Annotation of rpl/lapack/lapack/dsygv_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DSYGV_2STAGE
! 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 DSYGV_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygv_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygv_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygv_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSYGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
! 24: * WORK, LWORK, 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 A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
! 34: * ..
! 35: *
! 36: *
! 37: *> \par Purpose:
! 38: * =============
! 39: *>
! 40: *> \verbatim
! 41: *>
! 42: *> DSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
! 43: *> of a real generalized symmetric-definite eigenproblem, of the form
! 44: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 45: *> Here A and B are assumed to be symmetric and B is also
! 46: *> positive definite.
! 47: *> This routine use the 2stage technique for the reduction to tridiagonal
! 48: *> which showed higher performance on recent architecture and for large
! 49: * sizes N>2000.
! 50: *> \endverbatim
! 51: *
! 52: * Arguments:
! 53: * ==========
! 54: *
! 55: *> \param[in] ITYPE
! 56: *> \verbatim
! 57: *> ITYPE is INTEGER
! 58: *> Specifies the problem type to be solved:
! 59: *> = 1: A*x = (lambda)*B*x
! 60: *> = 2: A*B*x = (lambda)*x
! 61: *> = 3: B*A*x = (lambda)*x
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] JOBZ
! 65: *> \verbatim
! 66: *> JOBZ is CHARACTER*1
! 67: *> = 'N': Compute eigenvalues only;
! 68: *> = 'V': Compute eigenvalues and eigenvectors.
! 69: *> Not available in this release.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] UPLO
! 73: *> \verbatim
! 74: *> UPLO is CHARACTER*1
! 75: *> = 'U': Upper triangles of A and B are stored;
! 76: *> = 'L': Lower triangles of A and B are stored.
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] N
! 80: *> \verbatim
! 81: *> N is INTEGER
! 82: *> The order of the matrices A and B. N >= 0.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in,out] A
! 86: *> \verbatim
! 87: *> A is DOUBLE PRECISION array, dimension (LDA, N)
! 88: *> On entry, the symmetric matrix A. If UPLO = 'U', the
! 89: *> leading N-by-N upper triangular part of A contains the
! 90: *> upper triangular part of the matrix A. If UPLO = 'L',
! 91: *> the leading N-by-N lower triangular part of A contains
! 92: *> the lower triangular part of the matrix A.
! 93: *>
! 94: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 95: *> matrix Z of eigenvectors. The eigenvectors are normalized
! 96: *> as follows:
! 97: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
! 98: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
! 99: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 100: *> or the lower triangle (if UPLO='L') of A, including the
! 101: *> diagonal, is destroyed.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in] LDA
! 105: *> \verbatim
! 106: *> LDA is INTEGER
! 107: *> The leading dimension of the array A. LDA >= max(1,N).
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in,out] B
! 111: *> \verbatim
! 112: *> B is DOUBLE PRECISION array, dimension (LDB, N)
! 113: *> On entry, the symmetric positive definite matrix B.
! 114: *> If UPLO = 'U', the leading N-by-N upper triangular part of B
! 115: *> contains the upper triangular part of the matrix B.
! 116: *> If UPLO = 'L', the leading N-by-N lower triangular part of B
! 117: *> contains the lower triangular part of the matrix B.
! 118: *>
! 119: *> On exit, if INFO <= N, the part of B containing the matrix is
! 120: *> overwritten by the triangular factor U or L from the Cholesky
! 121: *> factorization B = U**T*U or B = L*L**T.
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[in] LDB
! 125: *> \verbatim
! 126: *> LDB is INTEGER
! 127: *> The leading dimension of the array B. LDB >= max(1,N).
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[out] W
! 131: *> \verbatim
! 132: *> W is DOUBLE PRECISION array, dimension (N)
! 133: *> If INFO = 0, the eigenvalues in ascending order.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[out] WORK
! 137: *> \verbatim
! 138: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 139: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] LWORK
! 143: *> \verbatim
! 144: *> LWORK is INTEGER
! 145: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 146: *> otherwise
! 147: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 148: *> LWORK = MAX(1, dimension) where
! 149: *> dimension = max(stage1,stage2) + (KD+1)*N + 2*N
! 150: *> = N*KD + N*max(KD+1,FACTOPTNB)
! 151: *> + max(2*KD*KD, KD*NTHREADS)
! 152: *> + (KD+1)*N + 2*N
! 153: *> where KD is the blocking size of the reduction,
! 154: *> FACTOPTNB is the blocking used by the QR or LQ
! 155: *> algorithm, usually FACTOPTNB=128 is a good choice
! 156: *> NTHREADS is the number of threads used when
! 157: *> openMP compilation is enabled, otherwise =1.
! 158: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
! 159: *>
! 160: *> If LWORK = -1, then a workspace query is assumed; the routine
! 161: *> only calculates the optimal size of the WORK array, returns
! 162: *> this value as the first entry of the WORK array, and no error
! 163: *> message related to LWORK is issued by XERBLA.
! 164: *> \endverbatim
! 165: *>
! 166: *> \param[out] INFO
! 167: *> \verbatim
! 168: *> INFO is INTEGER
! 169: *> = 0: successful exit
! 170: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 171: *> > 0: DPOTRF or DSYEV returned an error code:
! 172: *> <= N: if INFO = i, DSYEV failed to converge;
! 173: *> i off-diagonal elements of an intermediate
! 174: *> tridiagonal form did not converge to zero;
! 175: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 176: *> minor of order i of B is not positive definite.
! 177: *> The factorization of B could not be completed and
! 178: *> no eigenvalues or eigenvectors were computed.
! 179: *> \endverbatim
! 180: *
! 181: * Authors:
! 182: * ========
! 183: *
! 184: *> \author Univ. of Tennessee
! 185: *> \author Univ. of California Berkeley
! 186: *> \author Univ. of Colorado Denver
! 187: *> \author NAG Ltd.
! 188: *
! 189: *> \date December 2016
! 190: *
! 191: *> \ingroup doubleSYeigen
! 192: *
! 193: *> \par Further Details:
! 194: * =====================
! 195: *>
! 196: *> \verbatim
! 197: *>
! 198: *> All details about the 2stage techniques are available in:
! 199: *>
! 200: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 201: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 202: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 203: *> of 2011 International Conference for High Performance Computing,
! 204: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 205: *> Article 8 , 11 pages.
! 206: *> http://doi.acm.org/10.1145/2063384.2063394
! 207: *>
! 208: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 209: *> An improved parallel singular value algorithm and its implementation
! 210: *> for multicore hardware, In Proceedings of 2013 International Conference
! 211: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 212: *> Denver, Colorado, USA, 2013.
! 213: *> Article 90, 12 pages.
! 214: *> http://doi.acm.org/10.1145/2503210.2503292
! 215: *>
! 216: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 217: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 218: *> calculations based on fine-grained memory aware tasks.
! 219: *> International Journal of High Performance Computing Applications.
! 220: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 221: *> http://hpc.sagepub.com/content/28/2/196
! 222: *>
! 223: *> \endverbatim
! 224: *
! 225: * =====================================================================
! 226: SUBROUTINE DSYGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
! 227: $ WORK, LWORK, INFO )
! 228: *
! 229: IMPLICIT NONE
! 230: *
! 231: * -- LAPACK driver routine (version 3.7.0) --
! 232: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 233: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 234: * December 2016
! 235: *
! 236: * .. Scalar Arguments ..
! 237: CHARACTER JOBZ, UPLO
! 238: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
! 239: * ..
! 240: * .. Array Arguments ..
! 241: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
! 242: * ..
! 243: *
! 244: * =====================================================================
! 245: *
! 246: * .. Parameters ..
! 247: DOUBLE PRECISION ONE
! 248: PARAMETER ( ONE = 1.0D+0 )
! 249: * ..
! 250: * .. Local Scalars ..
! 251: LOGICAL LQUERY, UPPER, WANTZ
! 252: CHARACTER TRANS
! 253: INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
! 254: * ..
! 255: * .. External Functions ..
! 256: LOGICAL LSAME
! 257: INTEGER ILAENV
! 258: EXTERNAL LSAME, ILAENV
! 259: * ..
! 260: * .. External Subroutines ..
! 261: EXTERNAL DPOTRF, DSYGST, DTRMM, DTRSM, XERBLA,
! 262: $ DSYEV_2STAGE
! 263: * ..
! 264: * .. Intrinsic Functions ..
! 265: INTRINSIC MAX
! 266: * ..
! 267: * .. Executable Statements ..
! 268: *
! 269: * Test the input parameters.
! 270: *
! 271: WANTZ = LSAME( JOBZ, 'V' )
! 272: UPPER = LSAME( UPLO, 'U' )
! 273: LQUERY = ( LWORK.EQ.-1 )
! 274: *
! 275: INFO = 0
! 276: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 277: INFO = -1
! 278: ELSE IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 279: INFO = -2
! 280: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 281: INFO = -3
! 282: ELSE IF( N.LT.0 ) THEN
! 283: INFO = -4
! 284: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 285: INFO = -6
! 286: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 287: INFO = -8
! 288: END IF
! 289: *
! 290: IF( INFO.EQ.0 ) THEN
! 291: KD = ILAENV( 17, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 )
! 292: IB = ILAENV( 18, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
! 293: LHTRD = ILAENV( 19, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 294: LWTRD = ILAENV( 20, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
! 295: LWMIN = 2*N + LHTRD + LWTRD
! 296: WORK( 1 ) = LWMIN
! 297: *
! 298: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 299: INFO = -11
! 300: END IF
! 301: END IF
! 302: *
! 303: IF( INFO.NE.0 ) THEN
! 304: CALL XERBLA( 'DSYGV_2STAGE ', -INFO )
! 305: RETURN
! 306: ELSE IF( LQUERY ) THEN
! 307: RETURN
! 308: END IF
! 309: *
! 310: * Quick return if possible
! 311: *
! 312: IF( N.EQ.0 )
! 313: $ RETURN
! 314: *
! 315: * Form a Cholesky factorization of B.
! 316: *
! 317: CALL DPOTRF( UPLO, N, B, LDB, INFO )
! 318: IF( INFO.NE.0 ) THEN
! 319: INFO = N + INFO
! 320: RETURN
! 321: END IF
! 322: *
! 323: * Transform problem to standard eigenvalue problem and solve.
! 324: *
! 325: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 326: CALL DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
! 327: *
! 328: IF( WANTZ ) THEN
! 329: *
! 330: * Backtransform eigenvectors to the original problem.
! 331: *
! 332: NEIG = N
! 333: IF( INFO.GT.0 )
! 334: $ NEIG = INFO - 1
! 335: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 336: *
! 337: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 338: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
! 339: *
! 340: IF( UPPER ) THEN
! 341: TRANS = 'N'
! 342: ELSE
! 343: TRANS = 'T'
! 344: END IF
! 345: *
! 346: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 347: $ B, LDB, A, LDA )
! 348: *
! 349: ELSE IF( ITYPE.EQ.3 ) THEN
! 350: *
! 351: * For B*A*x=(lambda)*x;
! 352: * backtransform eigenvectors: x = L*y or U**T*y
! 353: *
! 354: IF( UPPER ) THEN
! 355: TRANS = 'T'
! 356: ELSE
! 357: TRANS = 'N'
! 358: END IF
! 359: *
! 360: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 361: $ B, LDB, A, LDA )
! 362: END IF
! 363: END IF
! 364: *
! 365: WORK( 1 ) = LWMIN
! 366: RETURN
! 367: *
! 368: * End of DSYGV_2STAGE
! 369: *
! 370: END
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