Annotation of rpl/lapack/lapack/zheevd.f, revision 1.16

1.8       bertrand    1: *> \brief <b> ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.14      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.8       bertrand    7: *
                      8: *> \htmlonly
1.14      bertrand    9: *> Download ZHEEVD + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheevd.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevd.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevd.f">
1.8       bertrand   15: *> [TXT]</a>
1.14      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
                     22: *                          LRWORK, IWORK, LIWORK, INFO )
1.14      bertrand   23: *
1.8       bertrand   24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          JOBZ, UPLO
                     26: *       INTEGER            INFO, LDA, LIWORK, LRWORK, LWORK, N
                     27: *       ..
                     28: *       .. Array Arguments ..
                     29: *       INTEGER            IWORK( * )
                     30: *       DOUBLE PRECISION   RWORK( * ), W( * )
                     31: *       COMPLEX*16         A( LDA, * ), WORK( * )
                     32: *       ..
1.14      bertrand   33: *
1.8       bertrand   34: *
                     35: *> \par Purpose:
                     36: *  =============
                     37: *>
                     38: *> \verbatim
                     39: *>
                     40: *> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
                     41: *> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
                     42: *> divide and conquer algorithm.
                     43: *>
                     44: *> The divide and conquer algorithm makes very mild assumptions about
                     45: *> floating point arithmetic. It will work on machines with a guard
                     46: *> digit in add/subtract, or on those binary machines without guard
                     47: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
                     48: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
                     49: *> without guard digits, but we know of none.
                     50: *> \endverbatim
                     51: *
                     52: *  Arguments:
                     53: *  ==========
                     54: *
                     55: *> \param[in] JOBZ
                     56: *> \verbatim
                     57: *>          JOBZ is CHARACTER*1
                     58: *>          = 'N':  Compute eigenvalues only;
                     59: *>          = 'V':  Compute eigenvalues and eigenvectors.
                     60: *> \endverbatim
                     61: *>
                     62: *> \param[in] UPLO
                     63: *> \verbatim
                     64: *>          UPLO is CHARACTER*1
                     65: *>          = 'U':  Upper triangle of A is stored;
                     66: *>          = 'L':  Lower triangle of A is stored.
                     67: *> \endverbatim
                     68: *>
                     69: *> \param[in] N
                     70: *> \verbatim
                     71: *>          N is INTEGER
                     72: *>          The order of the matrix A.  N >= 0.
                     73: *> \endverbatim
                     74: *>
                     75: *> \param[in,out] A
                     76: *> \verbatim
                     77: *>          A is COMPLEX*16 array, dimension (LDA, N)
                     78: *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
                     79: *>          leading N-by-N upper triangular part of A contains the
                     80: *>          upper triangular part of the matrix A.  If UPLO = 'L',
                     81: *>          the leading N-by-N lower triangular part of A contains
                     82: *>          the lower triangular part of the matrix A.
                     83: *>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
                     84: *>          orthonormal eigenvectors of the matrix A.
                     85: *>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
                     86: *>          or the upper triangle (if UPLO='U') of A, including the
                     87: *>          diagonal, is destroyed.
                     88: *> \endverbatim
                     89: *>
                     90: *> \param[in] LDA
                     91: *> \verbatim
                     92: *>          LDA is INTEGER
                     93: *>          The leading dimension of the array A.  LDA >= max(1,N).
                     94: *> \endverbatim
                     95: *>
                     96: *> \param[out] W
                     97: *> \verbatim
                     98: *>          W is DOUBLE PRECISION array, dimension (N)
                     99: *>          If INFO = 0, the eigenvalues in ascending order.
                    100: *> \endverbatim
                    101: *>
                    102: *> \param[out] WORK
                    103: *> \verbatim
                    104: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                    105: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
                    106: *> \endverbatim
                    107: *>
                    108: *> \param[in] LWORK
                    109: *> \verbatim
                    110: *>          LWORK is INTEGER
                    111: *>          The length of the array WORK.
                    112: *>          If N <= 1,                LWORK must be at least 1.
                    113: *>          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
                    114: *>          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.
                    115: *>
                    116: *>          If LWORK = -1, then a workspace query is assumed; the routine
                    117: *>          only calculates the optimal sizes of the WORK, RWORK and
                    118: *>          IWORK arrays, returns these values as the first entries of
                    119: *>          the WORK, RWORK and IWORK arrays, and no error message
                    120: *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
                    121: *> \endverbatim
                    122: *>
                    123: *> \param[out] RWORK
                    124: *> \verbatim
                    125: *>          RWORK is DOUBLE PRECISION array,
                    126: *>                                         dimension (LRWORK)
                    127: *>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
                    128: *> \endverbatim
                    129: *>
                    130: *> \param[in] LRWORK
                    131: *> \verbatim
                    132: *>          LRWORK is INTEGER
                    133: *>          The dimension of the array RWORK.
                    134: *>          If N <= 1,                LRWORK must be at least 1.
                    135: *>          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
                    136: *>          If JOBZ  = 'V' and N > 1, LRWORK must be at least
                    137: *>                         1 + 5*N + 2*N**2.
                    138: *>
                    139: *>          If LRWORK = -1, then a workspace query is assumed; the
                    140: *>          routine only calculates the optimal sizes of the WORK, RWORK
                    141: *>          and IWORK arrays, returns these values as the first entries
                    142: *>          of the WORK, RWORK and IWORK arrays, and no error message
                    143: *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
                    144: *> \endverbatim
                    145: *>
                    146: *> \param[out] IWORK
                    147: *> \verbatim
                    148: *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                    149: *>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
                    150: *> \endverbatim
                    151: *>
                    152: *> \param[in] LIWORK
                    153: *> \verbatim
                    154: *>          LIWORK is INTEGER
                    155: *>          The dimension of the array IWORK.
                    156: *>          If N <= 1,                LIWORK must be at least 1.
                    157: *>          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
                    158: *>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
                    159: *>
                    160: *>          If LIWORK = -1, then a workspace query is assumed; the
                    161: *>          routine only calculates the optimal sizes of the WORK, RWORK
                    162: *>          and IWORK arrays, returns these values as the first entries
                    163: *>          of the WORK, RWORK and IWORK arrays, and no error message
                    164: *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
                    165: *> \endverbatim
                    166: *>
                    167: *> \param[out] INFO
                    168: *> \verbatim
                    169: *>          INFO is INTEGER
                    170: *>          = 0:  successful exit
                    171: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
                    172: *>          > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
                    173: *>                to converge; i off-diagonal elements of an intermediate
                    174: *>                tridiagonal form did not converge to zero;
                    175: *>                if INFO = i and JOBZ = 'V', then the algorithm failed
                    176: *>                to compute an eigenvalue while working on the submatrix
                    177: *>                lying in rows and columns INFO/(N+1) through
                    178: *>                mod(INFO,N+1).
                    179: *> \endverbatim
                    180: *
                    181: *  Authors:
                    182: *  ========
                    183: *
1.14      bertrand  184: *> \author Univ. of Tennessee
                    185: *> \author Univ. of California Berkeley
                    186: *> \author Univ. of Colorado Denver
                    187: *> \author NAG Ltd.
1.8       bertrand  188: *
1.14      bertrand  189: *> \date December 2016
1.8       bertrand  190: *
                    191: *> \ingroup complex16HEeigen
                    192: *
                    193: *> \par Further Details:
                    194: *  =====================
                    195: *>
                    196: *>  Modified description of INFO. Sven, 16 Feb 05.
                    197: *
                    198: *> \par Contributors:
                    199: *  ==================
                    200: *>
                    201: *> Jeff Rutter, Computer Science Division, University of California
                    202: *> at Berkeley, USA
                    203: *>
                    204: *  =====================================================================
1.1       bertrand  205:       SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
                    206:      $                   LRWORK, IWORK, LIWORK, INFO )
                    207: *
1.14      bertrand  208: *  -- LAPACK driver routine (version 3.7.0) --
1.1       bertrand  209: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    210: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14      bertrand  211: *     December 2016
1.1       bertrand  212: *
                    213: *     .. Scalar Arguments ..
                    214:       CHARACTER          JOBZ, UPLO
                    215:       INTEGER            INFO, LDA, LIWORK, LRWORK, LWORK, N
                    216: *     ..
                    217: *     .. Array Arguments ..
                    218:       INTEGER            IWORK( * )
                    219:       DOUBLE PRECISION   RWORK( * ), W( * )
                    220:       COMPLEX*16         A( LDA, * ), WORK( * )
                    221: *     ..
                    222: *
                    223: *  =====================================================================
                    224: *
                    225: *     .. Parameters ..
                    226:       DOUBLE PRECISION   ZERO, ONE
                    227:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
                    228:       COMPLEX*16         CONE
                    229:       PARAMETER          ( CONE = ( 1.0D0, 0.0D0 ) )
                    230: *     ..
                    231: *     .. Local Scalars ..
                    232:       LOGICAL            LOWER, LQUERY, WANTZ
                    233:       INTEGER            IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
                    234:      $                   INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK,
                    235:      $                   LLWRK2, LOPT, LROPT, LRWMIN, LWMIN
                    236:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
                    237:      $                   SMLNUM
                    238: *     ..
                    239: *     .. External Functions ..
                    240:       LOGICAL            LSAME
                    241:       INTEGER            ILAENV
                    242:       DOUBLE PRECISION   DLAMCH, ZLANHE
                    243:       EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANHE
                    244: *     ..
                    245: *     .. External Subroutines ..
                    246:       EXTERNAL           DSCAL, DSTERF, XERBLA, ZHETRD, ZLACPY, ZLASCL,
                    247:      $                   ZSTEDC, ZUNMTR
                    248: *     ..
                    249: *     .. Intrinsic Functions ..
                    250:       INTRINSIC          MAX, SQRT
                    251: *     ..
                    252: *     .. Executable Statements ..
                    253: *
                    254: *     Test the input parameters.
                    255: *
                    256:       WANTZ = LSAME( JOBZ, 'V' )
                    257:       LOWER = LSAME( UPLO, 'L' )
                    258:       LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
                    259: *
                    260:       INFO = 0
                    261:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
                    262:          INFO = -1
                    263:       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
                    264:          INFO = -2
                    265:       ELSE IF( N.LT.0 ) THEN
                    266:          INFO = -3
                    267:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                    268:          INFO = -5
                    269:       END IF
                    270: *
                    271:       IF( INFO.EQ.0 ) THEN
                    272:          IF( N.LE.1 ) THEN
                    273:             LWMIN = 1
                    274:             LRWMIN = 1
                    275:             LIWMIN = 1
                    276:             LOPT = LWMIN
                    277:             LROPT = LRWMIN
                    278:             LIOPT = LIWMIN
                    279:          ELSE
                    280:             IF( WANTZ ) THEN
                    281:                LWMIN = 2*N + N*N
                    282:                LRWMIN = 1 + 5*N + 2*N**2
                    283:                LIWMIN = 3 + 5*N
                    284:             ELSE
                    285:                LWMIN = N + 1
                    286:                LRWMIN = N
                    287:                LIWMIN = 1
                    288:             END IF
                    289:             LOPT = MAX( LWMIN, N +
                    290:      $                  ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) )
                    291:             LROPT = LRWMIN
                    292:             LIOPT = LIWMIN
                    293:          END IF
                    294:          WORK( 1 ) = LOPT
                    295:          RWORK( 1 ) = LROPT
                    296:          IWORK( 1 ) = LIOPT
                    297: *
                    298:          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                    299:             INFO = -8
                    300:          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
                    301:             INFO = -10
                    302:          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
                    303:             INFO = -12
                    304:          END IF
                    305:       END IF
                    306: *
                    307:       IF( INFO.NE.0 ) THEN
                    308:          CALL XERBLA( 'ZHEEVD', -INFO )
                    309:          RETURN
                    310:       ELSE IF( LQUERY ) THEN
                    311:          RETURN
                    312:       END IF
                    313: *
                    314: *     Quick return if possible
                    315: *
                    316:       IF( N.EQ.0 )
                    317:      $   RETURN
                    318: *
                    319:       IF( N.EQ.1 ) THEN
                    320:          W( 1 ) = A( 1, 1 )
                    321:          IF( WANTZ )
                    322:      $      A( 1, 1 ) = CONE
                    323:          RETURN
                    324:       END IF
                    325: *
                    326: *     Get machine constants.
                    327: *
                    328:       SAFMIN = DLAMCH( 'Safe minimum' )
                    329:       EPS = DLAMCH( 'Precision' )
                    330:       SMLNUM = SAFMIN / EPS
                    331:       BIGNUM = ONE / SMLNUM
                    332:       RMIN = SQRT( SMLNUM )
                    333:       RMAX = SQRT( BIGNUM )
                    334: *
                    335: *     Scale matrix to allowable range, if necessary.
                    336: *
                    337:       ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
                    338:       ISCALE = 0
                    339:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
                    340:          ISCALE = 1
                    341:          SIGMA = RMIN / ANRM
                    342:       ELSE IF( ANRM.GT.RMAX ) THEN
                    343:          ISCALE = 1
                    344:          SIGMA = RMAX / ANRM
                    345:       END IF
                    346:       IF( ISCALE.EQ.1 )
                    347:      $   CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
                    348: *
                    349: *     Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
                    350: *
                    351:       INDE = 1
                    352:       INDTAU = 1
                    353:       INDWRK = INDTAU + N
                    354:       INDRWK = INDE + N
                    355:       INDWK2 = INDWRK + N*N
                    356:       LLWORK = LWORK - INDWRK + 1
                    357:       LLWRK2 = LWORK - INDWK2 + 1
                    358:       LLRWK = LRWORK - INDRWK + 1
                    359:       CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
                    360:      $             WORK( INDWRK ), LLWORK, IINFO )
                    361: *
                    362: *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
                    363: *     ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
                    364: *     tridiagonal matrix, then call ZUNMTR to multiply it to the
                    365: *     Householder transformations represented as Householder vectors in
                    366: *     A.
                    367: *
                    368:       IF( .NOT.WANTZ ) THEN
                    369:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
                    370:       ELSE
                    371:          CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N,
                    372:      $                WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK,
                    373:      $                IWORK, LIWORK, INFO )
                    374:          CALL ZUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
                    375:      $                WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
                    376:          CALL ZLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
                    377:       END IF
                    378: *
                    379: *     If matrix was scaled, then rescale eigenvalues appropriately.
                    380: *
                    381:       IF( ISCALE.EQ.1 ) THEN
                    382:          IF( INFO.EQ.0 ) THEN
                    383:             IMAX = N
                    384:          ELSE
                    385:             IMAX = INFO - 1
                    386:          END IF
                    387:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
                    388:       END IF
                    389: *
                    390:       WORK( 1 ) = LOPT
                    391:       RWORK( 1 ) = LROPT
                    392:       IWORK( 1 ) = LIOPT
                    393: *
                    394:       RETURN
                    395: *
                    396: *     End of ZHEEVD
                    397: *
                    398:       END

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