Annotation of rpl/lapack/lapack/zheevx_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> ZHEEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
! 2: *
! 3: * @precisions fortran z -> s d c
! 4: *
! 5: * =========== DOCUMENTATION ===========
! 6: *
! 7: * Online html documentation available at
! 8: * http://www.netlib.org/lapack/explore-html/
! 9: *
! 10: *> \htmlonly
! 11: *> Download ZHEEVX_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheevx_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevx_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevx_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE ZHEEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
! 24: * IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 25: * LWORK, RWORK, 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 RWORK( * ), W( * )
! 37: * COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * )
! 38: * ..
! 39: *
! 40: *
! 41: *> \par Purpose:
! 42: * =============
! 43: *>
! 44: *> \verbatim
! 45: *>
! 46: *> ZHEEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
! 47: *> of a complex Hermitian matrix A using the 2stage technique for
! 48: *> the reduction to tridiagonal. Eigenvalues and eigenvectors can
! 49: *> be selected by specifying either a range of values or a range of
! 50: *> indices for the desired eigenvalues.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] JOBZ
! 57: *> \verbatim
! 58: *> JOBZ is CHARACTER*1
! 59: *> = 'N': Compute eigenvalues only;
! 60: *> = 'V': Compute eigenvalues and eigenvectors.
! 61: *> Not available in this release.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] RANGE
! 65: *> \verbatim
! 66: *> RANGE is CHARACTER*1
! 67: *> = 'A': all eigenvalues will be found.
! 68: *> = 'V': all eigenvalues in the half-open interval (VL,VU]
! 69: *> will be found.
! 70: *> = 'I': the IL-th through IU-th eigenvalues will be found.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] UPLO
! 74: *> \verbatim
! 75: *> UPLO is CHARACTER*1
! 76: *> = 'U': Upper triangle of A is stored;
! 77: *> = 'L': Lower triangle of A is stored.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] N
! 81: *> \verbatim
! 82: *> N is INTEGER
! 83: *> The order of the matrix A. N >= 0.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in,out] A
! 87: *> \verbatim
! 88: *> A is COMPLEX*16 array, dimension (LDA, N)
! 89: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
! 90: *> leading N-by-N upper triangular part of A contains the
! 91: *> upper triangular part of the matrix A. If UPLO = 'L',
! 92: *> the leading N-by-N lower triangular part of A contains
! 93: *> the lower triangular part of the matrix A.
! 94: *> On exit, the lower triangle (if UPLO='L') or the upper
! 95: *> triangle (if UPLO='U') of A, including the diagonal, is
! 96: *> destroyed.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] LDA
! 100: *> \verbatim
! 101: *> LDA is INTEGER
! 102: *> The leading dimension of the array A. LDA >= max(1,N).
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in] VL
! 106: *> \verbatim
! 107: *> VL is DOUBLE PRECISION
! 108: *> If RANGE='V', the lower bound of the interval to
! 109: *> be searched for eigenvalues. VL < VU.
! 110: *> Not referenced if RANGE = 'A' or 'I'.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] VU
! 114: *> \verbatim
! 115: *> VU is DOUBLE PRECISION
! 116: *> If RANGE='V', the upper bound of the interval to
! 117: *> be searched for eigenvalues. VL < VU.
! 118: *> Not referenced if RANGE = 'A' or 'I'.
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] IL
! 122: *> \verbatim
! 123: *> IL is INTEGER
! 124: *> If RANGE='I', the index of the
! 125: *> smallest eigenvalue to be returned.
! 126: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 127: *> Not referenced if RANGE = 'A' or 'V'.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] IU
! 131: *> \verbatim
! 132: *> IU is INTEGER
! 133: *> If RANGE='I', the index of the
! 134: *> largest eigenvalue to be returned.
! 135: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 136: *> Not referenced if RANGE = 'A' or 'V'.
! 137: *> \endverbatim
! 138: *>
! 139: *> \param[in] ABSTOL
! 140: *> \verbatim
! 141: *> ABSTOL is DOUBLE PRECISION
! 142: *> The absolute error tolerance for the eigenvalues.
! 143: *> An approximate eigenvalue is accepted as converged
! 144: *> when it is determined to lie in an interval [a,b]
! 145: *> of width less than or equal to
! 146: *>
! 147: *> ABSTOL + EPS * max( |a|,|b| ) ,
! 148: *>
! 149: *> where EPS is the machine precision. If ABSTOL is less than
! 150: *> or equal to zero, then EPS*|T| will be used in its place,
! 151: *> where |T| is the 1-norm of the tridiagonal matrix obtained
! 152: *> by reducing A to tridiagonal form.
! 153: *>
! 154: *> Eigenvalues will be computed most accurately when ABSTOL is
! 155: *> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 156: *> If this routine returns with INFO>0, indicating that some
! 157: *> eigenvectors did not converge, try setting ABSTOL to
! 158: *> 2*DLAMCH('S').
! 159: *>
! 160: *> See "Computing Small Singular Values of Bidiagonal Matrices
! 161: *> with Guaranteed High Relative Accuracy," by Demmel and
! 162: *> Kahan, LAPACK Working Note #3.
! 163: *> \endverbatim
! 164: *>
! 165: *> \param[out] M
! 166: *> \verbatim
! 167: *> M is INTEGER
! 168: *> The total number of eigenvalues found. 0 <= M <= N.
! 169: *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 170: *> \endverbatim
! 171: *>
! 172: *> \param[out] W
! 173: *> \verbatim
! 174: *> W is DOUBLE PRECISION array, dimension (N)
! 175: *> On normal exit, the first M elements contain the selected
! 176: *> eigenvalues in ascending order.
! 177: *> \endverbatim
! 178: *>
! 179: *> \param[out] Z
! 180: *> \verbatim
! 181: *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
! 182: *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 183: *> contain the orthonormal eigenvectors of the matrix A
! 184: *> corresponding to the selected eigenvalues, with the i-th
! 185: *> column of Z holding the eigenvector associated with W(i).
! 186: *> If an eigenvector fails to converge, then that column of Z
! 187: *> contains the latest approximation to the eigenvector, and the
! 188: *> index of the eigenvector is returned in IFAIL.
! 189: *> If JOBZ = 'N', then Z is not referenced.
! 190: *> Note: the user must ensure that at least max(1,M) columns are
! 191: *> supplied in the array Z; if RANGE = 'V', the exact value of M
! 192: *> is not known in advance and an upper bound must be used.
! 193: *> \endverbatim
! 194: *>
! 195: *> \param[in] LDZ
! 196: *> \verbatim
! 197: *> LDZ is INTEGER
! 198: *> The leading dimension of the array Z. LDZ >= 1, and if
! 199: *> JOBZ = 'V', LDZ >= max(1,N).
! 200: *> \endverbatim
! 201: *>
! 202: *> \param[out] WORK
! 203: *> \verbatim
! 204: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 205: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 206: *> \endverbatim
! 207: *>
! 208: *> \param[in] LWORK
! 209: *> \verbatim
! 210: *> LWORK is INTEGER
! 211: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 212: *> otherwise
! 213: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 214: *> LWORK = MAX(1, 8*N, dimension) where
! 215: *> dimension = max(stage1,stage2) + (KD+1)*N + N
! 216: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 217: *> + max(2*KD*KD, KD*NTHREADS)
! 218: *> + (KD+1)*N + N
! 219: *> where KD is the blocking size of the reduction,
! 220: *> FACTOPTNB is the blocking used by the QR or LQ
! 221: *> algorithm, usually FACTOPTNB=128 is a good choice
! 222: *> NTHREADS is the number of threads used when
! 223: *> openMP compilation is enabled, otherwise =1.
! 224: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
! 225: *>
! 226: *> If LWORK = -1, then a workspace query is assumed; the routine
! 227: *> only calculates the optimal size of the WORK array, returns
! 228: *> this value as the first entry of the WORK array, and no error
! 229: *> message related to LWORK is issued by XERBLA.
! 230: *> \endverbatim
! 231: *>
! 232: *> \param[out] RWORK
! 233: *> \verbatim
! 234: *> RWORK is DOUBLE PRECISION array, dimension (7*N)
! 235: *> \endverbatim
! 236: *>
! 237: *> \param[out] IWORK
! 238: *> \verbatim
! 239: *> IWORK is INTEGER array, dimension (5*N)
! 240: *> \endverbatim
! 241: *>
! 242: *> \param[out] IFAIL
! 243: *> \verbatim
! 244: *> IFAIL is INTEGER array, dimension (N)
! 245: *> If JOBZ = 'V', then if INFO = 0, the first M elements of
! 246: *> IFAIL are zero. If INFO > 0, then IFAIL contains the
! 247: *> indices of the eigenvectors that failed to converge.
! 248: *> If JOBZ = 'N', then IFAIL is not referenced.
! 249: *> \endverbatim
! 250: *>
! 251: *> \param[out] INFO
! 252: *> \verbatim
! 253: *> INFO is INTEGER
! 254: *> = 0: successful exit
! 255: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 256: *> > 0: if INFO = i, then i eigenvectors failed to converge.
! 257: *> Their indices are stored in array IFAIL.
! 258: *> \endverbatim
! 259: *
! 260: * Authors:
! 261: * ========
! 262: *
! 263: *> \author Univ. of Tennessee
! 264: *> \author Univ. of California Berkeley
! 265: *> \author Univ. of Colorado Denver
! 266: *> \author NAG Ltd.
! 267: *
! 268: *> \date June 2016
! 269: *
! 270: *> \ingroup complex16HEeigen
! 271: *
! 272: *> \par Further Details:
! 273: * =====================
! 274: *>
! 275: *> \verbatim
! 276: *>
! 277: *> All details about the 2stage techniques are available in:
! 278: *>
! 279: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 280: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 281: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 282: *> of 2011 International Conference for High Performance Computing,
! 283: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 284: *> Article 8 , 11 pages.
! 285: *> http://doi.acm.org/10.1145/2063384.2063394
! 286: *>
! 287: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 288: *> An improved parallel singular value algorithm and its implementation
! 289: *> for multicore hardware, In Proceedings of 2013 International Conference
! 290: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 291: *> Denver, Colorado, USA, 2013.
! 292: *> Article 90, 12 pages.
! 293: *> http://doi.acm.org/10.1145/2503210.2503292
! 294: *>
! 295: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 296: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 297: *> calculations based on fine-grained memory aware tasks.
! 298: *> International Journal of High Performance Computing Applications.
! 299: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 300: *> http://hpc.sagepub.com/content/28/2/196
! 301: *>
! 302: *> \endverbatim
! 303: *
! 304: * =====================================================================
! 305: SUBROUTINE ZHEEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
! 306: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 307: $ LWORK, RWORK, IWORK, IFAIL, INFO )
! 308: *
! 309: IMPLICIT NONE
! 310: *
! 311: * -- LAPACK driver routine (version 3.7.0) --
! 312: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 313: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 314: * June 2016
! 315: *
! 316: * .. Scalar Arguments ..
! 317: CHARACTER JOBZ, RANGE, UPLO
! 318: INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N
! 319: DOUBLE PRECISION ABSTOL, VL, VU
! 320: * ..
! 321: * .. Array Arguments ..
! 322: INTEGER IFAIL( * ), IWORK( * )
! 323: DOUBLE PRECISION RWORK( * ), W( * )
! 324: COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * )
! 325: * ..
! 326: *
! 327: * =====================================================================
! 328: *
! 329: * .. Parameters ..
! 330: DOUBLE PRECISION ZERO, ONE
! 331: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 332: COMPLEX*16 CONE
! 333: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 334: * ..
! 335: * .. Local Scalars ..
! 336: LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
! 337: $ WANTZ
! 338: CHARACTER ORDER
! 339: INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
! 340: $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
! 341: $ ITMP1, J, JJ, LLWORK,
! 342: $ NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
! 343: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
! 344: $ SIGMA, SMLNUM, TMP1, VLL, VUU
! 345: * ..
! 346: * .. External Functions ..
! 347: LOGICAL LSAME
! 348: INTEGER ILAENV
! 349: DOUBLE PRECISION DLAMCH, ZLANHE
! 350: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE
! 351: * ..
! 352: * .. External Subroutines ..
! 353: EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL,
! 354: $ ZLACPY, ZSTEIN, ZSTEQR, ZSWAP, ZUNGTR, ZUNMTR,
! 355: $ ZHETRD_2STAGE
! 356: * ..
! 357: * .. Intrinsic Functions ..
! 358: INTRINSIC DBLE, MAX, MIN, SQRT
! 359: * ..
! 360: * .. Executable Statements ..
! 361: *
! 362: * Test the input parameters.
! 363: *
! 364: LOWER = LSAME( UPLO, 'L' )
! 365: WANTZ = LSAME( JOBZ, 'V' )
! 366: ALLEIG = LSAME( RANGE, 'A' )
! 367: VALEIG = LSAME( RANGE, 'V' )
! 368: INDEIG = LSAME( RANGE, 'I' )
! 369: LQUERY = ( LWORK.EQ.-1 )
! 370: *
! 371: INFO = 0
! 372: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 373: INFO = -1
! 374: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 375: INFO = -2
! 376: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 377: INFO = -3
! 378: ELSE IF( N.LT.0 ) THEN
! 379: INFO = -4
! 380: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 381: INFO = -6
! 382: ELSE
! 383: IF( VALEIG ) THEN
! 384: IF( N.GT.0 .AND. VU.LE.VL )
! 385: $ INFO = -8
! 386: ELSE IF( INDEIG ) THEN
! 387: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 388: INFO = -9
! 389: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 390: INFO = -10
! 391: END IF
! 392: END IF
! 393: END IF
! 394: IF( INFO.EQ.0 ) THEN
! 395: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 396: INFO = -15
! 397: END IF
! 398: END IF
! 399: *
! 400: IF( INFO.EQ.0 ) THEN
! 401: IF( N.LE.1 ) THEN
! 402: LWMIN = 1
! 403: WORK( 1 ) = LWMIN
! 404: ELSE
! 405: KD = ILAENV( 17, 'ZHETRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 406: IB = ILAENV( 18, 'ZHETRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 407: LHTRD = ILAENV( 19, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 408: LWTRD = ILAENV( 20, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 409: LWMIN = N + LHTRD + LWTRD
! 410: WORK( 1 ) = LWMIN
! 411: END IF
! 412: *
! 413: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
! 414: $ INFO = -17
! 415: END IF
! 416: *
! 417: IF( INFO.NE.0 ) THEN
! 418: CALL XERBLA( 'ZHEEVX_2STAGE', -INFO )
! 419: RETURN
! 420: ELSE IF( LQUERY ) THEN
! 421: RETURN
! 422: END IF
! 423: *
! 424: * Quick return if possible
! 425: *
! 426: M = 0
! 427: IF( N.EQ.0 ) THEN
! 428: RETURN
! 429: END IF
! 430: *
! 431: IF( N.EQ.1 ) THEN
! 432: IF( ALLEIG .OR. INDEIG ) THEN
! 433: M = 1
! 434: W( 1 ) = DBLE( A( 1, 1 ) )
! 435: ELSE IF( VALEIG ) THEN
! 436: IF( VL.LT.DBLE( A( 1, 1 ) ) .AND. VU.GE.DBLE( A( 1, 1 ) ) )
! 437: $ THEN
! 438: M = 1
! 439: W( 1 ) = DBLE( A( 1, 1 ) )
! 440: END IF
! 441: END IF
! 442: IF( WANTZ )
! 443: $ Z( 1, 1 ) = CONE
! 444: RETURN
! 445: END IF
! 446: *
! 447: * Get machine constants.
! 448: *
! 449: SAFMIN = DLAMCH( 'Safe minimum' )
! 450: EPS = DLAMCH( 'Precision' )
! 451: SMLNUM = SAFMIN / EPS
! 452: BIGNUM = ONE / SMLNUM
! 453: RMIN = SQRT( SMLNUM )
! 454: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
! 455: *
! 456: * Scale matrix to allowable range, if necessary.
! 457: *
! 458: ISCALE = 0
! 459: ABSTLL = ABSTOL
! 460: IF( VALEIG ) THEN
! 461: VLL = VL
! 462: VUU = VU
! 463: END IF
! 464: ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
! 465: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 466: ISCALE = 1
! 467: SIGMA = RMIN / ANRM
! 468: ELSE IF( ANRM.GT.RMAX ) THEN
! 469: ISCALE = 1
! 470: SIGMA = RMAX / ANRM
! 471: END IF
! 472: IF( ISCALE.EQ.1 ) THEN
! 473: IF( LOWER ) THEN
! 474: DO 10 J = 1, N
! 475: CALL ZDSCAL( N-J+1, SIGMA, A( J, J ), 1 )
! 476: 10 CONTINUE
! 477: ELSE
! 478: DO 20 J = 1, N
! 479: CALL ZDSCAL( J, SIGMA, A( 1, J ), 1 )
! 480: 20 CONTINUE
! 481: END IF
! 482: IF( ABSTOL.GT.0 )
! 483: $ ABSTLL = ABSTOL*SIGMA
! 484: IF( VALEIG ) THEN
! 485: VLL = VL*SIGMA
! 486: VUU = VU*SIGMA
! 487: END IF
! 488: END IF
! 489: *
! 490: * Call ZHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
! 491: *
! 492: INDD = 1
! 493: INDE = INDD + N
! 494: INDRWK = INDE + N
! 495: INDTAU = 1
! 496: INDHOUS = INDTAU + N
! 497: INDWRK = INDHOUS + LHTRD
! 498: LLWORK = LWORK - INDWRK + 1
! 499: *
! 500: CALL ZHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDD ),
! 501: $ RWORK( INDE ), WORK( INDTAU ),
! 502: $ WORK( INDHOUS ), LHTRD, WORK( INDWRK ),
! 503: $ LLWORK, IINFO )
! 504: *
! 505: * If all eigenvalues are desired and ABSTOL is less than or equal to
! 506: * zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for
! 507: * some eigenvalue, then try DSTEBZ.
! 508: *
! 509: TEST = .FALSE.
! 510: IF( INDEIG ) THEN
! 511: IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
! 512: TEST = .TRUE.
! 513: END IF
! 514: END IF
! 515: IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
! 516: CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
! 517: INDEE = INDRWK + 2*N
! 518: IF( .NOT.WANTZ ) THEN
! 519: CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
! 520: CALL DSTERF( N, W, RWORK( INDEE ), INFO )
! 521: ELSE
! 522: CALL ZLACPY( 'A', N, N, A, LDA, Z, LDZ )
! 523: CALL ZUNGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
! 524: $ WORK( INDWRK ), LLWORK, IINFO )
! 525: CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
! 526: CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
! 527: $ RWORK( INDRWK ), INFO )
! 528: IF( INFO.EQ.0 ) THEN
! 529: DO 30 I = 1, N
! 530: IFAIL( I ) = 0
! 531: 30 CONTINUE
! 532: END IF
! 533: END IF
! 534: IF( INFO.EQ.0 ) THEN
! 535: M = N
! 536: GO TO 40
! 537: END IF
! 538: INFO = 0
! 539: END IF
! 540: *
! 541: * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN.
! 542: *
! 543: IF( WANTZ ) THEN
! 544: ORDER = 'B'
! 545: ELSE
! 546: ORDER = 'E'
! 547: END IF
! 548: INDIBL = 1
! 549: INDISP = INDIBL + N
! 550: INDIWK = INDISP + N
! 551: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
! 552: $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
! 553: $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
! 554: $ IWORK( INDIWK ), INFO )
! 555: *
! 556: IF( WANTZ ) THEN
! 557: CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
! 558: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
! 559: $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
! 560: *
! 561: * Apply unitary matrix used in reduction to tridiagonal
! 562: * form to eigenvectors returned by ZSTEIN.
! 563: *
! 564: CALL ZUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
! 565: $ LDZ, WORK( INDWRK ), LLWORK, IINFO )
! 566: END IF
! 567: *
! 568: * If matrix was scaled, then rescale eigenvalues appropriately.
! 569: *
! 570: 40 CONTINUE
! 571: IF( ISCALE.EQ.1 ) THEN
! 572: IF( INFO.EQ.0 ) THEN
! 573: IMAX = M
! 574: ELSE
! 575: IMAX = INFO - 1
! 576: END IF
! 577: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 578: END IF
! 579: *
! 580: * If eigenvalues are not in order, then sort them, along with
! 581: * eigenvectors.
! 582: *
! 583: IF( WANTZ ) THEN
! 584: DO 60 J = 1, M - 1
! 585: I = 0
! 586: TMP1 = W( J )
! 587: DO 50 JJ = J + 1, M
! 588: IF( W( JJ ).LT.TMP1 ) THEN
! 589: I = JJ
! 590: TMP1 = W( JJ )
! 591: END IF
! 592: 50 CONTINUE
! 593: *
! 594: IF( I.NE.0 ) THEN
! 595: ITMP1 = IWORK( INDIBL+I-1 )
! 596: W( I ) = W( J )
! 597: IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
! 598: W( J ) = TMP1
! 599: IWORK( INDIBL+J-1 ) = ITMP1
! 600: CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
! 601: IF( INFO.NE.0 ) THEN
! 602: ITMP1 = IFAIL( I )
! 603: IFAIL( I ) = IFAIL( J )
! 604: IFAIL( J ) = ITMP1
! 605: END IF
! 606: END IF
! 607: 60 CONTINUE
! 608: END IF
! 609: *
! 610: * Set WORK(1) to optimal complex workspace size.
! 611: *
! 612: WORK( 1 ) = LWMIN
! 613: *
! 614: RETURN
! 615: *
! 616: * End of ZHEEVX_2STAGE
! 617: *
! 618: END
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