MINF_PARABOLIC

       Minimize a function using Brent's method with parabolic interpolation

       Find a local minimum of a 1-D function up to specified tolerance.
       This routine assumes that the function has a minimum nearby.
       (recommend first calling minF_bracket, xa,xb,xc, to bracket minimum).
       Routine can also be applied to a scalar function of many variables,
       for such case the local minimum in a specified direction is found,
       This routine is called by minF_conj_grad, to locate minimum in the
       direction of the conjugate gradient of function of many variables.

       minF_parabolic, xa,xb,xc, xmin, fmin, FUNC_NAME="name"  ;for 1-D func.
  or:
       minF_parabolic, xa,xb,xc, xmin, fmin, FUNC="name", $
                                         POINT=[0,1,1],   $
                                         DIRECTION=[2,1,1]     ;for 3-D func.

       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.

      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, x_min are then relative distances from POINT_NDIM)
      MAX_ITER = maximum allowed number iterations, default=100.
      TOLERANCE = desired accuracy of minimum location, default=sqrt(1.e-7).

       xmin = estimated location of minimum.
               When working with function of N variables,
               xmin is the relative distance from POINT_NDIM,
               in the direction specified by keyword DIRECTION,
               with scale factor given by magnitude of DIRECTION,
               so that min. Loc. Pmin = Point_Ndim + xmin * Direction.
       fmin = value of function at xmin (or Pmin).

       Brent's method to minimize a function by using parabolic interpolation.
       Based on function BRENT in Numerical Recipes in FORTRAN (Press et al.
       1992),  sec.10.2 (p. 397).

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

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