Statistiques
| Révision :

root / src / lapack / double / dlasr.f @ 1

Historique | Voir | Annoter | Télécharger (12,98 ko)

1 1 equemene
      SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
2 1 equemene
*
3 1 equemene
*  -- LAPACK auxiliary routine (version 3.2) --
4 1 equemene
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
5 1 equemene
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 1 equemene
*     November 2006
7 1 equemene
*
8 1 equemene
*     .. Scalar Arguments ..
9 1 equemene
      CHARACTER          DIRECT, PIVOT, SIDE
10 1 equemene
      INTEGER            LDA, M, N
11 1 equemene
*     ..
12 1 equemene
*     .. Array Arguments ..
13 1 equemene
      DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
14 1 equemene
*     ..
15 1 equemene
*
16 1 equemene
*  Purpose
17 1 equemene
*  =======
18 1 equemene
*
19 1 equemene
*  DLASR applies a sequence of plane rotations to a real matrix A,
20 1 equemene
*  from either the left or the right.
21 1 equemene
*
22 1 equemene
*  When SIDE = 'L', the transformation takes the form
23 1 equemene
*
24 1 equemene
*     A := P*A
25 1 equemene
*
26 1 equemene
*  and when SIDE = 'R', the transformation takes the form
27 1 equemene
*
28 1 equemene
*     A := A*P**T
29 1 equemene
*
30 1 equemene
*  where P is an orthogonal matrix consisting of a sequence of z plane
31 1 equemene
*  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
32 1 equemene
*  and P**T is the transpose of P.
33 1 equemene
*
34 1 equemene
*  When DIRECT = 'F' (Forward sequence), then
35 1 equemene
*
36 1 equemene
*     P = P(z-1) * ... * P(2) * P(1)
37 1 equemene
*
38 1 equemene
*  and when DIRECT = 'B' (Backward sequence), then
39 1 equemene
*
40 1 equemene
*     P = P(1) * P(2) * ... * P(z-1)
41 1 equemene
*
42 1 equemene
*  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
43 1 equemene
*
44 1 equemene
*     R(k) = (  c(k)  s(k) )
45 1 equemene
*          = ( -s(k)  c(k) ).
46 1 equemene
*
47 1 equemene
*  When PIVOT = 'V' (Variable pivot), the rotation is performed
48 1 equemene
*  for the plane (k,k+1), i.e., P(k) has the form
49 1 equemene
*
50 1 equemene
*     P(k) = (  1                                            )
51 1 equemene
*            (       ...                                     )
52 1 equemene
*            (              1                                )
53 1 equemene
*            (                   c(k)  s(k)                  )
54 1 equemene
*            (                  -s(k)  c(k)                  )
55 1 equemene
*            (                                1              )
56 1 equemene
*            (                                     ...       )
57 1 equemene
*            (                                            1  )
58 1 equemene
*
59 1 equemene
*  where R(k) appears as a rank-2 modification to the identity matrix in
60 1 equemene
*  rows and columns k and k+1.
61 1 equemene
*
62 1 equemene
*  When PIVOT = 'T' (Top pivot), the rotation is performed for the
63 1 equemene
*  plane (1,k+1), so P(k) has the form
64 1 equemene
*
65 1 equemene
*     P(k) = (  c(k)                    s(k)                 )
66 1 equemene
*            (         1                                     )
67 1 equemene
*            (              ...                              )
68 1 equemene
*            (                     1                         )
69 1 equemene
*            ( -s(k)                    c(k)                 )
70 1 equemene
*            (                                 1             )
71 1 equemene
*            (                                      ...      )
72 1 equemene
*            (                                             1 )
73 1 equemene
*
74 1 equemene
*  where R(k) appears in rows and columns 1 and k+1.
75 1 equemene
*
76 1 equemene
*  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
77 1 equemene
*  performed for the plane (k,z), giving P(k) the form
78 1 equemene
*
79 1 equemene
*     P(k) = ( 1                                             )
80 1 equemene
*            (      ...                                      )
81 1 equemene
*            (             1                                 )
82 1 equemene
*            (                  c(k)                    s(k) )
83 1 equemene
*            (                         1                     )
84 1 equemene
*            (                              ...              )
85 1 equemene
*            (                                     1         )
86 1 equemene
*            (                 -s(k)                    c(k) )
87 1 equemene
*
88 1 equemene
*  where R(k) appears in rows and columns k and z.  The rotations are
89 1 equemene
*  performed without ever forming P(k) explicitly.
90 1 equemene
*
91 1 equemene
*  Arguments
92 1 equemene
*  =========
93 1 equemene
*
94 1 equemene
*  SIDE    (input) CHARACTER*1
95 1 equemene
*          Specifies whether the plane rotation matrix P is applied to
96 1 equemene
*          A on the left or the right.
97 1 equemene
*          = 'L':  Left, compute A := P*A
98 1 equemene
*          = 'R':  Right, compute A:= A*P**T
99 1 equemene
*
100 1 equemene
*  PIVOT   (input) CHARACTER*1
101 1 equemene
*          Specifies the plane for which P(k) is a plane rotation
102 1 equemene
*          matrix.
103 1 equemene
*          = 'V':  Variable pivot, the plane (k,k+1)
104 1 equemene
*          = 'T':  Top pivot, the plane (1,k+1)
105 1 equemene
*          = 'B':  Bottom pivot, the plane (k,z)
106 1 equemene
*
107 1 equemene
*  DIRECT  (input) CHARACTER*1
108 1 equemene
*          Specifies whether P is a forward or backward sequence of
109 1 equemene
*          plane rotations.
110 1 equemene
*          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
111 1 equemene
*          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
112 1 equemene
*
113 1 equemene
*  M       (input) INTEGER
114 1 equemene
*          The number of rows of the matrix A.  If m <= 1, an immediate
115 1 equemene
*          return is effected.
116 1 equemene
*
117 1 equemene
*  N       (input) INTEGER
118 1 equemene
*          The number of columns of the matrix A.  If n <= 1, an
119 1 equemene
*          immediate return is effected.
120 1 equemene
*
121 1 equemene
*  C       (input) DOUBLE PRECISION array, dimension
122 1 equemene
*                  (M-1) if SIDE = 'L'
123 1 equemene
*                  (N-1) if SIDE = 'R'
124 1 equemene
*          The cosines c(k) of the plane rotations.
125 1 equemene
*
126 1 equemene
*  S       (input) DOUBLE PRECISION array, dimension
127 1 equemene
*                  (M-1) if SIDE = 'L'
128 1 equemene
*                  (N-1) if SIDE = 'R'
129 1 equemene
*          The sines s(k) of the plane rotations.  The 2-by-2 plane
130 1 equemene
*          rotation part of the matrix P(k), R(k), has the form
131 1 equemene
*          R(k) = (  c(k)  s(k) )
132 1 equemene
*                 ( -s(k)  c(k) ).
133 1 equemene
*
134 1 equemene
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
135 1 equemene
*          The M-by-N matrix A.  On exit, A is overwritten by P*A if
136 1 equemene
*          SIDE = 'R' or by A*P**T if SIDE = 'L'.
137 1 equemene
*
138 1 equemene
*  LDA     (input) INTEGER
139 1 equemene
*          The leading dimension of the array A.  LDA >= max(1,M).
140 1 equemene
*
141 1 equemene
*  =====================================================================
142 1 equemene
*
143 1 equemene
*     .. Parameters ..
144 1 equemene
      DOUBLE PRECISION   ONE, ZERO
145 1 equemene
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
146 1 equemene
*     ..
147 1 equemene
*     .. Local Scalars ..
148 1 equemene
      INTEGER            I, INFO, J
149 1 equemene
      DOUBLE PRECISION   CTEMP, STEMP, TEMP
150 1 equemene
*     ..
151 1 equemene
*     .. External Functions ..
152 1 equemene
      LOGICAL            LSAME
153 1 equemene
      EXTERNAL           LSAME
154 1 equemene
*     ..
155 1 equemene
*     .. External Subroutines ..
156 1 equemene
      EXTERNAL           XERBLA
157 1 equemene
*     ..
158 1 equemene
*     .. Intrinsic Functions ..
159 1 equemene
      INTRINSIC          MAX
160 1 equemene
*     ..
161 1 equemene
*     .. Executable Statements ..
162 1 equemene
*
163 1 equemene
*     Test the input parameters
164 1 equemene
*
165 1 equemene
      INFO = 0
166 1 equemene
      IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
167 1 equemene
         INFO = 1
168 1 equemene
      ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
169 1 equemene
     $         'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
170 1 equemene
         INFO = 2
171 1 equemene
      ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
172 1 equemene
     $          THEN
173 1 equemene
         INFO = 3
174 1 equemene
      ELSE IF( M.LT.0 ) THEN
175 1 equemene
         INFO = 4
176 1 equemene
      ELSE IF( N.LT.0 ) THEN
177 1 equemene
         INFO = 5
178 1 equemene
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
179 1 equemene
         INFO = 9
180 1 equemene
      END IF
181 1 equemene
      IF( INFO.NE.0 ) THEN
182 1 equemene
         CALL XERBLA( 'DLASR ', INFO )
183 1 equemene
         RETURN
184 1 equemene
      END IF
185 1 equemene
*
186 1 equemene
*     Quick return if possible
187 1 equemene
*
188 1 equemene
      IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
189 1 equemene
     $   RETURN
190 1 equemene
      IF( LSAME( SIDE, 'L' ) ) THEN
191 1 equemene
*
192 1 equemene
*        Form  P * A
193 1 equemene
*
194 1 equemene
         IF( LSAME( PIVOT, 'V' ) ) THEN
195 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
196 1 equemene
               DO 20 J = 1, M - 1
197 1 equemene
                  CTEMP = C( J )
198 1 equemene
                  STEMP = S( J )
199 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
200 1 equemene
                     DO 10 I = 1, N
201 1 equemene
                        TEMP = A( J+1, I )
202 1 equemene
                        A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
203 1 equemene
                        A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
204 1 equemene
   10                CONTINUE
205 1 equemene
                  END IF
206 1 equemene
   20          CONTINUE
207 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
208 1 equemene
               DO 40 J = M - 1, 1, -1
209 1 equemene
                  CTEMP = C( J )
210 1 equemene
                  STEMP = S( J )
211 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
212 1 equemene
                     DO 30 I = 1, N
213 1 equemene
                        TEMP = A( J+1, I )
214 1 equemene
                        A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
215 1 equemene
                        A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
216 1 equemene
   30                CONTINUE
217 1 equemene
                  END IF
218 1 equemene
   40          CONTINUE
219 1 equemene
            END IF
220 1 equemene
         ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
221 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
222 1 equemene
               DO 60 J = 2, M
223 1 equemene
                  CTEMP = C( J-1 )
224 1 equemene
                  STEMP = S( J-1 )
225 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
226 1 equemene
                     DO 50 I = 1, N
227 1 equemene
                        TEMP = A( J, I )
228 1 equemene
                        A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
229 1 equemene
                        A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
230 1 equemene
   50                CONTINUE
231 1 equemene
                  END IF
232 1 equemene
   60          CONTINUE
233 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
234 1 equemene
               DO 80 J = M, 2, -1
235 1 equemene
                  CTEMP = C( J-1 )
236 1 equemene
                  STEMP = S( J-1 )
237 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
238 1 equemene
                     DO 70 I = 1, N
239 1 equemene
                        TEMP = A( J, I )
240 1 equemene
                        A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
241 1 equemene
                        A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
242 1 equemene
   70                CONTINUE
243 1 equemene
                  END IF
244 1 equemene
   80          CONTINUE
245 1 equemene
            END IF
246 1 equemene
         ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
247 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
248 1 equemene
               DO 100 J = 1, M - 1
249 1 equemene
                  CTEMP = C( J )
250 1 equemene
                  STEMP = S( J )
251 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
252 1 equemene
                     DO 90 I = 1, N
253 1 equemene
                        TEMP = A( J, I )
254 1 equemene
                        A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
255 1 equemene
                        A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
256 1 equemene
   90                CONTINUE
257 1 equemene
                  END IF
258 1 equemene
  100          CONTINUE
259 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
260 1 equemene
               DO 120 J = M - 1, 1, -1
261 1 equemene
                  CTEMP = C( J )
262 1 equemene
                  STEMP = S( J )
263 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
264 1 equemene
                     DO 110 I = 1, N
265 1 equemene
                        TEMP = A( J, I )
266 1 equemene
                        A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
267 1 equemene
                        A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
268 1 equemene
  110                CONTINUE
269 1 equemene
                  END IF
270 1 equemene
  120          CONTINUE
271 1 equemene
            END IF
272 1 equemene
         END IF
273 1 equemene
      ELSE IF( LSAME( SIDE, 'R' ) ) THEN
274 1 equemene
*
275 1 equemene
*        Form A * P'
276 1 equemene
*
277 1 equemene
         IF( LSAME( PIVOT, 'V' ) ) THEN
278 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
279 1 equemene
               DO 140 J = 1, N - 1
280 1 equemene
                  CTEMP = C( J )
281 1 equemene
                  STEMP = S( J )
282 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
283 1 equemene
                     DO 130 I = 1, M
284 1 equemene
                        TEMP = A( I, J+1 )
285 1 equemene
                        A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
286 1 equemene
                        A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
287 1 equemene
  130                CONTINUE
288 1 equemene
                  END IF
289 1 equemene
  140          CONTINUE
290 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
291 1 equemene
               DO 160 J = N - 1, 1, -1
292 1 equemene
                  CTEMP = C( J )
293 1 equemene
                  STEMP = S( J )
294 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
295 1 equemene
                     DO 150 I = 1, M
296 1 equemene
                        TEMP = A( I, J+1 )
297 1 equemene
                        A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
298 1 equemene
                        A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
299 1 equemene
  150                CONTINUE
300 1 equemene
                  END IF
301 1 equemene
  160          CONTINUE
302 1 equemene
            END IF
303 1 equemene
         ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
304 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
305 1 equemene
               DO 180 J = 2, N
306 1 equemene
                  CTEMP = C( J-1 )
307 1 equemene
                  STEMP = S( J-1 )
308 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
309 1 equemene
                     DO 170 I = 1, M
310 1 equemene
                        TEMP = A( I, J )
311 1 equemene
                        A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
312 1 equemene
                        A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
313 1 equemene
  170                CONTINUE
314 1 equemene
                  END IF
315 1 equemene
  180          CONTINUE
316 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
317 1 equemene
               DO 200 J = N, 2, -1
318 1 equemene
                  CTEMP = C( J-1 )
319 1 equemene
                  STEMP = S( J-1 )
320 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
321 1 equemene
                     DO 190 I = 1, M
322 1 equemene
                        TEMP = A( I, J )
323 1 equemene
                        A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
324 1 equemene
                        A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
325 1 equemene
  190                CONTINUE
326 1 equemene
                  END IF
327 1 equemene
  200          CONTINUE
328 1 equemene
            END IF
329 1 equemene
         ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
330 1 equemene
            IF( LSAME( DIRECT, 'F' ) ) THEN
331 1 equemene
               DO 220 J = 1, N - 1
332 1 equemene
                  CTEMP = C( J )
333 1 equemene
                  STEMP = S( J )
334 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
335 1 equemene
                     DO 210 I = 1, M
336 1 equemene
                        TEMP = A( I, J )
337 1 equemene
                        A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
338 1 equemene
                        A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
339 1 equemene
  210                CONTINUE
340 1 equemene
                  END IF
341 1 equemene
  220          CONTINUE
342 1 equemene
            ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
343 1 equemene
               DO 240 J = N - 1, 1, -1
344 1 equemene
                  CTEMP = C( J )
345 1 equemene
                  STEMP = S( J )
346 1 equemene
                  IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
347 1 equemene
                     DO 230 I = 1, M
348 1 equemene
                        TEMP = A( I, J )
349 1 equemene
                        A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
350 1 equemene
                        A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
351 1 equemene
  230                CONTINUE
352 1 equemene
                  END IF
353 1 equemene
  240          CONTINUE
354 1 equemene
            END IF
355 1 equemene
         END IF
356 1 equemene
      END IF
357 1 equemene
*
358 1 equemene
      RETURN
359 1 equemene
*
360 1 equemene
*     End of DLASR
361 1 equemene
*
362 1 equemene
      END