 = 1
217 I3 = -NB
218 END IF
219 *
220 IF( LEFT ) THEN
221 NI = N
222 JC = 1
223 ELSE
224 MI = M
225 IC = 1
226 END IF
227 *
228 IF( NOTRAN ) THEN
229 TRANST = 'T'
230 ELSE
231 TRANST = 'N'
232 END IF
233 *
234 DO 10 I = I1, I2, I3
235 IB = MIN( NB, K-I+1 )
236 *
237 * Form the triangular factor of the block reflector
238 * H = H(i) H(i+1) . . . H(i+ib-1)
239 *
240 CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
241 $ LDA, TAU( I ), T, LDT )
242 IF( LEFT ) THEN
243 *
244 * H or H**T is applied to C(i:m,1:n)
245 *
246 MI = M - I + 1
247 IC = I
248 ELSE
249 *
250 * H or H**T is applied to C(1:m,i:n)
251 *
252 NI = N - I + 1
253 JC = I
254 END IF
255 *
256 * Apply H or H**T
257 *
258 CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
259 $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
260 $ LDWORK )
261 10 CONTINUE
262 END IF
263 WORK( 1 ) = LWKOPT
264 RETURN
265 *
266 * End of DORMLQ
267 *
268 END