LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dlarz.f
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1*> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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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*> \ingroup larz
131*
132*> \par Contributors:
133* ==================
134*>
135*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
136*
137*> \par Further Details:
138* =====================
139*>
140*> \verbatim
141*> \endverbatim
142*>
143* =====================================================================
144 SUBROUTINE dlarz( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
145*
146* -- LAPACK computational routine --
147* -- LAPACK is a software package provided by Univ. of Tennessee, --
148* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149*
150* .. Scalar Arguments ..
151 CHARACTER SIDE
152 INTEGER INCV, L, LDC, M, N
153 DOUBLE PRECISION TAU
154* ..
155* .. Array Arguments ..
156 DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
157* ..
158*
159* =====================================================================
160*
161* .. Parameters ..
162 DOUBLE PRECISION ONE, ZERO
163 parameter( one = 1.0d+0, zero = 0.0d+0 )
164* ..
165* .. External Subroutines ..
166 EXTERNAL daxpy, dcopy, dgemv, dger
167* ..
168* .. External Functions ..
169 LOGICAL LSAME
170 EXTERNAL lsame
171* ..
172* .. Executable Statements ..
173*
174 IF( lsame( side, 'L' ) ) THEN
175*
176* Form H * C
177*
178 IF( tau.NE.zero ) THEN
179*
180* w( 1:n ) = C( 1, 1:n )
181*
182 CALL dcopy( n, c, ldc, work, 1 )
183*
184* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
185*
186 CALL dgemv( 'Transpose', l, n, one, c( m-l+1, 1 ), ldc, v,
187 \$ incv, one, work, 1 )
188*
189* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
190*
191 CALL daxpy( n, -tau, work, 1, c, ldc )
192*
193* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
194* tau * v( 1:l ) * w( 1:n )**T
195*
196 CALL dger( l, n, -tau, v, incv, work, 1, c( m-l+1, 1 ),
197 \$ ldc )
198 END IF
199*
200 ELSE
201*
202* Form C * H
203*
204 IF( tau.NE.zero ) THEN
205*
206* w( 1:m ) = C( 1:m, 1 )
207*
208 CALL dcopy( m, c, 1, work, 1 )
209*
210* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
211*
212 CALL dgemv( 'No transpose', m, l, one, c( 1, n-l+1 ), ldc,
213 \$ v, incv, one, work, 1 )
214*
215* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
216*
217 CALL daxpy( m, -tau, work, 1, c, 1 )
218*
219* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
220* tau * w( 1:m ) * v( 1:l )**T
221*
222 CALL dger( m, l, -tau, work, 1, v, incv, c( 1, n-l+1 ),
223 \$ ldc )
224*
225 END IF
226*
227 END IF
228*
229 RETURN
230*
231* End of DLARZ
232*
233 END
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
subroutine dgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
DGEMV
Definition dgemv.f:158
subroutine dger(m, n, alpha, x, incx, y, incy, a, lda)
DGER
Definition dger.f:130
subroutine dlarz(side, m, n, l, v, incv, tau, c, ldc, work)
DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition dlarz.f:145