Annotation of rpl/lapack/lapack/dsyevx_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> DSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
! 2: *
! 3: * @precisions fortran d -> s
! 4: *
! 5: * =========== DOCUMENTATION ===========
! 6: *
! 7: * Online html documentation available at
! 8: * http://www.netlib.org/lapack/explore-html/
! 9: *
! 10: *> \htmlonly
! 11: *> Download DSYEVX_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevx_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevx_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevx_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSYEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
! 24: * IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 25: * LWORK, IWORK, IFAIL, INFO )
! 26: *
! 27: * IMPLICIT NONE
! 28: *
! 29: * .. Scalar Arguments ..
! 30: * CHARACTER JOBZ, RANGE, UPLO
! 31: * INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N
! 32: * DOUBLE PRECISION ABSTOL, VL, VU
! 33: * ..
! 34: * .. Array Arguments ..
! 35: * INTEGER IFAIL( * ), IWORK( * )
! 36: * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
! 37: * ..
! 38: *
! 39: *
! 40: *> \par Purpose:
! 41: * =============
! 42: *>
! 43: *> \verbatim
! 44: *>
! 45: *> DSYEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
! 46: *> of a real symmetric matrix A using the 2stage technique for
! 47: *> the reduction to tridiagonal. Eigenvalues and eigenvectors can be
! 48: *> selected by specifying either a range of values or a range of indices
! 49: *> for the desired eigenvalues.
! 50: *> \endverbatim
! 51: *
! 52: * Arguments:
! 53: * ==========
! 54: *
! 55: *> \param[in] JOBZ
! 56: *> \verbatim
! 57: *> JOBZ is CHARACTER*1
! 58: *> = 'N': Compute eigenvalues only;
! 59: *> = 'V': Compute eigenvalues and eigenvectors.
! 60: *> Not available in this release.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] RANGE
! 64: *> \verbatim
! 65: *> RANGE is CHARACTER*1
! 66: *> = 'A': all eigenvalues will be found.
! 67: *> = 'V': all eigenvalues in the half-open interval (VL,VU]
! 68: *> will be found.
! 69: *> = 'I': the IL-th through IU-th eigenvalues will be found.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] UPLO
! 73: *> \verbatim
! 74: *> UPLO is CHARACTER*1
! 75: *> = 'U': Upper triangle of A is stored;
! 76: *> = 'L': Lower triangle of A is stored.
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] N
! 80: *> \verbatim
! 81: *> N is INTEGER
! 82: *> The order of the matrix A. N >= 0.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in,out] A
! 86: *> \verbatim
! 87: *> A is DOUBLE PRECISION array, dimension (LDA, N)
! 88: *> On entry, the symmetric matrix A. If UPLO = 'U', the
! 89: *> leading N-by-N upper triangular part of A contains the
! 90: *> upper triangular part of the matrix A. If UPLO = 'L',
! 91: *> the leading N-by-N lower triangular part of A contains
! 92: *> the lower triangular part of the matrix A.
! 93: *> On exit, the lower triangle (if UPLO='L') or the upper
! 94: *> triangle (if UPLO='U') of A, including the diagonal, is
! 95: *> destroyed.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] LDA
! 99: *> \verbatim
! 100: *> LDA is INTEGER
! 101: *> The leading dimension of the array A. LDA >= max(1,N).
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in] VL
! 105: *> \verbatim
! 106: *> VL is DOUBLE PRECISION
! 107: *> If RANGE='V', the lower bound of the interval to
! 108: *> be searched for eigenvalues. VL < VU.
! 109: *> Not referenced if RANGE = 'A' or 'I'.
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[in] VU
! 113: *> \verbatim
! 114: *> VU is DOUBLE PRECISION
! 115: *> If RANGE='V', the upper bound of the interval to
! 116: *> be searched for eigenvalues. VL < VU.
! 117: *> Not referenced if RANGE = 'A' or 'I'.
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[in] IL
! 121: *> \verbatim
! 122: *> IL is INTEGER
! 123: *> If RANGE='I', the index of the
! 124: *> smallest eigenvalue to be returned.
! 125: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 126: *> Not referenced if RANGE = 'A' or 'V'.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] IU
! 130: *> \verbatim
! 131: *> IU is INTEGER
! 132: *> If RANGE='I', the index of the
! 133: *> largest eigenvalue to be returned.
! 134: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 135: *> Not referenced if RANGE = 'A' or 'V'.
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[in] ABSTOL
! 139: *> \verbatim
! 140: *> ABSTOL is DOUBLE PRECISION
! 141: *> The absolute error tolerance for the eigenvalues.
! 142: *> An approximate eigenvalue is accepted as converged
! 143: *> when it is determined to lie in an interval [a,b]
! 144: *> of width less than or equal to
! 145: *>
! 146: *> ABSTOL + EPS * max( |a|,|b| ) ,
! 147: *>
! 148: *> where EPS is the machine precision. If ABSTOL is less than
! 149: *> or equal to zero, then EPS*|T| will be used in its place,
! 150: *> where |T| is the 1-norm of the tridiagonal matrix obtained
! 151: *> by reducing A to tridiagonal form.
! 152: *>
! 153: *> Eigenvalues will be computed most accurately when ABSTOL is
! 154: *> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 155: *> If this routine returns with INFO>0, indicating that some
! 156: *> eigenvectors did not converge, try setting ABSTOL to
! 157: *> 2*DLAMCH('S').
! 158: *>
! 159: *> See "Computing Small Singular Values of Bidiagonal Matrices
! 160: *> with Guaranteed High Relative Accuracy," by Demmel and
! 161: *> Kahan, LAPACK Working Note #3.
! 162: *> \endverbatim
! 163: *>
! 164: *> \param[out] M
! 165: *> \verbatim
! 166: *> M is INTEGER
! 167: *> The total number of eigenvalues found. 0 <= M <= N.
! 168: *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 169: *> \endverbatim
! 170: *>
! 171: *> \param[out] W
! 172: *> \verbatim
! 173: *> W is DOUBLE PRECISION array, dimension (N)
! 174: *> On normal exit, the first M elements contain the selected
! 175: *> eigenvalues in ascending order.
! 176: *> \endverbatim
! 177: *>
! 178: *> \param[out] Z
! 179: *> \verbatim
! 180: *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
! 181: *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 182: *> contain the orthonormal eigenvectors of the matrix A
! 183: *> corresponding to the selected eigenvalues, with the i-th
! 184: *> column of Z holding the eigenvector associated with W(i).
! 185: *> If an eigenvector fails to converge, then that column of Z
! 186: *> contains the latest approximation to the eigenvector, and the
! 187: *> index of the eigenvector is returned in IFAIL.
! 188: *> If JOBZ = 'N', then Z is not referenced.
! 189: *> Note: the user must ensure that at least max(1,M) columns are
! 190: *> supplied in the array Z; if RANGE = 'V', the exact value of M
! 191: *> is not known in advance and an upper bound must be used.
! 192: *> \endverbatim
! 193: *>
! 194: *> \param[in] LDZ
! 195: *> \verbatim
! 196: *> LDZ is INTEGER
! 197: *> The leading dimension of the array Z. LDZ >= 1, and if
! 198: *> JOBZ = 'V', LDZ >= max(1,N).
! 199: *> \endverbatim
! 200: *>
! 201: *> \param[out] WORK
! 202: *> \verbatim
! 203: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 204: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 205: *> \endverbatim
! 206: *>
! 207: *> \param[in] LWORK
! 208: *> \verbatim
! 209: *> LWORK is INTEGER
! 210: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 211: *> otherwise
! 212: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 213: *> LWORK = MAX(1, 8*N, dimension) where
! 214: *> dimension = max(stage1,stage2) + (KD+1)*N + 3*N
! 215: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 216: *> + max(2*KD*KD, KD*NTHREADS)
! 217: *> + (KD+1)*N + 3*N
! 218: *> where KD is the blocking size of the reduction,
! 219: *> FACTOPTNB is the blocking used by the QR or LQ
! 220: *> algorithm, usually FACTOPTNB=128 is a good choice
! 221: *> NTHREADS is the number of threads used when
! 222: *> openMP compilation is enabled, otherwise =1.
! 223: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
! 224: *>
! 225: *> If LWORK = -1, then a workspace query is assumed; the routine
! 226: *> only calculates the optimal size of the WORK array, returns
! 227: *> this value as the first entry of the WORK array, and no error
! 228: *> message related to LWORK is issued by XERBLA.
! 229: *> \endverbatim
! 230: *>
! 231: *> \param[out] IWORK
! 232: *> \verbatim
! 233: *> IWORK is INTEGER array, dimension (5*N)
! 234: *> \endverbatim
! 235: *>
! 236: *> \param[out] IFAIL
! 237: *> \verbatim
! 238: *> IFAIL is INTEGER array, dimension (N)
! 239: *> If JOBZ = 'V', then if INFO = 0, the first M elements of
! 240: *> IFAIL are zero. If INFO > 0, then IFAIL contains the
! 241: *> indices of the eigenvectors that failed to converge.
! 242: *> If JOBZ = 'N', then IFAIL is not referenced.
! 243: *> \endverbatim
! 244: *>
! 245: *> \param[out] INFO
! 246: *> \verbatim
! 247: *> INFO is INTEGER
! 248: *> = 0: successful exit
! 249: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 250: *> > 0: if INFO = i, then i eigenvectors failed to converge.
! 251: *> Their indices are stored in array IFAIL.
! 252: *> \endverbatim
! 253: *
! 254: * Authors:
! 255: * ========
! 256: *
! 257: *> \author Univ. of Tennessee
! 258: *> \author Univ. of California Berkeley
! 259: *> \author Univ. of Colorado Denver
! 260: *> \author NAG Ltd.
! 261: *
! 262: *> \date June 2016
! 263: *
! 264: *> \ingroup doubleSYeigen
! 265: *
! 266: *> \par Further Details:
! 267: * =====================
! 268: *>
! 269: *> \verbatim
! 270: *>
! 271: *> All details about the 2stage techniques are available in:
! 272: *>
! 273: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 274: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 275: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 276: *> of 2011 International Conference for High Performance Computing,
! 277: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 278: *> Article 8 , 11 pages.
! 279: *> http://doi.acm.org/10.1145/2063384.2063394
! 280: *>
! 281: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 282: *> An improved parallel singular value algorithm and its implementation
! 283: *> for multicore hardware, In Proceedings of 2013 International Conference
! 284: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 285: *> Denver, Colorado, USA, 2013.
! 286: *> Article 90, 12 pages.
! 287: *> http://doi.acm.org/10.1145/2503210.2503292
! 288: *>
! 289: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 290: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 291: *> calculations based on fine-grained memory aware tasks.
! 292: *> International Journal of High Performance Computing Applications.
! 293: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 294: *> http://hpc.sagepub.com/content/28/2/196
! 295: *>
! 296: *> \endverbatim
! 297: *
! 298: * =====================================================================
! 299: SUBROUTINE DSYEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
! 300: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 301: $ LWORK, IWORK, IFAIL, INFO )
! 302: *
! 303: IMPLICIT NONE
! 304: *
! 305: * -- LAPACK driver routine (version 3.7.0) --
! 306: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 307: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 308: * June 2016
! 309: *
! 310: * .. Scalar Arguments ..
! 311: CHARACTER JOBZ, RANGE, UPLO
! 312: INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N
! 313: DOUBLE PRECISION ABSTOL, VL, VU
! 314: * ..
! 315: * .. Array Arguments ..
! 316: INTEGER IFAIL( * ), IWORK( * )
! 317: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
! 318: * ..
! 319: *
! 320: * =====================================================================
! 321: *
! 322: * .. Parameters ..
! 323: DOUBLE PRECISION ZERO, ONE
! 324: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 325: * ..
! 326: * .. Local Scalars ..
! 327: LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
! 328: $ WANTZ
! 329: CHARACTER ORDER
! 330: INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
! 331: $ INDISP, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
! 332: $ ITMP1, J, JJ, LLWORK, LLWRKN,
! 333: $ NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
! 334: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
! 335: $ SIGMA, SMLNUM, TMP1, VLL, VUU
! 336: * ..
! 337: * .. External Functions ..
! 338: LOGICAL LSAME
! 339: INTEGER ILAENV
! 340: DOUBLE PRECISION DLAMCH, DLANSY
! 341: EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY
! 342: * ..
! 343: * .. External Subroutines ..
! 344: EXTERNAL DCOPY, DLACPY, DORGTR, DORMTR, DSCAL, DSTEBZ,
! 345: $ DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA,
! 346: $ DSYTRD_2STAGE
! 347: * ..
! 348: * .. Intrinsic Functions ..
! 349: INTRINSIC MAX, MIN, SQRT
! 350: * ..
! 351: * .. Executable Statements ..
! 352: *
! 353: * Test the input parameters.
! 354: *
! 355: LOWER = LSAME( UPLO, 'L' )
! 356: WANTZ = LSAME( JOBZ, 'V' )
! 357: ALLEIG = LSAME( RANGE, 'A' )
! 358: VALEIG = LSAME( RANGE, 'V' )
! 359: INDEIG = LSAME( RANGE, 'I' )
! 360: LQUERY = ( LWORK.EQ.-1 )
! 361: *
! 362: INFO = 0
! 363: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 364: INFO = -1
! 365: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 366: INFO = -2
! 367: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 368: INFO = -3
! 369: ELSE IF( N.LT.0 ) THEN
! 370: INFO = -4
! 371: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 372: INFO = -6
! 373: ELSE
! 374: IF( VALEIG ) THEN
! 375: IF( N.GT.0 .AND. VU.LE.VL )
! 376: $ INFO = -8
! 377: ELSE IF( INDEIG ) THEN
! 378: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 379: INFO = -9
! 380: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 381: INFO = -10
! 382: END IF
! 383: END IF
! 384: END IF
! 385: IF( INFO.EQ.0 ) THEN
! 386: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 387: INFO = -15
! 388: END IF
! 389: END IF
! 390: *
! 391: IF( INFO.EQ.0 ) THEN
! 392: IF( N.LE.1 ) THEN
! 393: LWMIN = 1
! 394: WORK( 1 ) = LWMIN
! 395: ELSE
! 396: KD = ILAENV( 17, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 397: IB = ILAENV( 18, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 398: LHTRD = ILAENV( 19, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 399: LWTRD = ILAENV( 20, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 400: LWMIN = MAX( 8*N, 3*N + LHTRD + LWTRD )
! 401: WORK( 1 ) = LWMIN
! 402: END IF
! 403: *
! 404: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
! 405: $ INFO = -17
! 406: END IF
! 407: *
! 408: IF( INFO.NE.0 ) THEN
! 409: CALL XERBLA( 'DSYEVX_2STAGE', -INFO )
! 410: RETURN
! 411: ELSE IF( LQUERY ) THEN
! 412: RETURN
! 413: END IF
! 414: *
! 415: * Quick return if possible
! 416: *
! 417: M = 0
! 418: IF( N.EQ.0 ) THEN
! 419: RETURN
! 420: END IF
! 421: *
! 422: IF( N.EQ.1 ) THEN
! 423: IF( ALLEIG .OR. INDEIG ) THEN
! 424: M = 1
! 425: W( 1 ) = A( 1, 1 )
! 426: ELSE
! 427: IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN
! 428: M = 1
! 429: W( 1 ) = A( 1, 1 )
! 430: END IF
! 431: END IF
! 432: IF( WANTZ )
! 433: $ Z( 1, 1 ) = ONE
! 434: RETURN
! 435: END IF
! 436: *
! 437: * Get machine constants.
! 438: *
! 439: SAFMIN = DLAMCH( 'Safe minimum' )
! 440: EPS = DLAMCH( 'Precision' )
! 441: SMLNUM = SAFMIN / EPS
! 442: BIGNUM = ONE / SMLNUM
! 443: RMIN = SQRT( SMLNUM )
! 444: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
! 445: *
! 446: * Scale matrix to allowable range, if necessary.
! 447: *
! 448: ISCALE = 0
! 449: ABSTLL = ABSTOL
! 450: IF( VALEIG ) THEN
! 451: VLL = VL
! 452: VUU = VU
! 453: END IF
! 454: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
! 455: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 456: ISCALE = 1
! 457: SIGMA = RMIN / ANRM
! 458: ELSE IF( ANRM.GT.RMAX ) THEN
! 459: ISCALE = 1
! 460: SIGMA = RMAX / ANRM
! 461: END IF
! 462: IF( ISCALE.EQ.1 ) THEN
! 463: IF( LOWER ) THEN
! 464: DO 10 J = 1, N
! 465: CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 )
! 466: 10 CONTINUE
! 467: ELSE
! 468: DO 20 J = 1, N
! 469: CALL DSCAL( J, SIGMA, A( 1, J ), 1 )
! 470: 20 CONTINUE
! 471: END IF
! 472: IF( ABSTOL.GT.0 )
! 473: $ ABSTLL = ABSTOL*SIGMA
! 474: IF( VALEIG ) THEN
! 475: VLL = VL*SIGMA
! 476: VUU = VU*SIGMA
! 477: END IF
! 478: END IF
! 479: *
! 480: * Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
! 481: *
! 482: INDTAU = 1
! 483: INDE = INDTAU + N
! 484: INDD = INDE + N
! 485: INDHOUS = INDD + N
! 486: INDWRK = INDHOUS + LHTRD
! 487: LLWORK = LWORK - INDWRK + 1
! 488: *
! 489: CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, WORK( INDD ),
! 490: $ WORK( INDE ), WORK( INDTAU ), WORK( INDHOUS ),
! 491: $ LHTRD, WORK( INDWRK ), LLWORK, IINFO )
! 492: *
! 493: * If all eigenvalues are desired and ABSTOL is less than or equal to
! 494: * zero, then call DSTERF or DORGTR and SSTEQR. If this fails for
! 495: * some eigenvalue, then try DSTEBZ.
! 496: *
! 497: TEST = .FALSE.
! 498: IF( INDEIG ) THEN
! 499: IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
! 500: TEST = .TRUE.
! 501: END IF
! 502: END IF
! 503: IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
! 504: CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
! 505: INDEE = INDWRK + 2*N
! 506: IF( .NOT.WANTZ ) THEN
! 507: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 508: CALL DSTERF( N, W, WORK( INDEE ), INFO )
! 509: ELSE
! 510: CALL DLACPY( 'A', N, N, A, LDA, Z, LDZ )
! 511: CALL DORGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
! 512: $ WORK( INDWRK ), LLWORK, IINFO )
! 513: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 514: CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
! 515: $ WORK( INDWRK ), INFO )
! 516: IF( INFO.EQ.0 ) THEN
! 517: DO 30 I = 1, N
! 518: IFAIL( I ) = 0
! 519: 30 CONTINUE
! 520: END IF
! 521: END IF
! 522: IF( INFO.EQ.0 ) THEN
! 523: M = N
! 524: GO TO 40
! 525: END IF
! 526: INFO = 0
! 527: END IF
! 528: *
! 529: * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
! 530: *
! 531: IF( WANTZ ) THEN
! 532: ORDER = 'B'
! 533: ELSE
! 534: ORDER = 'E'
! 535: END IF
! 536: INDIBL = 1
! 537: INDISP = INDIBL + N
! 538: INDIWO = INDISP + N
! 539: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
! 540: $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
! 541: $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
! 542: $ IWORK( INDIWO ), INFO )
! 543: *
! 544: IF( WANTZ ) THEN
! 545: CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
! 546: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
! 547: $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
! 548: *
! 549: * Apply orthogonal matrix used in reduction to tridiagonal
! 550: * form to eigenvectors returned by DSTEIN.
! 551: *
! 552: INDWKN = INDE
! 553: LLWRKN = LWORK - INDWKN + 1
! 554: CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
! 555: $ LDZ, WORK( INDWKN ), LLWRKN, IINFO )
! 556: END IF
! 557: *
! 558: * If matrix was scaled, then rescale eigenvalues appropriately.
! 559: *
! 560: 40 CONTINUE
! 561: IF( ISCALE.EQ.1 ) THEN
! 562: IF( INFO.EQ.0 ) THEN
! 563: IMAX = M
! 564: ELSE
! 565: IMAX = INFO - 1
! 566: END IF
! 567: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 568: END IF
! 569: *
! 570: * If eigenvalues are not in order, then sort them, along with
! 571: * eigenvectors.
! 572: *
! 573: IF( WANTZ ) THEN
! 574: DO 60 J = 1, M - 1
! 575: I = 0
! 576: TMP1 = W( J )
! 577: DO 50 JJ = J + 1, M
! 578: IF( W( JJ ).LT.TMP1 ) THEN
! 579: I = JJ
! 580: TMP1 = W( JJ )
! 581: END IF
! 582: 50 CONTINUE
! 583: *
! 584: IF( I.NE.0 ) THEN
! 585: ITMP1 = IWORK( INDIBL+I-1 )
! 586: W( I ) = W( J )
! 587: IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
! 588: W( J ) = TMP1
! 589: IWORK( INDIBL+J-1 ) = ITMP1
! 590: CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
! 591: IF( INFO.NE.0 ) THEN
! 592: ITMP1 = IFAIL( I )
! 593: IFAIL( I ) = IFAIL( J )
! 594: IFAIL( J ) = ITMP1
! 595: END IF
! 596: END IF
! 597: 60 CONTINUE
! 598: END IF
! 599: *
! 600: * Set WORK(1) to optimal workspace size.
! 601: *
! 602: WORK( 1 ) = LWMIN
! 603: *
! 604: RETURN
! 605: *
! 606: * End of DSYEVX_2STAGE
! 607: *
! 608: END
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