Return to dlarrk.f CVS log

Up to [local] / rpl / lapack / lapack

Annotation of rpl/lapack/lapack/dlarrk.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DLARRK( N, IW, GL, GU,
        !             2:      $                    D, E2, PIVMIN, RELTOL, W, WERR, INFO)
        !             3:       IMPLICIT NONE
        !             4: *
        !             5: *  -- LAPACK auxiliary routine (version 3.2) --
        !             6: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             7: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             8: *     November 2006
        !             9: *
        !            10: *     .. Scalar Arguments ..
        !            11:       INTEGER   INFO, IW, N
        !            12:       DOUBLE PRECISION    PIVMIN, RELTOL, GL, GU, W, WERR
        !            13: *     ..
        !            14: *     .. Array Arguments ..
        !            15:       DOUBLE PRECISION   D( * ), E2( * )
        !            16: *     ..
        !            17: *
        !            18: *  Purpose
        !            19: *  =======
        !            20: *
        !            21: *  DLARRK computes one eigenvalue of a symmetric tridiagonal
        !            22: *  matrix T to suitable accuracy. This is an auxiliary code to be
        !            23: *  called from DSTEMR.
        !            24: *
        !            25: *  To avoid overflow, the matrix must be scaled so that its
        !            26: *  largest element is no greater than overflow**(1/2) *
        !            27: *  underflow**(1/4) in absolute value, and for greatest
        !            28: *  accuracy, it should not be much smaller than that.
        !            29: *
        !            30: *  See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
        !            31: *  Matrix", Report CS41, Computer Science Dept., Stanford
        !            32: *  University, July 21, 1966.
        !            33: *
        !            34: *  Arguments
        !            35: *  =========
        !            36: *
        !            37: *  N       (input) INTEGER
        !            38: *          The order of the tridiagonal matrix T.  N >= 0.
        !            39: *
        !            40: *  IW      (input) INTEGER
        !            41: *          The index of the eigenvalues to be returned.
        !            42: *
        !            43: *  GL      (input) DOUBLE PRECISION
        !            44: *  GU      (input) DOUBLE PRECISION
        !            45: *          An upper and a lower bound on the eigenvalue.
        !            46: *
        !            47: *  D       (input) DOUBLE PRECISION array, dimension (N)
        !            48: *          The n diagonal elements of the tridiagonal matrix T.
        !            49: *
        !            50: *  E2      (input) DOUBLE PRECISION array, dimension (N-1)
        !            51: *          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
        !            52: *
        !            53: *  PIVMIN  (input) DOUBLE PRECISION
        !            54: *          The minimum pivot allowed in the Sturm sequence for T.
        !            55: *
        !            56: *  RELTOL  (input) DOUBLE PRECISION
        !            57: *          The minimum relative width of an interval.  When an interval
        !            58: *          is narrower than RELTOL times the larger (in
        !            59: *          magnitude) endpoint, then it is considered to be
        !            60: *          sufficiently small, i.e., converged.  Note: this should
        !            61: *          always be at least radix*machine epsilon.
        !            62: *
        !            63: *  W       (output) DOUBLE PRECISION
        !            64: *
        !            65: *  WERR    (output) DOUBLE PRECISION
        !            66: *          The error bound on the corresponding eigenvalue approximation
        !            67: *          in W.
        !            68: *
        !            69: *  INFO    (output) INTEGER
        !            70: *          = 0:       Eigenvalue converged
        !            71: *          = -1:      Eigenvalue did NOT converge
        !            72: *
        !            73: *  Internal Parameters
        !            74: *  ===================
        !            75: *
        !            76: *  FUDGE   DOUBLE PRECISION, default = 2
        !            77: *          A "fudge factor" to widen the Gershgorin intervals.
        !            78: *
        !            79: *  =====================================================================
        !            80: *
        !            81: *     .. Parameters ..
        !            82:       DOUBLE PRECISION   FUDGE, HALF, TWO, ZERO
        !            83:       PARAMETER          ( HALF = 0.5D0, TWO = 2.0D0,
        !            84:      $                     FUDGE = TWO, ZERO = 0.0D0 )
        !            85: *     ..
        !            86: *     .. Local Scalars ..
        !            87:       INTEGER   I, IT, ITMAX, NEGCNT
        !            88:       DOUBLE PRECISION   ATOLI, EPS, LEFT, MID, RIGHT, RTOLI, TMP1,
        !            89:      $                   TMP2, TNORM
        !            90: *     ..
        !            91: *     .. External Functions ..
        !            92:       DOUBLE PRECISION   DLAMCH
        !            93:       EXTERNAL   DLAMCH
        !            94: *     ..
        !            95: *     .. Intrinsic Functions ..
        !            96:       INTRINSIC          ABS, INT, LOG, MAX
        !            97: *     ..
        !            98: *     .. Executable Statements ..
        !            99: *
        !           100: *     Get machine constants
        !           101:       EPS = DLAMCH( 'P' )
        !           102: 
        !           103:       TNORM = MAX( ABS( GL ), ABS( GU ) )
        !           104:       RTOLI = RELTOL
        !           105:       ATOLI = FUDGE*TWO*PIVMIN
        !           106: 
        !           107:       ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) /
        !           108:      $           LOG( TWO ) ) + 2
        !           109: 
        !           110:       INFO = -1
        !           111: 
        !           112:       LEFT = GL - FUDGE*TNORM*EPS*N - FUDGE*TWO*PIVMIN
        !           113:       RIGHT = GU + FUDGE*TNORM*EPS*N + FUDGE*TWO*PIVMIN
        !           114:       IT = 0
        !           115: 
        !           116:  10   CONTINUE
        !           117: *
        !           118: *     Check if interval converged or maximum number of iterations reached
        !           119: *
        !           120:       TMP1 = ABS( RIGHT - LEFT )
        !           121:       TMP2 = MAX( ABS(RIGHT), ABS(LEFT) )
        !           122:       IF( TMP1.LT.MAX( ATOLI, PIVMIN, RTOLI*TMP2 ) ) THEN
        !           123:          INFO = 0
        !           124:          GOTO 30
        !           125:       ENDIF
        !           126:       IF(IT.GT.ITMAX)
        !           127:      $   GOTO 30
        !           128: 
        !           129: *
        !           130: *     Count number of negative pivots for mid-point
        !           131: *
        !           132:       IT = IT + 1
        !           133:       MID = HALF * (LEFT + RIGHT)
        !           134:       NEGCNT = 0
        !           135:       TMP1 = D( 1 ) - MID
        !           136:       IF( ABS( TMP1 ).LT.PIVMIN )
        !           137:      $   TMP1 = -PIVMIN
        !           138:       IF( TMP1.LE.ZERO )
        !           139:      $   NEGCNT = NEGCNT + 1
        !           140: *
        !           141:       DO 20 I = 2, N
        !           142:          TMP1 = D( I ) - E2( I-1 ) / TMP1 - MID
        !           143:          IF( ABS( TMP1 ).LT.PIVMIN )
        !           144:      $      TMP1 = -PIVMIN
        !           145:          IF( TMP1.LE.ZERO )
        !           146:      $      NEGCNT = NEGCNT + 1
        !           147:  20   CONTINUE
        !           148: 
        !           149:       IF(NEGCNT.GE.IW) THEN
        !           150:          RIGHT = MID
        !           151:       ELSE
        !           152:          LEFT = MID
        !           153:       ENDIF
        !           154:       GOTO 10
        !           155: 
        !           156:  30   CONTINUE
        !           157: *
        !           158: *     Converged or maximum number of iterations reached
        !           159: *
        !           160:       W = HALF * (LEFT + RIGHT)
        !           161:       WERR = HALF * ABS( RIGHT - LEFT )
        !           162: 
        !           163:       RETURN
        !           164: *
        !           165: *     End of DLARRK
        !           166: *
        !           167:       END