Annotation of rpl/lapack/lapack/dlasr.f, revision 1.20
1.12 bertrand 1: *> \brief \b DLASR 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 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">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLASR( 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 A( LDA, * ), C( * ), S( * )
29: * ..
1.16 bertrand 30: *
1.9 bertrand 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.
1.16 bertrand 39: *>
1.9 bertrand 40: *> When SIDE = 'L', the transformation takes the form
1.16 bertrand 41: *>
1.9 bertrand 42: *> A := P*A
1.16 bertrand 43: *>
1.9 bertrand 44: *> and when SIDE = 'R', the transformation takes the form
1.16 bertrand 45: *>
1.9 bertrand 46: *> A := A*P**T
1.16 bertrand 47: *>
1.9 bertrand 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.
1.16 bertrand 51: *>
1.9 bertrand 52: *> When DIRECT = 'F' (Forward sequence), then
1.16 bertrand 53: *>
1.9 bertrand 54: *> P = P(z-1) * ... * P(2) * P(1)
1.16 bertrand 55: *>
1.9 bertrand 56: *> and when DIRECT = 'B' (Backward sequence), then
1.16 bertrand 57: *>
1.9 bertrand 58: *> P = P(1) * P(2) * ... * P(z-1)
1.16 bertrand 59: *>
1.9 bertrand 60: *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
1.16 bertrand 61: *>
1.9 bertrand 62: *> R(k) = ( c(k) s(k) )
63: *> = ( -s(k) c(k) ).
1.16 bertrand 64: *>
1.9 bertrand 65: *> When PIVOT = 'V' (Variable pivot), the rotation is performed
66: *> for the plane (k,k+1), i.e., P(k) has the form
1.16 bertrand 67: *>
1.9 bertrand 68: *> P(k) = ( 1 )
69: *> ( ... )
70: *> ( 1 )
71: *> ( c(k) s(k) )
72: *> ( -s(k) c(k) )
73: *> ( 1 )
74: *> ( ... )
75: *> ( 1 )
1.16 bertrand 76: *>
1.9 bertrand 77: *> where R(k) appears as a rank-2 modification to the identity matrix in
78: *> rows and columns k and k+1.
1.16 bertrand 79: *>
1.9 bertrand 80: *> When PIVOT = 'T' (Top pivot), the rotation is performed for the
81: *> plane (1,k+1), so P(k) has the form
1.16 bertrand 82: *>
1.9 bertrand 83: *> P(k) = ( c(k) s(k) )
84: *> ( 1 )
85: *> ( ... )
86: *> ( 1 )
87: *> ( -s(k) c(k) )
88: *> ( 1 )
89: *> ( ... )
90: *> ( 1 )
1.16 bertrand 91: *>
1.9 bertrand 92: *> where R(k) appears in rows and columns 1 and k+1.
1.16 bertrand 93: *>
1.9 bertrand 94: *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
95: *> performed for the plane (k,z), giving P(k) the form
1.16 bertrand 96: *>
1.9 bertrand 97: *> P(k) = ( 1 )
98: *> ( ... )
99: *> ( 1 )
100: *> ( c(k) s(k) )
101: *> ( 1 )
102: *> ( ... )
103: *> ( 1 )
104: *> ( -s(k) c(k) )
1.16 bertrand 105: *>
1.9 bertrand 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
1.19 bertrand 178: *> SIDE = 'L' or by A*P**T if SIDE = 'R'.
1.9 bertrand 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: *
1.16 bertrand 190: *> \author Univ. of Tennessee
191: *> \author Univ. of California Berkeley
192: *> \author Univ. of Colorado Denver
193: *> \author NAG Ltd.
1.9 bertrand 194: *
1.16 bertrand 195: *> \ingroup OTHERauxiliary
1.9 bertrand 196: *
197: * =====================================================================
1.1 bertrand 198: SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
199: *
1.20 ! bertrand 200: * -- LAPACK auxiliary routine --
1.1 bertrand 201: * -- LAPACK is a software package provided by Univ. of Tennessee, --
202: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203: *
204: * .. Scalar Arguments ..
205: CHARACTER DIRECT, PIVOT, SIDE
206: INTEGER LDA, M, N
207: * ..
208: * .. Array Arguments ..
209: DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
210: * ..
211: *
212: * =====================================================================
213: *
214: * .. Parameters ..
215: DOUBLE PRECISION ONE, ZERO
216: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
217: * ..
218: * .. Local Scalars ..
219: INTEGER I, INFO, J
220: DOUBLE PRECISION CTEMP, STEMP, TEMP
221: * ..
222: * .. External Functions ..
223: LOGICAL LSAME
224: EXTERNAL LSAME
225: * ..
226: * .. External Subroutines ..
227: EXTERNAL XERBLA
228: * ..
229: * .. Intrinsic Functions ..
230: INTRINSIC MAX
231: * ..
232: * .. Executable Statements ..
233: *
234: * Test the input parameters
235: *
236: INFO = 0
237: IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
238: INFO = 1
239: ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
240: $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
241: INFO = 2
242: ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
243: $ THEN
244: INFO = 3
245: ELSE IF( M.LT.0 ) THEN
246: INFO = 4
247: ELSE IF( N.LT.0 ) THEN
248: INFO = 5
249: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
250: INFO = 9
251: END IF
252: IF( INFO.NE.0 ) THEN
253: CALL XERBLA( 'DLASR ', INFO )
254: RETURN
255: END IF
256: *
257: * Quick return if possible
258: *
259: IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
260: $ RETURN
261: IF( LSAME( SIDE, 'L' ) ) THEN
262: *
263: * Form P * A
264: *
265: IF( LSAME( PIVOT, 'V' ) ) THEN
266: IF( LSAME( DIRECT, 'F' ) ) THEN
267: DO 20 J = 1, M - 1
268: CTEMP = C( J )
269: STEMP = S( J )
270: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
271: DO 10 I = 1, N
272: TEMP = A( J+1, I )
273: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
274: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
275: 10 CONTINUE
276: END IF
277: 20 CONTINUE
278: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
279: DO 40 J = M - 1, 1, -1
280: CTEMP = C( J )
281: STEMP = S( J )
282: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
283: DO 30 I = 1, N
284: TEMP = A( J+1, I )
285: A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
286: A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
287: 30 CONTINUE
288: END IF
289: 40 CONTINUE
290: END IF
291: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
292: IF( LSAME( DIRECT, 'F' ) ) THEN
293: DO 60 J = 2, M
294: CTEMP = C( J-1 )
295: STEMP = S( J-1 )
296: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
297: DO 50 I = 1, N
298: TEMP = A( J, I )
299: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
300: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
301: 50 CONTINUE
302: END IF
303: 60 CONTINUE
304: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
305: DO 80 J = M, 2, -1
306: CTEMP = C( J-1 )
307: STEMP = S( J-1 )
308: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
309: DO 70 I = 1, N
310: TEMP = A( J, I )
311: A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
312: A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
313: 70 CONTINUE
314: END IF
315: 80 CONTINUE
316: END IF
317: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
318: IF( LSAME( DIRECT, 'F' ) ) THEN
319: DO 100 J = 1, M - 1
320: CTEMP = C( J )
321: STEMP = S( J )
322: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
323: DO 90 I = 1, N
324: TEMP = A( J, I )
325: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
326: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
327: 90 CONTINUE
328: END IF
329: 100 CONTINUE
330: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
331: DO 120 J = M - 1, 1, -1
332: CTEMP = C( J )
333: STEMP = S( J )
334: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
335: DO 110 I = 1, N
336: TEMP = A( J, I )
337: A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
338: A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
339: 110 CONTINUE
340: END IF
341: 120 CONTINUE
342: END IF
343: END IF
344: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
345: *
1.8 bertrand 346: * Form A * P**T
1.1 bertrand 347: *
348: IF( LSAME( PIVOT, 'V' ) ) THEN
349: IF( LSAME( DIRECT, 'F' ) ) THEN
350: DO 140 J = 1, N - 1
351: CTEMP = C( J )
352: STEMP = S( J )
353: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
354: DO 130 I = 1, M
355: TEMP = A( I, J+1 )
356: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
357: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
358: 130 CONTINUE
359: END IF
360: 140 CONTINUE
361: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
362: DO 160 J = N - 1, 1, -1
363: CTEMP = C( J )
364: STEMP = S( J )
365: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
366: DO 150 I = 1, M
367: TEMP = A( I, J+1 )
368: A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
369: A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
370: 150 CONTINUE
371: END IF
372: 160 CONTINUE
373: END IF
374: ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
375: IF( LSAME( DIRECT, 'F' ) ) THEN
376: DO 180 J = 2, N
377: CTEMP = C( J-1 )
378: STEMP = S( J-1 )
379: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
380: DO 170 I = 1, M
381: TEMP = A( I, J )
382: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
383: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
384: 170 CONTINUE
385: END IF
386: 180 CONTINUE
387: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
388: DO 200 J = N, 2, -1
389: CTEMP = C( J-1 )
390: STEMP = S( J-1 )
391: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
392: DO 190 I = 1, M
393: TEMP = A( I, J )
394: A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
395: A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
396: 190 CONTINUE
397: END IF
398: 200 CONTINUE
399: END IF
400: ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
401: IF( LSAME( DIRECT, 'F' ) ) THEN
402: DO 220 J = 1, N - 1
403: CTEMP = C( J )
404: STEMP = S( J )
405: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
406: DO 210 I = 1, M
407: TEMP = A( I, J )
408: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
409: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
410: 210 CONTINUE
411: END IF
412: 220 CONTINUE
413: ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
414: DO 240 J = N - 1, 1, -1
415: CTEMP = C( J )
416: STEMP = S( J )
417: IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
418: DO 230 I = 1, M
419: TEMP = A( I, J )
420: A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
421: A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
422: 230 CONTINUE
423: END IF
424: 240 CONTINUE
425: END IF
426: END IF
427: END IF
428: *
429: RETURN
430: *
431: * End of DLASR
432: *
433: END
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