Annotation of rpl/lapack/lapack/dlasr.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLASR
! 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 November 2011
! 196: *
! 197: *> \ingroup auxOTHERauxiliary
! 198: *
! 199: * =====================================================================
1.1 bertrand 200: SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
201: *
1.9 ! bertrand 202: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 203: * -- LAPACK is a software package provided by Univ. of Tennessee, --
204: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 205: * November 2011
1.1 bertrand 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: *
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 DLASR
435: *
436: END
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