Annotation of rpl/lapack/lapack/dsbevd_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> DSBEVD_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 DSBEVD_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbevd_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbevd_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbevd_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSBEVD_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 24: * WORK, LWORK, IWORK, LIWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER JOBZ, UPLO
! 30: * INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * INTEGER IWORK( * )
! 34: * DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 35: * ..
! 36: *
! 37: *
! 38: *> \par Purpose:
! 39: * =============
! 40: *>
! 41: *> \verbatim
! 42: *>
! 43: *> DSBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
! 44: *> a real symmetric band matrix A using the 2stage technique for
! 45: *> the reduction to tridiagonal. If eigenvectors are desired, it uses
! 46: *> a 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] KD
! 81: *> \verbatim
! 82: *> KD is INTEGER
! 83: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 84: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in,out] AB
! 88: *> \verbatim
! 89: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
! 90: *> On entry, the upper or lower triangle of the symmetric band
! 91: *> matrix A, stored in the first KD+1 rows of the array. The
! 92: *> j-th column of A is stored in the j-th column of the array AB
! 93: *> as follows:
! 94: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 95: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 96: *>
! 97: *> On exit, AB is overwritten by values generated during the
! 98: *> reduction to tridiagonal form. If UPLO = 'U', the first
! 99: *> superdiagonal and the diagonal of the tridiagonal matrix T
! 100: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 101: *> the diagonal and first subdiagonal of T are returned in the
! 102: *> first two rows of AB.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in] LDAB
! 106: *> \verbatim
! 107: *> LDAB is INTEGER
! 108: *> The leading dimension of the array AB. LDAB >= KD + 1.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[out] W
! 112: *> \verbatim
! 113: *> W is DOUBLE PRECISION array, dimension (N)
! 114: *> If INFO = 0, the eigenvalues in ascending order.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[out] Z
! 118: *> \verbatim
! 119: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
! 120: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 121: *> eigenvectors of the matrix A, with the i-th column of Z
! 122: *> holding the eigenvector associated with W(i).
! 123: *> If JOBZ = 'N', then Z is not referenced.
! 124: *> \endverbatim
! 125: *>
! 126: *> \param[in] LDZ
! 127: *> \verbatim
! 128: *> LDZ is INTEGER
! 129: *> The leading dimension of the array Z. LDZ >= 1, and if
! 130: *> JOBZ = 'V', LDZ >= max(1,N).
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[out] WORK
! 134: *> \verbatim
! 135: *> WORK is DOUBLE PRECISION array, dimension LWORK
! 136: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 137: *> \endverbatim
! 138: *>
! 139: *> \param[in] LWORK
! 140: *> \verbatim
! 141: *> LWORK is INTEGER
! 142: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 143: *> otherwise
! 144: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 145: *> LWORK = MAX(1, dimension) where
! 146: *> dimension = (2KD+1)*N + KD*NTHREADS + N
! 147: *> where KD is the size of the band.
! 148: *> NTHREADS is the number of threads used when
! 149: *> openMP compilation is enabled, otherwise =1.
! 150: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
! 151: *>
! 152: *> If LWORK = -1, then a workspace query is assumed; the routine
! 153: *> only calculates the optimal sizes of the WORK and IWORK
! 154: *> arrays, returns these values as the first entries of the WORK
! 155: *> and IWORK arrays, and no error message related to LWORK or
! 156: *> LIWORK is issued by XERBLA.
! 157: *> \endverbatim
! 158: *>
! 159: *> \param[out] IWORK
! 160: *> \verbatim
! 161: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 162: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 163: *> \endverbatim
! 164: *>
! 165: *> \param[in] LIWORK
! 166: *> \verbatim
! 167: *> LIWORK is INTEGER
! 168: *> The dimension of the array IWORK.
! 169: *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
! 170: *> If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
! 171: *>
! 172: *> If LIWORK = -1, then a workspace query is assumed; the
! 173: *> routine only calculates the optimal sizes of the WORK and
! 174: *> IWORK arrays, returns these values as the first entries of
! 175: *> the WORK and IWORK arrays, and no error message related to
! 176: *> LWORK or LIWORK is issued by XERBLA.
! 177: *> \endverbatim
! 178: *>
! 179: *> \param[out] INFO
! 180: *> \verbatim
! 181: *> INFO is INTEGER
! 182: *> = 0: successful exit
! 183: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 184: *> > 0: if INFO = i, the algorithm failed to converge; i
! 185: *> off-diagonal elements of an intermediate tridiagonal
! 186: *> form did not converge to zero.
! 187: *> \endverbatim
! 188: *
! 189: * Authors:
! 190: * ========
! 191: *
! 192: *> \author Univ. of Tennessee
! 193: *> \author Univ. of California Berkeley
! 194: *> \author Univ. of Colorado Denver
! 195: *> \author NAG Ltd.
! 196: *
! 197: *> \date December 2016
! 198: *
! 199: *> \ingroup doubleOTHEReigen
! 200: *
! 201: *> \par Further Details:
! 202: * =====================
! 203: *>
! 204: *> \verbatim
! 205: *>
! 206: *> All details about the 2stage techniques are available in:
! 207: *>
! 208: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 209: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 210: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 211: *> of 2011 International Conference for High Performance Computing,
! 212: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 213: *> Article 8 , 11 pages.
! 214: *> http://doi.acm.org/10.1145/2063384.2063394
! 215: *>
! 216: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 217: *> An improved parallel singular value algorithm and its implementation
! 218: *> for multicore hardware, In Proceedings of 2013 International Conference
! 219: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 220: *> Denver, Colorado, USA, 2013.
! 221: *> Article 90, 12 pages.
! 222: *> http://doi.acm.org/10.1145/2503210.2503292
! 223: *>
! 224: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 225: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 226: *> calculations based on fine-grained memory aware tasks.
! 227: *> International Journal of High Performance Computing Applications.
! 228: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 229: *> http://hpc.sagepub.com/content/28/2/196
! 230: *>
! 231: *> \endverbatim
! 232: *
! 233: * =====================================================================
! 234: SUBROUTINE DSBEVD_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 235: $ WORK, LWORK, IWORK, LIWORK, INFO )
! 236: *
! 237: IMPLICIT NONE
! 238: *
! 239: * -- LAPACK driver routine (version 3.7.0) --
! 240: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 241: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 242: * December 2016
! 243: *
! 244: * .. Scalar Arguments ..
! 245: CHARACTER JOBZ, UPLO
! 246: INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
! 247: * ..
! 248: * .. Array Arguments ..
! 249: INTEGER IWORK( * )
! 250: DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 251: * ..
! 252: *
! 253: * =====================================================================
! 254: *
! 255: * .. Parameters ..
! 256: DOUBLE PRECISION ZERO, ONE
! 257: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 258: * ..
! 259: * .. Local Scalars ..
! 260: LOGICAL LOWER, LQUERY, WANTZ
! 261: INTEGER IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
! 262: $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
! 263: $ LLWRK2
! 264: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 265: $ SMLNUM
! 266: * ..
! 267: * .. External Functions ..
! 268: LOGICAL LSAME
! 269: INTEGER ILAENV
! 270: DOUBLE PRECISION DLAMCH, DLANSB
! 271: EXTERNAL LSAME, DLAMCH, DLANSB, ILAENV
! 272: * ..
! 273: * .. External Subroutines ..
! 274: EXTERNAL DGEMM, DLACPY, DLASCL, DSCAL, DSTEDC,
! 275: $ DSTERF, XERBLA, DSYTRD_SB2ST
! 276: * ..
! 277: * .. Intrinsic Functions ..
! 278: INTRINSIC SQRT
! 279: * ..
! 280: * .. Executable Statements ..
! 281: *
! 282: * Test the input parameters.
! 283: *
! 284: WANTZ = LSAME( JOBZ, 'V' )
! 285: LOWER = LSAME( UPLO, 'L' )
! 286: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 287: *
! 288: INFO = 0
! 289: IF( N.LE.1 ) THEN
! 290: LIWMIN = 1
! 291: LWMIN = 1
! 292: ELSE
! 293: IB = ILAENV( 18, 'DSYTRD_SB2ST', JOBZ, N, KD, -1, -1 )
! 294: LHTRD = ILAENV( 19, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 295: LWTRD = ILAENV( 20, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 296: IF( WANTZ ) THEN
! 297: LIWMIN = 3 + 5*N
! 298: LWMIN = 1 + 5*N + 2*N**2
! 299: ELSE
! 300: LIWMIN = 1
! 301: LWMIN = MAX( 2*N, N+LHTRD+LWTRD )
! 302: END IF
! 303: END IF
! 304: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 305: INFO = -1
! 306: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 307: INFO = -2
! 308: ELSE IF( N.LT.0 ) THEN
! 309: INFO = -3
! 310: ELSE IF( KD.LT.0 ) THEN
! 311: INFO = -4
! 312: ELSE IF( LDAB.LT.KD+1 ) THEN
! 313: INFO = -6
! 314: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 315: INFO = -9
! 316: END IF
! 317: *
! 318: IF( INFO.EQ.0 ) THEN
! 319: WORK( 1 ) = LWMIN
! 320: IWORK( 1 ) = LIWMIN
! 321: *
! 322: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 323: INFO = -11
! 324: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 325: INFO = -13
! 326: END IF
! 327: END IF
! 328: *
! 329: IF( INFO.NE.0 ) THEN
! 330: CALL XERBLA( 'DSBEVD_2STAGE', -INFO )
! 331: RETURN
! 332: ELSE IF( LQUERY ) THEN
! 333: RETURN
! 334: END IF
! 335: *
! 336: * Quick return if possible
! 337: *
! 338: IF( N.EQ.0 )
! 339: $ RETURN
! 340: *
! 341: IF( N.EQ.1 ) THEN
! 342: W( 1 ) = AB( 1, 1 )
! 343: IF( WANTZ )
! 344: $ Z( 1, 1 ) = ONE
! 345: RETURN
! 346: END IF
! 347: *
! 348: * Get machine constants.
! 349: *
! 350: SAFMIN = DLAMCH( 'Safe minimum' )
! 351: EPS = DLAMCH( 'Precision' )
! 352: SMLNUM = SAFMIN / EPS
! 353: BIGNUM = ONE / SMLNUM
! 354: RMIN = SQRT( SMLNUM )
! 355: RMAX = SQRT( BIGNUM )
! 356: *
! 357: * Scale matrix to allowable range, if necessary.
! 358: *
! 359: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
! 360: ISCALE = 0
! 361: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 362: ISCALE = 1
! 363: SIGMA = RMIN / ANRM
! 364: ELSE IF( ANRM.GT.RMAX ) THEN
! 365: ISCALE = 1
! 366: SIGMA = RMAX / ANRM
! 367: END IF
! 368: IF( ISCALE.EQ.1 ) THEN
! 369: IF( LOWER ) THEN
! 370: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 371: ELSE
! 372: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 373: END IF
! 374: END IF
! 375: *
! 376: * Call DSYTRD_SB2ST to reduce band symmetric matrix to tridiagonal form.
! 377: *
! 378: INDE = 1
! 379: INDHOUS = INDE + N
! 380: INDWRK = INDHOUS + LHTRD
! 381: LLWORK = LWORK - INDWRK + 1
! 382: INDWK2 = INDWRK + N*N
! 383: LLWRK2 = LWORK - INDWK2 + 1
! 384: *
! 385: CALL DSYTRD_SB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, W,
! 386: $ WORK( INDE ), WORK( INDHOUS ), LHTRD,
! 387: $ WORK( INDWRK ), LLWORK, IINFO )
! 388: *
! 389: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
! 390: *
! 391: IF( .NOT.WANTZ ) THEN
! 392: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 393: ELSE
! 394: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
! 395: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
! 396: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
! 397: $ ZERO, WORK( INDWK2 ), N )
! 398: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
! 399: END IF
! 400: *
! 401: * If matrix was scaled, then rescale eigenvalues appropriately.
! 402: *
! 403: IF( ISCALE.EQ.1 )
! 404: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
! 405: *
! 406: WORK( 1 ) = LWMIN
! 407: IWORK( 1 ) = LIWMIN
! 408: RETURN
! 409: *
! 410: * End of DSBEVD_2STAGE
! 411: *
! 412: END
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