LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
slasr.f
Go to the documentation of this file.
1 *> \brief \b SLASR applies a sequence of plane rotations to a general rectangular matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SLASR + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasr.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasr.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasr.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIRECT, PIVOT, SIDE
25 * INTEGER LDA, M, N
26 * ..
27 * .. Array Arguments ..
28 * REAL A( LDA, * ), C( * ), S( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SLASR applies a sequence of plane rotations to a real matrix A,
38 *> from either the left or the right.
39 *>
40 *> When SIDE = 'L', the transformation takes the form
41 *>
42 *> A := P*A
43 *>
44 *> and when SIDE = 'R', the transformation takes the form
45 *>
46 *> A := A*P**T
47 *>
48 *> where P is an orthogonal matrix consisting of a sequence of z plane
49 *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
50 *> and P**T is the transpose of P.
51 *>
52 *> When DIRECT = 'F' (Forward sequence), then
53 *>
54 *> P = P(z-1) * ... * P(2) * P(1)
55 *>
56 *> and when DIRECT = 'B' (Backward sequence), then
57 *>
58 *> P = P(1) * P(2) * ... * P(z-1)
59 *>
60 *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
61 *>
62 *> R(k) = ( c(k) s(k) )
63 *> = ( -s(k) c(k) ).
64 *>
65 *> When PIVOT = 'V' (Variable pivot), the rotation is performed
66 *> for the plane (k,k+1), i.e., P(k) has the form
67 *>
68 *> P(k) = ( 1 )
69 *> ( ... )
70 *> ( 1 )
71 *> ( c(k) s(k) )
72 *> ( -s(k) c(k) )
73 *> ( 1 )
74 *> ( ... )
75 *> ( 1 )
76 *>
77 *> where R(k) appears as a rank-2 modification to the identity matrix in
78 *> rows and columns k and k+1.
79 *>
80 *> When PIVOT = 'T' (Top pivot), the rotation is performed for the
81 *> plane (1,k+1), so P(k) has the form
82 *>
83 *> P(k) = ( c(k) s(k) )
84 *> ( 1 )
85 *> ( ... )
86 *> ( 1 )
87 *> ( -s(k) c(k) )
88 *> ( 1 )
89 *> ( ... )
90 *> ( 1 )
91 *>
92 *> where R(k) appears in rows and columns 1 and k+1.
93 *>
94 *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
95 *> performed for the plane (k,z), giving P(k) the form
96 *>
97 *> P(k) = ( 1 )
98 *> ( ... )
99 *> ( 1 )
100 *> ( c(k) s(k) )
101 *> ( 1 )
102 *> ( ... )
103 *> ( 1 )
104 *> ( -s(k) c(k) )
105 *>
106 *> where R(k) appears in rows and columns k and z. The rotations are
107 *> performed without ever forming P(k) explicitly.
108 *> \endverbatim
109 *
110 * Arguments:
111 * ==========
112 *
113 *> \param[in] SIDE
114 *> \verbatim
115 *> SIDE is CHARACTER*1
116 *> Specifies whether the plane rotation matrix P is applied to
117 *> A on the left or the right.
118 *> = 'L': Left, compute A := P*A
119 *> = 'R': Right, compute A:= A*P**T
120 *> \endverbatim
121 *>
122 *> \param[in] PIVOT
123 *> \verbatim
124 *> PIVOT is CHARACTER*1
125 *> Specifies the plane for which P(k) is a plane rotation
126 *> matrix.
127 *> = 'V': Variable pivot, the plane (k,k+1)
128 *> = 'T': Top pivot, the plane (1,k+1)
129 *> = 'B': Bottom pivot, the plane (k,z)
130 *> \endverbatim
131 *>
132 *> \param[in] DIRECT
133 *> \verbatim
134 *> DIRECT is CHARACTER*1
135 *> Specifies whether P is a forward or backward sequence of
136 *> plane rotations.
137 *> = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
138 *> = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
139 *> \endverbatim
140 *>
141 *> \param[in] M
142 *> \verbatim
143 *> M is INTEGER
144 *> The number of rows of the matrix A. If m <= 1, an immediate
145 *> return is effected.
146 *> \endverbatim
147 *>
148 *> \param[in] N
149 *> \verbatim
150 *> N is INTEGER
151 *> The number of columns of the matrix A. If n <= 1, an
152 *> immediate return is effected.
153 *> \endverbatim
154 *>
155 *> \param[in] C
156 *> \verbatim
157 *> C is REAL array, dimension
158 *> (M-1) if SIDE = 'L'
159 *> (N-1) if SIDE = 'R'
160 *> The cosines c(k) of the plane rotations.
161 *> \endverbatim
162 *>
163 *> \param[in] S
164 *> \verbatim
165 *> S is REAL array, dimension
166 *> (M-1) if SIDE = 'L'
167 *> (N-1) if SIDE = 'R'
168 *> The sines s(k) of the plane rotations. The 2-by-2 plane
169 *> rotation part of the matrix P(k), R(k), has the form
170 *> R(k) = ( c(k) s(k) )
171 *> ( -s(k) c(k) ).
172 *> \endverbatim
173 *>
174 *> \param[in,out] A
175 *> \verbatim
176 *> A is REAL array, dimension (LDA,N)
177 *> The M-by-N matrix A. On exit, A is overwritten by P*A if
178 *> SIDE = 'R' or by A*P**T if SIDE = 'L'.
179 *> \endverbatim
180 *>
181 *> \param[in] LDA
182 *> \verbatim
183 *> LDA is INTEGER
184 *> The leading dimension of the array A. LDA >= max(1,M).
185 *> \endverbatim
186 *
187 * Authors:
188 * ========
189 *
190 *> \author Univ. of Tennessee
191 *> \author Univ. of California Berkeley
192 *> \author Univ. of Colorado Denver
193 *> \author NAG Ltd.
194 *
195 *> \date September 2012
196 *
197 *> \ingroup auxOTHERauxiliary
198 *
199 * =====================================================================
200  SUBROUTINE slasr( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
201 *
202 * -- LAPACK auxiliary routine (version 3.4.2) --
203 * -- LAPACK is a software package provided by Univ. of Tennessee, --
204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205 * September 2012
206 *
207 * .. Scalar Arguments ..
208  CHARACTER DIRECT, PIVOT, SIDE
209  INTEGER LDA, M, N
210 * ..
211 * .. Array Arguments ..
212  REAL A( lda, * ), C( * ), S( * )
213 * ..
214 *
215 * =====================================================================
216 *
217 * .. Parameters ..
218  REAL ONE, ZERO
219  parameter ( one = 1.0e+0, zero = 0.0e+0 )
220 * ..
221 * .. Local Scalars ..
222  INTEGER I, INFO, J
223  REAL CTEMP, STEMP, TEMP
224 * ..
225 * .. External Functions ..
226  LOGICAL LSAME
227  EXTERNAL lsame
228 * ..
229 * .. External Subroutines ..
230  EXTERNAL xerbla
231 * ..
232 * .. Intrinsic Functions ..
233  INTRINSIC max
234 * ..
235 * .. Executable Statements ..
236 *
237 * Test the input parameters
238 *
239  info = 0
240  IF( .NOT.( lsame( side, 'L' ) .OR. lsame( side, 'R' ) ) ) THEN
241  info = 1
242  ELSE IF( .NOT.( lsame( pivot, 'V' ) .OR. lsame( pivot,
243  $ 'T' ) .OR. lsame( pivot, 'B' ) ) ) THEN
244  info = 2
245  ELSE IF( .NOT.( lsame( direct, 'F' ) .OR. lsame( direct, 'B' ) ) )
246  $ THEN
247  info = 3
248  ELSE IF( m.LT.0 ) THEN
249  info = 4
250  ELSE IF( n.LT.0 ) THEN
251  info = 5
252  ELSE IF( lda.LT.max( 1, m ) ) THEN
253  info = 9
254  END IF
255  IF( info.NE.0 ) THEN
256  CALL xerbla( 'SLASR ', info )
257  RETURN
258  END IF
259 *
260 * Quick return if possible
261 *
262  IF( ( m.EQ.0 ) .OR. ( n.EQ.0 ) )
263  $ RETURN
264  IF( lsame( side, 'L' ) ) THEN
265 *
266 * Form P * A
267 *
268  IF( lsame( pivot, 'V' ) ) THEN
269  IF( lsame( direct, 'F' ) ) THEN
270  DO 20 j = 1, m - 1
271  ctemp = c( j )
272  stemp = s( j )
273  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
274  DO 10 i = 1, n
275  temp = a( j+1, i )
276  a( j+1, i ) = ctemp*temp - stemp*a( j, i )
277  a( j, i ) = stemp*temp + ctemp*a( j, i )
278  10 CONTINUE
279  END IF
280  20 CONTINUE
281  ELSE IF( lsame( direct, 'B' ) ) THEN
282  DO 40 j = m - 1, 1, -1
283  ctemp = c( j )
284  stemp = s( j )
285  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
286  DO 30 i = 1, n
287  temp = a( j+1, i )
288  a( j+1, i ) = ctemp*temp - stemp*a( j, i )
289  a( j, i ) = stemp*temp + ctemp*a( j, i )
290  30 CONTINUE
291  END IF
292  40 CONTINUE
293  END IF
294  ELSE IF( lsame( pivot, 'T' ) ) THEN
295  IF( lsame( direct, 'F' ) ) THEN
296  DO 60 j = 2, m
297  ctemp = c( j-1 )
298  stemp = s( j-1 )
299  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
300  DO 50 i = 1, n
301  temp = a( j, i )
302  a( j, i ) = ctemp*temp - stemp*a( 1, i )
303  a( 1, i ) = stemp*temp + ctemp*a( 1, i )
304  50 CONTINUE
305  END IF
306  60 CONTINUE
307  ELSE IF( lsame( direct, 'B' ) ) THEN
308  DO 80 j = m, 2, -1
309  ctemp = c( j-1 )
310  stemp = s( j-1 )
311  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
312  DO 70 i = 1, n
313  temp = a( j, i )
314  a( j, i ) = ctemp*temp - stemp*a( 1, i )
315  a( 1, i ) = stemp*temp + ctemp*a( 1, i )
316  70 CONTINUE
317  END IF
318  80 CONTINUE
319  END IF
320  ELSE IF( lsame( pivot, 'B' ) ) THEN
321  IF( lsame( direct, 'F' ) ) THEN
322  DO 100 j = 1, m - 1
323  ctemp = c( j )
324  stemp = s( j )
325  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
326  DO 90 i = 1, n
327  temp = a( j, i )
328  a( j, i ) = stemp*a( m, i ) + ctemp*temp
329  a( m, i ) = ctemp*a( m, i ) - stemp*temp
330  90 CONTINUE
331  END IF
332  100 CONTINUE
333  ELSE IF( lsame( direct, 'B' ) ) THEN
334  DO 120 j = m - 1, 1, -1
335  ctemp = c( j )
336  stemp = s( j )
337  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
338  DO 110 i = 1, n
339  temp = a( j, i )
340  a( j, i ) = stemp*a( m, i ) + ctemp*temp
341  a( m, i ) = ctemp*a( m, i ) - stemp*temp
342  110 CONTINUE
343  END IF
344  120 CONTINUE
345  END IF
346  END IF
347  ELSE IF( lsame( side, 'R' ) ) THEN
348 *
349 * Form A * P**T
350 *
351  IF( lsame( pivot, 'V' ) ) THEN
352  IF( lsame( direct, 'F' ) ) THEN
353  DO 140 j = 1, n - 1
354  ctemp = c( j )
355  stemp = s( j )
356  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
357  DO 130 i = 1, m
358  temp = a( i, j+1 )
359  a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
360  a( i, j ) = stemp*temp + ctemp*a( i, j )
361  130 CONTINUE
362  END IF
363  140 CONTINUE
364  ELSE IF( lsame( direct, 'B' ) ) THEN
365  DO 160 j = n - 1, 1, -1
366  ctemp = c( j )
367  stemp = s( j )
368  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
369  DO 150 i = 1, m
370  temp = a( i, j+1 )
371  a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
372  a( i, j ) = stemp*temp + ctemp*a( i, j )
373  150 CONTINUE
374  END IF
375  160 CONTINUE
376  END IF
377  ELSE IF( lsame( pivot, 'T' ) ) THEN
378  IF( lsame( direct, 'F' ) ) THEN
379  DO 180 j = 2, n
380  ctemp = c( j-1 )
381  stemp = s( j-1 )
382  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
383  DO 170 i = 1, m
384  temp = a( i, j )
385  a( i, j ) = ctemp*temp - stemp*a( i, 1 )
386  a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
387  170 CONTINUE
388  END IF
389  180 CONTINUE
390  ELSE IF( lsame( direct, 'B' ) ) THEN
391  DO 200 j = n, 2, -1
392  ctemp = c( j-1 )
393  stemp = s( j-1 )
394  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
395  DO 190 i = 1, m
396  temp = a( i, j )
397  a( i, j ) = ctemp*temp - stemp*a( i, 1 )
398  a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
399  190 CONTINUE
400  END IF
401  200 CONTINUE
402  END IF
403  ELSE IF( lsame( pivot, 'B' ) ) THEN
404  IF( lsame( direct, 'F' ) ) THEN
405  DO 220 j = 1, n - 1
406  ctemp = c( j )
407  stemp = s( j )
408  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
409  DO 210 i = 1, m
410  temp = a( i, j )
411  a( i, j ) = stemp*a( i, n ) + ctemp*temp
412  a( i, n ) = ctemp*a( i, n ) - stemp*temp
413  210 CONTINUE
414  END IF
415  220 CONTINUE
416  ELSE IF( lsame( direct, 'B' ) ) THEN
417  DO 240 j = n - 1, 1, -1
418  ctemp = c( j )
419  stemp = s( j )
420  IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
421  DO 230 i = 1, m
422  temp = a( i, j )
423  a( i, j ) = stemp*a( i, n ) + ctemp*temp
424  a( i, n ) = ctemp*a( i, n ) - stemp*temp
425  230 CONTINUE
426  END IF
427  240 CONTINUE
428  END IF
429  END IF
430  END IF
431 *
432  RETURN
433 *
434 * End of SLASR
435 *
436  END
slasr
subroutine slasr(SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
SLASR applies a sequence of plane rotations to a general rectangular matrix.
Definition: slasr.f:201
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62