Annotation of rpl/lapack/lapack/zhbev_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 ZHBEV_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbev_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbev_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbev_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE ZHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 24: * WORK, LWORK, RWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER JOBZ, UPLO
! 30: * INTEGER INFO, KD, LDAB, LDZ, N, LWORK
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * DOUBLE PRECISION RWORK( * ), W( * )
! 34: * COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
! 35: * ..
! 36: *
! 37: *
! 38: *> \par Purpose:
! 39: * =============
! 40: *>
! 41: *> \verbatim
! 42: *>
! 43: *> ZHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
! 44: *> a complex Hermitian band matrix A using the 2stage technique for
! 45: *> the reduction to tridiagonal.
! 46: *> \endverbatim
! 47: *
! 48: * Arguments:
! 49: * ==========
! 50: *
! 51: *> \param[in] JOBZ
! 52: *> \verbatim
! 53: *> JOBZ is CHARACTER*1
! 54: *> = 'N': Compute eigenvalues only;
! 55: *> = 'V': Compute eigenvalues and eigenvectors.
! 56: *> Not available in this release.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] UPLO
! 60: *> \verbatim
! 61: *> UPLO is CHARACTER*1
! 62: *> = 'U': Upper triangle of A is stored;
! 63: *> = 'L': Lower triangle of A is stored.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] N
! 67: *> \verbatim
! 68: *> N is INTEGER
! 69: *> The order of the matrix A. N >= 0.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] KD
! 73: *> \verbatim
! 74: *> KD is INTEGER
! 75: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 76: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in,out] AB
! 80: *> \verbatim
! 81: *> AB is COMPLEX*16 array, dimension (LDAB, N)
! 82: *> On entry, the upper or lower triangle of the Hermitian band
! 83: *> matrix A, stored in the first KD+1 rows of the array. The
! 84: *> j-th column of A is stored in the j-th column of the array AB
! 85: *> as follows:
! 86: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 87: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 88: *>
! 89: *> On exit, AB is overwritten by values generated during the
! 90: *> reduction to tridiagonal form. If UPLO = 'U', the first
! 91: *> superdiagonal and the diagonal of the tridiagonal matrix T
! 92: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 93: *> the diagonal and first subdiagonal of T are returned in the
! 94: *> first two rows of AB.
! 95: *> \endverbatim
! 96: *>
! 97: *> \param[in] LDAB
! 98: *> \verbatim
! 99: *> LDAB is INTEGER
! 100: *> The leading dimension of the array AB. LDAB >= KD + 1.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[out] W
! 104: *> \verbatim
! 105: *> W is DOUBLE PRECISION array, dimension (N)
! 106: *> If INFO = 0, the eigenvalues in ascending order.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[out] Z
! 110: *> \verbatim
! 111: *> Z is COMPLEX*16 array, dimension (LDZ, N)
! 112: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 113: *> eigenvectors of the matrix A, with the i-th column of Z
! 114: *> holding the eigenvector associated with W(i).
! 115: *> If JOBZ = 'N', then Z is not referenced.
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in] LDZ
! 119: *> \verbatim
! 120: *> LDZ is INTEGER
! 121: *> The leading dimension of the array Z. LDZ >= 1, and if
! 122: *> JOBZ = 'V', LDZ >= max(1,N).
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[out] WORK
! 126: *> \verbatim
! 127: *> WORK is COMPLEX*16 array, dimension LWORK
! 128: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[in] LWORK
! 132: *> \verbatim
! 133: *> LWORK is INTEGER
! 134: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 135: *> otherwise
! 136: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 137: *> LWORK = MAX(1, dimension) where
! 138: *> dimension = (2KD+1)*N + KD*NTHREADS
! 139: *> where KD is the size of the band.
! 140: *> NTHREADS is the number of threads used when
! 141: *> openMP compilation is enabled, otherwise =1.
! 142: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
! 143: *>
! 144: *> If LWORK = -1, then a workspace query is assumed; the routine
! 145: *> only calculates the optimal sizes of the WORK, RWORK and
! 146: *> IWORK arrays, returns these values as the first entries of
! 147: *> the WORK, RWORK and IWORK arrays, and no error message
! 148: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 149: *> \endverbatim
! 150: *>
! 151: *> \param[out] RWORK
! 152: *> \verbatim
! 153: *> RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
! 154: *> \endverbatim
! 155: *>
! 156: *> \param[out] INFO
! 157: *> \verbatim
! 158: *> INFO is INTEGER
! 159: *> = 0: successful exit.
! 160: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 161: *> > 0: if INFO = i, the algorithm failed to converge; i
! 162: *> off-diagonal elements of an intermediate tridiagonal
! 163: *> form did not converge to zero.
! 164: *> \endverbatim
! 165: *
! 166: * Authors:
! 167: * ========
! 168: *
! 169: *> \author Univ. of Tennessee
! 170: *> \author Univ. of California Berkeley
! 171: *> \author Univ. of Colorado Denver
! 172: *> \author NAG Ltd.
! 173: *
! 174: *> \date December 2016
! 175: *
! 176: *> \ingroup complex16OTHEReigen
! 177: *
! 178: *> \par Further Details:
! 179: * =====================
! 180: *>
! 181: *> \verbatim
! 182: *>
! 183: *> All details about the 2stage techniques are available in:
! 184: *>
! 185: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 186: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 187: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 188: *> of 2011 International Conference for High Performance Computing,
! 189: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 190: *> Article 8 , 11 pages.
! 191: *> http://doi.acm.org/10.1145/2063384.2063394
! 192: *>
! 193: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 194: *> An improved parallel singular value algorithm and its implementation
! 195: *> for multicore hardware, In Proceedings of 2013 International Conference
! 196: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 197: *> Denver, Colorado, USA, 2013.
! 198: *> Article 90, 12 pages.
! 199: *> http://doi.acm.org/10.1145/2503210.2503292
! 200: *>
! 201: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 202: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 203: *> calculations based on fine-grained memory aware tasks.
! 204: *> International Journal of High Performance Computing Applications.
! 205: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 206: *> http://hpc.sagepub.com/content/28/2/196
! 207: *>
! 208: *> \endverbatim
! 209: *
! 210: * =====================================================================
! 211: SUBROUTINE ZHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 212: $ WORK, LWORK, RWORK, INFO )
! 213: *
! 214: IMPLICIT NONE
! 215: *
! 216: * -- LAPACK driver routine (version 3.7.0) --
! 217: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 218: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 219: * December 2016
! 220: *
! 221: * .. Scalar Arguments ..
! 222: CHARACTER JOBZ, UPLO
! 223: INTEGER INFO, KD, LDAB, LDZ, N, LWORK
! 224: * ..
! 225: * .. Array Arguments ..
! 226: DOUBLE PRECISION RWORK( * ), W( * )
! 227: COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
! 228: * ..
! 229: *
! 230: * =====================================================================
! 231: *
! 232: * .. Parameters ..
! 233: DOUBLE PRECISION ZERO, ONE
! 234: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 235: * ..
! 236: * .. Local Scalars ..
! 237: LOGICAL LOWER, WANTZ, LQUERY
! 238: INTEGER IINFO, IMAX, INDE, INDWRK, INDRWK, ISCALE,
! 239: $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS
! 240: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 241: $ SMLNUM
! 242: * ..
! 243: * .. External Functions ..
! 244: LOGICAL LSAME
! 245: INTEGER ILAENV
! 246: DOUBLE PRECISION DLAMCH, ZLANHB
! 247: EXTERNAL LSAME, DLAMCH, ZLANHB, ILAENV
! 248: * ..
! 249: * .. External Subroutines ..
! 250: EXTERNAL DSCAL, DSTERF, XERBLA, ZLASCL, ZSTEQR
! 251: $ ZHETRD_2STAGE
! 252: * ..
! 253: * .. Intrinsic Functions ..
! 254: INTRINSIC DBLE, SQRT
! 255: * ..
! 256: * .. Executable Statements ..
! 257: *
! 258: * Test the input parameters.
! 259: *
! 260: WANTZ = LSAME( JOBZ, 'V' )
! 261: LOWER = LSAME( UPLO, 'L' )
! 262: LQUERY = ( LWORK.EQ.-1 )
! 263: *
! 264: INFO = 0
! 265: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 266: INFO = -1
! 267: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 268: INFO = -2
! 269: ELSE IF( N.LT.0 ) THEN
! 270: INFO = -3
! 271: ELSE IF( KD.LT.0 ) THEN
! 272: INFO = -4
! 273: ELSE IF( LDAB.LT.KD+1 ) THEN
! 274: INFO = -6
! 275: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 276: INFO = -9
! 277: END IF
! 278: *
! 279: IF( INFO.EQ.0 ) THEN
! 280: IF( N.LE.1 ) THEN
! 281: LWMIN = 1
! 282: WORK( 1 ) = LWMIN
! 283: ELSE
! 284: IB = ILAENV( 18, 'ZHETRD_HB2ST', JOBZ, N, KD, -1, -1 )
! 285: LHTRD = ILAENV( 19, 'ZHETRD_HB2ST', JOBZ, N, KD, IB, -1 )
! 286: LWTRD = ILAENV( 20, 'ZHETRD_HB2ST', JOBZ, N, KD, IB, -1 )
! 287: LWMIN = LHTRD + LWTRD
! 288: WORK( 1 ) = LWMIN
! 289: ENDIF
! 290: *
! 291: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
! 292: $ INFO = -11
! 293: END IF
! 294: *
! 295: IF( INFO.NE.0 ) THEN
! 296: CALL XERBLA( 'ZHBEV_2STAGE ', -INFO )
! 297: RETURN
! 298: ELSE IF( LQUERY ) THEN
! 299: RETURN
! 300: END IF
! 301: *
! 302: * Quick return if possible
! 303: *
! 304: IF( N.EQ.0 )
! 305: $ RETURN
! 306: *
! 307: IF( N.EQ.1 ) THEN
! 308: IF( LOWER ) THEN
! 309: W( 1 ) = DBLE( AB( 1, 1 ) )
! 310: ELSE
! 311: W( 1 ) = DBLE( AB( KD+1, 1 ) )
! 312: END IF
! 313: IF( WANTZ )
! 314: $ Z( 1, 1 ) = ONE
! 315: RETURN
! 316: END IF
! 317: *
! 318: * Get machine constants.
! 319: *
! 320: SAFMIN = DLAMCH( 'Safe minimum' )
! 321: EPS = DLAMCH( 'Precision' )
! 322: SMLNUM = SAFMIN / EPS
! 323: BIGNUM = ONE / SMLNUM
! 324: RMIN = SQRT( SMLNUM )
! 325: RMAX = SQRT( BIGNUM )
! 326: *
! 327: * Scale matrix to allowable range, if necessary.
! 328: *
! 329: ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
! 330: ISCALE = 0
! 331: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 332: ISCALE = 1
! 333: SIGMA = RMIN / ANRM
! 334: ELSE IF( ANRM.GT.RMAX ) THEN
! 335: ISCALE = 1
! 336: SIGMA = RMAX / ANRM
! 337: END IF
! 338: IF( ISCALE.EQ.1 ) THEN
! 339: IF( LOWER ) THEN
! 340: CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 341: ELSE
! 342: CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 343: END IF
! 344: END IF
! 345: *
! 346: * Call ZHBTRD_HB2ST to reduce Hermitian band matrix to tridiagonal form.
! 347: *
! 348: INDE = 1
! 349: INDHOUS = 1
! 350: INDWRK = INDHOUS + LHTRD
! 351: LLWORK = LWORK - INDWRK + 1
! 352: *
! 353: CALL ZHETRD_HB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, W,
! 354: $ RWORK( INDE ), WORK( INDHOUS ), LHTRD,
! 355: $ WORK( INDWRK ), LLWORK, IINFO )
! 356: *
! 357: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
! 358: *
! 359: IF( .NOT.WANTZ ) THEN
! 360: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 361: ELSE
! 362: INDRWK = INDE + N
! 363: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
! 364: $ RWORK( INDRWK ), INFO )
! 365: END IF
! 366: *
! 367: * If matrix was scaled, then rescale eigenvalues appropriately.
! 368: *
! 369: IF( ISCALE.EQ.1 ) THEN
! 370: IF( INFO.EQ.0 ) THEN
! 371: IMAX = N
! 372: ELSE
! 373: IMAX = INFO - 1
! 374: END IF
! 375: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 376: END IF
! 377: *
! 378: * Set WORK(1) to optimal workspace size.
! 379: *
! 380: WORK( 1 ) = LWMIN
! 381: *
! 382: RETURN
! 383: *
! 384: * End of ZHBEV_2STAGE
! 385: *
! 386: END
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