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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, 00002 $ SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, 00003 $ LDVSR, WORK, LWORK, BWORK, INFO ) 00004 * 00005 * -- LAPACK driver routine (version 3.2) -- 00006 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00007 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00008 * November 2006 00009 * 00010 * .. Scalar Arguments .. 00011 CHARACTER JOBVSL, JOBVSR, SORT 00012 INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM 00013 * .. 00014 * .. Array Arguments .. 00015 LOGICAL BWORK( * ) 00016 DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), 00017 $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), 00018 $ VSR( LDVSR, * ), WORK( * ) 00019 * .. 00020 * .. Function Arguments .. 00021 LOGICAL SELCTG 00022 EXTERNAL SELCTG 00023 * .. 00024 * 00025 * Purpose 00026 * ======= 00027 * 00028 * DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B), 00029 * the generalized eigenvalues, the generalized real Schur form (S,T), 00030 * optionally, the left and/or right matrices of Schur vectors (VSL and 00031 * VSR). This gives the generalized Schur factorization 00032 * 00033 * (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) 00034 * 00035 * Optionally, it also orders the eigenvalues so that a selected cluster 00036 * of eigenvalues appears in the leading diagonal blocks of the upper 00037 * quasi-triangular matrix S and the upper triangular matrix T.The 00038 * leading columns of VSL and VSR then form an orthonormal basis for the 00039 * corresponding left and right eigenspaces (deflating subspaces). 00040 * 00041 * (If only the generalized eigenvalues are needed, use the driver 00042 * DGGEV instead, which is faster.) 00043 * 00044 * A generalized eigenvalue for a pair of matrices (A,B) is a scalar w 00045 * or a ratio alpha/beta = w, such that A - w*B is singular. It is 00046 * usually represented as the pair (alpha,beta), as there is a 00047 * reasonable interpretation for beta=0 or both being zero. 00048 * 00049 * A pair of matrices (S,T) is in generalized real Schur form if T is 00050 * upper triangular with non-negative diagonal and S is block upper 00051 * triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond 00052 * to real generalized eigenvalues, while 2-by-2 blocks of S will be 00053 * "standardized" by making the corresponding elements of T have the 00054 * form: 00055 * [ a 0 ] 00056 * [ 0 b ] 00057 * 00058 * and the pair of corresponding 2-by-2 blocks in S and T will have a 00059 * complex conjugate pair of generalized eigenvalues. 00060 * 00061 * 00062 * Arguments 00063 * ========= 00064 * 00065 * JOBVSL (input) CHARACTER*1 00066 * = 'N': do not compute the left Schur vectors; 00067 * = 'V': compute the left Schur vectors. 00068 * 00069 * JOBVSR (input) CHARACTER*1 00070 * = 'N': do not compute the right Schur vectors; 00071 * = 'V': compute the right Schur vectors. 00072 * 00073 * SORT (input) CHARACTER*1 00074 * Specifies whether or not to order the eigenvalues on the 00075 * diagonal of the generalized Schur form. 00076 * = 'N': Eigenvalues are not ordered; 00077 * = 'S': Eigenvalues are ordered (see SELCTG); 00078 * 00079 * SELCTG (external procedure) LOGICAL FUNCTION of three DOUBLE PRECISION arguments 00080 * SELCTG must be declared EXTERNAL in the calling subroutine. 00081 * If SORT = 'N', SELCTG is not referenced. 00082 * If SORT = 'S', SELCTG is used to select eigenvalues to sort 00083 * to the top left of the Schur form. 00084 * An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if 00085 * SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either 00086 * one of a complex conjugate pair of eigenvalues is selected, 00087 * then both complex eigenvalues are selected. 00088 * 00089 * Note that in the ill-conditioned case, a selected complex 00090 * eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), 00091 * BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 00092 * in this case. 00093 * 00094 * N (input) INTEGER 00095 * The order of the matrices A, B, VSL, and VSR. N >= 0. 00096 * 00097 * A (input/output) DOUBLE PRECISION array, dimension (LDA, N) 00098 * On entry, the first of the pair of matrices. 00099 * On exit, A has been overwritten by its generalized Schur 00100 * form S. 00101 * 00102 * LDA (input) INTEGER 00103 * The leading dimension of A. LDA >= max(1,N). 00104 * 00105 * B (input/output) DOUBLE PRECISION array, dimension (LDB, N) 00106 * On entry, the second of the pair of matrices. 00107 * On exit, B has been overwritten by its generalized Schur 00108 * form T. 00109 * 00110 * LDB (input) INTEGER 00111 * The leading dimension of B. LDB >= max(1,N). 00112 * 00113 * SDIM (output) INTEGER 00114 * If SORT = 'N', SDIM = 0. 00115 * If SORT = 'S', SDIM = number of eigenvalues (after sorting) 00116 * for which SELCTG is true. (Complex conjugate pairs for which 00117 * SELCTG is true for either eigenvalue count as 2.) 00118 * 00119 * ALPHAR (output) DOUBLE PRECISION array, dimension (N) 00120 * ALPHAI (output) DOUBLE PRECISION array, dimension (N) 00121 * BETA (output) DOUBLE PRECISION array, dimension (N) 00122 * On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will 00123 * be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i, 00124 * and BETA(j),j=1,...,N are the diagonals of the complex Schur 00125 * form (S,T) that would result if the 2-by-2 diagonal blocks of 00126 * the real Schur form of (A,B) were further reduced to 00127 * triangular form using 2-by-2 complex unitary transformations. 00128 * If ALPHAI(j) is zero, then the j-th eigenvalue is real; if 00129 * positive, then the j-th and (j+1)-st eigenvalues are a 00130 * complex conjugate pair, with ALPHAI(j+1) negative. 00131 * 00132 * Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) 00133 * may easily over- or underflow, and BETA(j) may even be zero. 00134 * Thus, the user should avoid naively computing the ratio. 00135 * However, ALPHAR and ALPHAI will be always less than and 00136 * usually comparable with norm(A) in magnitude, and BETA always 00137 * less than and usually comparable with norm(B). 00138 * 00139 * VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N) 00140 * If JOBVSL = 'V', VSL will contain the left Schur vectors. 00141 * Not referenced if JOBVSL = 'N'. 00142 * 00143 * LDVSL (input) INTEGER 00144 * The leading dimension of the matrix VSL. LDVSL >=1, and 00145 * if JOBVSL = 'V', LDVSL >= N. 00146 * 00147 * VSR (output) DOUBLE PRECISION array, dimension (LDVSR,N) 00148 * If JOBVSR = 'V', VSR will contain the right Schur vectors. 00149 * Not referenced if JOBVSR = 'N'. 00150 * 00151 * LDVSR (input) INTEGER 00152 * The leading dimension of the matrix VSR. LDVSR >= 1, and 00153 * if JOBVSR = 'V', LDVSR >= N. 00154 * 00155 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00156 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00157 * 00158 * LWORK (input) INTEGER 00159 * The dimension of the array WORK. 00160 * If N = 0, LWORK >= 1, else LWORK >= 8*N+16. 00161 * For good performance , LWORK must generally be larger. 00162 * 00163 * If LWORK = -1, then a workspace query is assumed; the routine 00164 * only calculates the optimal size of the WORK array, returns 00165 * this value as the first entry of the WORK array, and no error 00166 * message related to LWORK is issued by XERBLA. 00167 * 00168 * BWORK (workspace) LOGICAL array, dimension (N) 00169 * Not referenced if SORT = 'N'. 00170 * 00171 * INFO (output) INTEGER 00172 * = 0: successful exit 00173 * < 0: if INFO = -i, the i-th argument had an illegal value. 00174 * = 1,...,N: 00175 * The QZ iteration failed. (A,B) are not in Schur 00176 * form, but ALPHAR(j), ALPHAI(j), and BETA(j) should 00177 * be correct for j=INFO+1,...,N. 00178 * > N: =N+1: other than QZ iteration failed in DHGEQZ. 00179 * =N+2: after reordering, roundoff changed values of 00180 * some complex eigenvalues so that leading 00181 * eigenvalues in the Generalized Schur form no 00182 * longer satisfy SELCTG=.TRUE. This could also 00183 * be caused due to scaling. 00184 * =N+3: reordering failed in DTGSEN. 00185 * 00186 * ===================================================================== 00187 * 00188 * .. Parameters .. 00189 DOUBLE PRECISION ZERO, ONE 00190 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00191 * .. 00192 * .. Local Scalars .. 00193 LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL, 00194 $ LQUERY, LST2SL, WANTST 00195 INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, 00196 $ ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK, 00197 $ MINWRK 00198 DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL, 00199 $ PVSR, SAFMAX, SAFMIN, SMLNUM 00200 * .. 00201 * .. Local Arrays .. 00202 INTEGER IDUM( 1 ) 00203 DOUBLE PRECISION DIF( 2 ) 00204 * .. 00205 * .. External Subroutines .. 00206 EXTERNAL DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD, 00207 $ DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN, 00208 $ XERBLA 00209 * .. 00210 * .. External Functions .. 00211 LOGICAL LSAME 00212 INTEGER ILAENV 00213 DOUBLE PRECISION DLAMCH, DLANGE 00214 EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE 00215 * .. 00216 * .. Intrinsic Functions .. 00217 INTRINSIC ABS, MAX, SQRT 00218 * .. 00219 * .. Executable Statements .. 00220 * 00221 * Decode the input arguments 00222 * 00223 IF( LSAME( JOBVSL, 'N' ) ) THEN 00224 IJOBVL = 1 00225 ILVSL = .FALSE. 00226 ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN 00227 IJOBVL = 2 00228 ILVSL = .TRUE. 00229 ELSE 00230 IJOBVL = -1 00231 ILVSL = .FALSE. 00232 END IF 00233 * 00234 IF( LSAME( JOBVSR, 'N' ) ) THEN 00235 IJOBVR = 1 00236 ILVSR = .FALSE. 00237 ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN 00238 IJOBVR = 2 00239 ILVSR = .TRUE. 00240 ELSE 00241 IJOBVR = -1 00242 ILVSR = .FALSE. 00243 END IF 00244 * 00245 WANTST = LSAME( SORT, 'S' ) 00246 * 00247 * Test the input arguments 00248 * 00249 INFO = 0 00250 LQUERY = ( LWORK.EQ.-1 ) 00251 IF( IJOBVL.LE.0 ) THEN 00252 INFO = -1 00253 ELSE IF( IJOBVR.LE.0 ) THEN 00254 INFO = -2 00255 ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN 00256 INFO = -3 00257 ELSE IF( N.LT.0 ) THEN 00258 INFO = -5 00259 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00260 INFO = -7 00261 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00262 INFO = -9 00263 ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN 00264 INFO = -15 00265 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN 00266 INFO = -17 00267 END IF 00268 * 00269 * Compute workspace 00270 * (Note: Comments in the code beginning "Workspace:" describe the 00271 * minimal amount of workspace needed at that point in the code, 00272 * as well as the preferred amount for good performance. 00273 * NB refers to the optimal block size for the immediately 00274 * following subroutine, as returned by ILAENV.) 00275 * 00276 IF( INFO.EQ.0 ) THEN 00277 IF( N.GT.0 )THEN 00278 MINWRK = MAX( 8*N, 6*N + 16 ) 00279 MAXWRK = MINWRK - N + 00280 $ N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) 00281 MAXWRK = MAX( MAXWRK, MINWRK - N + 00282 $ N*ILAENV( 1, 'DORMQR', ' ', N, 1, N, -1 ) ) 00283 IF( ILVSL ) THEN 00284 MAXWRK = MAX( MAXWRK, MINWRK - N + 00285 $ N*ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) ) 00286 END IF 00287 ELSE 00288 MINWRK = 1 00289 MAXWRK = 1 00290 END IF 00291 WORK( 1 ) = MAXWRK 00292 * 00293 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) 00294 $ INFO = -19 00295 END IF 00296 * 00297 IF( INFO.NE.0 ) THEN 00298 CALL XERBLA( 'DGGES ', -INFO ) 00299 RETURN 00300 ELSE IF( LQUERY ) THEN 00301 RETURN 00302 END IF 00303 * 00304 * Quick return if possible 00305 * 00306 IF( N.EQ.0 ) THEN 00307 SDIM = 0 00308 RETURN 00309 END IF 00310 * 00311 * Get machine constants 00312 * 00313 EPS = DLAMCH( 'P' ) 00314 SAFMIN = DLAMCH( 'S' ) 00315 SAFMAX = ONE / SAFMIN 00316 CALL DLABAD( SAFMIN, SAFMAX ) 00317 SMLNUM = SQRT( SAFMIN ) / EPS 00318 BIGNUM = ONE / SMLNUM 00319 * 00320 * Scale A if max element outside range [SMLNUM,BIGNUM] 00321 * 00322 ANRM = DLANGE( 'M', N, N, A, LDA, WORK ) 00323 ILASCL = .FALSE. 00324 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 00325 ANRMTO = SMLNUM 00326 ILASCL = .TRUE. 00327 ELSE IF( ANRM.GT.BIGNUM ) THEN 00328 ANRMTO = BIGNUM 00329 ILASCL = .TRUE. 00330 END IF 00331 IF( ILASCL ) 00332 $ CALL DLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR ) 00333 * 00334 * Scale B if max element outside range [SMLNUM,BIGNUM] 00335 * 00336 BNRM = DLANGE( 'M', N, N, B, LDB, WORK ) 00337 ILBSCL = .FALSE. 00338 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN 00339 BNRMTO = SMLNUM 00340 ILBSCL = .TRUE. 00341 ELSE IF( BNRM.GT.BIGNUM ) THEN 00342 BNRMTO = BIGNUM 00343 ILBSCL = .TRUE. 00344 END IF 00345 IF( ILBSCL ) 00346 $ CALL DLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR ) 00347 * 00348 * Permute the matrix to make it more nearly triangular 00349 * (Workspace: need 6*N + 2*N space for storing balancing factors) 00350 * 00351 ILEFT = 1 00352 IRIGHT = N + 1 00353 IWRK = IRIGHT + N 00354 CALL DGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ), 00355 $ WORK( IRIGHT ), WORK( IWRK ), IERR ) 00356 * 00357 * Reduce B to triangular form (QR decomposition of B) 00358 * (Workspace: need N, prefer N*NB) 00359 * 00360 IROWS = IHI + 1 - ILO 00361 ICOLS = N + 1 - ILO 00362 ITAU = IWRK 00363 IWRK = ITAU + IROWS 00364 CALL DGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), 00365 $ WORK( IWRK ), LWORK+1-IWRK, IERR ) 00366 * 00367 * Apply the orthogonal transformation to matrix A 00368 * (Workspace: need N, prefer N*NB) 00369 * 00370 CALL DORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, 00371 $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ), 00372 $ LWORK+1-IWRK, IERR ) 00373 * 00374 * Initialize VSL 00375 * (Workspace: need N, prefer N*NB) 00376 * 00377 IF( ILVSL ) THEN 00378 CALL DLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL ) 00379 IF( IROWS.GT.1 ) THEN 00380 CALL DLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, 00381 $ VSL( ILO+1, ILO ), LDVSL ) 00382 END IF 00383 CALL DORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL, 00384 $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR ) 00385 END IF 00386 * 00387 * Initialize VSR 00388 * 00389 IF( ILVSR ) 00390 $ CALL DLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR ) 00391 * 00392 * Reduce to generalized Hessenberg form 00393 * (Workspace: none needed) 00394 * 00395 CALL DGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL, 00396 $ LDVSL, VSR, LDVSR, IERR ) 00397 * 00398 * Perform QZ algorithm, computing Schur vectors if desired 00399 * (Workspace: need N) 00400 * 00401 IWRK = ITAU 00402 CALL DHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, 00403 $ ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, 00404 $ WORK( IWRK ), LWORK+1-IWRK, IERR ) 00405 IF( IERR.NE.0 ) THEN 00406 IF( IERR.GT.0 .AND. IERR.LE.N ) THEN 00407 INFO = IERR 00408 ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN 00409 INFO = IERR - N 00410 ELSE 00411 INFO = N + 1 00412 END IF 00413 GO TO 50 00414 END IF 00415 * 00416 * Sort eigenvalues ALPHA/BETA if desired 00417 * (Workspace: need 4*N+16 ) 00418 * 00419 SDIM = 0 00420 IF( WANTST ) THEN 00421 * 00422 * Undo scaling on eigenvalues before SELCTGing 00423 * 00424 IF( ILASCL ) THEN 00425 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, 00426 $ IERR ) 00427 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, 00428 $ IERR ) 00429 END IF 00430 IF( ILBSCL ) 00431 $ CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) 00432 * 00433 * Select eigenvalues 00434 * 00435 DO 10 I = 1, N 00436 BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) ) 00437 10 CONTINUE 00438 * 00439 CALL DTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHAR, 00440 $ ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, 00441 $ PVSR, DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, 00442 $ IERR ) 00443 IF( IERR.EQ.1 ) 00444 $ INFO = N + 3 00445 * 00446 END IF 00447 * 00448 * Apply back-permutation to VSL and VSR 00449 * (Workspace: none needed) 00450 * 00451 IF( ILVSL ) 00452 $ CALL DGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ), 00453 $ WORK( IRIGHT ), N, VSL, LDVSL, IERR ) 00454 * 00455 IF( ILVSR ) 00456 $ CALL DGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ), 00457 $ WORK( IRIGHT ), N, VSR, LDVSR, IERR ) 00458 * 00459 * Check if unscaling would cause over/underflow, if so, rescale 00460 * (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of 00461 * B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) 00462 * 00463 IF( ILASCL ) THEN 00464 DO 20 I = 1, N 00465 IF( ALPHAI( I ).NE.ZERO ) THEN 00466 IF( ( ALPHAR( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) .OR. 00467 $ ( SAFMIN / ALPHAR( I ) ).GT.( ANRM / ANRMTO ) ) THEN 00468 WORK( 1 ) = ABS( A( I, I ) / ALPHAR( I ) ) 00469 BETA( I ) = BETA( I )*WORK( 1 ) 00470 ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) 00471 ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) 00472 ELSE IF( ( ALPHAI( I ) / SAFMAX ).GT. 00473 $ ( ANRMTO / ANRM ) .OR. 00474 $ ( SAFMIN / ALPHAI( I ) ).GT.( ANRM / ANRMTO ) ) 00475 $ THEN 00476 WORK( 1 ) = ABS( A( I, I+1 ) / ALPHAI( I ) ) 00477 BETA( I ) = BETA( I )*WORK( 1 ) 00478 ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) 00479 ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) 00480 END IF 00481 END IF 00482 20 CONTINUE 00483 END IF 00484 * 00485 IF( ILBSCL ) THEN 00486 DO 30 I = 1, N 00487 IF( ALPHAI( I ).NE.ZERO ) THEN 00488 IF( ( BETA( I ) / SAFMAX ).GT.( BNRMTO / BNRM ) .OR. 00489 $ ( SAFMIN / BETA( I ) ).GT.( BNRM / BNRMTO ) ) THEN 00490 WORK( 1 ) = ABS( B( I, I ) / BETA( I ) ) 00491 BETA( I ) = BETA( I )*WORK( 1 ) 00492 ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) 00493 ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) 00494 END IF 00495 END IF 00496 30 CONTINUE 00497 END IF 00498 * 00499 * Undo scaling 00500 * 00501 IF( ILASCL ) THEN 00502 CALL DLASCL( 'H', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR ) 00503 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR ) 00504 CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR ) 00505 END IF 00506 * 00507 IF( ILBSCL ) THEN 00508 CALL DLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR ) 00509 CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) 00510 END IF 00511 * 00512 IF( WANTST ) THEN 00513 * 00514 * Check if reordering is correct 00515 * 00516 LASTSL = .TRUE. 00517 LST2SL = .TRUE. 00518 SDIM = 0 00519 IP = 0 00520 DO 40 I = 1, N 00521 CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) ) 00522 IF( ALPHAI( I ).EQ.ZERO ) THEN 00523 IF( CURSL ) 00524 $ SDIM = SDIM + 1 00525 IP = 0 00526 IF( CURSL .AND. .NOT.LASTSL ) 00527 $ INFO = N + 2 00528 ELSE 00529 IF( IP.EQ.1 ) THEN 00530 * 00531 * Last eigenvalue of conjugate pair 00532 * 00533 CURSL = CURSL .OR. LASTSL 00534 LASTSL = CURSL 00535 IF( CURSL ) 00536 $ SDIM = SDIM + 2 00537 IP = -1 00538 IF( CURSL .AND. .NOT.LST2SL ) 00539 $ INFO = N + 2 00540 ELSE 00541 * 00542 * First eigenvalue of conjugate pair 00543 * 00544 IP = 1 00545 END IF 00546 END IF 00547 LST2SL = LASTSL 00548 LASTSL = CURSL 00549 40 CONTINUE 00550 * 00551 END IF 00552 * 00553 50 CONTINUE 00554 * 00555 WORK( 1 ) = MAXWRK 00556 * 00557 RETURN 00558 * 00559 * End of DGGES 00560 * 00561 END
1.7.3 
