1*> \brief \b DLASR 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 DLASR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DLASR( 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*       DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> DLASR 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 December 2016
196*
197*> \ingroup OTHERauxiliary
198*
199*  =====================================================================
200      SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
201*
202*  -- LAPACK auxiliary routine (version 3.7.0) --
203*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
204*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205*     December 2016
206*
207*     .. Scalar Arguments ..
208      CHARACTER          DIRECT, PIVOT, SIDE
209      INTEGER            LDA, M, N
210*     ..
211*     .. Array Arguments ..
212      DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
213*     ..
214*
215*  =====================================================================
216*
217*     .. Parameters ..
218      DOUBLE PRECISION   ONE, ZERO
219      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
220*     ..
221*     .. Local Scalars ..
222      INTEGER            I, INFO, J
223      DOUBLE PRECISION   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( 'DLASR ', 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 DLASR
435*
436      END
437