Annotation of rpl/lapack/lapack/dstevd.f, revision 1.17

1.8       bertrand    1: *> \brief <b> DSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 DSTEVD + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstevd.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstevd.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstevd.f">
1.8       bertrand   15: *> [TXT]</a>
1.14      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
                     22: *                          LIWORK, INFO )
1.14      bertrand   23: *
1.8       bertrand   24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          JOBZ
                     26: *       INTEGER            INFO, LDZ, LIWORK, LWORK, N
                     27: *       ..
                     28: *       .. Array Arguments ..
                     29: *       INTEGER            IWORK( * )
                     30: *       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
                     31: *       ..
1.14      bertrand   32: *
1.8       bertrand   33: *
                     34: *> \par Purpose:
                     35: *  =============
                     36: *>
                     37: *> \verbatim
                     38: *>
                     39: *> DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
                     40: *> real symmetric tridiagonal matrix. If eigenvectors are desired, it
                     41: *> uses a divide and conquer algorithm.
                     42: *>
                     43: *> The divide and conquer algorithm makes very mild assumptions about
                     44: *> floating point arithmetic. It will work on machines with a guard
                     45: *> digit in add/subtract, or on those binary machines without guard
                     46: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
                     47: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
                     48: *> without guard digits, but we know of none.
                     49: *> \endverbatim
                     50: *
                     51: *  Arguments:
                     52: *  ==========
                     53: *
                     54: *> \param[in] JOBZ
                     55: *> \verbatim
                     56: *>          JOBZ is CHARACTER*1
                     57: *>          = 'N':  Compute eigenvalues only;
                     58: *>          = 'V':  Compute eigenvalues and eigenvectors.
                     59: *> \endverbatim
                     60: *>
                     61: *> \param[in] N
                     62: *> \verbatim
                     63: *>          N is INTEGER
                     64: *>          The order of the matrix.  N >= 0.
                     65: *> \endverbatim
                     66: *>
                     67: *> \param[in,out] D
                     68: *> \verbatim
                     69: *>          D is DOUBLE PRECISION array, dimension (N)
                     70: *>          On entry, the n diagonal elements of the tridiagonal matrix
                     71: *>          A.
                     72: *>          On exit, if INFO = 0, the eigenvalues in ascending order.
                     73: *> \endverbatim
                     74: *>
                     75: *> \param[in,out] E
                     76: *> \verbatim
                     77: *>          E is DOUBLE PRECISION array, dimension (N-1)
                     78: *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
                     79: *>          matrix A, stored in elements 1 to N-1 of E.
                     80: *>          On exit, the contents of E are destroyed.
                     81: *> \endverbatim
                     82: *>
                     83: *> \param[out] Z
                     84: *> \verbatim
                     85: *>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
                     86: *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
                     87: *>          eigenvectors of the matrix A, with the i-th column of Z
                     88: *>          holding the eigenvector associated with D(i).
                     89: *>          If JOBZ = 'N', then Z is not referenced.
                     90: *> \endverbatim
                     91: *>
                     92: *> \param[in] LDZ
                     93: *> \verbatim
                     94: *>          LDZ is INTEGER
                     95: *>          The leading dimension of the array Z.  LDZ >= 1, and if
                     96: *>          JOBZ = 'V', LDZ >= max(1,N).
                     97: *> \endverbatim
                     98: *>
                     99: *> \param[out] WORK
                    100: *> \verbatim
                    101: *>          WORK is DOUBLE PRECISION array,
                    102: *>                                         dimension (LWORK)
                    103: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
                    104: *> \endverbatim
                    105: *>
                    106: *> \param[in] LWORK
                    107: *> \verbatim
                    108: *>          LWORK is INTEGER
                    109: *>          The dimension of the array WORK.
                    110: *>          If JOBZ  = 'N' or N <= 1 then LWORK must be at least 1.
                    111: *>          If JOBZ  = 'V' and N > 1 then LWORK must be at least
                    112: *>                         ( 1 + 4*N + N**2 ).
                    113: *>
                    114: *>          If LWORK = -1, then a workspace query is assumed; the routine
                    115: *>          only calculates the optimal sizes of the WORK and IWORK
                    116: *>          arrays, returns these values as the first entries of the WORK
                    117: *>          and IWORK arrays, and no error message related to LWORK or
                    118: *>          LIWORK is issued by XERBLA.
                    119: *> \endverbatim
                    120: *>
                    121: *> \param[out] IWORK
                    122: *> \verbatim
                    123: *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                    124: *>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
                    125: *> \endverbatim
                    126: *>
                    127: *> \param[in] LIWORK
                    128: *> \verbatim
                    129: *>          LIWORK is INTEGER
                    130: *>          The dimension of the array IWORK.
                    131: *>          If JOBZ  = 'N' or N <= 1 then LIWORK must be at least 1.
                    132: *>          If JOBZ  = 'V' and N > 1 then LIWORK must be at least 3+5*N.
                    133: *>
                    134: *>          If LIWORK = -1, then a workspace query is assumed; the
                    135: *>          routine only calculates the optimal sizes of the WORK and
                    136: *>          IWORK arrays, returns these values as the first entries of
                    137: *>          the WORK and IWORK arrays, and no error message related to
                    138: *>          LWORK or LIWORK is issued by XERBLA.
                    139: *> \endverbatim
                    140: *>
                    141: *> \param[out] INFO
                    142: *> \verbatim
                    143: *>          INFO is INTEGER
                    144: *>          = 0:  successful exit
                    145: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
                    146: *>          > 0:  if INFO = i, the algorithm failed to converge; i
                    147: *>                off-diagonal elements of E did not converge to zero.
                    148: *> \endverbatim
                    149: *
                    150: *  Authors:
                    151: *  ========
                    152: *
1.14      bertrand  153: *> \author Univ. of Tennessee
                    154: *> \author Univ. of California Berkeley
                    155: *> \author Univ. of Colorado Denver
                    156: *> \author NAG Ltd.
1.8       bertrand  157: *
                    158: *> \ingroup doubleOTHEReigen
                    159: *
                    160: *  =====================================================================
1.1       bertrand  161:       SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
                    162:      $                   LIWORK, INFO )
                    163: *
1.17    ! bertrand  164: *  -- LAPACK driver routine --
1.1       bertrand  165: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    166: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    167: *
                    168: *     .. Scalar Arguments ..
                    169:       CHARACTER          JOBZ
                    170:       INTEGER            INFO, LDZ, LIWORK, LWORK, N
                    171: *     ..
                    172: *     .. Array Arguments ..
                    173:       INTEGER            IWORK( * )
                    174:       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
                    175: *     ..
                    176: *
                    177: *  =====================================================================
                    178: *
                    179: *     .. Parameters ..
                    180:       DOUBLE PRECISION   ZERO, ONE
                    181:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
                    182: *     ..
                    183: *     .. Local Scalars ..
                    184:       LOGICAL            LQUERY, WANTZ
                    185:       INTEGER            ISCALE, LIWMIN, LWMIN
                    186:       DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
                    187:      $                   TNRM
                    188: *     ..
                    189: *     .. External Functions ..
                    190:       LOGICAL            LSAME
                    191:       DOUBLE PRECISION   DLAMCH, DLANST
                    192:       EXTERNAL           LSAME, DLAMCH, DLANST
                    193: *     ..
                    194: *     .. External Subroutines ..
                    195:       EXTERNAL           DSCAL, DSTEDC, DSTERF, XERBLA
                    196: *     ..
                    197: *     .. Intrinsic Functions ..
                    198:       INTRINSIC          SQRT
                    199: *     ..
                    200: *     .. Executable Statements ..
                    201: *
                    202: *     Test the input parameters.
                    203: *
                    204:       WANTZ = LSAME( JOBZ, 'V' )
                    205:       LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
                    206: *
                    207:       INFO = 0
                    208:       LIWMIN = 1
                    209:       LWMIN = 1
                    210:       IF( N.GT.1 .AND. WANTZ ) THEN
                    211:          LWMIN = 1 + 4*N + N**2
                    212:          LIWMIN = 3 + 5*N
                    213:       END IF
                    214: *
                    215:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
                    216:          INFO = -1
                    217:       ELSE IF( N.LT.0 ) THEN
                    218:          INFO = -2
                    219:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
                    220:          INFO = -6
                    221:       END IF
                    222: *
                    223:       IF( INFO.EQ.0 ) THEN
                    224:          WORK( 1 ) = LWMIN
                    225:          IWORK( 1 ) = LIWMIN
                    226: *
                    227:          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                    228:             INFO = -8
                    229:          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
                    230:             INFO = -10
                    231:          END IF
                    232:       END IF
                    233: *
                    234:       IF( INFO.NE.0 ) THEN
                    235:          CALL XERBLA( 'DSTEVD', -INFO )
                    236:          RETURN
                    237:       ELSE IF( LQUERY ) THEN
                    238:          RETURN
                    239:       END IF
                    240: *
                    241: *     Quick return if possible
                    242: *
                    243:       IF( N.EQ.0 )
                    244:      $   RETURN
                    245: *
                    246:       IF( N.EQ.1 ) THEN
                    247:          IF( WANTZ )
                    248:      $      Z( 1, 1 ) = ONE
                    249:          RETURN
                    250:       END IF
                    251: *
                    252: *     Get machine constants.
                    253: *
                    254:       SAFMIN = DLAMCH( 'Safe minimum' )
                    255:       EPS = DLAMCH( 'Precision' )
                    256:       SMLNUM = SAFMIN / EPS
                    257:       BIGNUM = ONE / SMLNUM
                    258:       RMIN = SQRT( SMLNUM )
                    259:       RMAX = SQRT( BIGNUM )
                    260: *
                    261: *     Scale matrix to allowable range, if necessary.
                    262: *
                    263:       ISCALE = 0
                    264:       TNRM = DLANST( 'M', N, D, E )
                    265:       IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
                    266:          ISCALE = 1
                    267:          SIGMA = RMIN / TNRM
                    268:       ELSE IF( TNRM.GT.RMAX ) THEN
                    269:          ISCALE = 1
                    270:          SIGMA = RMAX / TNRM
                    271:       END IF
                    272:       IF( ISCALE.EQ.1 ) THEN
                    273:          CALL DSCAL( N, SIGMA, D, 1 )
                    274:          CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
                    275:       END IF
                    276: *
                    277: *     For eigenvalues only, call DSTERF.  For eigenvalues and
                    278: *     eigenvectors, call DSTEDC.
                    279: *
                    280:       IF( .NOT.WANTZ ) THEN
                    281:          CALL DSTERF( N, D, E, INFO )
                    282:       ELSE
                    283:          CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
                    284:      $                INFO )
                    285:       END IF
                    286: *
                    287: *     If matrix was scaled, then rescale eigenvalues appropriately.
                    288: *
                    289:       IF( ISCALE.EQ.1 )
                    290:      $   CALL DSCAL( N, ONE / SIGMA, D, 1 )
                    291: *
                    292:       WORK( 1 ) = LWMIN
                    293:       IWORK( 1 ) = LIWMIN
                    294: *
                    295:       RETURN
                    296: *
                    297: *     End of DSTEVD
                    298: *
                    299:       END

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