brute
Syntax
brute(func, ranges, [ns=20], [finish=fmin])
Details
Minimize a function over a given range by brute force. Use the "brute force" method, i.e., compute the function's value at each point of a multidimensional grid of points, to find the global minimum of the function.
Arguments
func is the name of the function to be minimized. Note that its return value must be a numeric scalar.
ranges is a tuple of tuples. Each tuple element can take the following forms:
-
(low, high): Specifies the minimum and maximum values for a parameter.
-
(low, high, num): Also includes the number of grid points between low and high.
ns (optional) is a positive number indicating the number of grid points along the axes. If ranges is specified as (low, high, num), num determines the number of points. Otherwise, ns is used, defaulting to 20 if not provided.
finish (optional) is an optimization function that is called with the result
of brute force minimization as initial guess. finish should be a function
that returns a dictionary that contains keys 'xopt' and 'fopt' and their values
should be numeric. The default value is the fmin function. If set
to NULL, no "polishing" function is applied and the result of brute
is returned directly.
Return Values
It returns a dictionary with the following members:
-
xopt: Parameter that minimizes function.
-
fopt: Value of function at minimum:
fopt = f(xopt).
Examples
Calculate the minimum of function f within ranges.
def f(z) {
a = 2
b = 3
c = 7
d = 8
ee = 9
f = 10
g = 44
h = -1
i = 2
j = 26
k = 1
l = -2
scale = 0.5
x = z[0]
y = z[1]
f1 = a * square(x) + b * x * y + c * square(y) + d * x + ee* y + f
f2 = -g * exp(-(square(x-h)+square(y-i)) / scale)
f3 = -j * exp(-(square(x-k)+square(y-l)) / scale)
return f1+f2+f3
}
ranges=((-4, 3.75),(-4, 3.75))
brute(f, ranges, 32)
/* Ouput:
fopt->-3.408581876799
xopt->[-1.056651921797,1.808348429512]
*/