is it possible (in Python) to define a polynomial type of function that has changing amount of parameters? Number of parameters should change according to number of data series that I have in my input file.
Currently I have something like this:
def y(x, a0, x2, x3, x4):
y = a0 + a1*x + a2*x**2 + a3*x**3
return y
I could of course set parameters of higher order to zero by extra parameter but would there be some better way.
You can loop over the arguments and evaluate the polynomial using Horners method, which is very efficient.
def y(x, *args):
y = 0
for a in reversed(args):
y = y*x+a
return y
You can find a heap more details about variable numbers of arguments in this question.
an even simpler version using a generator expression
def y(x, *args):
return sum(a * x ** i for i, a in enumerate(args))
and a Horner version using reduce
def horn(x, *args):
return reduce(lambda y, a: y * x + a, reversed(args))
def y(x, *args):
y = 0
i = 0
for a in args:
y += a * x ** i
i += 1
return y
print y(2, 1, 2) # 2 * 2 ^ 0 + 2 * 2 ^ 1 = 5
In this particular case it would be much cleaner to provide polynomial as a single argument, namely a list of coefficients:
def eval_poly(x, poly):
....
eval_poly(10, [1, 2, 3]) # evaluate (1 + 2x + 3x^2)(10)
This way you can handle polynomials like ordinary values, for example:
def add_poly(p1, p2):
"""Add two polynomials together"""
...
p1 = [1,2,3]
p2 = [4,5,6]
print eval_poly(10, add_poly(p1, p2))
If you're working with data files and evaluating polynomials, you could probably benefit from using numpy, which also includes numpy.polyval for evaluating polynomials.
