Annotation of rpl/lapack/lapack/zlarz.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZLARZ
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
! 22: *
! 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: * ..
! 31: *
! 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: *
! 127: *> \author Univ. of Tennessee
! 128: *> \author Univ. of California Berkeley
! 129: *> \author Univ. of Colorado Denver
! 130: *> \author NAG Ltd.
! 131: *
! 132: *> \date November 2011
! 133: *
! 134: *> \ingroup complex16OTHERcomputational
! 135: *
! 136: *> \par Contributors:
! 137: * ==================
! 138: *>
! 139: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 140: *
! 141: *> \par Further Details:
! 142: * =====================
! 143: *>
! 144: *> \verbatim
! 145: *> \endverbatim
! 146: *>
! 147: * =====================================================================
1.1 bertrand 148: SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
149: *
1.9 ! bertrand 150: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 151: * -- LAPACK is a software package provided by Univ. of Tennessee, --
152: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 153: * November 2011
1.1 bertrand 154: *
155: * .. Scalar Arguments ..
156: CHARACTER SIDE
157: INTEGER INCV, L, LDC, M, N
158: COMPLEX*16 TAU
159: * ..
160: * .. Array Arguments ..
161: COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
162: * ..
163: *
164: * =====================================================================
165: *
166: * .. Parameters ..
167: COMPLEX*16 ONE, ZERO
168: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
169: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
170: * ..
171: * .. External Subroutines ..
172: EXTERNAL ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
173: * ..
174: * .. External Functions ..
175: LOGICAL LSAME
176: EXTERNAL LSAME
177: * ..
178: * .. Executable Statements ..
179: *
180: IF( LSAME( SIDE, 'L' ) ) THEN
181: *
182: * Form H * C
183: *
184: IF( TAU.NE.ZERO ) THEN
185: *
186: * w( 1:n ) = conjg( C( 1, 1:n ) )
187: *
188: CALL ZCOPY( N, C, LDC, WORK, 1 )
189: CALL ZLACGV( N, WORK, 1 )
190: *
1.8 bertrand 191: * w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
1.1 bertrand 192: *
193: CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
194: $ LDC, V, INCV, ONE, WORK, 1 )
195: CALL ZLACGV( N, WORK, 1 )
196: *
197: * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
198: *
199: CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
200: *
201: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
1.8 bertrand 202: * tau * v( 1:l ) * w( 1:n )**H
1.1 bertrand 203: *
204: CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
205: $ LDC )
206: END IF
207: *
208: ELSE
209: *
210: * Form C * H
211: *
212: IF( TAU.NE.ZERO ) THEN
213: *
214: * w( 1:m ) = C( 1:m, 1 )
215: *
216: CALL ZCOPY( M, C, 1, WORK, 1 )
217: *
218: * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
219: *
220: CALL ZGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
221: $ V, INCV, ONE, WORK, 1 )
222: *
223: * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
224: *
225: CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
226: *
227: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
1.8 bertrand 228: * tau * w( 1:m ) * v( 1:l )**H
1.1 bertrand 229: *
230: CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
231: $ LDC )
232: *
233: END IF
234: *
235: END IF
236: *
237: RETURN
238: *
239: * End of ZLARZ
240: *
241: END
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