1*> \brief \b DGGBAK 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DGGBAK + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggbak.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggbak.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggbak.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, 22* LDV, INFO ) 23* 24* .. Scalar Arguments .. 25* CHARACTER JOB, SIDE 26* INTEGER IHI, ILO, INFO, LDV, M, N 27* .. 28* .. Array Arguments .. 29* DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * ) 30* .. 31* 32* 33*> \par Purpose: 34* ============= 35*> 36*> \verbatim 37*> 38*> DGGBAK forms the right or left eigenvectors of a real generalized 39*> eigenvalue problem A*x = lambda*B*x, by backward transformation on 40*> the computed eigenvectors of the balanced pair of matrices output by 41*> DGGBAL. 42*> \endverbatim 43* 44* Arguments: 45* ========== 46* 47*> \param[in] JOB 48*> \verbatim 49*> JOB is CHARACTER*1 50*> Specifies the type of backward transformation required: 51*> = 'N': do nothing, return immediately; 52*> = 'P': do backward transformation for permutation only; 53*> = 'S': do backward transformation for scaling only; 54*> = 'B': do backward transformations for both permutation and 55*> scaling. 56*> JOB must be the same as the argument JOB supplied to DGGBAL. 57*> \endverbatim 58*> 59*> \param[in] SIDE 60*> \verbatim 61*> SIDE is CHARACTER*1 62*> = 'R': V contains right eigenvectors; 63*> = 'L': V contains left eigenvectors. 64*> \endverbatim 65*> 66*> \param[in] N 67*> \verbatim 68*> N is INTEGER 69*> The number of rows of the matrix V. N >= 0. 70*> \endverbatim 71*> 72*> \param[in] ILO 73*> \verbatim 74*> ILO is INTEGER 75*> \endverbatim 76*> 77*> \param[in] IHI 78*> \verbatim 79*> IHI is INTEGER 80*> The integers ILO and IHI determined by DGGBAL. 81*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. 82*> \endverbatim 83*> 84*> \param[in] LSCALE 85*> \verbatim 86*> LSCALE is DOUBLE PRECISION array, dimension (N) 87*> Details of the permutations and/or scaling factors applied 88*> to the left side of A and B, as returned by DGGBAL. 89*> \endverbatim 90*> 91*> \param[in] RSCALE 92*> \verbatim 93*> RSCALE is DOUBLE PRECISION array, dimension (N) 94*> Details of the permutations and/or scaling factors applied 95*> to the right side of A and B, as returned by DGGBAL. 96*> \endverbatim 97*> 98*> \param[in] M 99*> \verbatim 100*> M is INTEGER 101*> The number of columns of the matrix V. M >= 0. 102*> \endverbatim 103*> 104*> \param[in,out] V 105*> \verbatim 106*> V is DOUBLE PRECISION array, dimension (LDV,M) 107*> On entry, the matrix of right or left eigenvectors to be 108*> transformed, as returned by DTGEVC. 109*> On exit, V is overwritten by the transformed eigenvectors. 110*> \endverbatim 111*> 112*> \param[in] LDV 113*> \verbatim 114*> LDV is INTEGER 115*> The leading dimension of the matrix V. LDV >= max(1,N). 116*> \endverbatim 117*> 118*> \param[out] INFO 119*> \verbatim 120*> INFO is INTEGER 121*> = 0: successful exit. 122*> < 0: if INFO = -i, the i-th argument had an illegal value. 123*> \endverbatim 124* 125* Authors: 126* ======== 127* 128*> \author Univ. of Tennessee 129*> \author Univ. of California Berkeley 130*> \author Univ. of Colorado Denver 131*> \author NAG Ltd. 132* 133*> \ingroup doubleGBcomputational 134* 135*> \par Further Details: 136* ===================== 137*> 138*> \verbatim 139*> 140*> See R.C. Ward, Balancing the generalized eigenvalue problem, 141*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. 142*> \endverbatim 143*> 144* ===================================================================== 145 SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, 146 $ LDV, INFO ) 147* 148* -- LAPACK computational routine -- 149* -- LAPACK is a software package provided by Univ. of Tennessee, -- 150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 151* 152* .. Scalar Arguments .. 153 CHARACTER JOB, SIDE 154 INTEGER IHI, ILO, INFO, LDV, M, N 155* .. 156* .. Array Arguments .. 157 DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * ) 158* .. 159* 160* ===================================================================== 161* 162* .. Local Scalars .. 163 LOGICAL LEFTV, RIGHTV 164 INTEGER I, K 165* .. 166* .. External Functions .. 167 LOGICAL LSAME 168 EXTERNAL LSAME 169* .. 170* .. External Subroutines .. 171 EXTERNAL DSCAL, DSWAP, XERBLA 172* .. 173* .. Intrinsic Functions .. 174 INTRINSIC MAX, INT 175* .. 176* .. Executable Statements .. 177* 178* Test the input parameters 179* 180 RIGHTV = LSAME( SIDE, 'R' ) 181 LEFTV = LSAME( SIDE, 'L' ) 182* 183 INFO = 0 184 IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND. 185 $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN 186 INFO = -1 187 ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN 188 INFO = -2 189 ELSE IF( N.LT.0 ) THEN 190 INFO = -3 191 ELSE IF( ILO.LT.1 ) THEN 192 INFO = -4 193 ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN 194 INFO = -4 195 ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) ) 196 $ THEN 197 INFO = -5 198 ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN 199 INFO = -5 200 ELSE IF( M.LT.0 ) THEN 201 INFO = -8 202 ELSE IF( LDV.LT.MAX( 1, N ) ) THEN 203 INFO = -10 204 END IF 205 IF( INFO.NE.0 ) THEN 206 CALL XERBLA( 'DGGBAK', -INFO ) 207 RETURN 208 END IF 209* 210* Quick return if possible 211* 212 IF( N.EQ.0 ) 213 $ RETURN 214 IF( M.EQ.0 ) 215 $ RETURN 216 IF( LSAME( JOB, 'N' ) ) 217 $ RETURN 218* 219 IF( ILO.EQ.IHI ) 220 $ GO TO 30 221* 222* Backward balance 223* 224 IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN 225* 226* Backward transformation on right eigenvectors 227* 228 IF( RIGHTV ) THEN 229 DO 10 I = ILO, IHI 230 CALL DSCAL( M, RSCALE( I ), V( I, 1 ), LDV ) 231 10 CONTINUE 232 END IF 233* 234* Backward transformation on left eigenvectors 235* 236 IF( LEFTV ) THEN 237 DO 20 I = ILO, IHI 238 CALL DSCAL( M, LSCALE( I ), V( I, 1 ), LDV ) 239 20 CONTINUE 240 END IF 241 END IF 242* 243* Backward permutation 244* 245 30 CONTINUE 246 IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN 247* 248* Backward permutation on right eigenvectors 249* 250 IF( RIGHTV ) THEN 251 IF( ILO.EQ.1 ) 252 $ GO TO 50 253* 254 DO 40 I = ILO - 1, 1, -1 255 K = INT(RSCALE( I )) 256 IF( K.EQ.I ) 257 $ GO TO 40 258 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 259 40 CONTINUE 260* 261 50 CONTINUE 262 IF( IHI.EQ.N ) 263 $ GO TO 70 264 DO 60 I = IHI + 1, N 265 K = INT(RSCALE( I )) 266 IF( K.EQ.I ) 267 $ GO TO 60 268 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 269 60 CONTINUE 270 END IF 271* 272* Backward permutation on left eigenvectors 273* 274 70 CONTINUE 275 IF( LEFTV ) THEN 276 IF( ILO.EQ.1 ) 277 $ GO TO 90 278 DO 80 I = ILO - 1, 1, -1 279 K = INT(LSCALE( I )) 280 IF( K.EQ.I ) 281 $ GO TO 80 282 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 283 80 CONTINUE 284* 285 90 CONTINUE 286 IF( IHI.EQ.N ) 287 $ GO TO 110 288 DO 100 I = IHI + 1, N 289 K = INT(LSCALE( I )) 290 IF( K.EQ.I ) 291 $ GO TO 100 292 CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 293 100 CONTINUE 294 END IF 295 END IF 296* 297 110 CONTINUE 298* 299 RETURN 300* 301* End of DGGBAK 302* 303 END 304