Annotation of rpl/lapack/lapack/zlarz.f, revision 1.19
1.12 bertrand 1: *> \brief \b ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download ZLARZ + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarz.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarz.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarz.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER SIDE
25: * INTEGER INCV, L, LDC, M, N
26: * COMPLEX*16 TAU
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
30: * ..
1.16 bertrand 31: *
1.9 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLARZ applies a complex elementary reflector H to a complex
39: *> M-by-N matrix C, from either the left or the right. H is represented
40: *> in the form
41: *>
42: *> H = I - tau * v * v**H
43: *>
44: *> where tau is a complex scalar and v is a complex vector.
45: *>
46: *> If tau = 0, then H is taken to be the unit matrix.
47: *>
48: *> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
49: *> tau.
50: *>
51: *> H is a product of k elementary reflectors as returned by ZTZRZF.
52: *> \endverbatim
53: *
54: * Arguments:
55: * ==========
56: *
57: *> \param[in] SIDE
58: *> \verbatim
59: *> SIDE is CHARACTER*1
60: *> = 'L': form H * C
61: *> = 'R': form C * H
62: *> \endverbatim
63: *>
64: *> \param[in] M
65: *> \verbatim
66: *> M is INTEGER
67: *> The number of rows of the matrix C.
68: *> \endverbatim
69: *>
70: *> \param[in] N
71: *> \verbatim
72: *> N is INTEGER
73: *> The number of columns of the matrix C.
74: *> \endverbatim
75: *>
76: *> \param[in] L
77: *> \verbatim
78: *> L is INTEGER
79: *> The number of entries of the vector V containing
80: *> the meaningful part of the Householder vectors.
81: *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
82: *> \endverbatim
83: *>
84: *> \param[in] V
85: *> \verbatim
86: *> V is COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
87: *> The vector v in the representation of H as returned by
88: *> ZTZRZF. V is not used if TAU = 0.
89: *> \endverbatim
90: *>
91: *> \param[in] INCV
92: *> \verbatim
93: *> INCV is INTEGER
94: *> The increment between elements of v. INCV <> 0.
95: *> \endverbatim
96: *>
97: *> \param[in] TAU
98: *> \verbatim
99: *> TAU is COMPLEX*16
100: *> The value tau in the representation of H.
101: *> \endverbatim
102: *>
103: *> \param[in,out] C
104: *> \verbatim
105: *> C is COMPLEX*16 array, dimension (LDC,N)
106: *> On entry, the M-by-N matrix C.
107: *> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
108: *> or C * H if SIDE = 'R'.
109: *> \endverbatim
110: *>
111: *> \param[in] LDC
112: *> \verbatim
113: *> LDC is INTEGER
114: *> The leading dimension of the array C. LDC >= max(1,M).
115: *> \endverbatim
116: *>
117: *> \param[out] WORK
118: *> \verbatim
119: *> WORK is COMPLEX*16 array, dimension
120: *> (N) if SIDE = 'L'
121: *> or (M) if SIDE = 'R'
122: *> \endverbatim
123: *
124: * Authors:
125: * ========
126: *
1.16 bertrand 127: *> \author Univ. of Tennessee
128: *> \author Univ. of California Berkeley
129: *> \author Univ. of Colorado Denver
130: *> \author NAG Ltd.
1.9 bertrand 131: *
132: *> \ingroup complex16OTHERcomputational
133: *
134: *> \par Contributors:
135: * ==================
136: *>
137: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
138: *
139: *> \par Further Details:
140: * =====================
141: *>
142: *> \verbatim
143: *> \endverbatim
144: *>
145: * =====================================================================
1.1 bertrand 146: SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
147: *
1.19 ! bertrand 148: * -- LAPACK computational routine --
1.1 bertrand 149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: *
152: * .. Scalar Arguments ..
153: CHARACTER SIDE
154: INTEGER INCV, L, LDC, M, N
155: COMPLEX*16 TAU
156: * ..
157: * .. Array Arguments ..
158: COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
159: * ..
160: *
161: * =====================================================================
162: *
163: * .. Parameters ..
164: COMPLEX*16 ONE, ZERO
165: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
166: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
167: * ..
168: * .. External Subroutines ..
169: EXTERNAL ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. Executable Statements ..
176: *
177: IF( LSAME( SIDE, 'L' ) ) THEN
178: *
179: * Form H * C
180: *
181: IF( TAU.NE.ZERO ) THEN
182: *
183: * w( 1:n ) = conjg( C( 1, 1:n ) )
184: *
185: CALL ZCOPY( N, C, LDC, WORK, 1 )
186: CALL ZLACGV( N, WORK, 1 )
187: *
1.8 bertrand 188: * w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
1.1 bertrand 189: *
190: CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
191: $ LDC, V, INCV, ONE, WORK, 1 )
192: CALL ZLACGV( N, WORK, 1 )
193: *
194: * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
195: *
196: CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
197: *
198: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
1.8 bertrand 199: * tau * v( 1:l ) * w( 1:n )**H
1.1 bertrand 200: *
201: CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
202: $ LDC )
203: END IF
204: *
205: ELSE
206: *
207: * Form C * H
208: *
209: IF( TAU.NE.ZERO ) THEN
210: *
211: * w( 1:m ) = C( 1:m, 1 )
212: *
213: CALL ZCOPY( M, C, 1, WORK, 1 )
214: *
215: * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
216: *
217: CALL ZGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
218: $ V, INCV, ONE, WORK, 1 )
219: *
220: * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
221: *
222: CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
223: *
224: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
1.8 bertrand 225: * tau * w( 1:m ) * v( 1:l )**H
1.1 bertrand 226: *
227: CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
228: $ LDC )
229: *
230: END IF
231: *
232: END IF
233: *
234: RETURN
235: *
236: * End of ZLARZ
237: *
238: END
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