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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLASR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DLASR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER DIRECT, PIVOT, SIDE 00025 * INTEGER LDA, M, N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DLASR applies a sequence of plane rotations to a real matrix A, 00038 *> from either the left or the right. 00039 *> 00040 *> When SIDE = 'L', the transformation takes the form 00041 *> 00042 *> A := P*A 00043 *> 00044 *> and when SIDE = 'R', the transformation takes the form 00045 *> 00046 *> A := A*P**T 00047 *> 00048 *> where P is an orthogonal matrix consisting of a sequence of z plane 00049 *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', 00050 *> and P**T is the transpose of P. 00051 *> 00052 *> When DIRECT = 'F' (Forward sequence), then 00053 *> 00054 *> P = P(z-1) * ... * P(2) * P(1) 00055 *> 00056 *> and when DIRECT = 'B' (Backward sequence), then 00057 *> 00058 *> P = P(1) * P(2) * ... * P(z-1) 00059 *> 00060 *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation 00061 *> 00062 *> R(k) = ( c(k) s(k) ) 00063 *> = ( -s(k) c(k) ). 00064 *> 00065 *> When PIVOT = 'V' (Variable pivot), the rotation is performed 00066 *> for the plane (k,k+1), i.e., P(k) has the form 00067 *> 00068 *> P(k) = ( 1 ) 00069 *> ( ... ) 00070 *> ( 1 ) 00071 *> ( c(k) s(k) ) 00072 *> ( -s(k) c(k) ) 00073 *> ( 1 ) 00074 *> ( ... ) 00075 *> ( 1 ) 00076 *> 00077 *> where R(k) appears as a rank-2 modification to the identity matrix in 00078 *> rows and columns k and k+1. 00079 *> 00080 *> When PIVOT = 'T' (Top pivot), the rotation is performed for the 00081 *> plane (1,k+1), so P(k) has the form 00082 *> 00083 *> P(k) = ( c(k) s(k) ) 00084 *> ( 1 ) 00085 *> ( ... ) 00086 *> ( 1 ) 00087 *> ( -s(k) c(k) ) 00088 *> ( 1 ) 00089 *> ( ... ) 00090 *> ( 1 ) 00091 *> 00092 *> where R(k) appears in rows and columns 1 and k+1. 00093 *> 00094 *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is 00095 *> performed for the plane (k,z), giving P(k) the form 00096 *> 00097 *> P(k) = ( 1 ) 00098 *> ( ... ) 00099 *> ( 1 ) 00100 *> ( c(k) s(k) ) 00101 *> ( 1 ) 00102 *> ( ... ) 00103 *> ( 1 ) 00104 *> ( -s(k) c(k) ) 00105 *> 00106 *> where R(k) appears in rows and columns k and z. The rotations are 00107 *> performed without ever forming P(k) explicitly. 00108 *> \endverbatim 00109 * 00110 * Arguments: 00111 * ========== 00112 * 00113 *> \param[in] SIDE 00114 *> \verbatim 00115 *> SIDE is CHARACTER*1 00116 *> Specifies whether the plane rotation matrix P is applied to 00117 *> A on the left or the right. 00118 *> = 'L': Left, compute A := P*A 00119 *> = 'R': Right, compute A:= A*P**T 00120 *> \endverbatim 00121 *> 00122 *> \param[in] PIVOT 00123 *> \verbatim 00124 *> PIVOT is CHARACTER*1 00125 *> Specifies the plane for which P(k) is a plane rotation 00126 *> matrix. 00127 *> = 'V': Variable pivot, the plane (k,k+1) 00128 *> = 'T': Top pivot, the plane (1,k+1) 00129 *> = 'B': Bottom pivot, the plane (k,z) 00130 *> \endverbatim 00131 *> 00132 *> \param[in] DIRECT 00133 *> \verbatim 00134 *> DIRECT is CHARACTER*1 00135 *> Specifies whether P is a forward or backward sequence of 00136 *> plane rotations. 00137 *> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) 00138 *> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) 00139 *> \endverbatim 00140 *> 00141 *> \param[in] M 00142 *> \verbatim 00143 *> M is INTEGER 00144 *> The number of rows of the matrix A. If m <= 1, an immediate 00145 *> return is effected. 00146 *> \endverbatim 00147 *> 00148 *> \param[in] N 00149 *> \verbatim 00150 *> N is INTEGER 00151 *> The number of columns of the matrix A. If n <= 1, an 00152 *> immediate return is effected. 00153 *> \endverbatim 00154 *> 00155 *> \param[in] C 00156 *> \verbatim 00157 *> C is DOUBLE PRECISION array, dimension 00158 *> (M-1) if SIDE = 'L' 00159 *> (N-1) if SIDE = 'R' 00160 *> The cosines c(k) of the plane rotations. 00161 *> \endverbatim 00162 *> 00163 *> \param[in] S 00164 *> \verbatim 00165 *> S is DOUBLE PRECISION array, dimension 00166 *> (M-1) if SIDE = 'L' 00167 *> (N-1) if SIDE = 'R' 00168 *> The sines s(k) of the plane rotations. The 2-by-2 plane 00169 *> rotation part of the matrix P(k), R(k), has the form 00170 *> R(k) = ( c(k) s(k) ) 00171 *> ( -s(k) c(k) ). 00172 *> \endverbatim 00173 *> 00174 *> \param[in,out] A 00175 *> \verbatim 00176 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00177 *> The M-by-N matrix A. On exit, A is overwritten by P*A if 00178 *> SIDE = 'R' or by A*P**T if SIDE = 'L'. 00179 *> \endverbatim 00180 *> 00181 *> \param[in] LDA 00182 *> \verbatim 00183 *> LDA is INTEGER 00184 *> The leading dimension of the array A. LDA >= max(1,M). 00185 *> \endverbatim 00186 * 00187 * Authors: 00188 * ======== 00189 * 00190 *> \author Univ. of Tennessee 00191 *> \author Univ. of California Berkeley 00192 *> \author Univ. of Colorado Denver 00193 *> \author NAG Ltd. 00194 * 00195 *> \date November 2011 00196 * 00197 *> \ingroup auxOTHERauxiliary 00198 * 00199 * ===================================================================== 00200 SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) 00201 * 00202 * -- LAPACK auxiliary routine (version 3.4.0) -- 00203 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00205 * November 2011 00206 * 00207 * .. Scalar Arguments .. 00208 CHARACTER DIRECT, PIVOT, SIDE 00209 INTEGER LDA, M, N 00210 * .. 00211 * .. Array Arguments .. 00212 DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) 00213 * .. 00214 * 00215 * ===================================================================== 00216 * 00217 * .. Parameters .. 00218 DOUBLE PRECISION ONE, ZERO 00219 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00220 * .. 00221 * .. Local Scalars .. 00222 INTEGER I, INFO, J 00223 DOUBLE PRECISION CTEMP, STEMP, TEMP 00224 * .. 00225 * .. External Functions .. 00226 LOGICAL LSAME 00227 EXTERNAL LSAME 00228 * .. 00229 * .. External Subroutines .. 00230 EXTERNAL XERBLA 00231 * .. 00232 * .. Intrinsic Functions .. 00233 INTRINSIC MAX 00234 * .. 00235 * .. Executable Statements .. 00236 * 00237 * Test the input parameters 00238 * 00239 INFO = 0 00240 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN 00241 INFO = 1 00242 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, 00243 $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN 00244 INFO = 2 00245 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) 00246 $ THEN 00247 INFO = 3 00248 ELSE IF( M.LT.0 ) THEN 00249 INFO = 4 00250 ELSE IF( N.LT.0 ) THEN 00251 INFO = 5 00252 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00253 INFO = 9 00254 END IF 00255 IF( INFO.NE.0 ) THEN 00256 CALL XERBLA( 'DLASR ', INFO ) 00257 RETURN 00258 END IF 00259 * 00260 * Quick return if possible 00261 * 00262 IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) 00263 $ RETURN 00264 IF( LSAME( SIDE, 'L' ) ) THEN 00265 * 00266 * Form P * A 00267 * 00268 IF( LSAME( PIVOT, 'V' ) ) THEN 00269 IF( LSAME( DIRECT, 'F' ) ) THEN 00270 DO 20 J = 1, M - 1 00271 CTEMP = C( J ) 00272 STEMP = S( J ) 00273 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00274 DO 10 I = 1, N 00275 TEMP = A( J+1, I ) 00276 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 00277 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 00278 10 CONTINUE 00279 END IF 00280 20 CONTINUE 00281 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00282 DO 40 J = M - 1, 1, -1 00283 CTEMP = C( J ) 00284 STEMP = S( J ) 00285 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00286 DO 30 I = 1, N 00287 TEMP = A( J+1, I ) 00288 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) 00289 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 00290 30 CONTINUE 00291 END IF 00292 40 CONTINUE 00293 END IF 00294 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 00295 IF( LSAME( DIRECT, 'F' ) ) THEN 00296 DO 60 J = 2, M 00297 CTEMP = C( J-1 ) 00298 STEMP = S( J-1 ) 00299 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00300 DO 50 I = 1, N 00301 TEMP = A( J, I ) 00302 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 00303 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 00304 50 CONTINUE 00305 END IF 00306 60 CONTINUE 00307 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00308 DO 80 J = M, 2, -1 00309 CTEMP = C( J-1 ) 00310 STEMP = S( J-1 ) 00311 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00312 DO 70 I = 1, N 00313 TEMP = A( J, I ) 00314 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) 00315 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 00316 70 CONTINUE 00317 END IF 00318 80 CONTINUE 00319 END IF 00320 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 00321 IF( LSAME( DIRECT, 'F' ) ) THEN 00322 DO 100 J = 1, M - 1 00323 CTEMP = C( J ) 00324 STEMP = S( J ) 00325 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00326 DO 90 I = 1, N 00327 TEMP = A( J, I ) 00328 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 00329 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 00330 90 CONTINUE 00331 END IF 00332 100 CONTINUE 00333 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00334 DO 120 J = M - 1, 1, -1 00335 CTEMP = C( J ) 00336 STEMP = S( J ) 00337 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00338 DO 110 I = 1, N 00339 TEMP = A( J, I ) 00340 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP 00341 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 00342 110 CONTINUE 00343 END IF 00344 120 CONTINUE 00345 END IF 00346 END IF 00347 ELSE IF( LSAME( SIDE, 'R' ) ) THEN 00348 * 00349 * Form A * P**T 00350 * 00351 IF( LSAME( PIVOT, 'V' ) ) THEN 00352 IF( LSAME( DIRECT, 'F' ) ) THEN 00353 DO 140 J = 1, N - 1 00354 CTEMP = C( J ) 00355 STEMP = S( J ) 00356 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00357 DO 130 I = 1, M 00358 TEMP = A( I, J+1 ) 00359 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 00360 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 00361 130 CONTINUE 00362 END IF 00363 140 CONTINUE 00364 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00365 DO 160 J = N - 1, 1, -1 00366 CTEMP = C( J ) 00367 STEMP = S( J ) 00368 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00369 DO 150 I = 1, M 00370 TEMP = A( I, J+1 ) 00371 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) 00372 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 00373 150 CONTINUE 00374 END IF 00375 160 CONTINUE 00376 END IF 00377 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN 00378 IF( LSAME( DIRECT, 'F' ) ) THEN 00379 DO 180 J = 2, N 00380 CTEMP = C( J-1 ) 00381 STEMP = S( J-1 ) 00382 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00383 DO 170 I = 1, M 00384 TEMP = A( I, J ) 00385 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 00386 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 00387 170 CONTINUE 00388 END IF 00389 180 CONTINUE 00390 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00391 DO 200 J = N, 2, -1 00392 CTEMP = C( J-1 ) 00393 STEMP = S( J-1 ) 00394 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00395 DO 190 I = 1, M 00396 TEMP = A( I, J ) 00397 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) 00398 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 00399 190 CONTINUE 00400 END IF 00401 200 CONTINUE 00402 END IF 00403 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN 00404 IF( LSAME( DIRECT, 'F' ) ) THEN 00405 DO 220 J = 1, N - 1 00406 CTEMP = C( J ) 00407 STEMP = S( J ) 00408 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00409 DO 210 I = 1, M 00410 TEMP = A( I, J ) 00411 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 00412 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 00413 210 CONTINUE 00414 END IF 00415 220 CONTINUE 00416 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN 00417 DO 240 J = N - 1, 1, -1 00418 CTEMP = C( J ) 00419 STEMP = S( J ) 00420 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN 00421 DO 230 I = 1, M 00422 TEMP = A( I, J ) 00423 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP 00424 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 00425 230 CONTINUE 00426 END IF 00427 240 CONTINUE 00428 END IF 00429 END IF 00430 END IF 00431 * 00432 RETURN 00433 * 00434 * End of DLASR 00435 * 00436 END