Annotation of rpl/lapack/lapack/dsbev_2stage.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> DSBEV_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 DSBEV_2STAGE + dependencies
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbev_2stage.f">
! 13: *> [TGZ]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbev_2stage.f">
! 15: *> [ZIP]</a>
! 16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbev_2stage.f">
! 17: *> [TXT]</a>
! 18: *> \endhtmlonly
! 19: *
! 20: * Definition:
! 21: * ===========
! 22: *
! 23: * SUBROUTINE DSBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 24: * WORK, LWORK, 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 AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 34: * ..
! 35: *
! 36: *
! 37: *> \par Purpose:
! 38: * =============
! 39: *>
! 40: *> \verbatim
! 41: *>
! 42: *> DSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
! 43: *> a real symmetric band matrix A using the 2stage technique for
! 44: *> the reduction to tridiagonal.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] JOBZ
! 51: *> \verbatim
! 52: *> JOBZ is CHARACTER*1
! 53: *> = 'N': Compute eigenvalues only;
! 54: *> = 'V': Compute eigenvalues and eigenvectors.
! 55: *> Not available in this release.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] UPLO
! 59: *> \verbatim
! 60: *> UPLO is CHARACTER*1
! 61: *> = 'U': Upper triangle of A is stored;
! 62: *> = 'L': Lower triangle of A is stored.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] N
! 66: *> \verbatim
! 67: *> N is INTEGER
! 68: *> The order of the matrix A. N >= 0.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] KD
! 72: *> \verbatim
! 73: *> KD is INTEGER
! 74: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 75: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in,out] AB
! 79: *> \verbatim
! 80: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
! 81: *> On entry, the upper or lower triangle of the symmetric band
! 82: *> matrix A, stored in the first KD+1 rows of the array. The
! 83: *> j-th column of A is stored in the j-th column of the array AB
! 84: *> as follows:
! 85: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 86: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 87: *>
! 88: *> On exit, AB is overwritten by values generated during the
! 89: *> reduction to tridiagonal form. If UPLO = 'U', the first
! 90: *> superdiagonal and the diagonal of the tridiagonal matrix T
! 91: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 92: *> the diagonal and first subdiagonal of T are returned in the
! 93: *> first two rows of AB.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDAB
! 97: *> \verbatim
! 98: *> LDAB is INTEGER
! 99: *> The leading dimension of the array AB. LDAB >= KD + 1.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] W
! 103: *> \verbatim
! 104: *> W is DOUBLE PRECISION array, dimension (N)
! 105: *> If INFO = 0, the eigenvalues in ascending order.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] Z
! 109: *> \verbatim
! 110: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
! 111: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 112: *> eigenvectors of the matrix A, with the i-th column of Z
! 113: *> holding the eigenvector associated with W(i).
! 114: *> If JOBZ = 'N', then Z is not referenced.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] LDZ
! 118: *> \verbatim
! 119: *> LDZ is INTEGER
! 120: *> The leading dimension of the array Z. LDZ >= 1, and if
! 121: *> JOBZ = 'V', LDZ >= max(1,N).
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[out] WORK
! 125: *> \verbatim
! 126: *> WORK is DOUBLE PRECISION array, dimension LWORK
! 127: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] LWORK
! 131: *> \verbatim
! 132: *> LWORK is INTEGER
! 133: *> The length of the array WORK. LWORK >= 1, when N <= 1;
! 134: *> otherwise
! 135: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
! 136: *> LWORK = MAX(1, dimension) where
! 137: *> dimension = (2KD+1)*N + KD*NTHREADS + N
! 138: *> where KD is the size of the band.
! 139: *> NTHREADS is the number of threads used when
! 140: *> openMP compilation is enabled, otherwise =1.
! 141: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
! 142: *>
! 143: *> If LWORK = -1, then a workspace query is assumed; the routine
! 144: *> only calculates the optimal size of the WORK array, returns
! 145: *> this value as the first entry of the WORK array, and no error
! 146: *> message related to LWORK is issued by XERBLA.
! 147: *> \endverbatim
! 148: *>
! 149: *> \param[out] INFO
! 150: *> \verbatim
! 151: *> INFO is INTEGER
! 152: *> = 0: successful exit
! 153: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 154: *> > 0: if INFO = i, the algorithm failed to converge; i
! 155: *> off-diagonal elements of an intermediate tridiagonal
! 156: *> form did not converge to zero.
! 157: *> \endverbatim
! 158: *
! 159: * Authors:
! 160: * ========
! 161: *
! 162: *> \author Univ. of Tennessee
! 163: *> \author Univ. of California Berkeley
! 164: *> \author Univ. of Colorado Denver
! 165: *> \author NAG Ltd.
! 166: *
! 167: *> \date December 2016
! 168: *
! 169: *> \ingroup doubleOTHEReigen
! 170: *
! 171: *> \par Further Details:
! 172: * =====================
! 173: *>
! 174: *> \verbatim
! 175: *>
! 176: *> All details about the 2stage techniques are available in:
! 177: *>
! 178: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
! 179: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
! 180: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
! 181: *> of 2011 International Conference for High Performance Computing,
! 182: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
! 183: *> Article 8 , 11 pages.
! 184: *> http://doi.acm.org/10.1145/2063384.2063394
! 185: *>
! 186: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
! 187: *> An improved parallel singular value algorithm and its implementation
! 188: *> for multicore hardware, In Proceedings of 2013 International Conference
! 189: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
! 190: *> Denver, Colorado, USA, 2013.
! 191: *> Article 90, 12 pages.
! 192: *> http://doi.acm.org/10.1145/2503210.2503292
! 193: *>
! 194: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
! 195: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
! 196: *> calculations based on fine-grained memory aware tasks.
! 197: *> International Journal of High Performance Computing Applications.
! 198: *> Volume 28 Issue 2, Pages 196-209, May 2014.
! 199: *> http://hpc.sagepub.com/content/28/2/196
! 200: *>
! 201: *> \endverbatim
! 202: *
! 203: * =====================================================================
! 204: SUBROUTINE DSBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
! 205: $ WORK, LWORK, INFO )
! 206: *
! 207: IMPLICIT NONE
! 208: *
! 209: * -- LAPACK driver routine (version 3.7.0) --
! 210: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 211: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 212: * December 2016
! 213: *
! 214: * .. Scalar Arguments ..
! 215: CHARACTER JOBZ, UPLO
! 216: INTEGER INFO, KD, LDAB, LDZ, N, LWORK
! 217: * ..
! 218: * .. Array Arguments ..
! 219: DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 220: * ..
! 221: *
! 222: * =====================================================================
! 223: *
! 224: * .. Parameters ..
! 225: DOUBLE PRECISION ZERO, ONE
! 226: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 227: * ..
! 228: * .. Local Scalars ..
! 229: LOGICAL LOWER, WANTZ, LQUERY
! 230: INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE,
! 231: $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS
! 232: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 233: $ SMLNUM
! 234: * ..
! 235: * .. External Functions ..
! 236: LOGICAL LSAME
! 237: INTEGER ILAENV
! 238: DOUBLE PRECISION DLAMCH, DLANSB
! 239: EXTERNAL LSAME, DLAMCH, DLANSB, ILAENV
! 240: * ..
! 241: * .. External Subroutines ..
! 242: EXTERNAL DLASCL, DSCAL, DSTEQR, DSTERF, XERBLA
! 243: $ DSYTRD_SB2ST
! 244: * ..
! 245: * .. Intrinsic Functions ..
! 246: INTRINSIC SQRT
! 247: * ..
! 248: * .. Executable Statements ..
! 249: *
! 250: * Test the input parameters.
! 251: *
! 252: WANTZ = LSAME( JOBZ, 'V' )
! 253: LOWER = LSAME( UPLO, 'L' )
! 254: LQUERY = ( LWORK.EQ.-1 )
! 255: *
! 256: INFO = 0
! 257: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
! 258: INFO = -1
! 259: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 260: INFO = -2
! 261: ELSE IF( N.LT.0 ) THEN
! 262: INFO = -3
! 263: ELSE IF( KD.LT.0 ) THEN
! 264: INFO = -4
! 265: ELSE IF( LDAB.LT.KD+1 ) THEN
! 266: INFO = -6
! 267: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 268: INFO = -9
! 269: END IF
! 270: *
! 271: IF( INFO.EQ.0 ) THEN
! 272: IF( N.LE.1 ) THEN
! 273: LWMIN = 1
! 274: WORK( 1 ) = LWMIN
! 275: ELSE
! 276: IB = ILAENV( 18, 'DSYTRD_SB2ST', JOBZ, N, KD, -1, -1 )
! 277: LHTRD = ILAENV( 19, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 278: LWTRD = ILAENV( 20, 'DSYTRD_SB2ST', JOBZ, N, KD, IB, -1 )
! 279: LWMIN = N + LHTRD + LWTRD
! 280: WORK( 1 ) = LWMIN
! 281: ENDIF
! 282: *
! 283: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
! 284: $ INFO = -11
! 285: END IF
! 286: *
! 287: IF( INFO.NE.0 ) THEN
! 288: CALL XERBLA( 'DSBEV_2STAGE ', -INFO )
! 289: RETURN
! 290: ELSE IF( LQUERY ) THEN
! 291: RETURN
! 292: END IF
! 293: *
! 294: * Quick return if possible
! 295: *
! 296: IF( N.EQ.0 )
! 297: $ RETURN
! 298: *
! 299: IF( N.EQ.1 ) THEN
! 300: IF( LOWER ) THEN
! 301: W( 1 ) = AB( 1, 1 )
! 302: ELSE
! 303: W( 1 ) = AB( KD+1, 1 )
! 304: END IF
! 305: IF( WANTZ )
! 306: $ Z( 1, 1 ) = ONE
! 307: RETURN
! 308: END IF
! 309: *
! 310: * Get machine constants.
! 311: *
! 312: SAFMIN = DLAMCH( 'Safe minimum' )
! 313: EPS = DLAMCH( 'Precision' )
! 314: SMLNUM = SAFMIN / EPS
! 315: BIGNUM = ONE / SMLNUM
! 316: RMIN = SQRT( SMLNUM )
! 317: RMAX = SQRT( BIGNUM )
! 318: *
! 319: * Scale matrix to allowable range, if necessary.
! 320: *
! 321: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
! 322: ISCALE = 0
! 323: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 324: ISCALE = 1
! 325: SIGMA = RMIN / ANRM
! 326: ELSE IF( ANRM.GT.RMAX ) THEN
! 327: ISCALE = 1
! 328: SIGMA = RMAX / ANRM
! 329: END IF
! 330: IF( ISCALE.EQ.1 ) THEN
! 331: IF( LOWER ) THEN
! 332: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 333: ELSE
! 334: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 335: END IF
! 336: END IF
! 337: *
! 338: * Call DSYTRD_SB2ST to reduce symmetric band matrix to tridiagonal form.
! 339: *
! 340: INDE = 1
! 341: INDHOUS = INDE + N
! 342: INDWRK = INDHOUS + LHTRD
! 343: LLWORK = LWORK - INDWRK + 1
! 344: *
! 345: CALL DSYTRD_SB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB, W,
! 346: $ WORK( INDE ), WORK( INDHOUS ), LHTRD,
! 347: $ WORK( INDWRK ), LLWORK, IINFO )
! 348: *
! 349: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
! 350: *
! 351: IF( .NOT.WANTZ ) THEN
! 352: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 353: ELSE
! 354: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
! 355: $ INFO )
! 356: END IF
! 357: *
! 358: * If matrix was scaled, then rescale eigenvalues appropriately.
! 359: *
! 360: IF( ISCALE.EQ.1 ) THEN
! 361: IF( INFO.EQ.0 ) THEN
! 362: IMAX = N
! 363: ELSE
! 364: IMAX = INFO - 1
! 365: END IF
! 366: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 367: END IF
! 368: *
! 369: * Set WORK(1) to optimal workspace size.
! 370: *
! 371: WORK( 1 ) = LWMIN
! 372: *
! 373: RETURN
! 374: *
! 375: * End of DSBEV_2STAGE
! 376: *
! 377: END
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