idlastro / Math and Statistics: MINF_BRACKET

[Source code]

NAME
MINF_BRACKET
PURPOSE
Bracket a local minimum of a 1-D function with 3 points,
EXPLANATION
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.

minF_bracket, xa,xb,xc, fa,fb,fc, FUNC="name",     $
                                  POINT=[0,1,1],   $
                                  DIRECTION=[2,1,1]     ;for 3-D func.
INPUTS
xa = scalar, guess for point bracketing location of minimum.
xb = scalar, second guess for point bracketing location of minimum.
KEYWORDS
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
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
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
algorithm from Numerical Recipes (by Press, et al.), sec.10.1 (p.281).
MODIFICATION HISTORY
Written, Frank Varosi NASA/GSFC 1992.
Converted to IDL V5.0   W. Landsman   September 1997