1 SUBROUTINE DORMQR( 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 * DORMQR 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(1) H(2) . . . H(k)
30 *
31 * as returned by DGEQRF. 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 * DGEQRF in the first 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 DGEQRF.
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, IC, IINFO, IWS, JC, LDWORK,
108 $ LWKOPT, 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, DORM2R, 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 = N
138 ELSE
139 NQ = N
140 NW = 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 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
157 INFO = -12
158 END IF
159 *
160 IF( INFO.EQ.0 ) THEN
161 *
162 * Determine the block size. NB may be at most NBMAX, where NBMAX
163 * is used to define the local array T.
164 *
165 NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K,
166 $ -1 ) )
167 LWKOPT = MAX( 1, NW )*NB
168 WORK( 1 ) = LWKOPT
169 END IF
170 *
171 IF( INFO.NE.0 ) THEN
172 CALL XERBLA( 'DORMQR', -INFO )
173 RETURN
174 ELSE IF( LQUERY ) THEN
175 RETURN
176 END IF
177 *
178 * Quick return if possible
179 *
180 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
181 WORK( 1 ) = 1
182 RETURN
183 END IF
184 *
185 NBMIN = 2
186 LDWORK = NW
187 IF( NB.GT.1 .AND. NB.LT.K ) THEN
188 IWS = NW*NB
189 IF( LWORK.LT.IWS ) THEN
190 NB = LWORK / LDWORK
191 NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K,
192 $ -1 ) )
193 END IF
194 ELSE
195 IWS = NW
196 END IF
197 *
198 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
199 *
200 * Use unblocked code
201 *
202 CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
203 $ IINFO )
204 ELSE
205 *
206 * Use blocked code
207 *
208 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
209 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
210 I1 = 1
211 I2 = K
212 I3 = NB
213 ELSE
214 I1 = ( ( K-1 ) / NB )*NB + 1
215 I2 = 1
216 I3 = -NB
217 END IF
218 *
219 IF( LEFT ) THEN
220 NI = N
221 JC = 1
222 ELSE
223 MI = M
224 IC = 1
225 END IF
226 *
227 DO 10 I = I1, I2, I3
228 IB = MIN( NB, K-I+1 )
229 *
230 * Form the triangular factor of the block reflector
231 * H = H(i) H(i+1) . . . H(i+ib-1)
232 *
233 CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
234 $ LDA, TAU( I ), T, LDT )
235 IF( LEFT ) THEN
236 *
237 * H or H**T is applied to C(i:m,1:n)
238 *
239 MI = M - I + 1
240 IC = I
241 ELSE
242 *
243 * H or H**T is applied to C(1:m,i:n)
244 *
245 NI = N - I + 1
246 JC = I
247 END IF
248 *
249 * Apply H or H**T
250 *
251 CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
252 $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
253 $ WORK, LDWORK )
254 10 CONTINUE
255 END IF
256 WORK( 1 ) = LWKOPT
257 RETURN
258 *
259 * End of DORMQR
260 *
261 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 * DORMQR 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(1) H(2) . . . H(k)
30 *
31 * as returned by DGEQRF. 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 * DGEQRF in the first 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 DGEQRF.
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, IC, IINFO, IWS, JC, LDWORK,
108 $ LWKOPT, 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, DORM2R, 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 = N
138 ELSE
139 NQ = N
140 NW = 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 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
157 INFO = -12
158 END IF
159 *
160 IF( INFO.EQ.0 ) THEN
161 *
162 * Determine the block size. NB may be at most NBMAX, where NBMAX
163 * is used to define the local array T.
164 *
165 NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K,
166 $ -1 ) )
167 LWKOPT = MAX( 1, NW )*NB
168 WORK( 1 ) = LWKOPT
169 END IF
170 *
171 IF( INFO.NE.0 ) THEN
172 CALL XERBLA( 'DORMQR', -INFO )
173 RETURN
174 ELSE IF( LQUERY ) THEN
175 RETURN
176 END IF
177 *
178 * Quick return if possible
179 *
180 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
181 WORK( 1 ) = 1
182 RETURN
183 END IF
184 *
185 NBMIN = 2
186 LDWORK = NW
187 IF( NB.GT.1 .AND. NB.LT.K ) THEN
188 IWS = NW*NB
189 IF( LWORK.LT.IWS ) THEN
190 NB = LWORK / LDWORK
191 NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K,
192 $ -1 ) )
193 END IF
194 ELSE
195 IWS = NW
196 END IF
197 *
198 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
199 *
200 * Use unblocked code
201 *
202 CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
203 $ IINFO )
204 ELSE
205 *
206 * Use blocked code
207 *
208 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
209 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
210 I1 = 1
211 I2 = K
212 I3 = NB
213 ELSE
214 I1 = ( ( K-1 ) / NB )*NB + 1
215 I2 = 1
216 I3 = -NB
217 END IF
218 *
219 IF( LEFT ) THEN
220 NI = N
221 JC = 1
222 ELSE
223 MI = M
224 IC = 1
225 END IF
226 *
227 DO 10 I = I1, I2, I3
228 IB = MIN( NB, K-I+1 )
229 *
230 * Form the triangular factor of the block reflector
231 * H = H(i) H(i+1) . . . H(i+ib-1)
232 *
233 CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
234 $ LDA, TAU( I ), T, LDT )
235 IF( LEFT ) THEN
236 *
237 * H or H**T is applied to C(i:m,1:n)
238 *
239 MI = M - I + 1
240 IC = I
241 ELSE
242 *
243 * H or H**T is applied to C(1:m,i:n)
244 *
245 NI = N - I + 1
246 JC = I
247 END IF
248 *
249 * Apply H or H**T
250 *
251 CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
252 $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
253 $ WORK, LDWORK )
254 10 CONTINUE
255 END IF
256 WORK( 1 ) = LWKOPT
257 RETURN
258 *
259 * End of DORMQR
260 *
261 END