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
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 September 2012
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: * =====================================================================
146: SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
147: *
148: * -- LAPACK computational routine (version 3.4.2) --
149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: * September 2012
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: *
187: * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
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 ) - ...
197: * tau * v( 1:l ) * w( 1:n )**T
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 ) - ...
223: * tau * w( 1:m ) * v( 1:l )**T
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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