Annotation of rpl/lapack/lapack/zlarf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZLARF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
! 22: *
! 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: * ..
! 31: *
! 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: *
! 119: *> \author Univ. of Tennessee
! 120: *> \author Univ. of California Berkeley
! 121: *> \author Univ. of Colorado Denver
! 122: *> \author NAG Ltd.
! 123: *
! 124: *> \date November 2011
! 125: *
! 126: *> \ingroup complex16OTHERauxiliary
! 127: *
! 128: * =====================================================================
1.1 bertrand 129: SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
130: *
1.9 ! bertrand 131: * -- LAPACK auxiliary routine (version 3.4.0) --
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..--
1.9 ! bertrand 134: * November 2011
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
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