Annotation of rpl/lapack/lapack/zlarf.f, revision 1.19
1.12 bertrand 1: *> \brief \b ZLARF applies an elementary reflector to a general rectangular 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 ZLARF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarf.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER SIDE
25: * INTEGER INCV, 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: *> ZLARF applies a complex elementary reflector H to a complex M-by-N
39: *> matrix C, from either the left or the right. H is represented in the
40: *> 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, supply conjg(tau) instead
49: *> tau.
50: *> \endverbatim
51: *
52: * Arguments:
53: * ==========
54: *
55: *> \param[in] SIDE
56: *> \verbatim
57: *> SIDE is CHARACTER*1
58: *> = 'L': form H * C
59: *> = 'R': form C * H
60: *> \endverbatim
61: *>
62: *> \param[in] M
63: *> \verbatim
64: *> M is INTEGER
65: *> The number of rows of the matrix C.
66: *> \endverbatim
67: *>
68: *> \param[in] N
69: *> \verbatim
70: *> N is INTEGER
71: *> The number of columns of the matrix C.
72: *> \endverbatim
73: *>
74: *> \param[in] V
75: *> \verbatim
76: *> V is COMPLEX*16 array, dimension
77: *> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
78: *> or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
79: *> The vector v in the representation of H. V is not used if
80: *> TAU = 0.
81: *> \endverbatim
82: *>
83: *> \param[in] INCV
84: *> \verbatim
85: *> INCV is INTEGER
86: *> The increment between elements of v. INCV <> 0.
87: *> \endverbatim
88: *>
89: *> \param[in] TAU
90: *> \verbatim
91: *> TAU is COMPLEX*16
92: *> The value tau in the representation of H.
93: *> \endverbatim
94: *>
95: *> \param[in,out] C
96: *> \verbatim
97: *> C is COMPLEX*16 array, dimension (LDC,N)
98: *> On entry, the M-by-N matrix C.
99: *> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
100: *> or C * H if SIDE = 'R'.
101: *> \endverbatim
102: *>
103: *> \param[in] LDC
104: *> \verbatim
105: *> LDC is INTEGER
106: *> The leading dimension of the array C. LDC >= max(1,M).
107: *> \endverbatim
108: *>
109: *> \param[out] WORK
110: *> \verbatim
111: *> WORK is COMPLEX*16 array, dimension
112: *> (N) if SIDE = 'L'
113: *> or (M) if SIDE = 'R'
114: *> \endverbatim
115: *
116: * Authors:
117: * ========
118: *
1.16 bertrand 119: *> \author Univ. of Tennessee
120: *> \author Univ. of California Berkeley
121: *> \author Univ. of Colorado Denver
122: *> \author NAG Ltd.
1.9 bertrand 123: *
124: *> \ingroup complex16OTHERauxiliary
125: *
126: * =====================================================================
1.1 bertrand 127: SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
128: *
1.19 ! bertrand 129: * -- LAPACK auxiliary routine --
1.1 bertrand 130: * -- LAPACK is a software package provided by Univ. of Tennessee, --
131: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132: *
133: * .. Scalar Arguments ..
134: CHARACTER SIDE
135: INTEGER INCV, LDC, M, N
136: COMPLEX*16 TAU
137: * ..
138: * .. Array Arguments ..
139: COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Parameters ..
145: COMPLEX*16 ONE, ZERO
146: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
147: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL APPLYLEFT
151: INTEGER I, LASTV, LASTC
152: * ..
153: * .. External Subroutines ..
154: EXTERNAL ZGEMV, ZGERC
155: * ..
156: * .. External Functions ..
157: LOGICAL LSAME
158: INTEGER ILAZLR, ILAZLC
159: EXTERNAL LSAME, ILAZLR, ILAZLC
160: * ..
161: * .. Executable Statements ..
162: *
163: APPLYLEFT = LSAME( SIDE, 'L' )
164: LASTV = 0
165: LASTC = 0
166: IF( TAU.NE.ZERO ) THEN
1.9 bertrand 167: * Set up variables for scanning V. LASTV begins pointing to the end
168: * of V.
1.1 bertrand 169: IF( APPLYLEFT ) THEN
170: LASTV = M
171: ELSE
172: LASTV = N
173: END IF
174: IF( INCV.GT.0 ) THEN
175: I = 1 + (LASTV-1) * INCV
176: ELSE
177: I = 1
178: END IF
1.9 bertrand 179: * Look for the last non-zero row in V.
1.1 bertrand 180: DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
181: LASTV = LASTV - 1
182: I = I - INCV
183: END DO
184: IF( APPLYLEFT ) THEN
1.9 bertrand 185: * Scan for the last non-zero column in C(1:lastv,:).
1.1 bertrand 186: LASTC = ILAZLC(LASTV, N, C, LDC)
187: ELSE
1.9 bertrand 188: * Scan for the last non-zero row in C(:,1:lastv).
1.1 bertrand 189: LASTC = ILAZLR(M, LASTV, C, LDC)
190: END IF
191: END IF
1.9 bertrand 192: * Note that lastc.eq.0 renders the BLAS operations null; no special
193: * case is needed at this level.
1.1 bertrand 194: IF( APPLYLEFT ) THEN
195: *
196: * Form H * C
197: *
198: IF( LASTV.GT.0 ) THEN
199: *
1.8 bertrand 200: * w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
1.1 bertrand 201: *
202: CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
203: $ C, LDC, V, INCV, ZERO, WORK, 1 )
204: *
1.8 bertrand 205: * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
1.1 bertrand 206: *
207: CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
208: END IF
209: ELSE
210: *
211: * Form C * H
212: *
213: IF( LASTV.GT.0 ) THEN
214: *
215: * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
216: *
217: CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
218: $ V, INCV, ZERO, WORK, 1 )
219: *
1.8 bertrand 220: * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
1.1 bertrand 221: *
222: CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
223: END IF
224: END IF
225: RETURN
226: *
227: * End of ZLARF
228: *
229: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlarf.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack