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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief <b> DSTEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b> 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DSTEVR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstevr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstevr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstevr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, 00022 * M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, 00023 * LIWORK, INFO ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER JOBZ, RANGE 00027 * INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N 00028 * DOUBLE PRECISION ABSTOL, VL, VU 00029 * .. 00030 * .. Array Arguments .. 00031 * INTEGER ISUPPZ( * ), IWORK( * ) 00032 * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) 00033 * .. 00034 * 00035 * 00036 *> \par Purpose: 00037 * ============= 00038 *> 00039 *> \verbatim 00040 *> 00041 *> DSTEVR computes selected eigenvalues and, optionally, eigenvectors 00042 *> of a real symmetric tridiagonal matrix T. Eigenvalues and 00043 *> eigenvectors can be selected by specifying either a range of values 00044 *> or a range of indices for the desired eigenvalues. 00045 *> 00046 *> Whenever possible, DSTEVR calls DSTEMR to compute the 00047 *> eigenspectrum using Relatively Robust Representations. DSTEMR 00048 *> computes eigenvalues by the dqds algorithm, while orthogonal 00049 *> eigenvectors are computed from various "good" L D L^T representations 00050 *> (also known as Relatively Robust Representations). Gram-Schmidt 00051 *> orthogonalization is avoided as far as possible. More specifically, 00052 *> the various steps of the algorithm are as follows. For the i-th 00053 *> unreduced block of T, 00054 *> (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T 00055 *> is a relatively robust representation, 00056 *> (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high 00057 *> relative accuracy by the dqds algorithm, 00058 *> (c) If there is a cluster of close eigenvalues, "choose" sigma_i 00059 *> close to the cluster, and go to step (a), 00060 *> (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, 00061 *> compute the corresponding eigenvector by forming a 00062 *> rank-revealing twisted factorization. 00063 *> The desired accuracy of the output can be specified by the input 00064 *> parameter ABSTOL. 00065 *> 00066 *> For more details, see "A new O(n^2) algorithm for the symmetric 00067 *> tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, 00068 *> Computer Science Division Technical Report No. UCB//CSD-97-971, 00069 *> UC Berkeley, May 1997. 00070 *> 00071 *> 00072 *> Note 1 : DSTEVR calls DSTEMR when the full spectrum is requested 00073 *> on machines which conform to the ieee-754 floating point standard. 00074 *> DSTEVR calls DSTEBZ and DSTEIN on non-ieee machines and 00075 *> when partial spectrum requests are made. 00076 *> 00077 *> Normal execution of DSTEMR may create NaNs and infinities and 00078 *> hence may abort due to a floating point exception in environments 00079 *> which do not handle NaNs and infinities in the ieee standard default 00080 *> manner. 00081 *> \endverbatim 00082 * 00083 * Arguments: 00084 * ========== 00085 * 00086 *> \param[in] JOBZ 00087 *> \verbatim 00088 *> JOBZ is CHARACTER*1 00089 *> = 'N': Compute eigenvalues only; 00090 *> = 'V': Compute eigenvalues and eigenvectors. 00091 *> \endverbatim 00092 *> 00093 *> \param[in] RANGE 00094 *> \verbatim 00095 *> RANGE is CHARACTER*1 00096 *> = 'A': all eigenvalues will be found. 00097 *> = 'V': all eigenvalues in the half-open interval (VL,VU] 00098 *> will be found. 00099 *> = 'I': the IL-th through IU-th eigenvalues will be found. 00100 *> For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and 00101 *> DSTEIN are called 00102 *> \endverbatim 00103 *> 00104 *> \param[in] N 00105 *> \verbatim 00106 *> N is INTEGER 00107 *> The order of the matrix. N >= 0. 00108 *> \endverbatim 00109 *> 00110 *> \param[in,out] D 00111 *> \verbatim 00112 *> D is DOUBLE PRECISION array, dimension (N) 00113 *> On entry, the n diagonal elements of the tridiagonal matrix 00114 *> A. 00115 *> On exit, D may be multiplied by a constant factor chosen 00116 *> to avoid over/underflow in computing the eigenvalues. 00117 *> \endverbatim 00118 *> 00119 *> \param[in,out] E 00120 *> \verbatim 00121 *> E is DOUBLE PRECISION array, dimension (max(1,N-1)) 00122 *> On entry, the (n-1) subdiagonal elements of the tridiagonal 00123 *> matrix A in elements 1 to N-1 of E. 00124 *> On exit, E may be multiplied by a constant factor chosen 00125 *> to avoid over/underflow in computing the eigenvalues. 00126 *> \endverbatim 00127 *> 00128 *> \param[in] VL 00129 *> \verbatim 00130 *> VL is DOUBLE PRECISION 00131 *> \endverbatim 00132 *> 00133 *> \param[in] VU 00134 *> \verbatim 00135 *> VU is DOUBLE PRECISION 00136 *> If RANGE='V', the lower and upper bounds of the interval to 00137 *> be searched for eigenvalues. VL < VU. 00138 *> Not referenced if RANGE = 'A' or 'I'. 00139 *> \endverbatim 00140 *> 00141 *> \param[in] IL 00142 *> \verbatim 00143 *> IL is INTEGER 00144 *> \endverbatim 00145 *> 00146 *> \param[in] IU 00147 *> \verbatim 00148 *> IU is INTEGER 00149 *> If RANGE='I', the indices (in ascending order) of the 00150 *> smallest and largest eigenvalues to be returned. 00151 *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 00152 *> Not referenced if RANGE = 'A' or 'V'. 00153 *> \endverbatim 00154 *> 00155 *> \param[in] ABSTOL 00156 *> \verbatim 00157 *> ABSTOL is DOUBLE PRECISION 00158 *> The absolute error tolerance for the eigenvalues. 00159 *> An approximate eigenvalue is accepted as converged 00160 *> when it is determined to lie in an interval [a,b] 00161 *> of width less than or equal to 00162 *> 00163 *> ABSTOL + EPS * max( |a|,|b| ) , 00164 *> 00165 *> where EPS is the machine precision. If ABSTOL is less than 00166 *> or equal to zero, then EPS*|T| will be used in its place, 00167 *> where |T| is the 1-norm of the tridiagonal matrix obtained 00168 *> by reducing A to tridiagonal form. 00169 *> 00170 *> See "Computing Small Singular Values of Bidiagonal Matrices 00171 *> with Guaranteed High Relative Accuracy," by Demmel and 00172 *> Kahan, LAPACK Working Note #3. 00173 *> 00174 *> If high relative accuracy is important, set ABSTOL to 00175 *> DLAMCH( 'Safe minimum' ). Doing so will guarantee that 00176 *> eigenvalues are computed to high relative accuracy when 00177 *> possible in future releases. The current code does not 00178 *> make any guarantees about high relative accuracy, but 00179 *> future releases will. See J. Barlow and J. Demmel, 00180 *> "Computing Accurate Eigensystems of Scaled Diagonally 00181 *> Dominant Matrices", LAPACK Working Note #7, for a discussion 00182 *> of which matrices define their eigenvalues to high relative 00183 *> accuracy. 00184 *> \endverbatim 00185 *> 00186 *> \param[out] M 00187 *> \verbatim 00188 *> M is INTEGER 00189 *> The total number of eigenvalues found. 0 <= M <= N. 00190 *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 00191 *> \endverbatim 00192 *> 00193 *> \param[out] W 00194 *> \verbatim 00195 *> W is DOUBLE PRECISION array, dimension (N) 00196 *> The first M elements contain the selected eigenvalues in 00197 *> ascending order. 00198 *> \endverbatim 00199 *> 00200 *> \param[out] Z 00201 *> \verbatim 00202 *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) 00203 *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z 00204 *> contain the orthonormal eigenvectors of the matrix A 00205 *> corresponding to the selected eigenvalues, with the i-th 00206 *> column of Z holding the eigenvector associated with W(i). 00207 *> Note: the user must ensure that at least max(1,M) columns are 00208 *> supplied in the array Z; if RANGE = 'V', the exact value of M 00209 *> is not known in advance and an upper bound must be used. 00210 *> \endverbatim 00211 *> 00212 *> \param[in] LDZ 00213 *> \verbatim 00214 *> LDZ is INTEGER 00215 *> The leading dimension of the array Z. LDZ >= 1, and if 00216 *> JOBZ = 'V', LDZ >= max(1,N). 00217 *> \endverbatim 00218 *> 00219 *> \param[out] ISUPPZ 00220 *> \verbatim 00221 *> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) ) 00222 *> The support of the eigenvectors in Z, i.e., the indices 00223 *> indicating the nonzero elements in Z. The i-th eigenvector 00224 *> is nonzero only in elements ISUPPZ( 2*i-1 ) through 00225 *> ISUPPZ( 2*i ). 00226 *> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 00227 *> \endverbatim 00228 *> 00229 *> \param[out] WORK 00230 *> \verbatim 00231 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00232 *> On exit, if INFO = 0, WORK(1) returns the optimal (and 00233 *> minimal) LWORK. 00234 *> \endverbatim 00235 *> 00236 *> \param[in] LWORK 00237 *> \verbatim 00238 *> LWORK is INTEGER 00239 *> The dimension of the array WORK. LWORK >= max(1,20*N). 00240 *> 00241 *> If LWORK = -1, then a workspace query is assumed; the routine 00242 *> only calculates the optimal sizes of the WORK and IWORK 00243 *> arrays, returns these values as the first entries of the WORK 00244 *> and IWORK arrays, and no error message related to LWORK or 00245 *> LIWORK is issued by XERBLA. 00246 *> \endverbatim 00247 *> 00248 *> \param[out] IWORK 00249 *> \verbatim 00250 *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) 00251 *> On exit, if INFO = 0, IWORK(1) returns the optimal (and 00252 *> minimal) LIWORK. 00253 *> \endverbatim 00254 *> 00255 *> \param[in] LIWORK 00256 *> \verbatim 00257 *> LIWORK is INTEGER 00258 *> The dimension of the array IWORK. LIWORK >= max(1,10*N). 00259 *> 00260 *> If LIWORK = -1, then a workspace query is assumed; the 00261 *> routine only calculates the optimal sizes of the WORK and 00262 *> IWORK arrays, returns these values as the first entries of 00263 *> the WORK and IWORK arrays, and no error message related to 00264 *> LWORK or LIWORK is issued by XERBLA. 00265 *> \endverbatim 00266 *> 00267 *> \param[out] INFO 00268 *> \verbatim 00269 *> INFO is INTEGER 00270 *> = 0: successful exit 00271 *> < 0: if INFO = -i, the i-th argument had an illegal value 00272 *> > 0: Internal error 00273 *> \endverbatim 00274 * 00275 * Authors: 00276 * ======== 00277 * 00278 *> \author Univ. of Tennessee 00279 *> \author Univ. of California Berkeley 00280 *> \author Univ. of Colorado Denver 00281 *> \author NAG Ltd. 00282 * 00283 *> \date November 2011 00284 * 00285 *> \ingroup doubleOTHEReigen 00286 * 00287 *> \par Contributors: 00288 * ================== 00289 *> 00290 *> Inderjit Dhillon, IBM Almaden, USA \n 00291 *> Osni Marques, LBNL/NERSC, USA \n 00292 *> Ken Stanley, Computer Science Division, University of 00293 *> California at Berkeley, USA \n 00294 *> 00295 * ===================================================================== 00296 SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, 00297 $ M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, 00298 $ LIWORK, INFO ) 00299 * 00300 * -- LAPACK driver routine (version 3.4.0) -- 00301 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00302 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00303 * November 2011 00304 * 00305 * .. Scalar Arguments .. 00306 CHARACTER JOBZ, RANGE 00307 INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N 00308 DOUBLE PRECISION ABSTOL, VL, VU 00309 * .. 00310 * .. Array Arguments .. 00311 INTEGER ISUPPZ( * ), IWORK( * ) 00312 DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) 00313 * .. 00314 * 00315 * ===================================================================== 00316 * 00317 * .. Parameters .. 00318 DOUBLE PRECISION ZERO, ONE, TWO 00319 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) 00320 * .. 00321 * .. Local Scalars .. 00322 LOGICAL ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ, 00323 $ TRYRAC 00324 CHARACTER ORDER 00325 INTEGER I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP, 00326 $ INDIWO, ISCALE, ITMP1, J, JJ, LIWMIN, LWMIN, 00327 $ NSPLIT 00328 DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM, 00329 $ TMP1, TNRM, VLL, VUU 00330 * .. 00331 * .. External Functions .. 00332 LOGICAL LSAME 00333 INTEGER ILAENV 00334 DOUBLE PRECISION DLAMCH, DLANST 00335 EXTERNAL LSAME, ILAENV, DLAMCH, DLANST 00336 * .. 00337 * .. External Subroutines .. 00338 EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTEMR, DSTEIN, DSTERF, 00339 $ DSWAP, XERBLA 00340 * .. 00341 * .. Intrinsic Functions .. 00342 INTRINSIC MAX, MIN, SQRT 00343 * .. 00344 * .. Executable Statements .. 00345 * 00346 * 00347 * Test the input parameters. 00348 * 00349 IEEEOK = ILAENV( 10, 'DSTEVR', 'N', 1, 2, 3, 4 ) 00350 * 00351 WANTZ = LSAME( JOBZ, 'V' ) 00352 ALLEIG = LSAME( RANGE, 'A' ) 00353 VALEIG = LSAME( RANGE, 'V' ) 00354 INDEIG = LSAME( RANGE, 'I' ) 00355 * 00356 LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) ) 00357 LWMIN = MAX( 1, 20*N ) 00358 LIWMIN = MAX( 1, 10*N ) 00359 * 00360 * 00361 INFO = 0 00362 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00363 INFO = -1 00364 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 00365 INFO = -2 00366 ELSE IF( N.LT.0 ) THEN 00367 INFO = -3 00368 ELSE 00369 IF( VALEIG ) THEN 00370 IF( N.GT.0 .AND. VU.LE.VL ) 00371 $ INFO = -7 00372 ELSE IF( INDEIG ) THEN 00373 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN 00374 INFO = -8 00375 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 00376 INFO = -9 00377 END IF 00378 END IF 00379 END IF 00380 IF( INFO.EQ.0 ) THEN 00381 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00382 INFO = -14 00383 END IF 00384 END IF 00385 * 00386 IF( INFO.EQ.0 ) THEN 00387 WORK( 1 ) = LWMIN 00388 IWORK( 1 ) = LIWMIN 00389 * 00390 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00391 INFO = -17 00392 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00393 INFO = -19 00394 END IF 00395 END IF 00396 * 00397 IF( INFO.NE.0 ) THEN 00398 CALL XERBLA( 'DSTEVR', -INFO ) 00399 RETURN 00400 ELSE IF( LQUERY ) THEN 00401 RETURN 00402 END IF 00403 * 00404 * Quick return if possible 00405 * 00406 M = 0 00407 IF( N.EQ.0 ) 00408 $ RETURN 00409 * 00410 IF( N.EQ.1 ) THEN 00411 IF( ALLEIG .OR. INDEIG ) THEN 00412 M = 1 00413 W( 1 ) = D( 1 ) 00414 ELSE 00415 IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN 00416 M = 1 00417 W( 1 ) = D( 1 ) 00418 END IF 00419 END IF 00420 IF( WANTZ ) 00421 $ Z( 1, 1 ) = ONE 00422 RETURN 00423 END IF 00424 * 00425 * Get machine constants. 00426 * 00427 SAFMIN = DLAMCH( 'Safe minimum' ) 00428 EPS = DLAMCH( 'Precision' ) 00429 SMLNUM = SAFMIN / EPS 00430 BIGNUM = ONE / SMLNUM 00431 RMIN = SQRT( SMLNUM ) 00432 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) 00433 * 00434 * 00435 * Scale matrix to allowable range, if necessary. 00436 * 00437 ISCALE = 0 00438 VLL = VL 00439 VUU = VU 00440 * 00441 TNRM = DLANST( 'M', N, D, E ) 00442 IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN 00443 ISCALE = 1 00444 SIGMA = RMIN / TNRM 00445 ELSE IF( TNRM.GT.RMAX ) THEN 00446 ISCALE = 1 00447 SIGMA = RMAX / TNRM 00448 END IF 00449 IF( ISCALE.EQ.1 ) THEN 00450 CALL DSCAL( N, SIGMA, D, 1 ) 00451 CALL DSCAL( N-1, SIGMA, E( 1 ), 1 ) 00452 IF( VALEIG ) THEN 00453 VLL = VL*SIGMA 00454 VUU = VU*SIGMA 00455 END IF 00456 END IF 00457 00458 * Initialize indices into workspaces. Note: These indices are used only 00459 * if DSTERF or DSTEMR fail. 00460 00461 * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and 00462 * stores the block indices of each of the M<=N eigenvalues. 00463 INDIBL = 1 00464 * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and 00465 * stores the starting and finishing indices of each block. 00466 INDISP = INDIBL + N 00467 * IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors 00468 * that corresponding to eigenvectors that fail to converge in 00469 * DSTEIN. This information is discarded; if any fail, the driver 00470 * returns INFO > 0. 00471 INDIFL = INDISP + N 00472 * INDIWO is the offset of the remaining integer workspace. 00473 INDIWO = INDISP + N 00474 * 00475 * If all eigenvalues are desired, then 00476 * call DSTERF or DSTEMR. If this fails for some eigenvalue, then 00477 * try DSTEBZ. 00478 * 00479 * 00480 TEST = .FALSE. 00481 IF( INDEIG ) THEN 00482 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN 00483 TEST = .TRUE. 00484 END IF 00485 END IF 00486 IF( ( ALLEIG .OR. TEST ) .AND. IEEEOK.EQ.1 ) THEN 00487 CALL DCOPY( N-1, E( 1 ), 1, WORK( 1 ), 1 ) 00488 IF( .NOT.WANTZ ) THEN 00489 CALL DCOPY( N, D, 1, W, 1 ) 00490 CALL DSTERF( N, W, WORK, INFO ) 00491 ELSE 00492 CALL DCOPY( N, D, 1, WORK( N+1 ), 1 ) 00493 IF (ABSTOL .LE. TWO*N*EPS) THEN 00494 TRYRAC = .TRUE. 00495 ELSE 00496 TRYRAC = .FALSE. 00497 END IF 00498 CALL DSTEMR( JOBZ, 'A', N, WORK( N+1 ), WORK, VL, VU, IL, 00499 $ IU, M, W, Z, LDZ, N, ISUPPZ, TRYRAC, 00500 $ WORK( 2*N+1 ), LWORK-2*N, IWORK, LIWORK, INFO ) 00501 * 00502 END IF 00503 IF( INFO.EQ.0 ) THEN 00504 M = N 00505 GO TO 10 00506 END IF 00507 INFO = 0 00508 END IF 00509 * 00510 * Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN. 00511 * 00512 IF( WANTZ ) THEN 00513 ORDER = 'B' 00514 ELSE 00515 ORDER = 'E' 00516 END IF 00517 00518 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E, M, 00519 $ NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ), WORK, 00520 $ IWORK( INDIWO ), INFO ) 00521 * 00522 IF( WANTZ ) THEN 00523 CALL DSTEIN( N, D, E, M, W, IWORK( INDIBL ), IWORK( INDISP ), 00524 $ Z, LDZ, WORK, IWORK( INDIWO ), IWORK( INDIFL ), 00525 $ INFO ) 00526 END IF 00527 * 00528 * If matrix was scaled, then rescale eigenvalues appropriately. 00529 * 00530 10 CONTINUE 00531 IF( ISCALE.EQ.1 ) THEN 00532 IF( INFO.EQ.0 ) THEN 00533 IMAX = M 00534 ELSE 00535 IMAX = INFO - 1 00536 END IF 00537 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) 00538 END IF 00539 * 00540 * If eigenvalues are not in order, then sort them, along with 00541 * eigenvectors. 00542 * 00543 IF( WANTZ ) THEN 00544 DO 30 J = 1, M - 1 00545 I = 0 00546 TMP1 = W( J ) 00547 DO 20 JJ = J + 1, M 00548 IF( W( JJ ).LT.TMP1 ) THEN 00549 I = JJ 00550 TMP1 = W( JJ ) 00551 END IF 00552 20 CONTINUE 00553 * 00554 IF( I.NE.0 ) THEN 00555 ITMP1 = IWORK( I ) 00556 W( I ) = W( J ) 00557 IWORK( I ) = IWORK( J ) 00558 W( J ) = TMP1 00559 IWORK( J ) = ITMP1 00560 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) 00561 END IF 00562 30 CONTINUE 00563 END IF 00564 * 00565 * Causes problems with tests 19 & 20: 00566 * IF (wantz .and. INDEIG ) Z( 1,1) = Z(1,1) / 1.002 + .002 00567 * 00568 * 00569 WORK( 1 ) = LWMIN 00570 IWORK( 1 ) = LIWMIN 00571 RETURN 00572 * 00573 * End of DSTEVR 00574 * 00575 END