noodling/max_val_algos.py

### Author: estelendur
# Find the maximum value k of a function f(X) where X = [x1,x2,...,xn]
# Each xi in a range [ai,bi]
# Uses shiftwidth=4 for tabs; foldmarker={{{,}}} for folds;

import random

### Methodical algorithm {{{
# Find the highest value of f varying only x1, then x2, then...

def methodical(f,x,ab,varyf,varyv):
	# initialize each xi to rand(ai, bi)
	for i in range(len(x)):
		a = ab[i][0]
		b = ab[i][1]
		rand = random.random()
		x[i] = (rand*(b-a)) + a
	for i in range(len(x)):
		x[i] = varyf(f,x,ab,i,varyv)
	return f(x)
### End Methodical }}}

### Step-wise vary function {{{
# Takes xi through its range in varyv steps of equal size
# Vary functions: take function, x[], ab[], i, varyv

def stepvary(f,x,ab,i,varyv):
	a = ab[i][0]
	b = ab[i][1]
	step = (b-a)/varyv
	currplace = a
	currmax = f(x) # the current highest value of f
	top = x[i] # the value of x[i] for which f is highest
	while(currplace <= b):
		x[i] = currplace
		if f(x) > currmax:
			currmax = f(x)
			top = x[i]
		currplace += step
	return top
### End Step-wise vary }}}