Annotation of rpl/lapack/lapack/dsyevd_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> DSYEVD_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 DSYEVD_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSYEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
! 24: * IWORK, LIWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER JOBZ, UPLO
! 30: * INTEGER INFO, LDA, LIWORK, LWORK, N
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * INTEGER IWORK( * )
! 34: * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
! 35: * ..
! 36: *
! 37: *
! 38: *> \par Purpose:
! 39: * =============
! 40: *>
! 41: *> \verbatim
! 42: *>
! 43: *> DSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
! 44: *> real symmetric matrix A using the 2stage technique for
! 45: *> the reduction to tridiagonal. If eigenvectors are desired, it uses a
! 46: *> divide and conquer algorithm.
! 47: *>
! 48: *> The divide and conquer algorithm makes very mild assumptions about
! 49: *> floating point arithmetic. It will work on machines with a guard
! 50: *> digit in add/subtract, or on those binary machines without guard
! 51: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 52: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 53: *> without guard digits, but we know of none.
! 54: *> \endverbatim
! 55: *
! 56: * Arguments:
! 57: * ==========
! 58: *
! 59: *> \param[in] JOBZ
! 60: *> \verbatim
! 61: *> JOBZ is CHARACTER*1
! 62: *> = 'N': Compute eigenvalues only;
! 63: *> = 'V': Compute eigenvalues and eigenvectors.
! 64: *> Not available in this release.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] UPLO
! 68: *> \verbatim
! 69: *> UPLO is CHARACTER*1
! 70: *> = 'U': Upper triangle of A is stored;
! 71: *> = 'L': Lower triangle of A is stored.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] N
! 75: *> \verbatim
! 76: *> N is INTEGER
! 77: *> The order of the matrix A. N >= 0.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in,out] A
! 81: *> \verbatim
! 82: *> A is DOUBLE PRECISION array, dimension (LDA, N)
! 83: *> On entry, the symmetric matrix A. If UPLO = 'U', the
! 84: *> leading N-by-N upper triangular part of A contains the
! 85: *> upper triangular part of the matrix A. If UPLO = 'L',
! 86: *> the leading N-by-N lower triangular part of A contains
! 87: *> the lower triangular part of the matrix A.
! 88: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 89: *> orthonormal eigenvectors of the matrix A.
! 90: *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
! 91: *> or the upper triangle (if UPLO='U') of A, including the
! 92: *> diagonal, is destroyed.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] LDA
! 96: *> \verbatim
! 97: *> LDA is INTEGER
! 98: *> The leading dimension of the array A. LDA >= max(1,N).
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[out] W
! 102: *> \verbatim
! 103: *> W is DOUBLE PRECISION array, dimension (N)
! 104: *> If INFO = 0, the eigenvalues in ascending order.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[out] WORK
! 108: *> \verbatim
! 109: *> WORK is DOUBLE PRECISION array,
! 110: *> dimension (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 + 2*N+1
! 122: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 123: *> + max(2*KD*KD, KD*NTHREADS)
! 124: *> + (KD+1)*N + 2*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
! 131: *> 1 + 6*N + 2*N**2.
! 132: *>
! 133: *> If LWORK = -1, then a workspace query is assumed; the routine
! 134: *> only calculates the optimal sizes of the WORK and IWORK
! 135: *> arrays, returns these values as the first entries of the WORK
! 136: *> and IWORK arrays, and no error message related to LWORK or
! 137: *> LIWORK is issued by XERBLA.
! 138: *> \endverbatim
! 139: *>
! 140: *> \param[out] IWORK
! 141: *> \verbatim
! 142: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 143: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 144: *> \endverbatim
! 145: *>
! 146: *> \param[in] LIWORK
! 147: *> \verbatim
! 148: *> LIWORK is INTEGER
! 149: *> The dimension of the array IWORK.
! 150: *> If N <= 1, LIWORK must be at least 1.
! 151: *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
! 152: *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
! 153: *>
! 154: *> If LIWORK = -1, then a workspace query is assumed; the
! 155: *> routine only calculates the optimal sizes of the WORK and
! 156: *> IWORK arrays, returns these values as the first entries of
! 157: *> the WORK and IWORK arrays, and no error message related to
! 158: *> LWORK or LIWORK is issued by XERBLA.
! 159: *> \endverbatim
! 160: *>
! 161: *> \param[out] INFO
! 162: *> \verbatim
! 163: *> INFO is INTEGER
! 164: *> = 0: successful exit
! 165: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 166: *> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
! 167: *> to converge; i off-diagonal elements of an intermediate
! 168: *> tridiagonal form did not converge to zero;
! 169: *> if INFO = i and JOBZ = 'V', then the algorithm failed
! 170: *> to compute an eigenvalue while working on the submatrix
! 171: *> lying in rows and columns INFO/(N+1) through
! 172: *> mod(INFO,N+1).
! 173: *> \endverbatim
! 174: *
! 175: * Authors:
! 176: * ========
! 177: *
! 178: *> \author Univ. of Tennessee
! 179: *> \author Univ. of California Berkeley
! 180: *> \author Univ. of Colorado Denver
! 181: *> \author NAG Ltd.
! 182: *
! 183: *> \date December 2016
! 184: *
! 185: *> \ingroup doubleSYeigen
! 186: *
! 187: *> \par Contributors:
! 188: * ==================
! 189: *>
! 190: *> Jeff Rutter, Computer Science Division, University of California
! 191: *> at Berkeley, USA \n
! 192: *> Modified by Francoise Tisseur, University of Tennessee \n
! 193: *> Modified description of INFO. Sven, 16 Feb 05. \n
! 194: *> \par Further Details:
! 195: * =====================
! 196: *>
! 197: *> \verbatim
! 198: *>
! 199: *> All details about the 2stage techniques are available in:
! 200: *>
! 201: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 202: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 203: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 204: *> of 2011 International Conference for High Performance Computing,
! 205: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 206: *> Article 8 , 11 pages.
! 207: *> http://doi.acm.org/10.1145/2063384.2063394
! 208: *>
! 209: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 210: *> An improved parallel singular value algorithm and its implementation
! 211: *> for multicore hardware, In Proceedings of 2013 International Conference
! 212: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 213: *> Denver, Colorado, USA, 2013.
! 214: *> Article 90, 12 pages.
! 215: *> http://doi.acm.org/10.1145/2503210.2503292
! 216: *>
! 217: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 218: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 219: *> calculations based on fine-grained memory aware tasks.
! 220: *> International Journal of High Performance Computing Applications.
! 221: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 222: *> http://hpc.sagepub.com/content/28/2/196
! 223: *>
! 224: *> \endverbatim
! 225: *
! 226: * =====================================================================
! 227: SUBROUTINE DSYEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
! 228: $ IWORK, LIWORK, INFO )
! 229: *
! 230: IMPLICIT NONE
! 231: *
! 232: * -- LAPACK driver routine (version 3.7.0) --
! 233: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 234: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 235: * December 2016
! 236: *
! 237: * .. Scalar Arguments ..
! 238: CHARACTER JOBZ, UPLO
! 239: INTEGER INFO, LDA, LIWORK, LWORK, N
! 240: * ..
! 241: * .. Array Arguments ..
! 242: INTEGER IWORK( * )
! 243: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
! 244: * ..
! 245: *
! 246: * =====================================================================
! 247: *
! 248: * .. Parameters ..
! 249: DOUBLE PRECISION ZERO, ONE
! 250: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 251: * ..
! 252: * .. Local Scalars ..
! 253: *
! 254: LOGICAL LOWER, LQUERY, WANTZ
! 255: INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
! 256: $ LIWMIN, LLWORK, LLWRK2, LWMIN,
! 257: $ LHTRD, LWTRD, KD, IB, INDHOUS
! 258: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 259: $ SMLNUM
! 260: * ..
! 261: * .. External Functions ..
! 262: LOGICAL LSAME
! 263: INTEGER ILAENV
! 264: DOUBLE PRECISION DLAMCH, DLANSY
! 265: EXTERNAL LSAME, DLAMCH, DLANSY, ILAENV
! 266: * ..
! 267: * .. External Subroutines ..
! 268: EXTERNAL DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF,
! 269: $ DSYTRD_2STAGE, XERBLA
! 270: * ..
! 271: * .. Intrinsic Functions ..
! 272: INTRINSIC MAX, SQRT
! 273: * ..
! 274: * .. Executable Statements ..
! 275: *
! 276: * Test the input parameters.
! 277: *
! 278: WANTZ = LSAME( JOBZ, 'V' )
! 279: LOWER = LSAME( UPLO, 'L' )
! 280: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 281: *
! 282: INFO = 0
! 283: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 284: INFO = -1
! 285: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 286: INFO = -2
! 287: ELSE IF( N.LT.0 ) THEN
! 288: INFO = -3
! 289: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 290: INFO = -5
! 291: END IF
! 292: *
! 293: IF( INFO.EQ.0 ) THEN
! 294: IF( N.LE.1 ) THEN
! 295: LIWMIN = 1
! 296: LWMIN = 1
! 297: ELSE
! 298: KD = ILAENV( 17, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 299: IB = ILAENV( 18, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 300: LHTRD = ILAENV( 19, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 301: LWTRD = ILAENV( 20, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 302: IF( WANTZ ) THEN
! 303: LIWMIN = 3 + 5*N
! 304: LWMIN = 1 + 6*N + 2*N**2
! 305: ELSE
! 306: LIWMIN = 1
! 307: LWMIN = 2*N + 1 + LHTRD + LWTRD
! 308: END IF
! 309: END IF
! 310: WORK( 1 ) = LWMIN
! 311: IWORK( 1 ) = LIWMIN
! 312: *
! 313: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 314: INFO = -8
! 315: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 316: INFO = -10
! 317: END IF
! 318: END IF
! 319: *
! 320: IF( INFO.NE.0 ) THEN
! 321: CALL XERBLA( 'DSYEVD_2STAGE', -INFO )
! 322: RETURN
! 323: ELSE IF( LQUERY ) THEN
! 324: RETURN
! 325: END IF
! 326: *
! 327: * Quick return if possible
! 328: *
! 329: IF( N.EQ.0 )
! 330: $ RETURN
! 331: *
! 332: IF( N.EQ.1 ) THEN
! 333: W( 1 ) = A( 1, 1 )
! 334: IF( WANTZ )
! 335: $ A( 1, 1 ) = ONE
! 336: RETURN
! 337: END IF
! 338: *
! 339: * Get machine constants.
! 340: *
! 341: SAFMIN = DLAMCH( 'Safe minimum' )
! 342: EPS = DLAMCH( 'Precision' )
! 343: SMLNUM = SAFMIN / EPS
! 344: BIGNUM = ONE / SMLNUM
! 345: RMIN = SQRT( SMLNUM )
! 346: RMAX = SQRT( BIGNUM )
! 347: *
! 348: * Scale matrix to allowable range, if necessary.
! 349: *
! 350: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
! 351: ISCALE = 0
! 352: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 353: ISCALE = 1
! 354: SIGMA = RMIN / ANRM
! 355: ELSE IF( ANRM.GT.RMAX ) THEN
! 356: ISCALE = 1
! 357: SIGMA = RMAX / ANRM
! 358: END IF
! 359: IF( ISCALE.EQ.1 )
! 360: $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
! 361: *
! 362: * Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
! 363: *
! 364: INDE = 1
! 365: INDTAU = INDE + N
! 366: INDHOUS = INDTAU + N
! 367: INDWRK = INDHOUS + LHTRD
! 368: LLWORK = LWORK - INDWRK + 1
! 369: INDWK2 = INDWRK + N*N
! 370: LLWRK2 = LWORK - INDWK2 + 1
! 371: *
! 372: CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK( INDE ),
! 373: $ WORK( INDTAU ), WORK( INDHOUS ), LHTRD,
! 374: $ WORK( INDWRK ), LLWORK, IINFO )
! 375: *
! 376: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 377: * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
! 378: * tridiagonal matrix, then call DORMTR to multiply it by the
! 379: * Householder transformations stored in A.
! 380: *
! 381: IF( .NOT.WANTZ ) THEN
! 382: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 383: ELSE
! 384: * Not available in this release, and agrument checking should not
! 385: * let it getting here
! 386: RETURN
! 387: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
! 388: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
! 389: CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
! 390: $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
! 391: CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
! 392: END IF
! 393: *
! 394: * If matrix was scaled, then rescale eigenvalues appropriately.
! 395: *
! 396: IF( ISCALE.EQ.1 )
! 397: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
! 398: *
! 399: WORK( 1 ) = LWMIN
! 400: IWORK( 1 ) = LIWMIN
! 401: *
! 402: RETURN
! 403: *
! 404: * End of DSYEVD_2STAGE
! 405: *
! 406: END
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