source: pacpussensors/trunk/Vislab/lib3dv/eigen/lapack/dlarft.f@ 137

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1*> \brief \b DLARFT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLARFT + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarft.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarft.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
22*
23* .. Scalar Arguments ..
24* CHARACTER DIRECT, STOREV
25* INTEGER K, LDT, LDV, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DLARFT forms the triangular factor T of a real block reflector H
38*> of order n, which is defined as a product of k elementary reflectors.
39*>
40*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
41*>
42*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
43*>
44*> If STOREV = 'C', the vector which defines the elementary reflector
45*> H(i) is stored in the i-th column of the array V, and
46*>
47*> H = I - V * T * V**T
48*>
49*> If STOREV = 'R', the vector which defines the elementary reflector
50*> H(i) is stored in the i-th row of the array V, and
51*>
52*> H = I - V**T * T * V
53*> \endverbatim
54*
55* Arguments:
56* ==========
57*
58*> \param[in] DIRECT
59*> \verbatim
60*> DIRECT is CHARACTER*1
61*> Specifies the order in which the elementary reflectors are
62*> multiplied to form the block reflector:
63*> = 'F': H = H(1) H(2) . . . H(k) (Forward)
64*> = 'B': H = H(k) . . . H(2) H(1) (Backward)
65*> \endverbatim
66*>
67*> \param[in] STOREV
68*> \verbatim
69*> STOREV is CHARACTER*1
70*> Specifies how the vectors which define the elementary
71*> reflectors are stored (see also Further Details):
72*> = 'C': columnwise
73*> = 'R': rowwise
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*> N is INTEGER
79*> The order of the block reflector H. N >= 0.
80*> \endverbatim
81*>
82*> \param[in] K
83*> \verbatim
84*> K is INTEGER
85*> The order of the triangular factor T (= the number of
86*> elementary reflectors). K >= 1.
87*> \endverbatim
88*>
89*> \param[in] V
90*> \verbatim
91*> V is DOUBLE PRECISION array, dimension
92*> (LDV,K) if STOREV = 'C'
93*> (LDV,N) if STOREV = 'R'
94*> The matrix V. See further details.
95*> \endverbatim
96*>
97*> \param[in] LDV
98*> \verbatim
99*> LDV is INTEGER
100*> The leading dimension of the array V.
101*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
102*> \endverbatim
103*>
104*> \param[in] TAU
105*> \verbatim
106*> TAU is DOUBLE PRECISION array, dimension (K)
107*> TAU(i) must contain the scalar factor of the elementary
108*> reflector H(i).
109*> \endverbatim
110*>
111*> \param[out] T
112*> \verbatim
113*> T is DOUBLE PRECISION array, dimension (LDT,K)
114*> The k by k triangular factor T of the block reflector.
115*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
116*> lower triangular. The rest of the array is not used.
117*> \endverbatim
118*>
119*> \param[in] LDT
120*> \verbatim
121*> LDT is INTEGER
122*> The leading dimension of the array T. LDT >= K.
123*> \endverbatim
124*
125* Authors:
126* ========
127*
128*> \author Univ. of Tennessee
129*> \author Univ. of California Berkeley
130*> \author Univ. of Colorado Denver
131*> \author NAG Ltd.
132*
133*> \date April 2012
134*
135*> \ingroup doubleOTHERauxiliary
136*
137*> \par Further Details:
138* =====================
139*>
140*> \verbatim
141*>
142*> The shape of the matrix V and the storage of the vectors which define
143*> the H(i) is best illustrated by the following example with n = 5 and
144*> k = 3. The elements equal to 1 are not stored.
145*>
146*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
147*>
148*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
149*> ( v1 1 ) ( 1 v2 v2 v2 )
150*> ( v1 v2 1 ) ( 1 v3 v3 )
151*> ( v1 v2 v3 )
152*> ( v1 v2 v3 )
153*>
154*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
155*>
156*> V = ( v1 v2 v3 ) V = ( v1 v1 1 )
157*> ( v1 v2 v3 ) ( v2 v2 v2 1 )
158*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
159*> ( 1 v3 )
160*> ( 1 )
161*> \endverbatim
162*>
163* =====================================================================
164 SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
165*
166* -- LAPACK auxiliary routine (version 3.4.1) --
167* -- LAPACK is a software package provided by Univ. of Tennessee, --
168* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169* April 2012
170*
171* .. Scalar Arguments ..
172 CHARACTER DIRECT, STOREV
173 INTEGER K, LDT, LDV, N
174* ..
175* .. Array Arguments ..
176 DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
177* ..
178*
179* =====================================================================
180*
181* .. Parameters ..
182 DOUBLE PRECISION ONE, ZERO
183 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
184* ..
185* .. Local Scalars ..
186 INTEGER I, J, PREVLASTV, LASTV
187* ..
188* .. External Subroutines ..
189 EXTERNAL DGEMV, DTRMV
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 EXTERNAL LSAME
194* ..
195* .. Executable Statements ..
196*
197* Quick return if possible
198*
199 IF( N.EQ.0 )
200 $ RETURN
201*
202 IF( LSAME( DIRECT, 'F' ) ) THEN
203 PREVLASTV = N
204 DO I = 1, K
205 PREVLASTV = MAX( I, PREVLASTV )
206 IF( TAU( I ).EQ.ZERO ) THEN
207*
208* H(i) = I
209*
210 DO J = 1, I
211 T( J, I ) = ZERO
212 END DO
213 ELSE
214*
215* general case
216*
217 IF( LSAME( STOREV, 'C' ) ) THEN
218* Skip any trailing zeros.
219 DO LASTV = N, I+1, -1
220 IF( V( LASTV, I ).NE.ZERO ) EXIT
221 END DO
222 DO J = 1, I-1
223 T( J, I ) = -TAU( I ) * V( I , J )
224 END DO
225 J = MIN( LASTV, PREVLASTV )
226*
227* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
228*
229 CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ),
230 $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE,
231 $ T( 1, I ), 1 )
232 ELSE
233* Skip any trailing zeros.
234 DO LASTV = N, I+1, -1
235 IF( V( I, LASTV ).NE.ZERO ) EXIT
236 END DO
237 DO J = 1, I-1
238 T( J, I ) = -TAU( I ) * V( J , I )
239 END DO
240 J = MIN( LASTV, PREVLASTV )
241*
242* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
243*
244 CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ),
245 $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE,
246 $ T( 1, I ), 1 )
247 END IF
248*
249* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
250*
251 CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
252 $ LDT, T( 1, I ), 1 )
253 T( I, I ) = TAU( I )
254 IF( I.GT.1 ) THEN
255 PREVLASTV = MAX( PREVLASTV, LASTV )
256 ELSE
257 PREVLASTV = LASTV
258 END IF
259 END IF
260 END DO
261 ELSE
262 PREVLASTV = 1
263 DO I = K, 1, -1
264 IF( TAU( I ).EQ.ZERO ) THEN
265*
266* H(i) = I
267*
268 DO J = I, K
269 T( J, I ) = ZERO
270 END DO
271 ELSE
272*
273* general case
274*
275 IF( I.LT.K ) THEN
276 IF( LSAME( STOREV, 'C' ) ) THEN
277* Skip any leading zeros.
278 DO LASTV = 1, I-1
279 IF( V( LASTV, I ).NE.ZERO ) EXIT
280 END DO
281 DO J = I+1, K
282 T( J, I ) = -TAU( I ) * V( N-K+I , J )
283 END DO
284 J = MAX( LASTV, PREVLASTV )
285*
286* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
287*
288 CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ),
289 $ V( J, I+1 ), LDV, V( J, I ), 1, ONE,
290 $ T( I+1, I ), 1 )
291 ELSE
292* Skip any leading zeros.
293 DO LASTV = 1, I-1
294 IF( V( I, LASTV ).NE.ZERO ) EXIT
295 END DO
296 DO J = I+1, K
297 T( J, I ) = -TAU( I ) * V( J, N-K+I )
298 END DO
299 J = MAX( LASTV, PREVLASTV )
300*
301* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
302*
303 CALL DGEMV( 'No transpose', K-I, N-K+I-J,
304 $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
305 $ ONE, T( I+1, I ), 1 )
306 END IF
307*
308* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
309*
310 CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
311 $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
312 IF( I.GT.1 ) THEN
313 PREVLASTV = MIN( PREVLASTV, LASTV )
314 ELSE
315 PREVLASTV = LASTV
316 END IF
317 END IF
318 T( I, I ) = TAU( I )
319 END IF
320 END DO
321 END IF
322 RETURN
323*
324* End of DLARFT
325*
326 END
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