Annotation of rpl/lapack/lapack/dlarz.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLARZ
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLARZ + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarz.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarz.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarz.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLARZ( 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: * DOUBLE PRECISION TAU
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DLARZ applies a real elementary reflector H to a real 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**T
! 43: *>
! 44: *> where tau is a real scalar and v is a real vector.
! 45: *>
! 46: *> If tau = 0, then H is taken to be the unit matrix.
! 47: *>
! 48: *>
! 49: *> H is a product of k elementary reflectors as returned by DTZRZF.
! 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] L
! 75: *> \verbatim
! 76: *> L is INTEGER
! 77: *> The number of entries of the vector V containing
! 78: *> the meaningful part of the Householder vectors.
! 79: *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] V
! 83: *> \verbatim
! 84: *> V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
! 85: *> The vector v in the representation of H as returned by
! 86: *> DTZRZF. V is not used if TAU = 0.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] INCV
! 90: *> \verbatim
! 91: *> INCV is INTEGER
! 92: *> The increment between elements of v. INCV <> 0.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] TAU
! 96: *> \verbatim
! 97: *> TAU is DOUBLE PRECISION
! 98: *> The value tau in the representation of H.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in,out] C
! 102: *> \verbatim
! 103: *> C is DOUBLE PRECISION array, dimension (LDC,N)
! 104: *> On entry, the M-by-N matrix C.
! 105: *> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
! 106: *> or C * H if SIDE = 'R'.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] LDC
! 110: *> \verbatim
! 111: *> LDC is INTEGER
! 112: *> The leading dimension of the array C. LDC >= max(1,M).
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[out] WORK
! 116: *> \verbatim
! 117: *> WORK is DOUBLE PRECISION array, dimension
! 118: *> (N) if SIDE = 'L'
! 119: *> or (M) if SIDE = 'R'
! 120: *> \endverbatim
! 121: *
! 122: * Authors:
! 123: * ========
! 124: *
! 125: *> \author Univ. of Tennessee
! 126: *> \author Univ. of California Berkeley
! 127: *> \author Univ. of Colorado Denver
! 128: *> \author NAG Ltd.
! 129: *
! 130: *> \date November 2011
! 131: *
! 132: *> \ingroup doubleOTHERcomputational
! 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 DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
147: *
1.9 ! bertrand 148: * -- LAPACK computational routine (version 3.4.0) --
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..--
1.9 ! bertrand 151: * November 2011
1.1 bertrand 152: *
153: * .. Scalar Arguments ..
154: CHARACTER SIDE
155: INTEGER INCV, L, LDC, M, N
156: DOUBLE PRECISION TAU
157: * ..
158: * .. Array Arguments ..
159: DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
160: * ..
161: *
162: * =====================================================================
163: *
164: * .. Parameters ..
165: DOUBLE PRECISION ONE, ZERO
166: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
167: * ..
168: * .. External Subroutines ..
169: EXTERNAL DAXPY, DCOPY, DGEMV, DGER
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 ) = C( 1, 1:n )
184: *
185: CALL DCOPY( N, C, LDC, WORK, 1 )
186: *
1.8 bertrand 187: * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
1.1 bertrand 188: *
189: CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
190: $ INCV, ONE, WORK, 1 )
191: *
192: * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
193: *
194: CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
195: *
196: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
1.8 bertrand 197: * tau * v( 1:l ) * w( 1:n )**T
1.1 bertrand 198: *
199: CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
200: $ LDC )
201: END IF
202: *
203: ELSE
204: *
205: * Form C * H
206: *
207: IF( TAU.NE.ZERO ) THEN
208: *
209: * w( 1:m ) = C( 1:m, 1 )
210: *
211: CALL DCOPY( M, C, 1, WORK, 1 )
212: *
213: * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
214: *
215: CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
216: $ V, INCV, ONE, WORK, 1 )
217: *
218: * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
219: *
220: CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
221: *
222: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
1.8 bertrand 223: * tau * w( 1:m ) * v( 1:l )**T
1.1 bertrand 224: *
225: CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
226: $ LDC )
227: *
228: END IF
229: *
230: END IF
231: *
232: RETURN
233: *
234: * End of DLARZ
235: *
236: END
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