Annotation of rpl/lapack/lapack/dsbevx_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> DSBEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 DSBEVX_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbevx_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbevx_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbevx_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q,
! 24: * LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
! 25: * LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
! 26: *
! 27: * IMPLICIT NONE
! 28: *
! 29: * .. Scalar Arguments ..
! 30: * CHARACTER JOBZ, RANGE, UPLO
! 31: * INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N, LWORK
! 32: * DOUBLE PRECISION ABSTOL, VL, VU
! 33: * ..
! 34: * .. Array Arguments ..
! 35: * INTEGER IFAIL( * ), IWORK( * )
! 36: * DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
! 37: * $ Z( LDZ, * )
! 38: * ..
! 39: *
! 40: *
! 41: *> \par Purpose:
! 42: * =============
! 43: *>
! 44: *> \verbatim
! 45: *>
! 46: *> DSBEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
! 47: *> of a real symmetric band 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] KD
! 87: *> \verbatim
! 88: *> KD is INTEGER
! 89: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 90: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in,out] AB
! 94: *> \verbatim
! 95: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
! 96: *> On entry, the upper or lower triangle of the symmetric band
! 97: *> matrix A, stored in the first KD+1 rows of the array. The
! 98: *> j-th column of A is stored in the j-th column of the array AB
! 99: *> as follows:
! 100: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 101: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 102: *>
! 103: *> On exit, AB is overwritten by values generated during the
! 104: *> reduction to tridiagonal form. If UPLO = 'U', the first
! 105: *> superdiagonal and the diagonal of the tridiagonal matrix T
! 106: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 107: *> the diagonal and first subdiagonal of T are returned in the
! 108: *> first two rows of AB.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] LDAB
! 112: *> \verbatim
! 113: *> LDAB is INTEGER
! 114: *> The leading dimension of the array AB. LDAB >= KD + 1.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[out] Q
! 118: *> \verbatim
! 119: *> Q is DOUBLE PRECISION array, dimension (LDQ, N)
! 120: *> If JOBZ = 'V', the N-by-N orthogonal matrix used in the
! 121: *> reduction to tridiagonal form.
! 122: *> If JOBZ = 'N', the array Q is not referenced.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in] LDQ
! 126: *> \verbatim
! 127: *> LDQ is INTEGER
! 128: *> The leading dimension of the array Q. If JOBZ = 'V', then
! 129: *> LDQ >= max(1,N).
! 130: *> \endverbatim
! 131: *>
! 132: *> \param[in] VL
! 133: *> \verbatim
! 134: *> VL is DOUBLE PRECISION
! 135: *> If RANGE='V', the lower bound of the interval to
! 136: *> be searched for eigenvalues. VL < VU.
! 137: *> Not referenced if RANGE = 'A' or 'I'.
! 138: *> \endverbatim
! 139: *>
! 140: *> \param[in] VU
! 141: *> \verbatim
! 142: *> VU is DOUBLE PRECISION
! 143: *> If RANGE='V', the upper bound of the interval to
! 144: *> be searched for eigenvalues. VL < VU.
! 145: *> Not referenced if RANGE = 'A' or 'I'.
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[in] IL
! 149: *> \verbatim
! 150: *> IL is INTEGER
! 151: *> If RANGE='I', the index of the
! 152: *> smallest eigenvalue to be returned.
! 153: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 154: *> Not referenced if RANGE = 'A' or 'V'.
! 155: *> \endverbatim
! 156: *>
! 157: *> \param[in] IU
! 158: *> \verbatim
! 159: *> IU is INTEGER
! 160: *> If RANGE='I', the index of the
! 161: *> largest eigenvalue to be returned.
! 162: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 163: *> Not referenced if RANGE = 'A' or 'V'.
! 164: *> \endverbatim
! 165: *>
! 166: *> \param[in] ABSTOL
! 167: *> \verbatim
! 168: *> ABSTOL is DOUBLE PRECISION
! 169: *> The absolute error tolerance for the eigenvalues.
! 170: *> An approximate eigenvalue is accepted as converged
! 171: *> when it is determined to lie in an interval [a,b]
! 172: *> of width less than or equal to
! 173: *>
! 174: *> ABSTOL + EPS * max( |a|,|b| ) ,
! 175: *>
! 176: *> where EPS is the machine precision. If ABSTOL is less than
! 177: *> or equal to zero, then EPS*|T| will be used in its place,
! 178: *> where |T| is the 1-norm of the tridiagonal matrix obtained
! 179: *> by reducing AB to tridiagonal form.
! 180: *>
! 181: *> Eigenvalues will be computed most accurately when ABSTOL is
! 182: *> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 183: *> If this routine returns with INFO>0, indicating that some
! 184: *> eigenvectors did not converge, try setting ABSTOL to
! 185: *> 2*DLAMCH('S').
! 186: *>
! 187: *> See "Computing Small Singular Values of Bidiagonal Matrices
! 188: *> with Guaranteed High Relative Accuracy," by Demmel and
! 189: *> Kahan, LAPACK Working Note #3.
! 190: *> \endverbatim
! 191: *>
! 192: *> \param[out] M
! 193: *> \verbatim
! 194: *> M is INTEGER
! 195: *> The total number of eigenvalues found. 0 <= M <= N.
! 196: *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 197: *> \endverbatim
! 198: *>
! 199: *> \param[out] W
! 200: *> \verbatim
! 201: *> W is DOUBLE PRECISION array, dimension (N)
! 202: *> The first M elements contain the selected eigenvalues in
! 203: *> ascending order.
! 204: *> \endverbatim
! 205: *>
! 206: *> \param[out] Z
! 207: *> \verbatim
! 208: *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
! 209: *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 210: *> contain the orthonormal eigenvectors of the matrix A
! 211: *> corresponding to the selected eigenvalues, with the i-th
! 212: *> column of Z holding the eigenvector associated with W(i).
! 213: *> If an eigenvector fails to converge, then that column of Z
! 214: *> contains the latest approximation to the eigenvector, and the
! 215: *> index of the eigenvector is returned in IFAIL.
! 216: *> If JOBZ = 'N', then Z is not referenced.
! 217: *> Note: the user must ensure that at least max(1,M) columns are
! 218: *> supplied in the array Z; if RANGE = 'V', the exact value of M
! 219: *> is not known in advance and an upper bound must be used.
! 220: *> \endverbatim
! 221: *>
! 222: *> \param[in] LDZ
! 223: *> \verbatim
! 224: *> LDZ is INTEGER
! 225: *> The leading dimension of the array Z. LDZ >= 1, and if
! 226: *> JOBZ = 'V', LDZ >= max(1,N).
! 227: *> \endverbatim
! 228: *>
! 229: *> \param[out] WORK
! 230: *> \verbatim
! 231: *> WORK is DOUBLE PRECISION array, dimension (LWORK)
! 232: *> \endverbatim
! 233: *>
! 234: *> \param[in] LWORK
! 235: *> \verbatim
! 236: *> LWORK is INTEGER
! 237: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 238: *> otherwise
! 239: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 240: *> LWORK = MAX(1, 7*N, dimension) where
! 241: *> dimension = (2KD+1)*N + KD*NTHREADS + 2*N
! 242: *> where KD is the size of the band.
! 243: *> NTHREADS is the number of threads used when
! 244: *> openMP compilation is enabled, otherwise =1.
! 245: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
! 246: *>
! 247: *> If LWORK = -1, then a workspace query is assumed; the routine
! 248: *> only calculates the optimal size of the WORK array, returns
! 249: *> this value as the first entry of the WORK array, and no error
! 250: *> message related to LWORK is issued by XERBLA.
! 251: *> \endverbatim
! 252: *>
! 253: *> \param[out] IWORK
! 254: *> \verbatim
! 255: *> IWORK is INTEGER array, dimension (5*N)
! 256: *> \endverbatim
! 257: *>
! 258: *> \param[out] IFAIL
! 259: *> \verbatim
! 260: *> IFAIL is INTEGER array, dimension (N)
! 261: *> If JOBZ = 'V', then if INFO = 0, the first M elements of
! 262: *> IFAIL are zero. If INFO > 0, then IFAIL contains the
! 263: *> indices of the eigenvectors that failed to converge.
! 264: *> If JOBZ = 'N', then IFAIL is not referenced.
! 265: *> \endverbatim
! 266: *>
! 267: *> \param[out] INFO
! 268: *> \verbatim
! 269: *> INFO is INTEGER
! 270: *> = 0: successful exit.
! 271: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 272: *> > 0: if INFO = i, then i eigenvectors failed to converge.
! 273: *> Their indices are stored in array IFAIL.
! 274: *> \endverbatim
! 275: *
! 276: * Authors:
! 277: * ========
! 278: *
! 279: *> \author Univ. of Tennessee
! 280: *> \author Univ. of California Berkeley
! 281: *> \author Univ. of Colorado Denver
! 282: *> \author NAG Ltd.
! 283: *
! 284: *> \date June 2016
! 285: *
! 286: *> \ingroup doubleOTHEReigen
! 287: *
! 288: *> \par Further Details:
! 289: * =====================
! 290: *>
! 291: *> \verbatim
! 292: *>
! 293: *> All details about the 2stage techniques are available in:
! 294: *>
! 295: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 296: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 297: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 298: *> of 2011 International Conference for High Performance Computing,
! 299: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 300: *> Article 8 , 11 pages.
! 301: *> http://doi.acm.org/10.1145/2063384.2063394
! 302: *>
! 303: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 304: *> An improved parallel singular value algorithm and its implementation
! 305: *> for multicore hardware, In Proceedings of 2013 International Conference
! 306: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 307: *> Denver, Colorado, USA, 2013.
! 308: *> Article 90, 12 pages.
! 309: *> http://doi.acm.org/10.1145/2503210.2503292
! 310: *>
! 311: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 312: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 313: *> calculations based on fine-grained memory aware tasks.
! 314: *> International Journal of High Performance Computing Applications.
! 315: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 316: *> http://hpc.sagepub.com/content/28/2/196
! 317: *>
! 318: *> \endverbatim
! 319: *
! 320: * =====================================================================
! 321: SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q,
! 322: $ LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
! 323: $ LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
! 324: *
! 325: IMPLICIT NONE
! 326: *
! 327: * -- LAPACK driver routine (version 3.7.0) --
! 328: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 329: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 330: * June 2016
! 331: *
! 332: * .. Scalar Arguments ..
! 333: CHARACTER JOBZ, RANGE, UPLO
! 334: INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N, LWORK
! 335: DOUBLE PRECISION ABSTOL, VL, VU
! 336: * ..
! 337: * .. Array Arguments ..
! 338: INTEGER IFAIL( * ), IWORK( * )
! 339: DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
! 340: $ Z( LDZ, * )
! 341: * ..
! 342: *
! 343: * =====================================================================
! 344: *
! 345: * .. Parameters ..
! 346: DOUBLE PRECISION ZERO, ONE
! 347: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 348: * ..
! 349: * .. Local Scalars ..
! 350: LOGICAL ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ,
! 351: $ LQUERY
! 352: CHARACTER ORDER
! 353: INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
! 354: $ INDISP, INDIWO, INDWRK, ISCALE, ITMP1, J, JJ,
! 355: $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
! 356: $ NSPLIT
! 357: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
! 358: $ SIGMA, SMLNUM, TMP1, VLL, VUU
! 359: * ..
! 360: * .. External Functions ..
! 361: LOGICAL LSAME
! 362: INTEGER ILAENV
! 363: DOUBLE PRECISION DLAMCH, DLANSB
! 364: EXTERNAL LSAME, DLAMCH, DLANSB, ILAENV
! 365: * ..
! 366: * .. External Subroutines ..
! 367: EXTERNAL DCOPY, DGEMV, DLACPY, DLASCL, DSCAL,
! 368: $ DSTEBZ, DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA,
! 369: $ DSYTRD_SB2ST
! 370: * ..
! 371: * .. Intrinsic Functions ..
! 372: INTRINSIC MAX, MIN, SQRT
! 373: * ..
! 374: * .. Executable Statements ..
! 375: *
! 376: * Test the input parameters.
! 377: *
! 378: WANTZ = LSAME( JOBZ, 'V' )
! 379: ALLEIG = LSAME( RANGE, 'A' )
! 380: VALEIG = LSAME( RANGE, 'V' )
! 381: INDEIG = LSAME( RANGE, 'I' )
! 382: LOWER = LSAME( UPLO, 'L' )
! 383: LQUERY = ( LWORK.EQ.-1 )
! 384: *
! 385: INFO = 0
! 386: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 387: INFO = -1
! 388: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 389: INFO = -2
! 390: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 391: INFO = -3
! 392: ELSE IF( N.LT.0 ) THEN
! 393: INFO = -4
! 394: ELSE IF( KD.LT.0 ) THEN
! 395: INFO = -5
! 396: ELSE IF( LDAB.LT.KD+1 ) THEN
! 397: INFO = -7
! 398: ELSE IF( WANTZ .AND. LDQ.LT.MAX( 1, N ) ) THEN
! 399: INFO = -9
! 400: ELSE
! 401: IF( VALEIG ) THEN
! 402: IF( N.GT.0 .AND. VU.LE.VL )
! 403: $ INFO = -11
! 404: ELSE IF( INDEIG ) THEN
! 405: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 406: INFO = -12
! 407: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 408: INFO = -13
! 409: END IF
! 410: END IF
! 411: END IF
! 412: IF( INFO.EQ.0 ) THEN
! 413: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
! 414: $ INFO = -18
! 415: END IF
! 416: *
! 417: IF( INFO.EQ.0 ) THEN
! 418: IF( N.LE.1 ) THEN
! 419: LWMIN = 1
! 420: WORK( 1 ) = LWMIN
! 421: ELSE
! 422: IB = ILAENV( 18, 'DSYTRD_SB2ST', JOBZ, N, KD, -1, -1 )
! 423: LHTRD = ILAENV( 19, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 424: LWTRD = ILAENV( 20, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 425: LWMIN = 2*N + LHTRD + LWTRD
! 426: WORK( 1 ) = LWMIN
! 427: ENDIF
! 428: *
! 429: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
! 430: $ INFO = -20
! 431: END IF
! 432: *
! 433: IF( INFO.NE.0 ) THEN
! 434: CALL XERBLA( 'DSBEVX_2STAGE ', -INFO )
! 435: RETURN
! 436: ELSE IF( LQUERY ) THEN
! 437: RETURN
! 438: END IF
! 439: *
! 440: * Quick return if possible
! 441: *
! 442: M = 0
! 443: IF( N.EQ.0 )
! 444: $ RETURN
! 445: *
! 446: IF( N.EQ.1 ) THEN
! 447: M = 1
! 448: IF( LOWER ) THEN
! 449: TMP1 = AB( 1, 1 )
! 450: ELSE
! 451: TMP1 = AB( KD+1, 1 )
! 452: END IF
! 453: IF( VALEIG ) THEN
! 454: IF( .NOT.( VL.LT.TMP1 .AND. VU.GE.TMP1 ) )
! 455: $ M = 0
! 456: END IF
! 457: IF( M.EQ.1 ) THEN
! 458: W( 1 ) = TMP1
! 459: IF( WANTZ )
! 460: $ Z( 1, 1 ) = ONE
! 461: END IF
! 462: RETURN
! 463: END IF
! 464: *
! 465: * Get machine constants.
! 466: *
! 467: SAFMIN = DLAMCH( 'Safe minimum' )
! 468: EPS = DLAMCH( 'Precision' )
! 469: SMLNUM = SAFMIN / EPS
! 470: BIGNUM = ONE / SMLNUM
! 471: RMIN = SQRT( SMLNUM )
! 472: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
! 473: *
! 474: * Scale matrix to allowable range, if necessary.
! 475: *
! 476: ISCALE = 0
! 477: ABSTLL = ABSTOL
! 478: IF( VALEIG ) THEN
! 479: VLL = VL
! 480: VUU = VU
! 481: ELSE
! 482: VLL = ZERO
! 483: VUU = ZERO
! 484: END IF
! 485: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
! 486: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 487: ISCALE = 1
! 488: SIGMA = RMIN / ANRM
! 489: ELSE IF( ANRM.GT.RMAX ) THEN
! 490: ISCALE = 1
! 491: SIGMA = RMAX / ANRM
! 492: END IF
! 493: IF( ISCALE.EQ.1 ) THEN
! 494: IF( LOWER ) THEN
! 495: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 496: ELSE
! 497: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 498: END IF
! 499: IF( ABSTOL.GT.0 )
! 500: $ ABSTLL = ABSTOL*SIGMA
! 501: IF( VALEIG ) THEN
! 502: VLL = VL*SIGMA
! 503: VUU = VU*SIGMA
! 504: END IF
! 505: END IF
! 506: *
! 507: * Call DSYTRD_SB2ST to reduce symmetric band matrix to tridiagonal form.
! 508: *
! 509: INDD = 1
! 510: INDE = INDD + N
! 511: INDHOUS = INDE + N
! 512: INDWRK = INDHOUS + LHTRD
! 513: LLWORK = LWORK - INDWRK + 1
! 514: *
! 515: CALL DSYTRD_SB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, WORK( INDD ),
! 516: $ WORK( INDE ), WORK( INDHOUS ), LHTRD,
! 517: $ WORK( INDWRK ), LLWORK, IINFO )
! 518: *
! 519: * If all eigenvalues are desired and ABSTOL is less than or equal
! 520: * to zero, then call DSTERF or SSTEQR. If this fails for some
! 521: * eigenvalue, then try DSTEBZ.
! 522: *
! 523: TEST = .FALSE.
! 524: IF (INDEIG) THEN
! 525: IF (IL.EQ.1 .AND. IU.EQ.N) THEN
! 526: TEST = .TRUE.
! 527: END IF
! 528: END IF
! 529: IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN
! 530: CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
! 531: INDEE = INDWRK + 2*N
! 532: IF( .NOT.WANTZ ) THEN
! 533: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 534: CALL DSTERF( N, W, WORK( INDEE ), INFO )
! 535: ELSE
! 536: CALL DLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
! 537: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 538: CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
! 539: $ WORK( INDWRK ), INFO )
! 540: IF( INFO.EQ.0 ) THEN
! 541: DO 10 I = 1, N
! 542: IFAIL( I ) = 0
! 543: 10 CONTINUE
! 544: END IF
! 545: END IF
! 546: IF( INFO.EQ.0 ) THEN
! 547: M = N
! 548: GO TO 30
! 549: END IF
! 550: INFO = 0
! 551: END IF
! 552: *
! 553: * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
! 554: *
! 555: IF( WANTZ ) THEN
! 556: ORDER = 'B'
! 557: ELSE
! 558: ORDER = 'E'
! 559: END IF
! 560: INDIBL = 1
! 561: INDISP = INDIBL + N
! 562: INDIWO = INDISP + N
! 563: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
! 564: $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
! 565: $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
! 566: $ IWORK( INDIWO ), INFO )
! 567: *
! 568: IF( WANTZ ) THEN
! 569: CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
! 570: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
! 571: $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
! 572: *
! 573: * Apply orthogonal matrix used in reduction to tridiagonal
! 574: * form to eigenvectors returned by DSTEIN.
! 575: *
! 576: DO 20 J = 1, M
! 577: CALL DCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
! 578: CALL DGEMV( 'N', N, N, ONE, Q, LDQ, WORK, 1, ZERO,
! 579: $ Z( 1, J ), 1 )
! 580: 20 CONTINUE
! 581: END IF
! 582: *
! 583: * If matrix was scaled, then rescale eigenvalues appropriately.
! 584: *
! 585: 30 CONTINUE
! 586: IF( ISCALE.EQ.1 ) THEN
! 587: IF( INFO.EQ.0 ) THEN
! 588: IMAX = M
! 589: ELSE
! 590: IMAX = INFO - 1
! 591: END IF
! 592: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 593: END IF
! 594: *
! 595: * If eigenvalues are not in order, then sort them, along with
! 596: * eigenvectors.
! 597: *
! 598: IF( WANTZ ) THEN
! 599: DO 50 J = 1, M - 1
! 600: I = 0
! 601: TMP1 = W( J )
! 602: DO 40 JJ = J + 1, M
! 603: IF( W( JJ ).LT.TMP1 ) THEN
! 604: I = JJ
! 605: TMP1 = W( JJ )
! 606: END IF
! 607: 40 CONTINUE
! 608: *
! 609: IF( I.NE.0 ) THEN
! 610: ITMP1 = IWORK( INDIBL+I-1 )
! 611: W( I ) = W( J )
! 612: IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
! 613: W( J ) = TMP1
! 614: IWORK( INDIBL+J-1 ) = ITMP1
! 615: CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
! 616: IF( INFO.NE.0 ) THEN
! 617: ITMP1 = IFAIL( I )
! 618: IFAIL( I ) = IFAIL( J )
! 619: IFAIL( J ) = ITMP1
! 620: END IF
! 621: END IF
! 622: 50 CONTINUE
! 623: END IF
! 624: *
! 625: * Set WORK(1) to optimal workspace size.
! 626: *
! 627: WORK( 1 ) = LWMIN
! 628: *
! 629: RETURN
! 630: *
! 631: * End of DSBEVX_2STAGE
! 632: *
! 633: END
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