001:       SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
002: *
003: *  -- LAPACK auxiliary routine (version 3.2) --
004: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
005: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
006: *     November 2006
007: *
008: *     .. Scalar Arguments ..
009:       CHARACTER          DIRECT, PIVOT, SIDE
010:       INTEGER            LDA, M, N
011: *     ..
012: *     .. Array Arguments ..
013:       DOUBLE PRECISION   C( * ), S( * )
014:       COMPLEX*16         A( LDA, * )
015: *     ..
016: *
017: *  Purpose
018: *  =======
019: *
020: *  ZLASR applies a sequence of real plane rotations to a complex matrix
021: *  A, from either the left or the right.
022: *
023: *  When SIDE = 'L', the transformation takes the form
024: *
025: *     A := P*A
026: *
027: *  and when SIDE = 'R', the transformation takes the form
028: *
029: *     A := A*P**T
030: *
031: *  where P is an orthogonal matrix consisting of a sequence of z plane
032: *  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
033: *  and P**T is the transpose of P.
034: *  
035: *  When DIRECT = 'F' (Forward sequence), then
036: *  
037: *     P = P(z-1) * ... * P(2) * P(1)
038: *  
039: *  and when DIRECT = 'B' (Backward sequence), then
040: *  
041: *     P = P(1) * P(2) * ... * P(z-1)
042: *  
043: *  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
044: *  
045: *     R(k) = (  c(k)  s(k) )
046: *          = ( -s(k)  c(k) ).
047: *  
048: *  When PIVOT = 'V' (Variable pivot), the rotation is performed
049: *  for the plane (k,k+1), i.e., P(k) has the form
050: *  
051: *     P(k) = (  1                                            )
052: *            (       ...                                     )
053: *            (              1                                )
054: *            (                   c(k)  s(k)                  )
055: *            (                  -s(k)  c(k)                  )
056: *            (                                1              )
057: *            (                                     ...       )
058: *            (                                            1  )
059: *  
060: *  where R(k) appears as a rank-2 modification to the identity matrix in
061: *  rows and columns k and k+1.
062: *  
063: *  When PIVOT = 'T' (Top pivot), the rotation is performed for the
064: *  plane (1,k+1), so P(k) has the form
065: *  
066: *     P(k) = (  c(k)                    s(k)                 )
067: *            (         1                                     )
068: *            (              ...                              )
069: *            (                     1                         )
070: *            ( -s(k)                    c(k)                 )
071: *            (                                 1             )
072: *            (                                      ...      )
073: *            (                                             1 )
074: *  
075: *  where R(k) appears in rows and columns 1 and k+1.
076: *  
077: *  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
078: *  performed for the plane (k,z), giving P(k) the form
079: *  
080: *     P(k) = ( 1                                             )
081: *            (      ...                                      )
082: *            (             1                                 )
083: *            (                  c(k)                    s(k) )
084: *            (                         1                     )
085: *            (                              ...              )
086: *            (                                     1         )
087: *            (                 -s(k)                    c(k) )
088: *  
089: *  where R(k) appears in rows and columns k and z.  The rotations are
090: *  performed without ever forming P(k) explicitly.
091: *
092: *  Arguments
093: *  =========
094: *
095: *  SIDE    (input) CHARACTER*1
096: *          Specifies whether the plane rotation matrix P is applied to
097: *          A on the left or the right.
098: *          = 'L':  Left, compute A := P*A
099: *          = 'R':  Right, compute A:= A*P**T
100: *
101: *  PIVOT   (input) CHARACTER*1
102: *          Specifies the plane for which P(k) is a plane rotation
103: *          matrix.
104: *          = 'V':  Variable pivot, the plane (k,k+1)
105: *          = 'T':  Top pivot, the plane (1,k+1)
106: *          = 'B':  Bottom pivot, the plane (k,z)
107: *
108: *  DIRECT  (input) CHARACTER*1
109: *          Specifies whether P is a forward or backward sequence of
110: *          plane rotations.
111: *          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
112: *          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
113: *
114: *  M       (input) INTEGER
115: *          The number of rows of the matrix A.  If m <= 1, an immediate
116: *          return is effected.
117: *
118: *  N       (input) INTEGER
119: *          The number of columns of the matrix A.  If n <= 1, an
120: *          immediate return is effected.
121: *
122: *  C       (input) DOUBLE PRECISION array, dimension
123: *                  (M-1) if SIDE = 'L'
124: *                  (N-1) if SIDE = 'R'
125: *          The cosines c(k) of the plane rotations.
126: *
127: *  S       (input) DOUBLE PRECISION array, dimension
128: *                  (M-1) if SIDE = 'L'
129: *                  (N-1) if SIDE = 'R'
130: *          The sines s(k) of the plane rotations.  The 2-by-2 plane
131: *          rotation part of the matrix P(k), R(k), has the form
132: *          R(k) = (  c(k)  s(k) )
133: *                 ( -s(k)  c(k) ).
134: *
135: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
136: *          The M-by-N matrix A.  On exit, A is overwritten by P*A if
137: *          SIDE = 'R' or by A*P**T if SIDE = 'L'.
138: *
139: *  LDA     (input) INTEGER
140: *          The leading dimension of the array A.  LDA >= max(1,M).
141: *
142: *  =====================================================================
143: *
144: *     .. Parameters ..
145:       DOUBLE PRECISION   ONE, ZERO
146:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
147: *     ..
148: *     .. Local Scalars ..
149:       INTEGER            I, INFO, J
150:       DOUBLE PRECISION   CTEMP, STEMP
151:       COMPLEX*16         TEMP
152: *     ..
153: *     .. Intrinsic Functions ..
154:       INTRINSIC          MAX
155: *     ..
156: *     .. External Functions ..
157:       LOGICAL            LSAME
158:       EXTERNAL           LSAME
159: *     ..
160: *     .. External Subroutines ..
161:       EXTERNAL           XERBLA
162: *     ..
163: *     .. Executable Statements ..
164: *
165: *     Test the input parameters
166: *
167:       INFO = 0
168:       IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
169:          INFO = 1
170:       ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
171:      $         'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
172:          INFO = 2
173:       ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
174:      $          THEN
175:          INFO = 3
176:       ELSE IF( M.LT.0 ) THEN
177:          INFO = 4
178:       ELSE IF( N.LT.0 ) THEN
179:          INFO = 5
180:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
181:          INFO = 9
182:       END IF
183:       IF( INFO.NE.0 ) THEN
184:          CALL XERBLA( 'ZLASR ', INFO )
185:          RETURN
186:       END IF
187: *
188: *     Quick return if possible
189: *
190:       IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
191:      $   RETURN
192:       IF( LSAME( SIDE, 'L' ) ) THEN
193: *
194: *        Form  P * A
195: *
196:          IF( LSAME( PIVOT, 'V' ) ) THEN
197:             IF( LSAME( DIRECT, 'F' ) ) THEN
198:                DO 20 J = 1, M - 1
199:                   CTEMP = C( J )
200:                   STEMP = S( J )
201:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
202:                      DO 10 I = 1, N
203:                         TEMP = A( J+1, I )
204:                         A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
205:                         A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
206:    10                CONTINUE
207:                   END IF
208:    20          CONTINUE
209:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
210:                DO 40 J = M - 1, 1, -1
211:                   CTEMP = C( J )
212:                   STEMP = S( J )
213:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
214:                      DO 30 I = 1, N
215:                         TEMP = A( J+1, I )
216:                         A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
217:                         A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
218:    30                CONTINUE
219:                   END IF
220:    40          CONTINUE
221:             END IF
222:          ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
223:             IF( LSAME( DIRECT, 'F' ) ) THEN
224:                DO 60 J = 2, M
225:                   CTEMP = C( J-1 )
226:                   STEMP = S( J-1 )
227:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
228:                      DO 50 I = 1, N
229:                         TEMP = A( J, I )
230:                         A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
231:                         A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
232:    50                CONTINUE
233:                   END IF
234:    60          CONTINUE
235:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
236:                DO 80 J = M, 2, -1
237:                   CTEMP = C( J-1 )
238:                   STEMP = S( J-1 )
239:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
240:                      DO 70 I = 1, N
241:                         TEMP = A( J, I )
242:                         A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
243:                         A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
244:    70                CONTINUE
245:                   END IF
246:    80          CONTINUE
247:             END IF
248:          ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
249:             IF( LSAME( DIRECT, 'F' ) ) THEN
250:                DO 100 J = 1, M - 1
251:                   CTEMP = C( J )
252:                   STEMP = S( J )
253:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
254:                      DO 90 I = 1, N
255:                         TEMP = A( J, I )
256:                         A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
257:                         A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
258:    90                CONTINUE
259:                   END IF
260:   100          CONTINUE
261:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
262:                DO 120 J = M - 1, 1, -1
263:                   CTEMP = C( J )
264:                   STEMP = S( J )
265:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
266:                      DO 110 I = 1, N
267:                         TEMP = A( J, I )
268:                         A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
269:                         A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
270:   110                CONTINUE
271:                   END IF
272:   120          CONTINUE
273:             END IF
274:          END IF
275:       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
276: *
277: *        Form A * P'
278: *
279:          IF( LSAME( PIVOT, 'V' ) ) THEN
280:             IF( LSAME( DIRECT, 'F' ) ) THEN
281:                DO 140 J = 1, N - 1
282:                   CTEMP = C( J )
283:                   STEMP = S( J )
284:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
285:                      DO 130 I = 1, M
286:                         TEMP = A( I, J+1 )
287:                         A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
288:                         A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
289:   130                CONTINUE
290:                   END IF
291:   140          CONTINUE
292:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
293:                DO 160 J = N - 1, 1, -1
294:                   CTEMP = C( J )
295:                   STEMP = S( J )
296:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
297:                      DO 150 I = 1, M
298:                         TEMP = A( I, J+1 )
299:                         A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
300:                         A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
301:   150                CONTINUE
302:                   END IF
303:   160          CONTINUE
304:             END IF
305:          ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
306:             IF( LSAME( DIRECT, 'F' ) ) THEN
307:                DO 180 J = 2, N
308:                   CTEMP = C( J-1 )
309:                   STEMP = S( J-1 )
310:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
311:                      DO 170 I = 1, M
312:                         TEMP = A( I, J )
313:                         A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
314:                         A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
315:   170                CONTINUE
316:                   END IF
317:   180          CONTINUE
318:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
319:                DO 200 J = N, 2, -1
320:                   CTEMP = C( J-1 )
321:                   STEMP = S( J-1 )
322:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
323:                      DO 190 I = 1, M
324:                         TEMP = A( I, J )
325:                         A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
326:                         A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
327:   190                CONTINUE
328:                   END IF
329:   200          CONTINUE
330:             END IF
331:          ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
332:             IF( LSAME( DIRECT, 'F' ) ) THEN
333:                DO 220 J = 1, N - 1
334:                   CTEMP = C( J )
335:                   STEMP = S( J )
336:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
337:                      DO 210 I = 1, M
338:                         TEMP = A( I, J )
339:                         A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
340:                         A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
341:   210                CONTINUE
342:                   END IF
343:   220          CONTINUE
344:             ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
345:                DO 240 J = N - 1, 1, -1
346:                   CTEMP = C( J )
347:                   STEMP = S( J )
348:                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
349:                      DO 230 I = 1, M
350:                         TEMP = A( I, J )
351:                         A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
352:                         A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
353:   230                CONTINUE
354:                   END IF
355:   240          CONTINUE
356:             END IF
357:          END IF
358:       END IF
359: *
360:       RETURN
361: *
362: *     End of ZLASR
363: *
364:       END
365: