1 SUBROUTINE ZUNMRQ( 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 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZUNMRQ overwrites the general complex M-by-N matrix C with
21 *
22 * SIDE = 'L' SIDE = 'R'
23 * TRANS = 'N': Q * C C * Q
24 * TRANS = 'C': Q**H * C C * Q**H
25 *
26 * where Q is a complex unitary matrix defined as the product of k
27 * elementary reflectors
28 *
29 * Q = H(1)**H H(2)**H . . . H(k)**H
30 *
31 * as returned by ZGERQF. 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**H from the Left;
39 * = 'R': apply Q or Q**H from the Right.
40 *
41 * TRANS (input) CHARACTER*1
42 * = 'N': No transpose, apply Q;
43 * = 'C': Transpose, apply Q**H.
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) COMPLEX*16 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 * ZGERQF in the last 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) COMPLEX*16 array, dimension (K)
69 * TAU(i) must contain the scalar factor of the elementary
70 * reflector H(i), as returned by ZGERQF.
71 *
72 * C (input/output) COMPLEX*16 array, dimension (LDC,N)
73 * On entry, the M-by-N matrix C.
74 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H 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) COMPLEX*16 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, IINFO, IWS, LDWORK, LWKOPT,
109 $ MI, NB, NBMIN, NI, NQ, NW
110 * ..
111 * .. Local Arrays ..
112 COMPLEX*16 T( LDT, NBMAX )
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 INTEGER ILAENV
117 EXTERNAL LSAME, ILAENV
118 * ..
119 * .. External Subroutines ..
120 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNMR2
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 = MAX( 1, N )
139 ELSE
140 NQ = N
141 NW = MAX( 1, 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, 'C' ) ) 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 END IF
158 *
159 IF( INFO.EQ.0 ) THEN
160 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
161 LWKOPT = 1
162 ELSE
163 *
164 * Determine the block size. NB may be at most NBMAX, where
165 * NBMAX is used to define the local array T.
166 *
167 NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
168 $ K, -1 ) )
169 LWKOPT = NW*NB
170 END IF
171 WORK( 1 ) = LWKOPT
172 *
173 IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
174 INFO = -12
175 END IF
176 END IF
177 *
178 IF( INFO.NE.0 ) THEN
179 CALL XERBLA( 'ZUNMRQ', -INFO )
180 RETURN
181 ELSE IF( LQUERY ) THEN
182 RETURN
183 END IF
184 *
185 * Quick return if possible
186 *
187 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
188 RETURN
189 END IF
190 *
191 NBMIN = 2
192 LDWORK = NW
193 IF( NB.GT.1 .AND. NB.LT.K ) THEN
194 IWS = NW*NB
195 IF( LWORK.LT.IWS ) THEN
196 NB = LWORK / LDWORK
197 NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
198 $ -1 ) )
199 END IF
200 ELSE
201 IWS = NW
202 END IF
203 *
204 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
205 *
206 * Use unblocked code
207 *
208 CALL ZUNMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
209 $ IINFO )
210 ELSE
211 *
212 * Use blocked code
213 *
214 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
215 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
216 I1 = 1
217 I2 = K
218 I3 = NB
219 ELSE
220 I1 = ( ( K-1 ) / NB )*NB + 1
221 I2 = 1
222 I3 = -NB
223 END IF
224 *
225 IF( LEFT ) THEN
226 NI = N
227 ELSE
228 MI = M
229 END IF
230 *
231 IF( NOTRAN ) THEN
232 TRANST = 'C'
233 ELSE
234 TRANST = 'N'
235 END IF
236 *
237 DO 10 I = I1, I2, I3
238 IB = MIN( NB, K-I+1 )
239 *
240 * Form the triangular factor of the block reflector
241 * H = H(i+ib-1) . . . H(i+1) H(i)
242 *
243 CALL ZLARFT( 'Backward', 'Rowwise', NQ-K+I+IB-1, IB,
244 $ A( I, 1 ), LDA, TAU( I ), T, LDT )
245 IF( LEFT ) THEN
246 *
247 * H or H**H is applied to C(1:m-k+i+ib-1,1:n)
248 *
249 MI = M - K + I + IB - 1
250 ELSE
251 *
252 * H or H**H is applied to C(1:m,1:n-k+i+ib-1)
253 *
254 NI = N - K + I + IB - 1
255 END IF
256 *
257 * Apply H or H**H
258 *
259 CALL ZLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
260 $ IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
261 $ LDWORK )
262 10 CONTINUE
263 END IF
264 WORK( 1 ) = LWKOPT
265 RETURN
266 *
267 * End of ZUNMRQ
268 *
269 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 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZUNMRQ overwrites the general complex M-by-N matrix C with
21 *
22 * SIDE = 'L' SIDE = 'R'
23 * TRANS = 'N': Q * C C * Q
24 * TRANS = 'C': Q**H * C C * Q**H
25 *
26 * where Q is a complex unitary matrix defined as the product of k
27 * elementary reflectors
28 *
29 * Q = H(1)**H H(2)**H . . . H(k)**H
30 *
31 * as returned by ZGERQF. 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**H from the Left;
39 * = 'R': apply Q or Q**H from the Right.
40 *
41 * TRANS (input) CHARACTER*1
42 * = 'N': No transpose, apply Q;
43 * = 'C': Transpose, apply Q**H.
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) COMPLEX*16 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 * ZGERQF in the last 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) COMPLEX*16 array, dimension (K)
69 * TAU(i) must contain the scalar factor of the elementary
70 * reflector H(i), as returned by ZGERQF.
71 *
72 * C (input/output) COMPLEX*16 array, dimension (LDC,N)
73 * On entry, the M-by-N matrix C.
74 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H 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) COMPLEX*16 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, IINFO, IWS, LDWORK, LWKOPT,
109 $ MI, NB, NBMIN, NI, NQ, NW
110 * ..
111 * .. Local Arrays ..
112 COMPLEX*16 T( LDT, NBMAX )
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 INTEGER ILAENV
117 EXTERNAL LSAME, ILAENV
118 * ..
119 * .. External Subroutines ..
120 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNMR2
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 = MAX( 1, N )
139 ELSE
140 NQ = N
141 NW = MAX( 1, 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, 'C' ) ) 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 END IF
158 *
159 IF( INFO.EQ.0 ) THEN
160 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
161 LWKOPT = 1
162 ELSE
163 *
164 * Determine the block size. NB may be at most NBMAX, where
165 * NBMAX is used to define the local array T.
166 *
167 NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
168 $ K, -1 ) )
169 LWKOPT = NW*NB
170 END IF
171 WORK( 1 ) = LWKOPT
172 *
173 IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
174 INFO = -12
175 END IF
176 END IF
177 *
178 IF( INFO.NE.0 ) THEN
179 CALL XERBLA( 'ZUNMRQ', -INFO )
180 RETURN
181 ELSE IF( LQUERY ) THEN
182 RETURN
183 END IF
184 *
185 * Quick return if possible
186 *
187 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
188 RETURN
189 END IF
190 *
191 NBMIN = 2
192 LDWORK = NW
193 IF( NB.GT.1 .AND. NB.LT.K ) THEN
194 IWS = NW*NB
195 IF( LWORK.LT.IWS ) THEN
196 NB = LWORK / LDWORK
197 NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
198 $ -1 ) )
199 END IF
200 ELSE
201 IWS = NW
202 END IF
203 *
204 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
205 *
206 * Use unblocked code
207 *
208 CALL ZUNMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
209 $ IINFO )
210 ELSE
211 *
212 * Use blocked code
213 *
214 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
215 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
216 I1 = 1
217 I2 = K
218 I3 = NB
219 ELSE
220 I1 = ( ( K-1 ) / NB )*NB + 1
221 I2 = 1
222 I3 = -NB
223 END IF
224 *
225 IF( LEFT ) THEN
226 NI = N
227 ELSE
228 MI = M
229 END IF
230 *
231 IF( NOTRAN ) THEN
232 TRANST = 'C'
233 ELSE
234 TRANST = 'N'
235 END IF
236 *
237 DO 10 I = I1, I2, I3
238 IB = MIN( NB, K-I+1 )
239 *
240 * Form the triangular factor of the block reflector
241 * H = H(i+ib-1) . . . H(i+1) H(i)
242 *
243 CALL ZLARFT( 'Backward', 'Rowwise', NQ-K+I+IB-1, IB,
244 $ A( I, 1 ), LDA, TAU( I ), T, LDT )
245 IF( LEFT ) THEN
246 *
247 * H or H**H is applied to C(1:m-k+i+ib-1,1:n)
248 *
249 MI = M - K + I + IB - 1
250 ELSE
251 *
252 * H or H**H is applied to C(1:m,1:n-k+i+ib-1)
253 *
254 NI = N - K + I + IB - 1
255 END IF
256 *
257 * Apply H or H**H
258 *
259 CALL ZLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
260 $ IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
261 $ LDWORK )
262 10 CONTINUE
263 END IF
264 WORK( 1 ) = LWKOPT
265 RETURN
266 *
267 * End of ZUNMRQ
268 *
269 END