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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief <b> CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE 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 CHEEVX + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevx.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevx.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevx.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, 00022 * ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, 00023 * IWORK, IFAIL, INFO ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER JOBZ, RANGE, UPLO 00027 * INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N 00028 * REAL ABSTOL, VL, VU 00029 * .. 00030 * .. Array Arguments .. 00031 * INTEGER IFAIL( * ), IWORK( * ) 00032 * REAL RWORK( * ), W( * ) 00033 * COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * ) 00034 * .. 00035 * 00036 * 00037 *> \par Purpose: 00038 * ============= 00039 *> 00040 *> \verbatim 00041 *> 00042 *> CHEEVX computes selected eigenvalues and, optionally, eigenvectors 00043 *> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can 00044 *> be selected by specifying either a range of values or a range of 00045 *> indices for the desired eigenvalues. 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \param[in] JOBZ 00052 *> \verbatim 00053 *> JOBZ is CHARACTER*1 00054 *> = 'N': Compute eigenvalues only; 00055 *> = 'V': Compute eigenvalues and eigenvectors. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] RANGE 00059 *> \verbatim 00060 *> RANGE is CHARACTER*1 00061 *> = 'A': all eigenvalues will be found. 00062 *> = 'V': all eigenvalues in the half-open interval (VL,VU] 00063 *> will be found. 00064 *> = 'I': the IL-th through IU-th eigenvalues will be found. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] UPLO 00068 *> \verbatim 00069 *> UPLO is CHARACTER*1 00070 *> = 'U': Upper triangle of A is stored; 00071 *> = 'L': Lower triangle of A is stored. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] N 00075 *> \verbatim 00076 *> N is INTEGER 00077 *> The order of the matrix A. N >= 0. 00078 *> \endverbatim 00079 *> 00080 *> \param[in,out] A 00081 *> \verbatim 00082 *> A is COMPLEX array, dimension (LDA, N) 00083 *> On entry, the Hermitian matrix A. If UPLO = 'U', the 00084 *> leading N-by-N upper triangular part of A contains the 00085 *> upper triangular part of the matrix A. If UPLO = 'L', 00086 *> the leading N-by-N lower triangular part of A contains 00087 *> the lower triangular part of the matrix A. 00088 *> On exit, the lower triangle (if UPLO='L') or the upper 00089 *> triangle (if UPLO='U') of A, including the diagonal, is 00090 *> destroyed. 00091 *> \endverbatim 00092 *> 00093 *> \param[in] LDA 00094 *> \verbatim 00095 *> LDA is INTEGER 00096 *> The leading dimension of the array A. LDA >= max(1,N). 00097 *> \endverbatim 00098 *> 00099 *> \param[in] VL 00100 *> \verbatim 00101 *> VL is REAL 00102 *> \endverbatim 00103 *> 00104 *> \param[in] VU 00105 *> \verbatim 00106 *> VU is REAL 00107 *> If RANGE='V', the lower and upper bounds of the interval to 00108 *> be searched for eigenvalues. VL < VU. 00109 *> Not referenced if RANGE = 'A' or 'I'. 00110 *> \endverbatim 00111 *> 00112 *> \param[in] IL 00113 *> \verbatim 00114 *> IL is INTEGER 00115 *> \endverbatim 00116 *> 00117 *> \param[in] IU 00118 *> \verbatim 00119 *> IU is INTEGER 00120 *> If RANGE='I', the indices (in ascending order) of the 00121 *> smallest and largest eigenvalues to be returned. 00122 *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 00123 *> Not referenced if RANGE = 'A' or 'V'. 00124 *> \endverbatim 00125 *> 00126 *> \param[in] ABSTOL 00127 *> \verbatim 00128 *> ABSTOL is REAL 00129 *> The absolute error tolerance for the eigenvalues. 00130 *> An approximate eigenvalue is accepted as converged 00131 *> when it is determined to lie in an interval [a,b] 00132 *> of width less than or equal to 00133 *> 00134 *> ABSTOL + EPS * max( |a|,|b| ) , 00135 *> 00136 *> where EPS is the machine precision. If ABSTOL is less than 00137 *> or equal to zero, then EPS*|T| will be used in its place, 00138 *> where |T| is the 1-norm of the tridiagonal matrix obtained 00139 *> by reducing A to tridiagonal form. 00140 *> 00141 *> Eigenvalues will be computed most accurately when ABSTOL is 00142 *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. 00143 *> If this routine returns with INFO>0, indicating that some 00144 *> eigenvectors did not converge, try setting ABSTOL to 00145 *> 2*SLAMCH('S'). 00146 *> 00147 *> See "Computing Small Singular Values of Bidiagonal Matrices 00148 *> with Guaranteed High Relative Accuracy," by Demmel and 00149 *> Kahan, LAPACK Working Note #3. 00150 *> \endverbatim 00151 *> 00152 *> \param[out] M 00153 *> \verbatim 00154 *> M is INTEGER 00155 *> The total number of eigenvalues found. 0 <= M <= N. 00156 *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 00157 *> \endverbatim 00158 *> 00159 *> \param[out] W 00160 *> \verbatim 00161 *> W is REAL array, dimension (N) 00162 *> On normal exit, the first M elements contain the selected 00163 *> eigenvalues in ascending order. 00164 *> \endverbatim 00165 *> 00166 *> \param[out] Z 00167 *> \verbatim 00168 *> Z is COMPLEX array, dimension (LDZ, max(1,M)) 00169 *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z 00170 *> contain the orthonormal eigenvectors of the matrix A 00171 *> corresponding to the selected eigenvalues, with the i-th 00172 *> column of Z holding the eigenvector associated with W(i). 00173 *> If an eigenvector fails to converge, then that column of Z 00174 *> contains the latest approximation to the eigenvector, and the 00175 *> index of the eigenvector is returned in IFAIL. 00176 *> If JOBZ = 'N', then Z is not referenced. 00177 *> Note: the user must ensure that at least max(1,M) columns are 00178 *> supplied in the array Z; if RANGE = 'V', the exact value of M 00179 *> is not known in advance and an upper bound must be used. 00180 *> \endverbatim 00181 *> 00182 *> \param[in] LDZ 00183 *> \verbatim 00184 *> LDZ is INTEGER 00185 *> The leading dimension of the array Z. LDZ >= 1, and if 00186 *> JOBZ = 'V', LDZ >= max(1,N). 00187 *> \endverbatim 00188 *> 00189 *> \param[out] WORK 00190 *> \verbatim 00191 *> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 00192 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00193 *> \endverbatim 00194 *> 00195 *> \param[in] LWORK 00196 *> \verbatim 00197 *> LWORK is INTEGER 00198 *> The length of the array WORK. LWORK >= 1, when N <= 1; 00199 *> otherwise 2*N. 00200 *> For optimal efficiency, LWORK >= (NB+1)*N, 00201 *> where NB is the max of the blocksize for CHETRD and for 00202 *> CUNMTR as returned by ILAENV. 00203 *> 00204 *> If LWORK = -1, then a workspace query is assumed; the routine 00205 *> only calculates the optimal size of the WORK array, returns 00206 *> this value as the first entry of the WORK array, and no error 00207 *> message related to LWORK is issued by XERBLA. 00208 *> \endverbatim 00209 *> 00210 *> \param[out] RWORK 00211 *> \verbatim 00212 *> RWORK is REAL array, dimension (7*N) 00213 *> \endverbatim 00214 *> 00215 *> \param[out] IWORK 00216 *> \verbatim 00217 *> IWORK is INTEGER array, dimension (5*N) 00218 *> \endverbatim 00219 *> 00220 *> \param[out] IFAIL 00221 *> \verbatim 00222 *> IFAIL is INTEGER array, dimension (N) 00223 *> If JOBZ = 'V', then if INFO = 0, the first M elements of 00224 *> IFAIL are zero. If INFO > 0, then IFAIL contains the 00225 *> indices of the eigenvectors that failed to converge. 00226 *> If JOBZ = 'N', then IFAIL is not referenced. 00227 *> \endverbatim 00228 *> 00229 *> \param[out] INFO 00230 *> \verbatim 00231 *> INFO is INTEGER 00232 *> = 0: successful exit 00233 *> < 0: if INFO = -i, the i-th argument had an illegal value 00234 *> > 0: if INFO = i, then i eigenvectors failed to converge. 00235 *> Their indices are stored in array IFAIL. 00236 *> \endverbatim 00237 * 00238 * Authors: 00239 * ======== 00240 * 00241 *> \author Univ. of Tennessee 00242 *> \author Univ. of California Berkeley 00243 *> \author Univ. of Colorado Denver 00244 *> \author NAG Ltd. 00245 * 00246 *> \date November 2011 00247 * 00248 *> \ingroup complexHEeigen 00249 * 00250 * ===================================================================== 00251 SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, 00252 $ ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, 00253 $ IWORK, IFAIL, INFO ) 00254 * 00255 * -- LAPACK driver routine (version 3.4.0) -- 00256 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00257 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00258 * November 2011 00259 * 00260 * .. Scalar Arguments .. 00261 CHARACTER JOBZ, RANGE, UPLO 00262 INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N 00263 REAL ABSTOL, VL, VU 00264 * .. 00265 * .. Array Arguments .. 00266 INTEGER IFAIL( * ), IWORK( * ) 00267 REAL RWORK( * ), W( * ) 00268 COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * ) 00269 * .. 00270 * 00271 * ===================================================================== 00272 * 00273 * .. Parameters .. 00274 REAL ZERO, ONE 00275 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00276 COMPLEX CONE 00277 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) 00278 * .. 00279 * .. Local Scalars .. 00280 LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG, 00281 $ WANTZ 00282 CHARACTER ORDER 00283 INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL, 00284 $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE, 00285 $ ITMP1, J, JJ, LLWORK, LWKMIN, LWKOPT, NB, 00286 $ NSPLIT 00287 REAL ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, 00288 $ SIGMA, SMLNUM, TMP1, VLL, VUU 00289 * .. 00290 * .. External Functions .. 00291 LOGICAL LSAME 00292 INTEGER ILAENV 00293 REAL SLAMCH, CLANHE 00294 EXTERNAL LSAME, ILAENV, SLAMCH, CLANHE 00295 * .. 00296 * .. External Subroutines .. 00297 EXTERNAL SCOPY, SSCAL, SSTEBZ, SSTERF, XERBLA, CSSCAL, 00298 $ CHETRD, CLACPY, CSTEIN, CSTEQR, CSWAP, CUNGTR, 00299 $ CUNMTR 00300 * .. 00301 * .. Intrinsic Functions .. 00302 INTRINSIC REAL, MAX, MIN, SQRT 00303 * .. 00304 * .. Executable Statements .. 00305 * 00306 * Test the input parameters. 00307 * 00308 LOWER = LSAME( UPLO, 'L' ) 00309 WANTZ = LSAME( JOBZ, 'V' ) 00310 ALLEIG = LSAME( RANGE, 'A' ) 00311 VALEIG = LSAME( RANGE, 'V' ) 00312 INDEIG = LSAME( RANGE, 'I' ) 00313 LQUERY = ( LWORK.EQ.-1 ) 00314 * 00315 INFO = 0 00316 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00317 INFO = -1 00318 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 00319 INFO = -2 00320 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN 00321 INFO = -3 00322 ELSE IF( N.LT.0 ) THEN 00323 INFO = -4 00324 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00325 INFO = -6 00326 ELSE 00327 IF( VALEIG ) THEN 00328 IF( N.GT.0 .AND. VU.LE.VL ) 00329 $ INFO = -8 00330 ELSE IF( INDEIG ) THEN 00331 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN 00332 INFO = -9 00333 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 00334 INFO = -10 00335 END IF 00336 END IF 00337 END IF 00338 IF( INFO.EQ.0 ) THEN 00339 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00340 INFO = -15 00341 END IF 00342 END IF 00343 * 00344 IF( INFO.EQ.0 ) THEN 00345 IF( N.LE.1 ) THEN 00346 LWKMIN = 1 00347 WORK( 1 ) = LWKMIN 00348 ELSE 00349 LWKMIN = 2*N 00350 NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) 00351 NB = MAX( NB, ILAENV( 1, 'CUNMTR', UPLO, N, -1, -1, -1 ) ) 00352 LWKOPT = MAX( 1, ( NB + 1 )*N ) 00353 WORK( 1 ) = LWKOPT 00354 END IF 00355 * 00356 IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) 00357 $ INFO = -17 00358 END IF 00359 * 00360 IF( INFO.NE.0 ) THEN 00361 CALL XERBLA( 'CHEEVX', -INFO ) 00362 RETURN 00363 ELSE IF( LQUERY ) THEN 00364 RETURN 00365 END IF 00366 * 00367 * Quick return if possible 00368 * 00369 M = 0 00370 IF( N.EQ.0 ) THEN 00371 RETURN 00372 END IF 00373 * 00374 IF( N.EQ.1 ) THEN 00375 IF( ALLEIG .OR. INDEIG ) THEN 00376 M = 1 00377 W( 1 ) = A( 1, 1 ) 00378 ELSE IF( VALEIG ) THEN 00379 IF( VL.LT.REAL( A( 1, 1 ) ) .AND. VU.GE.REAL( A( 1, 1 ) ) ) 00380 $ THEN 00381 M = 1 00382 W( 1 ) = A( 1, 1 ) 00383 END IF 00384 END IF 00385 IF( WANTZ ) 00386 $ Z( 1, 1 ) = CONE 00387 RETURN 00388 END IF 00389 * 00390 * Get machine constants. 00391 * 00392 SAFMIN = SLAMCH( 'Safe minimum' ) 00393 EPS = SLAMCH( 'Precision' ) 00394 SMLNUM = SAFMIN / EPS 00395 BIGNUM = ONE / SMLNUM 00396 RMIN = SQRT( SMLNUM ) 00397 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) 00398 * 00399 * Scale matrix to allowable range, if necessary. 00400 * 00401 ISCALE = 0 00402 ABSTLL = ABSTOL 00403 IF( VALEIG ) THEN 00404 VLL = VL 00405 VUU = VU 00406 END IF 00407 ANRM = CLANHE( 'M', UPLO, N, A, LDA, RWORK ) 00408 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN 00409 ISCALE = 1 00410 SIGMA = RMIN / ANRM 00411 ELSE IF( ANRM.GT.RMAX ) THEN 00412 ISCALE = 1 00413 SIGMA = RMAX / ANRM 00414 END IF 00415 IF( ISCALE.EQ.1 ) THEN 00416 IF( LOWER ) THEN 00417 DO 10 J = 1, N 00418 CALL CSSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 00419 10 CONTINUE 00420 ELSE 00421 DO 20 J = 1, N 00422 CALL CSSCAL( J, SIGMA, A( 1, J ), 1 ) 00423 20 CONTINUE 00424 END IF 00425 IF( ABSTOL.GT.0 ) 00426 $ ABSTLL = ABSTOL*SIGMA 00427 IF( VALEIG ) THEN 00428 VLL = VL*SIGMA 00429 VUU = VU*SIGMA 00430 END IF 00431 END IF 00432 * 00433 * Call CHETRD to reduce Hermitian matrix to tridiagonal form. 00434 * 00435 INDD = 1 00436 INDE = INDD + N 00437 INDRWK = INDE + N 00438 INDTAU = 1 00439 INDWRK = INDTAU + N 00440 LLWORK = LWORK - INDWRK + 1 00441 CALL CHETRD( UPLO, N, A, LDA, RWORK( INDD ), RWORK( INDE ), 00442 $ WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO ) 00443 * 00444 * If all eigenvalues are desired and ABSTOL is less than or equal to 00445 * zero, then call SSTERF or CUNGTR and CSTEQR. If this fails for 00446 * some eigenvalue, then try SSTEBZ. 00447 * 00448 TEST = .FALSE. 00449 IF( INDEIG ) THEN 00450 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN 00451 TEST = .TRUE. 00452 END IF 00453 END IF 00454 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN 00455 CALL SCOPY( N, RWORK( INDD ), 1, W, 1 ) 00456 INDEE = INDRWK + 2*N 00457 IF( .NOT.WANTZ ) THEN 00458 CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) 00459 CALL SSTERF( N, W, RWORK( INDEE ), INFO ) 00460 ELSE 00461 CALL CLACPY( 'A', N, N, A, LDA, Z, LDZ ) 00462 CALL CUNGTR( UPLO, N, Z, LDZ, WORK( INDTAU ), 00463 $ WORK( INDWRK ), LLWORK, IINFO ) 00464 CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) 00465 CALL CSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ, 00466 $ RWORK( INDRWK ), INFO ) 00467 IF( INFO.EQ.0 ) THEN 00468 DO 30 I = 1, N 00469 IFAIL( I ) = 0 00470 30 CONTINUE 00471 END IF 00472 END IF 00473 IF( INFO.EQ.0 ) THEN 00474 M = N 00475 GO TO 40 00476 END IF 00477 INFO = 0 00478 END IF 00479 * 00480 * Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. 00481 * 00482 IF( WANTZ ) THEN 00483 ORDER = 'B' 00484 ELSE 00485 ORDER = 'E' 00486 END IF 00487 INDIBL = 1 00488 INDISP = INDIBL + N 00489 INDIWK = INDISP + N 00490 CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, 00491 $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W, 00492 $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ), 00493 $ IWORK( INDIWK ), INFO ) 00494 * 00495 IF( WANTZ ) THEN 00496 CALL CSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W, 00497 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, 00498 $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO ) 00499 * 00500 * Apply unitary matrix used in reduction to tridiagonal 00501 * form to eigenvectors returned by CSTEIN. 00502 * 00503 CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, 00504 $ LDZ, WORK( INDWRK ), LLWORK, IINFO ) 00505 END IF 00506 * 00507 * If matrix was scaled, then rescale eigenvalues appropriately. 00508 * 00509 40 CONTINUE 00510 IF( ISCALE.EQ.1 ) THEN 00511 IF( INFO.EQ.0 ) THEN 00512 IMAX = M 00513 ELSE 00514 IMAX = INFO - 1 00515 END IF 00516 CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) 00517 END IF 00518 * 00519 * If eigenvalues are not in order, then sort them, along with 00520 * eigenvectors. 00521 * 00522 IF( WANTZ ) THEN 00523 DO 60 J = 1, M - 1 00524 I = 0 00525 TMP1 = W( J ) 00526 DO 50 JJ = J + 1, M 00527 IF( W( JJ ).LT.TMP1 ) THEN 00528 I = JJ 00529 TMP1 = W( JJ ) 00530 END IF 00531 50 CONTINUE 00532 * 00533 IF( I.NE.0 ) THEN 00534 ITMP1 = IWORK( INDIBL+I-1 ) 00535 W( I ) = W( J ) 00536 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) 00537 W( J ) = TMP1 00538 IWORK( INDIBL+J-1 ) = ITMP1 00539 CALL CSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) 00540 IF( INFO.NE.0 ) THEN 00541 ITMP1 = IFAIL( I ) 00542 IFAIL( I ) = IFAIL( J ) 00543 IFAIL( J ) = ITMP1 00544 END IF 00545 END IF 00546 60 CONTINUE 00547 END IF 00548 * 00549 * Set WORK(1) to optimal complex workspace size. 00550 * 00551 WORK( 1 ) = LWKOPT 00552 * 00553 RETURN 00554 * 00555 * End of CHEEVX 00556 * 00557 END