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ZBRENT

ZBRENT

Name


    ZBRENT

Purpose


    Find the zero of a 1-D function up to specified tolerance.

Explantion


    This routine assumes that the function is known to have a zero.
    Adapted from procedure of the same name in "Numerical Recipes" by
    Press et al. (1992), Section 9.3
  CALLING:
      x_zero = ZBRENT( x1, x2, FUNC_NAME="name", MaX_Iter=, Tolerance=,
                                _EXTRA = )

Inputs


      x1, x2 = scalars, 2 points which bracket location of function zero,
                                              that is, F(x1) < 0 < F(x2).
      Note: computations are performed with
      same precision (single/double) as the inputs and user supplied function.
  REQUIRED INPUT KEYWORD:
      FUNC_NAME = function name (string)
              Calling mechanism should be: F = func_name( px )
              where: px = scalar independent variable, input.
                      F = scalar value of function at px,
                          should be same precision (single/double) as input.

Optional Input Keywords


      MAX_ITER = maximum allowed number iterations, default=100.
      TOLERANCE = desired accuracy of minimum location, default = 1.e-3.
      Any other keywords are passed directly to the user-supplied function
      via the _EXTRA facility.

Outputs


      Returns the location of zero, with accuracy of specified tolerance.

Procedure


      Brent's method to find zero of a function by using bracketing,
      bisection, and inverse quadratic interpolation,

Example


      Find the root of the COSINE function between 1. and 2. radians
        IDL> print, zbrent( 1, 2, FUNC = 'COS')
      and the result will be !PI/2 within the specified tolerance

Modification History


      Written, Frank Varosi NASA/GSFC 1992.
      FV.1994, mod to check for single/double prec. and set zeps accordingly.
      Use MACHAR() to define machine precision W. Landsman September 2002
      Added _EXTRA keyword W. Landsman December 2011
      Need to check whether user function accepts keywords W.L. Jan 2012



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