LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
clatzm.f
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1 *> \brief \b CLATZM
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER SIDE
25 * INTEGER INCV, LDC, M, N
26 * COMPLEX TAU
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX 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 This routine is deprecated and has been replaced by routine CUNMRZ.
39 *>
40 *> CLATZM applies a Householder matrix generated by CTZRQF to a matrix.
41 *>
42 *> Let P = I - tau*u*u**H, 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 COMPLEX 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 COMPLEX
99 *> The value tau in the representation of P.
100 *> \endverbatim
101 *>
102 *> \param[in,out] C1
103 *> \verbatim
104 *> C1 is COMPLEX 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 COMPLEX 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.
130 *> LDC >= max(1,M).
131 *> \endverbatim
132 *>
133 *> \param[out] WORK
134 *> \verbatim
135 *> WORK is COMPLEX array, dimension
136 *> (N) if SIDE = 'L'
137 *> (M) if SIDE = 'R'
138 *> \endverbatim
139 *
140 * Authors:
141 * ========
142 *
143 *> \author Univ. of Tennessee
144 *> \author Univ. of California Berkeley
145 *> \author Univ. of Colorado Denver
146 *> \author NAG Ltd.
147 *
148 *> \date December 2016
149 *
150 *> \ingroup complexOTHERcomputational
151 *
152 * =====================================================================
153  SUBROUTINE clatzm( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
154 *
155 * -- LAPACK computational routine (version 3.7.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * December 2016
159 *
160 * .. Scalar Arguments ..
161  CHARACTER SIDE
162  INTEGER INCV, LDC, M, N
163  COMPLEX TAU
164 * ..
165 * .. Array Arguments ..
166  COMPLEX C1( ldc, * ), C2( ldc, * ), V( * ), WORK( * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  COMPLEX ONE, ZERO
173  parameter( one = ( 1.0e+0, 0.0e+0 ),
174  $ zero = ( 0.0e+0, 0.0e+0 ) )
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL caxpy, ccopy, cgemv, cgerc, cgeru, clacgv
178 * ..
179 * .. External Functions ..
180  LOGICAL LSAME
181  EXTERNAL lsame
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC min
185 * ..
186 * .. Executable Statements ..
187 *
188  IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
189  $ RETURN
190 *
191  IF( lsame( side, 'L' ) ) THEN
192 *
193 * w := ( C1 + v**H * C2 )**H
194 *
195  CALL ccopy( n, c1, ldc, work, 1 )
196  CALL clacgv( n, work, 1 )
197  CALL cgemv( 'Conjugate transpose', m-1, n, one, c2, ldc, v,
198  $ incv, one, work, 1 )
199 *
200 * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
201 * [ C2 ] [ C2 ] [ v ]
202 *
203  CALL clacgv( n, work, 1 )
204  CALL caxpy( n, -tau, work, 1, c1, ldc )
205  CALL cgeru( m-1, n, -tau, v, incv, work, 1, c2, ldc )
206 *
207  ELSE IF( lsame( side, 'R' ) ) THEN
208 *
209 * w := C1 + C2 * v
210 *
211  CALL ccopy( m, c1, 1, work, 1 )
212  CALL cgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
213  $ work, 1 )
214 *
215 * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
216 *
217  CALL caxpy( m, -tau, work, 1, c1, 1 )
218  CALL cgerc( m, n-1, -tau, work, 1, v, incv, c2, ldc )
219  END IF
220 *
221  RETURN
222 *
223 * End of CLATZM
224 *
225  END
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:160
subroutine cgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERU
Definition: cgeru.f:132
subroutine clatzm(SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK)
CLATZM
Definition: clatzm.f:154
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:76
subroutine cgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERC
Definition: cgerc.f:132