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sprince09
October 27th, 2009, 05:35 AM
Hi guys,

I'm writing some code for a project which needs to use mathematical constraints such as -1 <= x <= 3, f(x) > 50, -inf < 50 <= 400, etc...

So far, I've written a small class in Python which can check whether a given input value is within a certain range, and returns True or False. It's usage looks like (basically):

>>>c1 = constraint(0, 500)
>>>print c1(300), c1(0), c1(500), c1(2000)
True True True False

This works great so long as I'm looking at a single 1 dimensional function (ie f(x)). My problem is that I'm most definitely not using a single one dimensional function, and so I need some way to keep track of which constraints belong to which variables. For example, I might have a function of 3 variables, f(x,y,z) where I need to have constraint equations on x, y, z, and/or f(x,y,z).

Basically, I'm looking for suggestions on how I could go about implementing this in a nice way. It seems cumbersome to attach a variable name to each constraint and also to each variable as a way to identify them to each other, so I'm assuming there's an elegant way to do this, and that I just don't see it. Maybe there's even a standard module that implements something like this?

Reiger
October 27th, 2009, 06:50 AM
In JavaScript you can do something like this:

/* evaluate constraint objects with init(context), evaluate(), and get() */
function checkAll(constraints) {
// context property list
var context {
valid: true, // cumulative ‘validity’ check
constraints: constraints // enable constraints to access other constraints
};
var result= { }; //result property list
for(var c in constraints) {
constraints[c].init(context);
constraints[c].evaluate();
result[c] = constraints[c].get();
}
return result;
}

/* simple wrapper function returning a closure that calls realCheck as function() on evaluate(). */
function checkWrapper(realCheck) {
return function() {
this.context;
this.valid // is the constraint met?
this.init= function(env) { this.context = env; this.valid = env.valid; };
/* this implementation automatically fails if the previous constraint had set the context.valid field to false! */
this.evaluate() { if(this.valid) { this.valid= realCheck(); this.context.valid = this.valid; } };
this.get() { return this.valid; };
}
}

Closures like that can be modeled using objects with appropriate init() and callback() methods.

Python can probably use dictionaries or something to model the property lists.

For an idea of how you can write automated tests for your constraints implementation:

/* construct a simple test constraint checking whether or not intVal == 22 */
function testCase(intVal) {
return checkWrapper(function() { return intVal == 22; });
}

/* test the theory: run a couple of testCase() objects */
function run() {
return checkAll({
first: testCase(22), // should come out as valid
second:testCase(55) // should come out as invalid
});
}
/* test the result of run() against the expected values: */
function test() {
var vals = run();
return vals.first && ! vals.second;
}

diesch
October 27th, 2009, 07:38 AM
Maybe like that:

class Function(object):
def __call__(self, *args, **kwargs):
raise NotImplementedError

class Times(Function):

def __init__(self, n):
self.n = n

def __call__(self, x):
return self.n*x

class ThreeDFunc(Function):
def __call__(self, x,y,z):
return x+y+z

class Constraint(object):
def __init__(self, min, max, func):
self.min = min
self.max = max
self.func = func

def __call__(self, *args, **kwargs):
return self.min < self.func(*args, **kwargs) < self.max

c1 = Constraint(1, 10, Times(2))
print c1(0), c1(3), c1(10)

c2 = Constraint(1, 10, ThreeDFunc())
print c2(1,2,3), c2(4,5,6), c2(8,9,0),

sprince09
October 27th, 2009, 06:35 PM
Alright guys, here's what I came up with:

import math

################################################## ##############################
# class: constraint
################################################## ##############################

class Constraint(object):
"""fixme class documentation"""

def __init__(self, min, max, varname, min_mode='inc', max_mode='inc', logic='or'):

# cleanup input
if(min_mode == 'inclusive'):
min_mode = 'inc'
elif(min_mode == 'exclusive'):
min_mode = 'exc'

if(max_mode == 'inclusive'):
max_mode = 'inc'
elif(max_mode == 'exclusive'):
max_mode = 'exc'

# make sure modes are good
if((min_mode != 'inc') & (min_mode != 'exc')):
raise ValueError('Invalid value of Constraint.min_mode')

if((max_mode != 'inc') & (max_mode != 'exc')):
raise ValueError('Invalid value of Constraint.max_mode')

if((logic != 'and') & (logic != 'or')):
raise ValueError('Constraint.logic must be \'and\' or \'or\'')

# check that min < max
if(min > max):
raise ValueError('Constraint.min must be <= Constraint.max')

# check that varname is not ''
if(varname == ''):
raise ValueError('Constraint.varname cannot be \'\'');

self.min = min
self.max = max
self.min_mode = min_mode
self.max_mode = max_mode
self.varname = varname
self.logic = logic

def __call__(self, value):
"""Returns True if value is within the constraint, or False otherwise"""
if(self.min_mode == 'inc'):
if(self.max_mode == 'inc'):
if((value <= self.max) & (value >= self.min)):
return True
else:
return False
elif((value < self.max) & (value >= self.min)):
return True
else:
return False

elif(self.max_mode == 'inc'):
if((value <= self.max) & (value > self.min)):
return True
else:
return False
elif((value < self.max) & (value > self.min)):
return True
else:
return False

################################################## ##############################
# class: FitFunc
################################################## ##############################

class FitFunc(object):
"""fixme class documentation"""

def __init__(self, func, ivars, iconstraints, ovar=[], oconstraints=[]):

# make sure input is ok
# number of iconstraints must be greater than or equal to num of ivars
# number of oconstraints must be greater than or equal to num of ovar
if(len(ivars) > len(iconstraints)):
raise ValueError('len(FitFunc.ivars) must be <=len(FitFunc.iconstraints)');
elif(len(ovar) > len(oconstraints)):
raise ValueError('len(FitFunc.ovar) must be <= len(FitFunc.oconstraints)');

# assign values to class
self.func = func
self.ivars = ivars
self.ovar = ovar
self.iconstraintDict = {}
self.oconstraintDict = {}

# assign constraint, varname pairs to dictionary
for varname in ivars:
for constraint in iconstraints:
if(constraint.varname == varname):
self.iconstraintDict[constraint] = varname
for varname in ovar:
for constraint in oconstraints:
if(constraint.varname == varname):
self.oconstraintDict[constraint] = varname

def __call__(self, values):
"""Returns FitFunc.func(values) if all constraints (anded) are True,
otherwise returns float('nan').
"""

# check input constraints
c_check = 0
for constraint in self.iconstraintDict:
if(constraint.logic == 'and'):
for i in range(len(self.ivars)):
if(self.ivars[i] == self.iconstraintDict[constraint]):
if(constraint(values[i]) == False):
return float('nan')
else:
for i in range(len(self.ivars)):
if(self.ivars[i] == self.iconstraintDict[constraint]):
if(constraint(values[i]) == True):
c_check += 1

# if the 'or' logic is being used with the Constrain object, then
# c_check gets incremented once any time a Constraint object evaluates
# to True for a given variable name. So, if c_check >= the number of
# variable names in FitFunc, then the or operation was true.
if(c_check < len(self.ivars)):
return float('nan')

# evaluate func
output = self.func(values)

# check output constraints
for constraint in self.oconstraintDict:
if(constraint(output) == False):
return float('nan')

# all good, return output from function
return output

## Run test code if this module is run as a script
if __name__ == "__main__":

# dummy test function
def f(x):
""" Returns the value of the following function:

f(xi) = sum(2*xi^2 + xi^2 * sin(xi))

where xi is an n dimensional array of input values. This function has
exactly one global minimum at xi = 0, and is used to test the pso
module.
"""

out = 0
for value in x:
out += 2*value*value + value*value*math.sin(value)
return out

# run module test
var1 = 'x1'
var2 = 'x2'
vars = [var1, var2]
c1 = Constraint(0, 30.0, var1)
c2 = Constraint(-30, -1, var1)
c3 = Constraint(float('-inf'), 100, var2, max_mode='exclusive')
constraints = [c1, c2, c3]

ff = FitFunc(f, vars, constraints)
print ff([-40, 10]), ff([-30, 100]), ff([-10, 50])
#(prints: nan nan 4598.46497683 as expected)

That get's the logic down at least, now I need to do some optimization, documentation, etc... Thanks for the suggestions!

Can+~
October 28th, 2009, 03:36 AM
As someone mentioned before, a closure fits perfectly for this:

def constraint_range(min, max):

def closure(x):
return x > min and x < max

return closure

constraint1 = constraint_range(-5, 5)
constraint2 = constraint_range(-3, 8)

constraint3 = lambda x: constraint1(x) and constraint2(x)

print map(constraint3, [-7, -2, -1, 0, 1, 3, 5, 7, 15])

wmcbrine
October 28th, 2009, 11:40 AM
x > min and x < maxDon't forget, Python allows this notation:

min < x < max
Although, "min" and "max" are built-ins, so I wouldn't use those names.

sprince09
October 28th, 2009, 11:52 AM
I'll take a look at closures, they seem pretty useful...

sprince09
October 28th, 2009, 12:08 PM
Alright, I've got a question: what's the advantage of using a closure instead of just using __call__? Doesn't __call__ achieve the same affect in this case?