Name

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      MINF_BRACKET

Purpose

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      Bracket a local minimum of a 1-D function with 3 points,

Explanation

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      Brackets a local minimum of a 1-d function with 3 points,
      thus ensuring that a minimum exists somewhere in the interval.
      This routine assumes that the function has a minimum somewhere....
      Routine can also be applied to a scalar function of many variables,
      for such case the local minimum in a specified direction is bracketed,
      This routine is called by minF_conj_grad, to bracket minimum in the
      direction of the conjugate gradient of function of many variables
  CALLING EXAMPLE:
      xa=0 & xb=1
      minF_bracket, xa,xb,xc, fa,fb,fc, FUNC_NAME="name" ;for 1-D func.
  or:
      minF_bracket, xa,xb,xc, fa,fb,fc, FUNC="name", $
                                        POINT=[0,1,1], $
                                        DIRECTION=[2,1,1] ;for 3-D func.

Inputs

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      xa = scalar, guess for point bracketing location of minimum.
      xb = scalar, second guess for point bracketing location of minimum.

Keywords

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      FUNC_NAME = function name (string)
              Calling mechanism should be: F = func_name( px )
              where:
                      px = scalar or vector of independent variables, input.
                      F = scalar value of function at px.
      POINT_NDIM = when working with function of N variables,
              use this keyword to specify the starting point in N-dim space.
              Default = 0, which assumes function is 1-D.
      DIRECTION = when working with function of N variables,
              use this keyword to specify the direction in N-dim space
              along which to bracket the local minimum, (default=1 for 1-D).
              (xa,xb,xc) are then relative distances from POINT_NDIM.

Outputs

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      xa,xb,xc = scalars, 3 points which bracket location of minimum,
              that is, f(xb) < f(xa) and f(xb) < f(xc), so minimum exists.
              When working with function of N variables
              (xa,xb,xc) are then relative distances from POINT_NDIM,
              in the direction specified by keyword DIRECTION,
              with scale factor given by magnitude of DIRECTION.

Optional Output

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      fa,fb,fc = value of function at 3 points which bracket the minimum,
                      again note that fb < fa and fb < fc if minimum exists.

Procedure

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      algorithm from Numerical Recipes (by Press, et al.), sec.10.1 (p.281).

Modification History

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      Written, Frank Varosi NASA/GSFC 1992.
      Converted to IDL V5.0 W. Landsman September 1997