1 SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
2 $ LDV, T, LDT, C, LDC, WORK, LDWORK )
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 DIRECT, SIDE, STOREV, TRANS
11 INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DLARZB applies a real block reflector H or its transpose H**T to
22 * a real distributed M-by-N C from the left or the right.
23 *
24 * Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
25 *
26 * Arguments
27 * =========
28 *
29 * SIDE (input) CHARACTER*1
30 * = 'L': apply H or H**T from the Left
31 * = 'R': apply H or H**T from the Right
32 *
33 * TRANS (input) CHARACTER*1
34 * = 'N': apply H (No transpose)
35 * = 'C': apply H**T (Transpose)
36 *
37 * DIRECT (input) CHARACTER*1
38 * Indicates how H is formed from a product of elementary
39 * reflectors
40 * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
41 * = 'B': H = H(k) . . . H(2) H(1) (Backward)
42 *
43 * STOREV (input) CHARACTER*1
44 * Indicates how the vectors which define the elementary
45 * reflectors are stored:
46 * = 'C': Columnwise (not supported yet)
47 * = 'R': Rowwise
48 *
49 * M (input) INTEGER
50 * The number of rows of the matrix C.
51 *
52 * N (input) INTEGER
53 * The number of columns of the matrix C.
54 *
55 * K (input) INTEGER
56 * The order of the matrix T (= the number of elementary
57 * reflectors whose product defines the block reflector).
58 *
59 * L (input) INTEGER
60 * The number of columns of the matrix V containing the
61 * meaningful part of the Householder reflectors.
62 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
63 *
64 * V (input) DOUBLE PRECISION array, dimension (LDV,NV).
65 * If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
66 *
67 * LDV (input) INTEGER
68 * The leading dimension of the array V.
69 * If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
70 *
71 * T (input) DOUBLE PRECISION array, dimension (LDT,K)
72 * The triangular K-by-K matrix T in the representation of the
73 * block reflector.
74 *
75 * LDT (input) INTEGER
76 * The leading dimension of the array T. LDT >= K.
77 *
78 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
79 * On entry, the M-by-N matrix C.
80 * On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
81 *
82 * LDC (input) INTEGER
83 * The leading dimension of the array C. LDC >= max(1,M).
84 *
85 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
86 *
87 * LDWORK (input) INTEGER
88 * The leading dimension of the array WORK.
89 * If SIDE = 'L', LDWORK >= max(1,N);
90 * if SIDE = 'R', LDWORK >= max(1,M).
91 *
92 * Further Details
93 * ===============
94 *
95 * Based on contributions by
96 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
97 *
98 * =====================================================================
99 *
100 * .. Parameters ..
101 DOUBLE PRECISION ONE
102 PARAMETER ( ONE = 1.0D+0 )
103 * ..
104 * .. Local Scalars ..
105 CHARACTER TRANST
106 INTEGER I, INFO, J
107 * ..
108 * .. External Functions ..
109 LOGICAL LSAME
110 EXTERNAL LSAME
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA
114 * ..
115 * .. Executable Statements ..
116 *
117 * Quick return if possible
118 *
119 IF( M.LE.0 .OR. N.LE.0 )
120 $ RETURN
121 *
122 * Check for currently supported options
123 *
124 INFO = 0
125 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
126 INFO = -3
127 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
128 INFO = -4
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'DLARZB', -INFO )
132 RETURN
133 END IF
134 *
135 IF( LSAME( TRANS, 'N' ) ) THEN
136 TRANST = 'T'
137 ELSE
138 TRANST = 'N'
139 END IF
140 *
141 IF( LSAME( SIDE, 'L' ) ) THEN
142 *
143 * Form H * C or H**T * C
144 *
145 * W( 1:n, 1:k ) = C( 1:k, 1:n )**T
146 *
147 DO 10 J = 1, K
148 CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
149 10 CONTINUE
150 *
151 * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
152 * C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
153 *
154 IF( L.GT.0 )
155 $ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
156 $ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
157 *
158 * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
159 *
160 CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
161 $ LDT, WORK, LDWORK )
162 *
163 * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
164 *
165 DO 30 J = 1, N
166 DO 20 I = 1, K
167 C( I, J ) = C( I, J ) - WORK( J, I )
168 20 CONTINUE
169 30 CONTINUE
170 *
171 * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
172 * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
173 *
174 IF( L.GT.0 )
175 $ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
176 $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
177 *
178 ELSE IF( LSAME( SIDE, 'R' ) ) THEN
179 *
180 * Form C * H or C * H**T
181 *
182 * W( 1:m, 1:k ) = C( 1:m, 1:k )
183 *
184 DO 40 J = 1, K
185 CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
186 40 CONTINUE
187 *
188 * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
189 * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
190 *
191 IF( L.GT.0 )
192 $ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
193 $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
194 *
195 * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
196 *
197 CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
198 $ LDT, WORK, LDWORK )
199 *
200 * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
201 *
202 DO 60 J = 1, K
203 DO 50 I = 1, M
204 C( I, J ) = C( I, J ) - WORK( I, J )
205 50 CONTINUE
206 60 CONTINUE
207 *
208 * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
209 * W( 1:m, 1:k ) * V( 1:k, 1:l )
210 *
211 IF( L.GT.0 )
212 $ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
213 $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
214 *
215 END IF
216 *
217 RETURN
218 *
219 * End of DLARZB
220 *
221 END
2 $ LDV, T, LDT, C, LDC, WORK, LDWORK )
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 DIRECT, SIDE, STOREV, TRANS
11 INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DLARZB applies a real block reflector H or its transpose H**T to
22 * a real distributed M-by-N C from the left or the right.
23 *
24 * Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
25 *
26 * Arguments
27 * =========
28 *
29 * SIDE (input) CHARACTER*1
30 * = 'L': apply H or H**T from the Left
31 * = 'R': apply H or H**T from the Right
32 *
33 * TRANS (input) CHARACTER*1
34 * = 'N': apply H (No transpose)
35 * = 'C': apply H**T (Transpose)
36 *
37 * DIRECT (input) CHARACTER*1
38 * Indicates how H is formed from a product of elementary
39 * reflectors
40 * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
41 * = 'B': H = H(k) . . . H(2) H(1) (Backward)
42 *
43 * STOREV (input) CHARACTER*1
44 * Indicates how the vectors which define the elementary
45 * reflectors are stored:
46 * = 'C': Columnwise (not supported yet)
47 * = 'R': Rowwise
48 *
49 * M (input) INTEGER
50 * The number of rows of the matrix C.
51 *
52 * N (input) INTEGER
53 * The number of columns of the matrix C.
54 *
55 * K (input) INTEGER
56 * The order of the matrix T (= the number of elementary
57 * reflectors whose product defines the block reflector).
58 *
59 * L (input) INTEGER
60 * The number of columns of the matrix V containing the
61 * meaningful part of the Householder reflectors.
62 * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
63 *
64 * V (input) DOUBLE PRECISION array, dimension (LDV,NV).
65 * If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
66 *
67 * LDV (input) INTEGER
68 * The leading dimension of the array V.
69 * If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
70 *
71 * T (input) DOUBLE PRECISION array, dimension (LDT,K)
72 * The triangular K-by-K matrix T in the representation of the
73 * block reflector.
74 *
75 * LDT (input) INTEGER
76 * The leading dimension of the array T. LDT >= K.
77 *
78 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
79 * On entry, the M-by-N matrix C.
80 * On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
81 *
82 * LDC (input) INTEGER
83 * The leading dimension of the array C. LDC >= max(1,M).
84 *
85 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
86 *
87 * LDWORK (input) INTEGER
88 * The leading dimension of the array WORK.
89 * If SIDE = 'L', LDWORK >= max(1,N);
90 * if SIDE = 'R', LDWORK >= max(1,M).
91 *
92 * Further Details
93 * ===============
94 *
95 * Based on contributions by
96 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
97 *
98 * =====================================================================
99 *
100 * .. Parameters ..
101 DOUBLE PRECISION ONE
102 PARAMETER ( ONE = 1.0D+0 )
103 * ..
104 * .. Local Scalars ..
105 CHARACTER TRANST
106 INTEGER I, INFO, J
107 * ..
108 * .. External Functions ..
109 LOGICAL LSAME
110 EXTERNAL LSAME
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA
114 * ..
115 * .. Executable Statements ..
116 *
117 * Quick return if possible
118 *
119 IF( M.LE.0 .OR. N.LE.0 )
120 $ RETURN
121 *
122 * Check for currently supported options
123 *
124 INFO = 0
125 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
126 INFO = -3
127 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
128 INFO = -4
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'DLARZB', -INFO )
132 RETURN
133 END IF
134 *
135 IF( LSAME( TRANS, 'N' ) ) THEN
136 TRANST = 'T'
137 ELSE
138 TRANST = 'N'
139 END IF
140 *
141 IF( LSAME( SIDE, 'L' ) ) THEN
142 *
143 * Form H * C or H**T * C
144 *
145 * W( 1:n, 1:k ) = C( 1:k, 1:n )**T
146 *
147 DO 10 J = 1, K
148 CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
149 10 CONTINUE
150 *
151 * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
152 * C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
153 *
154 IF( L.GT.0 )
155 $ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
156 $ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
157 *
158 * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
159 *
160 CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
161 $ LDT, WORK, LDWORK )
162 *
163 * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
164 *
165 DO 30 J = 1, N
166 DO 20 I = 1, K
167 C( I, J ) = C( I, J ) - WORK( J, I )
168 20 CONTINUE
169 30 CONTINUE
170 *
171 * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
172 * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
173 *
174 IF( L.GT.0 )
175 $ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
176 $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
177 *
178 ELSE IF( LSAME( SIDE, 'R' ) ) THEN
179 *
180 * Form C * H or C * H**T
181 *
182 * W( 1:m, 1:k ) = C( 1:m, 1:k )
183 *
184 DO 40 J = 1, K
185 CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
186 40 CONTINUE
187 *
188 * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
189 * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
190 *
191 IF( L.GT.0 )
192 $ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
193 $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
194 *
195 * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
196 *
197 CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
198 $ LDT, WORK, LDWORK )
199 *
200 * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
201 *
202 DO 60 J = 1, K
203 DO 50 I = 1, M
204 C( I, J ) = C( I, J ) - WORK( I, J )
205 50 CONTINUE
206 60 CONTINUE
207 *
208 * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
209 * W( 1:m, 1:k ) * V( 1:k, 1:l )
210 *
211 IF( L.GT.0 )
212 $ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
213 $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
214 *
215 END IF
216 *
217 RETURN
218 *
219 * End of DLARZB
220 *
221 END