1: SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
2: $ LDV, T, LDT, C, LDC, WORK, LDWORK )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
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: COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
15: $ WORK( LDWORK, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLARZB applies a complex block reflector H or its transpose H**H
22: * to a complex 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' from the Left
31: * = 'R': apply H or H' from the Right
32: *
33: * TRANS (input) CHARACTER*1
34: * = 'N': apply H (No transpose)
35: * = 'C': apply H' (Conjugate 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (LDC,N)
79: * On entry, the M-by-N matrix C.
80: * On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
81: *
82: * LDC (input) INTEGER
83: * The leading dimension of the array C. LDC >= max(1,M).
84: *
85: * WORK (workspace) COMPLEX*16 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: COMPLEX*16 ONE
102: PARAMETER ( ONE = ( 1.0D+0, 0.0D+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 XERBLA, ZCOPY, ZGEMM, ZLACGV, ZTRMM
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( 'ZLARZB', -INFO )
132: RETURN
133: END IF
134: *
135: IF( LSAME( TRANS, 'N' ) ) THEN
136: TRANST = 'C'
137: ELSE
138: TRANST = 'N'
139: END IF
140: *
141: IF( LSAME( SIDE, 'L' ) ) THEN
142: *
143: * Form H * C or H' * C
144: *
145: * W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
146: *
147: DO 10 J = 1, K
148: CALL ZCOPY( 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: * conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
153: *
154: IF( L.GT.0 )
155: $ CALL ZGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
156: $ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
157: $ LDWORK )
158: *
159: * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T' or W( 1:m, 1:k ) * T
160: *
161: CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
162: $ LDT, WORK, LDWORK )
163: *
164: * C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
165: *
166: DO 30 J = 1, N
167: DO 20 I = 1, K
168: C( I, J ) = C( I, J ) - WORK( J, I )
169: 20 CONTINUE
170: 30 CONTINUE
171: *
172: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
173: * conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
174: *
175: IF( L.GT.0 )
176: $ CALL ZGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
177: $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
178: *
179: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
180: *
181: * Form C * H or C * H'
182: *
183: * W( 1:m, 1:k ) = C( 1:m, 1:k )
184: *
185: DO 40 J = 1, K
186: CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
187: 40 CONTINUE
188: *
189: * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
190: * C( 1:m, n-l+1:n ) * conjg( V( 1:k, 1:l )' )
191: *
192: IF( L.GT.0 )
193: $ CALL ZGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
194: $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
195: *
196: * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
197: * W( 1:m, 1:k ) * conjg( T' )
198: *
199: DO 50 J = 1, K
200: CALL ZLACGV( K-J+1, T( J, J ), 1 )
201: 50 CONTINUE
202: CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
203: $ LDT, WORK, LDWORK )
204: DO 60 J = 1, K
205: CALL ZLACGV( K-J+1, T( J, J ), 1 )
206: 60 CONTINUE
207: *
208: * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
209: *
210: DO 80 J = 1, K
211: DO 70 I = 1, M
212: C( I, J ) = C( I, J ) - WORK( I, J )
213: 70 CONTINUE
214: 80 CONTINUE
215: *
216: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
217: * W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
218: *
219: DO 90 J = 1, L
220: CALL ZLACGV( K, V( 1, J ), 1 )
221: 90 CONTINUE
222: IF( L.GT.0 )
223: $ CALL ZGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
224: $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
225: DO 100 J = 1, L
226: CALL ZLACGV( K, V( 1, J ), 1 )
227: 100 CONTINUE
228: *
229: END IF
230: *
231: RETURN
232: *
233: * End of ZLARZB
234: *
235: END
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