1: *> \brief \b ZLASR 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 ZLASR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlasr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlasr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlasr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLASR( 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 C( * ), S( * )
29: * COMPLEX*16 A( LDA, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLASR applies a sequence of real plane rotations to a complex matrix
39: *> A, from either the left or the right.
40: *>
41: *> When SIDE = 'L', the transformation takes the form
42: *>
43: *> A := P*A
44: *>
45: *> and when SIDE = 'R', the transformation takes the form
46: *>
47: *> A := A*P**T
48: *>
49: *> where P is an orthogonal matrix consisting of a sequence of z plane
50: *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
51: *> and P**T is the transpose of P.
52: *>
53: *> When DIRECT = 'F' (Forward sequence), then
54: *>
55: *> P = P(z-1) * ... * P(2) * P(1)
56: *>
57: *> and when DIRECT = 'B' (Backward sequence), then
58: *>
59: *> P = P(1) * P(2) * ... * P(z-1)
60: *>
61: *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
62: *>
63: *> R(k) = ( c(k) s(k) )
64: *> = ( -s(k) c(k) ).
65: *>
66: *> When PIVOT = 'V' (Variable pivot), the rotation is performed
67: *> for the plane (k,k+1), i.e., P(k) has the form
68: *>
69: *> P(k) = ( 1 )
70: *> ( ... )
71: *> ( 1 )
72: *> ( c(k) s(k) )
73: *> ( -s(k) c(k) )
74: *> ( 1 )
75: *> ( ... )
76: *> ( 1 )
77: *>
78: *> where R(k) appears as a rank-2 modification to the identity matrix in
79: *> rows and columns k and k+1.
80: *>
81: *> When PIVOT = 'T' (Top pivot), the rotation is performed for the
82: *> plane (1,k+1), so P(k) has the form
83: *>
84: *> P(k) = ( c(k) s(k) )
85: *> ( 1 )
86: *> ( ... )
87: *> ( 1 )
88: *> ( -s(k) c(k) )
89: *> ( 1 )
90: *> ( ... )
91: *> ( 1 )
92: *>
93: *> where R(k) appears in rows and columns 1 and k+1.
94: *>
95: *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
96: *> performed for the plane (k,z), giving P(k) the form
97: *>
98: *> P(k) = ( 1 )
99: *> ( ... )
100: *> ( 1 )
101: *> ( c(k) s(k) )
102: *> ( 1 )
103: *> ( ... )
104: *> ( 1 )
105: *> ( -s(k) c(k) )
106: *>
107: *> where R(k) appears in rows and columns k and z. The rotations are
108: *> performed without ever forming P(k) explicitly.
109: *> \endverbatim
110: *
111: * Arguments:
112: * ==========
113: *
114: *> \param[in] SIDE
115: *> \verbatim
116: *> SIDE is CHARACTER*1
117: *> Specifies whether the plane rotation matrix P is applied to
118: *> A on the left or the right.
119: *> = 'L': Left, compute A := P*A
120: *> = 'R': Right, compute A:= A*P**T
121: *> \endverbatim
122: *>
123: *> \param[in] PIVOT
124: *> \verbatim
125: *> PIVOT is CHARACTER*1
126: *> Specifies the plane for which P(k) is a plane rotation
127: *> matrix.
128: *> = 'V': Variable pivot, the plane (k,k+1)
129: *> = 'T': Top pivot, the plane (1,k+1)
130: *> = 'B': Bottom pivot, the plane (k,z)
131: *> \endverbatim
132: *>
133: *> \param[in] DIRECT
134: *> \verbatim
135: *> DIRECT is CHARACTER*1
136: *> Specifies whether P is a forward or backward sequence of
137: *> plane rotations.
138: *> = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
139: *> = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
140: *> \endverbatim
141: *>
142: *> \param[in] M
143: *> \verbatim
144: *> M is INTEGER
145: *> The number of rows of the matrix A. If m <= 1, an immediate
146: *> return is effected.
147: *> \endverbatim
148: *>
149: *> \param[in] N
150: *> \verbatim
151: *> N is INTEGER
152: *> The number of columns of the matrix A. If n <= 1, an
153: *> immediate return is effected.
154: *> \endverbatim
155: *>
156: *> \param[in] C
157: *> \verbatim
158: *> C is DOUBLE PRECISION array, dimension
159: *> (M-1) if SIDE = 'L'
160: *> (N-1) if SIDE = 'R'
161: *> The cosines c(k) of the plane rotations.
162: *> \endverbatim
163: *>
164: *> \param[in] S
165: *> \verbatim
166: *> S is DOUBLE PRECISION array, dimension
167: *> (M-1) if SIDE = 'L'
168: *> (N-1) if SIDE = 'R'
169: *> The sines s(k) of the plane rotations. The 2-by-2 plane
170: *> rotation part of the matrix P(k), R(k), has the form
171: *> R(k) = ( c(k) s(k) )
172: *> ( -s(k) c(k) ).
173: *> \endverbatim
174: *>
175: *> \param[in,out] A
176: *> \verbatim
177: *> A is COMPLEX*16 array, dimension (LDA,N)
178: *> The M-by-N matrix A. On exit, A is overwritten by P*A if
179: *> SIDE = 'R' or by A*P**T if SIDE = 'L'.
180: *> \endverbatim
181: *>
182: *> \param[in] LDA
183: *> \verbatim
184: *> LDA is INTEGER
185: *> The leading dimension of the array A. LDA >= max(1,M).
186: *> \endverbatim
187: *
188: * Authors:
189: * ========
190: *
191: *> \author Univ. of Tennessee
192: *> \author Univ. of California Berkeley
193: *> \author Univ. of Colorado Denver
194: *> \author NAG Ltd.
195: *
196: *> \date September 2012
197: *
198: *> \ingroup complex16OTHERauxiliary
199: *
200: * =====================================================================
201: SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
202: *
203: * -- LAPACK auxiliary routine (version 3.4.2) --
204: * -- LAPACK is a software package provided by Univ. of Tennessee, --
205: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
206: * September 2012
207: *
208: * .. Scalar Arguments ..
209: CHARACTER DIRECT, PIVOT, SIDE
210: INTEGER LDA, M, N
211: * ..
212: * .. Array Arguments ..
213: DOUBLE PRECISION C( * ), S( * )
214: COMPLEX*16 A( LDA, * )
215: * ..
216: *
217: * =====================================================================
218: *
219: * .. Parameters ..
220: DOUBLE PRECISION ONE, ZERO
221: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
222: * ..
223: * .. Local Scalars ..
224: INTEGER I, INFO, J
225: DOUBLE PRECISION CTEMP, STEMP
226: COMPLEX*16 TEMP
227: * ..
228: * .. Intrinsic Functions ..
229: INTRINSIC MAX
230: * ..
231: * .. External Functions ..
232: LOGICAL LSAME
233: EXTERNAL LSAME
234: * ..
235: * .. External Subroutines ..
236: EXTERNAL XERBLA
237: * ..
238: * .. Executable Statements ..
239: *
240: * Test the input parameters
241: *
242: INFO = 0
243: IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
244: INFO = 1
245: ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
246: $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
247: INFO = 2
248: ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
249: $ THEN
250: INFO = 3
251: ELSE IF( M.LT.0 ) THEN
252: INFO = 4
253: ELSE IF( N.LT.0 ) THEN
254: INFO = 5
255: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
256: INFO = 9
257: END IF
258: IF( INFO.NE.0 ) THEN
259: CALL XERBLA( 'ZLASR ', INFO )
260: RETURN
261: END IF
262: *
263: * Quick return if possible
264: *
265: IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
266: $ RETURN
267: IF( LSAME( SIDE, 'L' ) ) THEN
268: *
269: * Form P * A
270: *
271: IF( LSAME( PIVOT, 'V' ) ) THEN
272: IF( LSAME( DIRECT, 'F' ) ) THEN
273: DO 20 J = 1, M - 1
274: CTEMP = C( J )
275: STEMP = S( J )
276: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
277: DO 10 I = 1, N
278: TEMP = A( J+1, I )
279: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
280: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
281: 10 CONTINUE
282: END IF
283: 20 CONTINUE
284: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
285: DO 40 J = M - 1, 1, -1
286: CTEMP = C( J )
287: STEMP = S( J )
288: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
289: DO 30 I = 1, N
290: TEMP = A( J+1, I )
291: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
292: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
293: 30 CONTINUE
294: END IF
295: 40 CONTINUE
296: END IF
297: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
298: IF( LSAME( DIRECT, 'F' ) ) THEN
299: DO 60 J = 2, M
300: CTEMP = C( J-1 )
301: STEMP = S( J-1 )
302: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
303: DO 50 I = 1, N
304: TEMP = A( J, I )
305: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
306: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
307: 50 CONTINUE
308: END IF
309: 60 CONTINUE
310: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
311: DO 80 J = M, 2, -1
312: CTEMP = C( J-1 )
313: STEMP = S( J-1 )
314: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
315: DO 70 I = 1, N
316: TEMP = A( J, I )
317: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
318: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
319: 70 CONTINUE
320: END IF
321: 80 CONTINUE
322: END IF
323: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
324: IF( LSAME( DIRECT, 'F' ) ) THEN
325: DO 100 J = 1, M - 1
326: CTEMP = C( J )
327: STEMP = S( J )
328: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
329: DO 90 I = 1, N
330: TEMP = A( J, I )
331: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
332: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
333: 90 CONTINUE
334: END IF
335: 100 CONTINUE
336: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
337: DO 120 J = M - 1, 1, -1
338: CTEMP = C( J )
339: STEMP = S( J )
340: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
341: DO 110 I = 1, N
342: TEMP = A( J, I )
343: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
344: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
345: 110 CONTINUE
346: END IF
347: 120 CONTINUE
348: END IF
349: END IF
350: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
351: *
352: * Form A * P**T
353: *
354: IF( LSAME( PIVOT, 'V' ) ) THEN
355: IF( LSAME( DIRECT, 'F' ) ) THEN
356: DO 140 J = 1, N - 1
357: CTEMP = C( J )
358: STEMP = S( J )
359: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
360: DO 130 I = 1, M
361: TEMP = A( I, J+1 )
362: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
363: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
364: 130 CONTINUE
365: END IF
366: 140 CONTINUE
367: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
368: DO 160 J = N - 1, 1, -1
369: CTEMP = C( J )
370: STEMP = S( J )
371: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
372: DO 150 I = 1, M
373: TEMP = A( I, J+1 )
374: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
375: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
376: 150 CONTINUE
377: END IF
378: 160 CONTINUE
379: END IF
380: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
381: IF( LSAME( DIRECT, 'F' ) ) THEN
382: DO 180 J = 2, N
383: CTEMP = C( J-1 )
384: STEMP = S( J-1 )
385: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
386: DO 170 I = 1, M
387: TEMP = A( I, J )
388: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
389: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
390: 170 CONTINUE
391: END IF
392: 180 CONTINUE
393: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
394: DO 200 J = N, 2, -1
395: CTEMP = C( J-1 )
396: STEMP = S( J-1 )
397: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
398: DO 190 I = 1, M
399: TEMP = A( I, J )
400: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
401: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
402: 190 CONTINUE
403: END IF
404: 200 CONTINUE
405: END IF
406: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
407: IF( LSAME( DIRECT, 'F' ) ) THEN
408: DO 220 J = 1, N - 1
409: CTEMP = C( J )
410: STEMP = S( J )
411: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
412: DO 210 I = 1, M
413: TEMP = A( I, J )
414: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
415: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
416: 210 CONTINUE
417: END IF
418: 220 CONTINUE
419: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
420: DO 240 J = N - 1, 1, -1
421: CTEMP = C( J )
422: STEMP = S( J )
423: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
424: DO 230 I = 1, M
425: TEMP = A( I, J )
426: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
427: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
428: 230 CONTINUE
429: END IF
430: 240 CONTINUE
431: END IF
432: END IF
433: END IF
434: *
435: RETURN
436: *
437: * End of ZLASR
438: *
439: END
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