Annotation of rpl/lapack/lapack/dlarz.f, revision 1.19
1.12 bertrand 1: *> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 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">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
1.16 bertrand 22: *
1.9 bertrand 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: * ..
1.16 bertrand 31: *
1.9 bertrand 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: *
1.16 bertrand 125: *> \author Univ. of Tennessee
126: *> \author Univ. of California Berkeley
127: *> \author Univ. of Colorado Denver
128: *> \author NAG Ltd.
1.9 bertrand 129: *
130: *> \ingroup doubleOTHERcomputational
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: * =====================================================================
1.1 bertrand 144: SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
145: *
1.19 ! bertrand 146: * -- LAPACK computational routine --
1.1 bertrand 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: *
1.8 bertrand 184: * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
1.1 bertrand 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 ) - ...
1.8 bertrand 194: * tau * v( 1:l ) * w( 1:n )**T
1.1 bertrand 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 ) - ...
1.8 bertrand 220: * tau * w( 1:m ) * v( 1:l )**T
1.1 bertrand 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
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