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1.12 bertrand 1: *> \brief \b ZLASR applies a sequence of plane rotations to a general rectangular matrix.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 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">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
1.16 bertrand 22: *
1.9 bertrand 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: * ..
1.16 bertrand 31: *
1.9 bertrand 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.
1.16 bertrand 52: *>
1.9 bertrand 53: *> When DIRECT = 'F' (Forward sequence), then
1.16 bertrand 54: *>
1.9 bertrand 55: *> P = P(z-1) * ... * P(2) * P(1)
1.16 bertrand 56: *>
1.9 bertrand 57: *> and when DIRECT = 'B' (Backward sequence), then
1.16 bertrand 58: *>
1.9 bertrand 59: *> P = P(1) * P(2) * ... * P(z-1)
1.16 bertrand 60: *>
1.9 bertrand 61: *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
1.16 bertrand 62: *>
1.9 bertrand 63: *> R(k) = ( c(k) s(k) )
64: *> = ( -s(k) c(k) ).
1.16 bertrand 65: *>
1.9 bertrand 66: *> When PIVOT = 'V' (Variable pivot), the rotation is performed
67: *> for the plane (k,k+1), i.e., P(k) has the form
1.16 bertrand 68: *>
1.9 bertrand 69: *> P(k) = ( 1 )
70: *> ( ... )
71: *> ( 1 )
72: *> ( c(k) s(k) )
73: *> ( -s(k) c(k) )
74: *> ( 1 )
75: *> ( ... )
76: *> ( 1 )
1.16 bertrand 77: *>
1.9 bertrand 78: *> where R(k) appears as a rank-2 modification to the identity matrix in
79: *> rows and columns k and k+1.
1.16 bertrand 80: *>
1.9 bertrand 81: *> When PIVOT = 'T' (Top pivot), the rotation is performed for the
82: *> plane (1,k+1), so P(k) has the form
1.16 bertrand 83: *>
1.9 bertrand 84: *> P(k) = ( c(k) s(k) )
85: *> ( 1 )
86: *> ( ... )
87: *> ( 1 )
88: *> ( -s(k) c(k) )
89: *> ( 1 )
90: *> ( ... )
91: *> ( 1 )
1.16 bertrand 92: *>
1.9 bertrand 93: *> where R(k) appears in rows and columns 1 and k+1.
1.16 bertrand 94: *>
1.9 bertrand 95: *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
96: *> performed for the plane (k,z), giving P(k) the form
1.16 bertrand 97: *>
1.9 bertrand 98: *> P(k) = ( 1 )
99: *> ( ... )
100: *> ( 1 )
101: *> ( c(k) s(k) )
102: *> ( 1 )
103: *> ( ... )
104: *> ( 1 )
105: *> ( -s(k) c(k) )
1.16 bertrand 106: *>
1.9 bertrand 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: *
1.16 bertrand 191: *> \author Univ. of Tennessee
192: *> \author Univ. of California Berkeley
193: *> \author Univ. of Colorado Denver
194: *> \author NAG Ltd.
1.9 bertrand 195: *
196: *> \ingroup complex16OTHERauxiliary
197: *
198: * =====================================================================
1.1 bertrand 199: SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
200: *
1.19 ! bertrand 201: * -- LAPACK auxiliary routine --
1.1 bertrand 202: * -- LAPACK is a software package provided by Univ. of Tennessee, --
203: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
204: *
205: * .. Scalar Arguments ..
206: CHARACTER DIRECT, PIVOT, SIDE
207: INTEGER LDA, M, N
208: * ..
209: * .. Array Arguments ..
210: DOUBLE PRECISION C( * ), S( * )
211: COMPLEX*16 A( LDA, * )
212: * ..
213: *
214: * =====================================================================
215: *
216: * .. Parameters ..
217: DOUBLE PRECISION ONE, ZERO
218: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
219: * ..
220: * .. Local Scalars ..
221: INTEGER I, INFO, J
222: DOUBLE PRECISION CTEMP, STEMP
223: COMPLEX*16 TEMP
224: * ..
225: * .. Intrinsic Functions ..
226: INTRINSIC MAX
227: * ..
228: * .. External Functions ..
229: LOGICAL LSAME
230: EXTERNAL LSAME
231: * ..
232: * .. External Subroutines ..
233: EXTERNAL XERBLA
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( 'ZLASR ', 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: *
1.8 bertrand 349: * Form A * P**T
1.1 bertrand 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 ZLASR
435: *
436: END