Annotation of rpl/lapack/lapack/zlarf.f, revision 1.16
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: *
1.16 ! bertrand 124: *> \date December 2016
1.9 bertrand 125: *
126: *> \ingroup complex16OTHERauxiliary
127: *
128: * =====================================================================
1.1 bertrand 129: SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
130: *
1.16 ! bertrand 131: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.16 ! bertrand 134: * December 2016
1.1 bertrand 135: *
136: * .. Scalar Arguments ..
137: CHARACTER SIDE
138: INTEGER INCV, LDC, M, N
139: COMPLEX*16 TAU
140: * ..
141: * .. Array Arguments ..
142: COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
143: * ..
144: *
145: * =====================================================================
146: *
147: * .. Parameters ..
148: COMPLEX*16 ONE, ZERO
149: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
150: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL APPLYLEFT
154: INTEGER I, LASTV, LASTC
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL ZGEMV, ZGERC
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: INTEGER ILAZLR, ILAZLC
162: EXTERNAL LSAME, ILAZLR, ILAZLC
163: * ..
164: * .. Executable Statements ..
165: *
166: APPLYLEFT = LSAME( SIDE, 'L' )
167: LASTV = 0
168: LASTC = 0
169: IF( TAU.NE.ZERO ) THEN
1.9 bertrand 170: * Set up variables for scanning V. LASTV begins pointing to the end
171: * of V.
1.1 bertrand 172: IF( APPLYLEFT ) THEN
173: LASTV = M
174: ELSE
175: LASTV = N
176: END IF
177: IF( INCV.GT.0 ) THEN
178: I = 1 + (LASTV-1) * INCV
179: ELSE
180: I = 1
181: END IF
1.9 bertrand 182: * Look for the last non-zero row in V.
1.1 bertrand 183: DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
184: LASTV = LASTV - 1
185: I = I - INCV
186: END DO
187: IF( APPLYLEFT ) THEN
1.9 bertrand 188: * Scan for the last non-zero column in C(1:lastv,:).
1.1 bertrand 189: LASTC = ILAZLC(LASTV, N, C, LDC)
190: ELSE
1.9 bertrand 191: * Scan for the last non-zero row in C(:,1:lastv).
1.1 bertrand 192: LASTC = ILAZLR(M, LASTV, C, LDC)
193: END IF
194: END IF
1.9 bertrand 195: * Note that lastc.eq.0 renders the BLAS operations null; no special
196: * case is needed at this level.
1.1 bertrand 197: IF( APPLYLEFT ) THEN
198: *
199: * Form H * C
200: *
201: IF( LASTV.GT.0 ) THEN
202: *
1.8 bertrand 203: * w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
1.1 bertrand 204: *
205: CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
206: $ C, LDC, V, INCV, ZERO, WORK, 1 )
207: *
1.8 bertrand 208: * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
1.1 bertrand 209: *
210: CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
211: END IF
212: ELSE
213: *
214: * Form C * H
215: *
216: IF( LASTV.GT.0 ) THEN
217: *
218: * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
219: *
220: CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
221: $ V, INCV, ZERO, WORK, 1 )
222: *
1.8 bertrand 223: * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
1.1 bertrand 224: *
225: CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
226: END IF
227: END IF
228: RETURN
229: *
230: * End of ZLARF
231: *
232: 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