LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dlatzm.f
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1*> \brief \b DLATZM
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLATZM + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatzm.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatzm.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatzm.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER SIDE
25* INTEGER INCV, LDC, M, N
26* DOUBLE PRECISION TAU
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> This routine is deprecated and has been replaced by routine DORMRZ.
39*>
40*> DLATZM applies a Householder matrix generated by DTZRQF to a matrix.
41*>
42*> Let P = I - tau*u*u**T, u = ( 1 ),
43*> ( v )
44*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
45*> SIDE = 'R'.
46*>
47*> If SIDE equals 'L', let
48*> C = [ C1 ] 1
49*> [ C2 ] m-1
50*> n
51*> Then C is overwritten by P*C.
52*>
53*> If SIDE equals 'R', let
54*> C = [ C1, C2 ] m
55*> 1 n-1
56*> Then C is overwritten by C*P.
57*> \endverbatim
58*
59* Arguments:
60* ==========
61*
62*> \param[in] SIDE
63*> \verbatim
64*> SIDE is CHARACTER*1
65*> = 'L': form P * C
66*> = 'R': form C * P
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*> M is INTEGER
72*> The number of rows of the matrix C.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The number of columns of the matrix C.
79*> \endverbatim
80*>
81*> \param[in] V
82*> \verbatim
83*> V is DOUBLE PRECISION array, dimension
84*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
85*> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
86*> The vector v in the representation of P. V is not used
87*> if TAU = 0.
88*> \endverbatim
89*>
90*> \param[in] INCV
91*> \verbatim
92*> INCV is INTEGER
93*> The increment between elements of v. INCV <> 0
94*> \endverbatim
95*>
96*> \param[in] TAU
97*> \verbatim
98*> TAU is DOUBLE PRECISION
99*> The value tau in the representation of P.
100*> \endverbatim
101*>
102*> \param[in,out] C1
103*> \verbatim
104*> C1 is DOUBLE PRECISION array, dimension
105*> (LDC,N) if SIDE = 'L'
106*> (M,1) if SIDE = 'R'
107*> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
108*> if SIDE = 'R'.
109*>
110*> On exit, the first row of P*C if SIDE = 'L', or the first
111*> column of C*P if SIDE = 'R'.
112*> \endverbatim
113*>
114*> \param[in,out] C2
115*> \verbatim
116*> C2 is DOUBLE PRECISION array, dimension
117*> (LDC, N) if SIDE = 'L'
118*> (LDC, N-1) if SIDE = 'R'
119*> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
120*> m x (n - 1) matrix C2 if SIDE = 'R'.
121*>
122*> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
123*> if SIDE = 'R'.
124*> \endverbatim
125*>
126*> \param[in] LDC
127*> \verbatim
128*> LDC is INTEGER
129*> The leading dimension of the arrays C1 and C2. LDC >= (1,M).
130*> \endverbatim
131*>
132*> \param[out] WORK
133*> \verbatim
134*> WORK is DOUBLE PRECISION array, dimension
135*> (N) if SIDE = 'L'
136*> (M) if SIDE = 'R'
137*> \endverbatim
138*
139* Authors:
140* ========
141*
142*> \author Univ. of Tennessee
143*> \author Univ. of California Berkeley
144*> \author Univ. of Colorado Denver
145*> \author NAG Ltd.
146*
147*> \ingroup doubleOTHERcomputational
148*
149* =====================================================================
150 SUBROUTINE dlatzm( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
151*
152* -- LAPACK computational routine --
153* -- LAPACK is a software package provided by Univ. of Tennessee, --
154* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155*
156* .. Scalar Arguments ..
157 CHARACTER SIDE
158 INTEGER INCV, LDC, M, N
159 DOUBLE PRECISION TAU
160* ..
161* .. Array Arguments ..
162 DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
163* ..
164*
165* =====================================================================
166*
167* .. Parameters ..
168 DOUBLE PRECISION ONE, ZERO
169 parameter( one = 1.0d+0, zero = 0.0d+0 )
170* ..
171* .. External Subroutines ..
172 EXTERNAL daxpy, dcopy, dgemv, dger
173* ..
174* .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL lsame
177* ..
178* .. Intrinsic Functions ..
179 INTRINSIC min
180* ..
181* .. Executable Statements ..
182*
183 IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
184 $ RETURN
185*
186 IF( lsame( side, 'L' ) ) THEN
187*
188* w := (C1 + v**T * C2)**T
189*
190 CALL dcopy( n, c1, ldc, work, 1 )
191 CALL dgemv( 'Transpose', m-1, n, one, c2, ldc, v, incv, one,
192 $ work, 1 )
193*
194* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
195* [ C2 ] [ C2 ] [ v ]
196*
197 CALL daxpy( n, -tau, work, 1, c1, ldc )
198 CALL dger( m-1, n, -tau, v, incv, work, 1, c2, ldc )
199*
200 ELSE IF( lsame( side, 'R' ) ) THEN
201*
202* w := C1 + C2 * v
203*
204 CALL dcopy( m, c1, 1, work, 1 )
205 CALL dgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
206 $ work, 1 )
207*
208* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
209*
210 CALL daxpy( m, -tau, work, 1, c1, 1 )
211 CALL dger( m, n-1, -tau, work, 1, v, incv, c2, ldc )
212 END IF
213*
214 RETURN
215*
216* End of DLATZM
217*
218 END
subroutine dlatzm(side, m, n, v, incv, tau, c1, c2, ldc, work)
DLATZM
Definition dlatzm.f:151
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