Annotation of rpl/lapack/lapack/zheevd_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> ZHEEVD_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 ZHEEVD_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheevd_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevd_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevd_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE ZHEEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
! 24: * RWORK, LRWORK, IWORK, LIWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER JOBZ, UPLO
! 30: * INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * INTEGER IWORK( * )
! 34: * DOUBLE PRECISION RWORK( * ), W( * )
! 35: * COMPLEX*16 A( LDA, * ), WORK( * )
! 36: * ..
! 37: *
! 38: *
! 39: *> \par Purpose:
! 40: * =============
! 41: *>
! 42: *> \verbatim
! 43: *>
! 44: *> ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
! 45: *> complex Hermitian matrix A using the 2stage technique for
! 46: *> the reduction to tridiagonal. If eigenvectors are desired, it uses a
! 47: *> divide and conquer algorithm.
! 48: *>
! 49: *> The divide and conquer algorithm makes very mild assumptions about
! 50: *> floating point arithmetic. It will work on machines with a guard
! 51: *> digit in add/subtract, or on those binary machines without guard
! 52: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 53: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 54: *> without guard digits, but we know of none.
! 55: *> \endverbatim
! 56: *
! 57: * Arguments:
! 58: * ==========
! 59: *
! 60: *> \param[in] JOBZ
! 61: *> \verbatim
! 62: *> JOBZ is CHARACTER*1
! 63: *> = 'N': Compute eigenvalues only;
! 64: *> = 'V': Compute eigenvalues and eigenvectors.
! 65: *> Not available in this release.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] UPLO
! 69: *> \verbatim
! 70: *> UPLO is CHARACTER*1
! 71: *> = 'U': Upper triangle of A is stored;
! 72: *> = 'L': Lower triangle of A is stored.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] N
! 76: *> \verbatim
! 77: *> N is INTEGER
! 78: *> The order of the matrix A. N >= 0.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in,out] A
! 82: *> \verbatim
! 83: *> A is COMPLEX*16 array, dimension (LDA, N)
! 84: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
! 85: *> leading N-by-N upper triangular part of A contains the
! 86: *> upper triangular part of the matrix A. If UPLO = 'L',
! 87: *> the leading N-by-N lower triangular part of A contains
! 88: *> the lower triangular part of the matrix A.
! 89: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 90: *> orthonormal eigenvectors of the matrix A.
! 91: *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
! 92: *> or the upper triangle (if UPLO='U') of A, including the
! 93: *> diagonal, is destroyed.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDA
! 97: *> \verbatim
! 98: *> LDA is INTEGER
! 99: *> The leading dimension of the array A. LDA >= max(1,N).
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] W
! 103: *> \verbatim
! 104: *> W is DOUBLE PRECISION array, dimension (N)
! 105: *> If INFO = 0, the eigenvalues in ascending order.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] WORK
! 109: *> \verbatim
! 110: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 111: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in] LWORK
! 115: *> \verbatim
! 116: *> LWORK is INTEGER
! 117: *> The dimension of the array WORK.
! 118: *> If N <= 1, LWORK must be at least 1.
! 119: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 120: *> LWORK = MAX(1, dimension) where
! 121: *> dimension = max(stage1,stage2) + (KD+1)*N + N+1
! 122: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 123: *> + max(2*KD*KD, KD*NTHREADS)
! 124: *> + (KD+1)*N + N+1
! 125: *> where KD is the blocking size of the reduction,
! 126: *> FACTOPTNB is the blocking used by the QR or LQ
! 127: *> algorithm, usually FACTOPTNB=128 is a good choice
! 128: *> NTHREADS is the number of threads used when
! 129: *> openMP compilation is enabled, otherwise =1.
! 130: *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2
! 131: *>
! 132: *> If LWORK = -1, then a workspace query is assumed; the routine
! 133: *> only calculates the optimal sizes of the WORK, RWORK and
! 134: *> IWORK arrays, returns these values as the first entries of
! 135: *> the WORK, RWORK and IWORK arrays, and no error message
! 136: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 137: *> \endverbatim
! 138: *>
! 139: *> \param[out] RWORK
! 140: *> \verbatim
! 141: *> RWORK is DOUBLE PRECISION array,
! 142: *> dimension (LRWORK)
! 143: *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
! 144: *> \endverbatim
! 145: *>
! 146: *> \param[in] LRWORK
! 147: *> \verbatim
! 148: *> LRWORK is INTEGER
! 149: *> The dimension of the array RWORK.
! 150: *> If N <= 1, LRWORK must be at least 1.
! 151: *> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
! 152: *> If JOBZ = 'V' and N > 1, LRWORK must be at least
! 153: *> 1 + 5*N + 2*N**2.
! 154: *>
! 155: *> If LRWORK = -1, then a workspace query is assumed; the
! 156: *> routine only calculates the optimal sizes of the WORK, RWORK
! 157: *> and IWORK arrays, returns these values as the first entries
! 158: *> of the WORK, RWORK and IWORK arrays, and no error message
! 159: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 160: *> \endverbatim
! 161: *>
! 162: *> \param[out] IWORK
! 163: *> \verbatim
! 164: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 165: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 166: *> \endverbatim
! 167: *>
! 168: *> \param[in] LIWORK
! 169: *> \verbatim
! 170: *> LIWORK is INTEGER
! 171: *> The dimension of the array IWORK.
! 172: *> If N <= 1, LIWORK must be at least 1.
! 173: *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
! 174: *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
! 175: *>
! 176: *> If LIWORK = -1, then a workspace query is assumed; the
! 177: *> routine only calculates the optimal sizes of the WORK, RWORK
! 178: *> and IWORK arrays, returns these values as the first entries
! 179: *> of the WORK, RWORK and IWORK arrays, and no error message
! 180: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 181: *> \endverbatim
! 182: *>
! 183: *> \param[out] INFO
! 184: *> \verbatim
! 185: *> INFO is INTEGER
! 186: *> = 0: successful exit
! 187: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 188: *> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
! 189: *> to converge; i off-diagonal elements of an intermediate
! 190: *> tridiagonal form did not converge to zero;
! 191: *> if INFO = i and JOBZ = 'V', then the algorithm failed
! 192: *> to compute an eigenvalue while working on the submatrix
! 193: *> lying in rows and columns INFO/(N+1) through
! 194: *> mod(INFO,N+1).
! 195: *> \endverbatim
! 196: *
! 197: * Authors:
! 198: * ========
! 199: *
! 200: *> \author Univ. of Tennessee
! 201: *> \author Univ. of California Berkeley
! 202: *> \author Univ. of Colorado Denver
! 203: *> \author NAG Ltd.
! 204: *
! 205: *> \date December 2016
! 206: *
! 207: *> \ingroup complex16HEeigen
! 208: *
! 209: *> \par Further Details:
! 210: * =====================
! 211: *>
! 212: *> Modified description of INFO. Sven, 16 Feb 05.
! 213: *
! 214: *> \par Contributors:
! 215: * ==================
! 216: *>
! 217: *> Jeff Rutter, Computer Science Division, University of California
! 218: *> at Berkeley, USA
! 219: *>
! 220: *> \par Further Details:
! 221: * =====================
! 222: *>
! 223: *> \verbatim
! 224: *>
! 225: *> All details about the 2stage techniques are available in:
! 226: *>
! 227: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 228: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 229: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 230: *> of 2011 International Conference for High Performance Computing,
! 231: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 232: *> Article 8 , 11 pages.
! 233: *> http://doi.acm.org/10.1145/2063384.2063394
! 234: *>
! 235: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 236: *> An improved parallel singular value algorithm and its implementation
! 237: *> for multicore hardware, In Proceedings of 2013 International Conference
! 238: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 239: *> Denver, Colorado, USA, 2013.
! 240: *> Article 90, 12 pages.
! 241: *> http://doi.acm.org/10.1145/2503210.2503292
! 242: *>
! 243: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 244: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 245: *> calculations based on fine-grained memory aware tasks.
! 246: *> International Journal of High Performance Computing Applications.
! 247: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 248: *> http://hpc.sagepub.com/content/28/2/196
! 249: *>
! 250: *> \endverbatim
! 251: *
! 252: * =====================================================================
! 253: SUBROUTINE ZHEEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
! 254: $ RWORK, LRWORK, IWORK, LIWORK, INFO )
! 255: *
! 256: IMPLICIT NONE
! 257: *
! 258: * -- LAPACK driver routine (version 3.7.0) --
! 259: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 260: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 261: * December 2016
! 262: *
! 263: * .. Scalar Arguments ..
! 264: CHARACTER JOBZ, UPLO
! 265: INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
! 266: * ..
! 267: * .. Array Arguments ..
! 268: INTEGER IWORK( * )
! 269: DOUBLE PRECISION RWORK( * ), W( * )
! 270: COMPLEX*16 A( LDA, * ), WORK( * )
! 271: * ..
! 272: *
! 273: * =====================================================================
! 274: *
! 275: * .. Parameters ..
! 276: DOUBLE PRECISION ZERO, ONE
! 277: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 278: COMPLEX*16 CONE
! 279: PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) )
! 280: * ..
! 281: * .. Local Scalars ..
! 282: LOGICAL LOWER, LQUERY, WANTZ
! 283: INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
! 284: $ INDWRK, ISCALE, LIWMIN, LLRWK, LLWORK,
! 285: $ LLWRK2, LRWMIN, LWMIN,
! 286: $ LHTRD, LWTRD, KD, IB, INDHOUS
! 287:
! 288:
! 289: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 290: $ SMLNUM
! 291: * ..
! 292: * .. External Functions ..
! 293: LOGICAL LSAME
! 294: INTEGER ILAENV
! 295: DOUBLE PRECISION DLAMCH, ZLANHE
! 296: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE
! 297: * ..
! 298: * .. External Subroutines ..
! 299: EXTERNAL DSCAL, DSTERF, XERBLA, ZLACPY, ZLASCL,
! 300: $ ZSTEDC, ZUNMTR, ZHETRD_2STAGE
! 301: * ..
! 302: * .. Intrinsic Functions ..
! 303: INTRINSIC DBLE, MAX, SQRT
! 304: * ..
! 305: * .. Executable Statements ..
! 306: *
! 307: * Test the input parameters.
! 308: *
! 309: WANTZ = LSAME( JOBZ, 'V' )
! 310: LOWER = LSAME( UPLO, 'L' )
! 311: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 312: *
! 313: INFO = 0
! 314: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 315: INFO = -1
! 316: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 317: INFO = -2
! 318: ELSE IF( N.LT.0 ) THEN
! 319: INFO = -3
! 320: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 321: INFO = -5
! 322: END IF
! 323: *
! 324: IF( INFO.EQ.0 ) THEN
! 325: IF( N.LE.1 ) THEN
! 326: LWMIN = 1
! 327: LRWMIN = 1
! 328: LIWMIN = 1
! 329: ELSE
! 330: KD = ILAENV( 17, 'ZHETRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 331: IB = ILAENV( 18, 'ZHETRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 332: LHTRD = ILAENV( 19, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 333: LWTRD = ILAENV( 20, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 334: IF( WANTZ ) THEN
! 335: LWMIN = 2*N + N*N
! 336: LRWMIN = 1 + 5*N + 2*N**2
! 337: LIWMIN = 3 + 5*N
! 338: ELSE
! 339: LWMIN = N + 1 + LHTRD + LWTRD
! 340: LRWMIN = N
! 341: LIWMIN = 1
! 342: END IF
! 343: END IF
! 344: WORK( 1 ) = LWMIN
! 345: RWORK( 1 ) = LRWMIN
! 346: IWORK( 1 ) = LIWMIN
! 347: *
! 348: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 349: INFO = -8
! 350: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
! 351: INFO = -10
! 352: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 353: INFO = -12
! 354: END IF
! 355: END IF
! 356: *
! 357: IF( INFO.NE.0 ) THEN
! 358: CALL XERBLA( 'ZHEEVD_2STAGE', -INFO )
! 359: RETURN
! 360: ELSE IF( LQUERY ) THEN
! 361: RETURN
! 362: END IF
! 363: *
! 364: * Quick return if possible
! 365: *
! 366: IF( N.EQ.0 )
! 367: $ RETURN
! 368: *
! 369: IF( N.EQ.1 ) THEN
! 370: W( 1 ) = DBLE( A( 1, 1 ) )
! 371: IF( WANTZ )
! 372: $ A( 1, 1 ) = CONE
! 373: RETURN
! 374: END IF
! 375: *
! 376: * Get machine constants.
! 377: *
! 378: SAFMIN = DLAMCH( 'Safe minimum' )
! 379: EPS = DLAMCH( 'Precision' )
! 380: SMLNUM = SAFMIN / EPS
! 381: BIGNUM = ONE / SMLNUM
! 382: RMIN = SQRT( SMLNUM )
! 383: RMAX = SQRT( BIGNUM )
! 384: *
! 385: * Scale matrix to allowable range, if necessary.
! 386: *
! 387: ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
! 388: ISCALE = 0
! 389: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 390: ISCALE = 1
! 391: SIGMA = RMIN / ANRM
! 392: ELSE IF( ANRM.GT.RMAX ) THEN
! 393: ISCALE = 1
! 394: SIGMA = RMAX / ANRM
! 395: END IF
! 396: IF( ISCALE.EQ.1 )
! 397: $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
! 398: *
! 399: * Call ZHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
! 400: *
! 401: INDE = 1
! 402: INDRWK = INDE + N
! 403: LLRWK = LRWORK - INDRWK + 1
! 404: INDTAU = 1
! 405: INDHOUS = INDTAU + N
! 406: INDWRK = INDHOUS + LHTRD
! 407: LLWORK = LWORK - INDWRK + 1
! 408: INDWK2 = INDWRK + N*N
! 409: LLWRK2 = LWORK - INDWK2 + 1
! 410: *
! 411: CALL ZHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, RWORK( INDE ),
! 412: $ WORK( INDTAU ), WORK( INDHOUS ), LHTRD,
! 413: $ WORK( INDWRK ), LLWORK, IINFO )
! 414: *
! 415: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 416: * ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
! 417: * tridiagonal matrix, then call ZUNMTR to multiply it to the
! 418: * Householder transformations represented as Householder vectors in
! 419: * A.
! 420: *
! 421: IF( .NOT.WANTZ ) THEN
! 422: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 423: ELSE
! 424: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N,
! 425: $ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK,
! 426: $ IWORK, LIWORK, INFO )
! 427: CALL ZUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
! 428: $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
! 429: CALL ZLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
! 430: END IF
! 431: *
! 432: * If matrix was scaled, then rescale eigenvalues appropriately.
! 433: *
! 434: IF( ISCALE.EQ.1 ) THEN
! 435: IF( INFO.EQ.0 ) THEN
! 436: IMAX = N
! 437: ELSE
! 438: IMAX = INFO - 1
! 439: END IF
! 440: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 441: END IF
! 442: *
! 443: WORK( 1 ) = LWMIN
! 444: RWORK( 1 ) = LRWMIN
! 445: IWORK( 1 ) = LIWMIN
! 446: *
! 447: RETURN
! 448: *
! 449: * End of ZHEEVD_2STAGE
! 450: *
! 451: END
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