1*> \brief \b SLASR 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 SLASR + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasr.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasr.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasr.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE SLASR( 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* REAL A( LDA, * ), C( * ), S( * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> SLASR 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 REAL 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 REAL 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 REAL 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 September 2012 196* 197*> \ingroup auxOTHERauxiliary 198* 199* ===================================================================== 200 SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 201* 202* -- LAPACK auxiliary routine (version 3.4.2) -- 203* -- LAPACK is a software package provided by Univ. of Tennessee, -- 204* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 205* September 2012 206* 207* .. Scalar Arguments .. 208 CHARACTER DIRECT, PIVOT, SIDE 209 INTEGER LDA, M, N 210* .. 211* .. Array Arguments .. 212 REAL A( LDA, * ), C( * ), S( * ) 213* .. 214* 215* ===================================================================== 216* 217* .. Parameters .. 218 REAL ONE, ZERO 219 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 220* .. 221* .. Local Scalars .. 222 INTEGER I, INFO, J 223 REAL 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( 'SLASR ', 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* 349* Form A * P**T 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 SLASR 435* 436 END 437