Annotation of rpl/lapack/lapack/zhegv_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZHEGV_2STAGE
! 2: *
! 3: * @precisions fortran z -> c
! 4: *
! 5: * =========== DOCUMENTATION ===========
! 6: *
! 7: * Online html documentation available at
! 8: * http://www.netlib.org/lapack/explore-html/
! 9: *
! 10: *> \htmlonly
! 11: *> Download ZHEGV_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegv_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegv_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegv_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE ZHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
! 24: * WORK, LWORK, RWORK, INFO )
! 25: *
! 26: * IMPLICIT NONE
! 27: *
! 28: * .. Scalar Arguments ..
! 29: * CHARACTER JOBZ, UPLO
! 30: * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * DOUBLE PRECISION RWORK( * ), W( * )
! 34: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 35: * ..
! 36: *
! 37: *
! 38: *> \par Purpose:
! 39: * =============
! 40: *>
! 41: *> \verbatim
! 42: *>
! 43: *> ZHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
! 44: *> of a complex generalized Hermitian-definite eigenproblem, of the form
! 45: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 46: *> Here A and B are assumed to be Hermitian and B is also
! 47: *> positive definite.
! 48: *> This routine use the 2stage technique for the reduction to tridiagonal
! 49: *> which showed higher performance on recent architecture and for large
! 50: * sizes N>2000.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] ITYPE
! 57: *> \verbatim
! 58: *> ITYPE is INTEGER
! 59: *> Specifies the problem type to be solved:
! 60: *> = 1: A*x = (lambda)*B*x
! 61: *> = 2: A*B*x = (lambda)*x
! 62: *> = 3: B*A*x = (lambda)*x
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] JOBZ
! 66: *> \verbatim
! 67: *> JOBZ is CHARACTER*1
! 68: *> = 'N': Compute eigenvalues only;
! 69: *> = 'V': Compute eigenvalues and eigenvectors.
! 70: *> Not available in this release.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] UPLO
! 74: *> \verbatim
! 75: *> UPLO is CHARACTER*1
! 76: *> = 'U': Upper triangles of A and B are stored;
! 77: *> = 'L': Lower triangles of A and B are stored.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] N
! 81: *> \verbatim
! 82: *> N is INTEGER
! 83: *> The order of the matrices A and B. N >= 0.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in,out] A
! 87: *> \verbatim
! 88: *> A is COMPLEX*16 array, dimension (LDA, N)
! 89: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
! 90: *> leading N-by-N upper triangular part of A contains the
! 91: *> upper triangular part of the matrix A. If UPLO = 'L',
! 92: *> the leading N-by-N lower triangular part of A contains
! 93: *> the lower triangular part of the matrix A.
! 94: *>
! 95: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 96: *> matrix Z of eigenvectors. The eigenvectors are normalized
! 97: *> as follows:
! 98: *> if ITYPE = 1 or 2, Z**H*B*Z = I;
! 99: *> if ITYPE = 3, Z**H*inv(B)*Z = I.
! 100: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 101: *> or the lower triangle (if UPLO='L') of A, including the
! 102: *> diagonal, is destroyed.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in] LDA
! 106: *> \verbatim
! 107: *> LDA is INTEGER
! 108: *> The leading dimension of the array A. LDA >= max(1,N).
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in,out] B
! 112: *> \verbatim
! 113: *> B is COMPLEX*16 array, dimension (LDB, N)
! 114: *> On entry, the Hermitian positive definite matrix B.
! 115: *> If UPLO = 'U', the leading N-by-N upper triangular part of B
! 116: *> contains the upper triangular part of the matrix B.
! 117: *> If UPLO = 'L', the leading N-by-N lower triangular part of B
! 118: *> contains the lower triangular part of the matrix B.
! 119: *>
! 120: *> On exit, if INFO <= N, the part of B containing the matrix is
! 121: *> overwritten by the triangular factor U or L from the Cholesky
! 122: *> factorization B = U**H*U or B = L*L**H.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in] LDB
! 126: *> \verbatim
! 127: *> LDB is INTEGER
! 128: *> The leading dimension of the array B. LDB >= max(1,N).
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[out] W
! 132: *> \verbatim
! 133: *> W is DOUBLE PRECISION array, dimension (N)
! 134: *> If INFO = 0, the eigenvalues in ascending order.
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[out] WORK
! 138: *> \verbatim
! 139: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 140: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 141: *> \endverbatim
! 142: *>
! 143: *> \param[in] LWORK
! 144: *> \verbatim
! 145: *> LWORK is INTEGER
! 146: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 147: *> otherwise
! 148: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 149: *> LWORK = MAX(1, dimension) where
! 150: *> dimension = max(stage1,stage2) + (KD+1)*N + N
! 151: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 152: *> + max(2*KD*KD, KD*NTHREADS)
! 153: *> + (KD+1)*N + N
! 154: *> where KD is the blocking size of the reduction,
! 155: *> FACTOPTNB is the blocking used by the QR or LQ
! 156: *> algorithm, usually FACTOPTNB=128 is a good choice
! 157: *> NTHREADS is the number of threads used when
! 158: *> openMP compilation is enabled, otherwise =1.
! 159: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
! 160: *>
! 161: *> If LWORK = -1, then a workspace query is assumed; the routine
! 162: *> only calculates the optimal size of the WORK array, returns
! 163: *> this value as the first entry of the WORK array, and no error
! 164: *> message related to LWORK is issued by XERBLA.
! 165: *> \endverbatim
! 166: *>
! 167: *> \param[out] RWORK
! 168: *> \verbatim
! 169: *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
! 170: *> \endverbatim
! 171: *>
! 172: *> \param[out] INFO
! 173: *> \verbatim
! 174: *> INFO is INTEGER
! 175: *> = 0: successful exit
! 176: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 177: *> > 0: ZPOTRF or ZHEEV returned an error code:
! 178: *> <= N: if INFO = i, ZHEEV failed to converge;
! 179: *> i off-diagonal elements of an intermediate
! 180: *> tridiagonal form did not converge to zero;
! 181: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 182: *> minor of order i of B is not positive definite.
! 183: *> The factorization of B could not be completed and
! 184: *> no eigenvalues or eigenvectors were computed.
! 185: *> \endverbatim
! 186: *
! 187: * Authors:
! 188: * ========
! 189: *
! 190: *> \author Univ. of Tennessee
! 191: *> \author Univ. of California Berkeley
! 192: *> \author Univ. of Colorado Denver
! 193: *> \author NAG Ltd.
! 194: *
! 195: *> \date December 2016
! 196: *
! 197: *> \ingroup complex16HEeigen
! 198: *
! 199: *> \par Further Details:
! 200: * =====================
! 201: *>
! 202: *> \verbatim
! 203: *>
! 204: *> All details about the 2stage techniques are available in:
! 205: *>
! 206: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 207: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 208: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 209: *> of 2011 International Conference for High Performance Computing,
! 210: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 211: *> Article 8 , 11 pages.
! 212: *> http://doi.acm.org/10.1145/2063384.2063394
! 213: *>
! 214: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 215: *> An improved parallel singular value algorithm and its implementation
! 216: *> for multicore hardware, In Proceedings of 2013 International Conference
! 217: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 218: *> Denver, Colorado, USA, 2013.
! 219: *> Article 90, 12 pages.
! 220: *> http://doi.acm.org/10.1145/2503210.2503292
! 221: *>
! 222: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 223: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 224: *> calculations based on fine-grained memory aware tasks.
! 225: *> International Journal of High Performance Computing Applications.
! 226: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 227: *> http://hpc.sagepub.com/content/28/2/196
! 228: *>
! 229: *> \endverbatim
! 230: *
! 231: * =====================================================================
! 232: SUBROUTINE ZHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
! 233: $ WORK, LWORK, RWORK, INFO )
! 234: *
! 235: IMPLICIT NONE
! 236: *
! 237: * -- LAPACK driver routine (version 3.7.0) --
! 238: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 239: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 240: * December 2016
! 241: *
! 242: * .. Scalar Arguments ..
! 243: CHARACTER JOBZ, UPLO
! 244: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
! 245: * ..
! 246: * .. Array Arguments ..
! 247: DOUBLE PRECISION RWORK( * ), W( * )
! 248: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 249: * ..
! 250: *
! 251: * =====================================================================
! 252: *
! 253: * .. Parameters ..
! 254: COMPLEX*16 ONE
! 255: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 256: * ..
! 257: * .. Local Scalars ..
! 258: LOGICAL LQUERY, UPPER, WANTZ
! 259: CHARACTER TRANS
! 260: INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
! 261: * ..
! 262: * .. External Functions ..
! 263: LOGICAL LSAME
! 264: INTEGER ILAENV
! 265: EXTERNAL LSAME, ILAENV
! 266: * ..
! 267: * .. External Subroutines ..
! 268: EXTERNAL XERBLA, ZHEGST, ZPOTRF, ZTRMM, ZTRSM,
! 269: $ ZHEEV_2STAGE
! 270: * ..
! 271: * .. Intrinsic Functions ..
! 272: INTRINSIC MAX
! 273: * ..
! 274: * .. Executable Statements ..
! 275: *
! 276: * Test the input parameters.
! 277: *
! 278: WANTZ = LSAME( JOBZ, 'V' )
! 279: UPPER = LSAME( UPLO, 'U' )
! 280: LQUERY = ( LWORK.EQ.-1 )
! 281: *
! 282: INFO = 0
! 283: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 284: INFO = -1
! 285: ELSE IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 286: INFO = -2
! 287: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 288: INFO = -3
! 289: ELSE IF( N.LT.0 ) THEN
! 290: INFO = -4
! 291: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 292: INFO = -6
! 293: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 294: INFO = -8
! 295: END IF
! 296: *
! 297: IF( INFO.EQ.0 ) THEN
! 298: KD = ILAENV( 17, 'ZHETRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 299: IB = ILAENV( 18, 'ZHETRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 300: LHTRD = ILAENV( 19, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 301: LWTRD = ILAENV( 20, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 302: LWMIN = N + LHTRD + LWTRD
! 303: WORK( 1 ) = LWMIN
! 304: *
! 305: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 306: INFO = -11
! 307: END IF
! 308: END IF
! 309: *
! 310: IF( INFO.NE.0 ) THEN
! 311: CALL XERBLA( 'ZHEGV_2STAGE ', -INFO )
! 312: RETURN
! 313: ELSE IF( LQUERY ) THEN
! 314: RETURN
! 315: END IF
! 316: *
! 317: * Quick return if possible
! 318: *
! 319: IF( N.EQ.0 )
! 320: $ RETURN
! 321: *
! 322: * Form a Cholesky factorization of B.
! 323: *
! 324: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
! 325: IF( INFO.NE.0 ) THEN
! 326: INFO = N + INFO
! 327: RETURN
! 328: END IF
! 329: *
! 330: * Transform problem to standard eigenvalue problem and solve.
! 331: *
! 332: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 333: CALL ZHEEV_2STAGE( JOBZ, UPLO, N, A, LDA, W,
! 334: $ WORK, LWORK, RWORK, INFO )
! 335: *
! 336: IF( WANTZ ) THEN
! 337: *
! 338: * Backtransform eigenvectors to the original problem.
! 339: *
! 340: NEIG = N
! 341: IF( INFO.GT.0 )
! 342: $ NEIG = INFO - 1
! 343: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 344: *
! 345: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 346: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
! 347: *
! 348: IF( UPPER ) THEN
! 349: TRANS = 'N'
! 350: ELSE
! 351: TRANS = 'C'
! 352: END IF
! 353: *
! 354: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 355: $ B, LDB, A, LDA )
! 356: *
! 357: ELSE IF( ITYPE.EQ.3 ) THEN
! 358: *
! 359: * For B*A*x=(lambda)*x;
! 360: * backtransform eigenvectors: x = L*y or U**H *y
! 361: *
! 362: IF( UPPER ) THEN
! 363: TRANS = 'C'
! 364: ELSE
! 365: TRANS = 'N'
! 366: END IF
! 367: *
! 368: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 369: $ B, LDB, A, LDA )
! 370: END IF
! 371: END IF
! 372: *
! 373: WORK( 1 ) = LWMIN
! 374: *
! 375: RETURN
! 376: *
! 377: * End of ZHEGV_2STAGE
! 378: *
! 379: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zhegv_2stage.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack