1 SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, 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, L, 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 * DORMRZ 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 DTZRZF. 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 * L (input) INTEGER
58 * The number of columns of the matrix A containing
59 * the meaningful part of the Householder reflectors.
60 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
61 *
62 * A (input) DOUBLE PRECISION array, dimension
63 * (LDA,M) if SIDE = 'L',
64 * (LDA,N) if SIDE = 'R'
65 * The i-th row must contain the vector which defines the
66 * elementary reflector H(i), for i = 1,2,...,k, as returned by
67 * DTZRZF in the last k rows of its array argument A.
68 * A is modified by the routine but restored on exit.
69 *
70 * LDA (input) INTEGER
71 * The leading dimension of the array A. LDA >= max(1,K).
72 *
73 * TAU (input) DOUBLE PRECISION array, dimension (K)
74 * TAU(i) must contain the scalar factor of the elementary
75 * reflector H(i), as returned by DTZRZF.
76 *
77 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
78 * On entry, the M-by-N matrix C.
79 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
80 *
81 * LDC (input) INTEGER
82 * The leading dimension of the array C. LDC >= max(1,M).
83 *
84 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
85 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
86 *
87 * LWORK (input) INTEGER
88 * The dimension of the array WORK.
89 * If SIDE = 'L', LWORK >= max(1,N);
90 * if SIDE = 'R', LWORK >= max(1,M).
91 * For optimum performance LWORK >= N*NB if SIDE = 'L', and
92 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
93 * blocksize.
94 *
95 * If LWORK = -1, then a workspace query is assumed; the routine
96 * only calculates the optimal size of the WORK array, returns
97 * this value as the first entry of the WORK array, and no error
98 * message related to LWORK is issued by XERBLA.
99 *
100 * INFO (output) INTEGER
101 * = 0: successful exit
102 * < 0: if INFO = -i, the i-th argument had an illegal value
103 *
104 * Further Details
105 * ===============
106 *
107 * Based on contributions by
108 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113 INTEGER NBMAX, LDT
114 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
115 * ..
116 * .. Local Scalars ..
117 LOGICAL LEFT, LQUERY, NOTRAN
118 CHARACTER TRANST
119 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC,
120 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
121 * ..
122 * .. Local Arrays ..
123 DOUBLE PRECISION T( LDT, NBMAX )
124 * ..
125 * .. External Functions ..
126 LOGICAL LSAME
127 INTEGER ILAENV
128 EXTERNAL LSAME, ILAENV
129 * ..
130 * .. External Subroutines ..
131 EXTERNAL DLARZB, DLARZT, DORMR3, XERBLA
132 * ..
133 * .. Intrinsic Functions ..
134 INTRINSIC MAX, MIN
135 * ..
136 * .. Executable Statements ..
137 *
138 * Test the input arguments
139 *
140 INFO = 0
141 LEFT = LSAME( SIDE, 'L' )
142 NOTRAN = LSAME( TRANS, 'N' )
143 LQUERY = ( LWORK.EQ.-1 )
144 *
145 * NQ is the order of Q and NW is the minimum dimension of WORK
146 *
147 IF( LEFT ) THEN
148 NQ = M
149 NW = MAX( 1, N )
150 ELSE
151 NQ = N
152 NW = MAX( 1, M )
153 END IF
154 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
155 INFO = -1
156 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
157 INFO = -2
158 ELSE IF( M.LT.0 ) THEN
159 INFO = -3
160 ELSE IF( N.LT.0 ) THEN
161 INFO = -4
162 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
163 INFO = -5
164 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
165 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
166 INFO = -6
167 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
168 INFO = -8
169 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
170 INFO = -11
171 END IF
172 *
173 IF( INFO.EQ.0 ) THEN
174 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
175 LWKOPT = 1
176 ELSE
177 *
178 * Determine the block size. NB may be at most NBMAX, where
179 * NBMAX is used to define the local array T.
180 *
181 NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N,
182 $ K, -1 ) )
183 LWKOPT = NW*NB
184 END IF
185 WORK( 1 ) = LWKOPT
186 *
187 IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
188 INFO = -13
189 END IF
190 END IF
191 *
192 IF( INFO.NE.0 ) THEN
193 CALL XERBLA( 'DORMRZ', -INFO )
194 RETURN
195 ELSE IF( LQUERY ) THEN
196 RETURN
197 END IF
198 *
199 * Quick return if possible
200 *
201 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
202 WORK( 1 ) = 1
203 RETURN
204 END IF
205 *
206 NBMIN = 2
207 LDWORK = NW
208 IF( NB.GT.1 .AND. NB.LT.K ) THEN
209 IWS = NW*NB
210 IF( LWORK.LT.IWS ) THEN
211 NB = LWORK / LDWORK
212 NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K,
213 $ -1 ) )
214 END IF
215 ELSE
216 IWS = NW
217 END IF
218 *
219 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
220 *
221 * Use unblocked code
222 *
223 CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
224 $ WORK, IINFO )
225 ELSE
226 *
227 * Use blocked code
228 *
229 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
230 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
231 I1 = 1
232 I2 = K
233 I3 = NB
234 ELSE
235 I1 = ( ( K-1 ) / NB )*NB + 1
236 I2 = 1
237 I3 = -NB
238 END IF
239 *
240 IF( LEFT ) THEN
241 NI = N
242 JC = 1
243 JA = M - L + 1
244 ELSE
245 MI = M
246 IC = 1
247 JA = N - L + 1
248 END IF
249 *
250 IF( NOTRAN ) THEN
251 TRANST = 'T'
252 ELSE
253 TRANST = 'N'
254 END IF
255 *
256 DO 10 I = I1, I2, I3
257 IB = MIN( NB, K-I+1 )
258 *
259 * Form the triangular factor of the block reflector
260 * H = H(i+ib-1) . . . H(i+1) H(i)
261 *
262 CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
263 $ TAU( I ), T, LDT )
264 *
265 IF( LEFT ) THEN
266 *
267 * H or H**T is applied to C(i:m,1:n)
268 *
269 MI = M - I + 1
270 IC = I
271 ELSE
272 *
273 * H or H**T is applied to C(1:m,i:n)
274 *
275 NI = N - I + 1
276 JC = I
277 END IF
278 *
279 * Apply H or H**T
280 *
281 CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
282 $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
283 $ LDC, WORK, LDWORK )
284 10 CONTINUE
285 *
286 END IF
287 *
288 WORK( 1 ) = LWKOPT
289 *
290 RETURN
291 *
292 * End of DORMRZ
293 *
294 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, L, 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 * DORMRZ 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 DTZRZF. 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 * L (input) INTEGER
58 * The number of columns of the matrix A containing
59 * the meaningful part of the Householder reflectors.
60 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
61 *
62 * A (input) DOUBLE PRECISION array, dimension
63 * (LDA,M) if SIDE = 'L',
64 * (LDA,N) if SIDE = 'R'
65 * The i-th row must contain the vector which defines the
66 * elementary reflector H(i), for i = 1,2,...,k, as returned by
67 * DTZRZF in the last k rows of its array argument A.
68 * A is modified by the routine but restored on exit.
69 *
70 * LDA (input) INTEGER
71 * The leading dimension of the array A. LDA >= max(1,K).
72 *
73 * TAU (input) DOUBLE PRECISION array, dimension (K)
74 * TAU(i) must contain the scalar factor of the elementary
75 * reflector H(i), as returned by DTZRZF.
76 *
77 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
78 * On entry, the M-by-N matrix C.
79 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
80 *
81 * LDC (input) INTEGER
82 * The leading dimension of the array C. LDC >= max(1,M).
83 *
84 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
85 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
86 *
87 * LWORK (input) INTEGER
88 * The dimension of the array WORK.
89 * If SIDE = 'L', LWORK >= max(1,N);
90 * if SIDE = 'R', LWORK >= max(1,M).
91 * For optimum performance LWORK >= N*NB if SIDE = 'L', and
92 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
93 * blocksize.
94 *
95 * If LWORK = -1, then a workspace query is assumed; the routine
96 * only calculates the optimal size of the WORK array, returns
97 * this value as the first entry of the WORK array, and no error
98 * message related to LWORK is issued by XERBLA.
99 *
100 * INFO (output) INTEGER
101 * = 0: successful exit
102 * < 0: if INFO = -i, the i-th argument had an illegal value
103 *
104 * Further Details
105 * ===============
106 *
107 * Based on contributions by
108 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113 INTEGER NBMAX, LDT
114 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
115 * ..
116 * .. Local Scalars ..
117 LOGICAL LEFT, LQUERY, NOTRAN
118 CHARACTER TRANST
119 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC,
120 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
121 * ..
122 * .. Local Arrays ..
123 DOUBLE PRECISION T( LDT, NBMAX )
124 * ..
125 * .. External Functions ..
126 LOGICAL LSAME
127 INTEGER ILAENV
128 EXTERNAL LSAME, ILAENV
129 * ..
130 * .. External Subroutines ..
131 EXTERNAL DLARZB, DLARZT, DORMR3, XERBLA
132 * ..
133 * .. Intrinsic Functions ..
134 INTRINSIC MAX, MIN
135 * ..
136 * .. Executable Statements ..
137 *
138 * Test the input arguments
139 *
140 INFO = 0
141 LEFT = LSAME( SIDE, 'L' )
142 NOTRAN = LSAME( TRANS, 'N' )
143 LQUERY = ( LWORK.EQ.-1 )
144 *
145 * NQ is the order of Q and NW is the minimum dimension of WORK
146 *
147 IF( LEFT ) THEN
148 NQ = M
149 NW = MAX( 1, N )
150 ELSE
151 NQ = N
152 NW = MAX( 1, M )
153 END IF
154 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
155 INFO = -1
156 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
157 INFO = -2
158 ELSE IF( M.LT.0 ) THEN
159 INFO = -3
160 ELSE IF( N.LT.0 ) THEN
161 INFO = -4
162 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
163 INFO = -5
164 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
165 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
166 INFO = -6
167 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
168 INFO = -8
169 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
170 INFO = -11
171 END IF
172 *
173 IF( INFO.EQ.0 ) THEN
174 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
175 LWKOPT = 1
176 ELSE
177 *
178 * Determine the block size. NB may be at most NBMAX, where
179 * NBMAX is used to define the local array T.
180 *
181 NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N,
182 $ K, -1 ) )
183 LWKOPT = NW*NB
184 END IF
185 WORK( 1 ) = LWKOPT
186 *
187 IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
188 INFO = -13
189 END IF
190 END IF
191 *
192 IF( INFO.NE.0 ) THEN
193 CALL XERBLA( 'DORMRZ', -INFO )
194 RETURN
195 ELSE IF( LQUERY ) THEN
196 RETURN
197 END IF
198 *
199 * Quick return if possible
200 *
201 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
202 WORK( 1 ) = 1
203 RETURN
204 END IF
205 *
206 NBMIN = 2
207 LDWORK = NW
208 IF( NB.GT.1 .AND. NB.LT.K ) THEN
209 IWS = NW*NB
210 IF( LWORK.LT.IWS ) THEN
211 NB = LWORK / LDWORK
212 NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K,
213 $ -1 ) )
214 END IF
215 ELSE
216 IWS = NW
217 END IF
218 *
219 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
220 *
221 * Use unblocked code
222 *
223 CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
224 $ WORK, IINFO )
225 ELSE
226 *
227 * Use blocked code
228 *
229 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
230 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
231 I1 = 1
232 I2 = K
233 I3 = NB
234 ELSE
235 I1 = ( ( K-1 ) / NB )*NB + 1
236 I2 = 1
237 I3 = -NB
238 END IF
239 *
240 IF( LEFT ) THEN
241 NI = N
242 JC = 1
243 JA = M - L + 1
244 ELSE
245 MI = M
246 IC = 1
247 JA = N - L + 1
248 END IF
249 *
250 IF( NOTRAN ) THEN
251 TRANST = 'T'
252 ELSE
253 TRANST = 'N'
254 END IF
255 *
256 DO 10 I = I1, I2, I3
257 IB = MIN( NB, K-I+1 )
258 *
259 * Form the triangular factor of the block reflector
260 * H = H(i+ib-1) . . . H(i+1) H(i)
261 *
262 CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
263 $ TAU( I ), T, LDT )
264 *
265 IF( LEFT ) THEN
266 *
267 * H or H**T is applied to C(i:m,1:n)
268 *
269 MI = M - I + 1
270 IC = I
271 ELSE
272 *
273 * H or H**T is applied to C(1:m,i:n)
274 *
275 NI = N - I + 1
276 JC = I
277 END IF
278 *
279 * Apply H or H**T
280 *
281 CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
282 $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
283 $ LDC, WORK, LDWORK )
284 10 CONTINUE
285 *
286 END IF
287 *
288 WORK( 1 ) = LWKOPT
289 *
290 RETURN
291 *
292 * End of DORMRZ
293 *
294 END