Merged in f5soh/librepilot/update_credits (pull request #529)
[librepilot.git] / ground / gcs / src / libs / eigen / lapack / slarft.f
blob30b0668e4f7e59fd3fb5015a21fe9529c9666a98
1 *> \brief \b SLARFT
3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
8 *> \htmlonly
9 *> Download SLARFT + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarft.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarft.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarft.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
18 * Definition:
19 * ===========
21 * SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
23 * .. Scalar Arguments ..
24 * CHARACTER DIRECT, STOREV
25 * INTEGER K, LDT, LDV, N
26 * ..
27 * .. Array Arguments ..
28 * REAL T( LDT, * ), TAU( * ), V( LDV, * )
29 * ..
32 *> \par Purpose:
33 * =============
35 *> \verbatim
37 *> SLARFT 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.
40 *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
42 *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
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
47 *> H = I - V * T * V**T
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
52 *> H = I - V**T * T * V
53 *> \endverbatim
55 * Arguments:
56 * ==========
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
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
76 *> \param[in] N
77 *> \verbatim
78 *> N is INTEGER
79 *> The order of the block reflector H. N >= 0.
80 *> \endverbatim
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
89 *> \param[in] V
90 *> \verbatim
91 *> V is REAL array, dimension
92 *> (LDV,K) if STOREV = 'C'
93 *> (LDV,N) if STOREV = 'R'
94 *> The matrix V. See further details.
95 *> \endverbatim
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
104 *> \param[in] TAU
105 *> \verbatim
106 *> TAU is REAL array, dimension (K)
107 *> TAU(i) must contain the scalar factor of the elementary
108 *> reflector H(i).
109 *> \endverbatim
111 *> \param[out] T
112 *> \verbatim
113 *> T is REAL 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
119 *> \param[in] LDT
120 *> \verbatim
121 *> LDT is INTEGER
122 *> The leading dimension of the array T. LDT >= K.
123 *> \endverbatim
125 * Authors:
126 * ========
128 *> \author Univ. of Tennessee
129 *> \author Univ. of California Berkeley
130 *> \author Univ. of Colorado Denver
131 *> \author NAG Ltd.
133 *> \date April 2012
135 *> \ingroup realOTHERauxiliary
137 *> \par Further Details:
138 * =====================
140 *> \verbatim
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.
146 *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
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 )
154 *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
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
163 * =====================================================================
164 SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
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
171 * .. Scalar Arguments ..
172 CHARACTER DIRECT, STOREV
173 INTEGER K, LDT, LDV, N
174 * ..
175 * .. Array Arguments ..
176 REAL T( LDT, * ), TAU( * ), V( LDV, * )
177 * ..
179 * =====================================================================
181 * .. Parameters ..
182 REAL ONE, ZERO
183 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
184 * ..
185 * .. Local Scalars ..
186 INTEGER I, J, PREVLASTV, LASTV
187 * ..
188 * .. External Subroutines ..
189 EXTERNAL SGEMV, STRMV
190 * ..
191 * .. External Functions ..
192 LOGICAL LSAME
193 EXTERNAL LSAME
194 * ..
195 * .. Executable Statements ..
197 * Quick return if possible
199 IF( N.EQ.0 )
200 $ RETURN
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
208 * H(i) = I
210 DO J = 1, I
211 T( J, I ) = ZERO
212 END DO
213 ELSE
215 * general case
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 )
227 * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
229 CALL SGEMV( '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 )
242 * T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
244 CALL SGEMV( 'No transpose', I-1, J-I, -TAU( I ),
245 $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV,
246 $ ONE, T( 1, I ), 1 )
247 END IF
249 * T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
251 CALL STRMV( '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
266 * H(i) = I
268 DO J = I, K
269 T( J, I ) = ZERO
270 END DO
271 ELSE
273 * general case
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 )
286 * T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
288 CALL SGEMV( '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 )
301 * T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
303 CALL SGEMV( '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
308 * T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
310 CALL STRMV( '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
324 * End of SLARFT