NAME: MINF_PARABOLIC PURPOSE: Minimize a function using Brent's method with parabolic interpolation EXPLANATION: 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. CALLING EXAMPLES: 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. INPUTS: 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. INPUT 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, 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). OUTPUTS: 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). PROCEDURE: 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). MODIFICATION HISTORY: Written, Frank Varosi NASA/GSFC 1992. Converted to IDL V5.0 W. Landsman September 1997 DEPENDENCIES None