DifferForward_Newton_Class.py

from mpmath import *
# mpmath Option
mp.dps = 5; mp.pretty = True

class DifferForward_Newton_Func:
    def __init__(self, xi , fi):
        """x_i , f_i"""
        self.xi = xi
        self.fi = fi
        self.ls = []

    def _C(s, k):
##        s = mpf(s)
##        if s-k < 0 and s-int(s) == 0: return 0
##        return fac(s) / ( fac(k) * fac(s - k) )
        return binomial(s,k)

    def _f(self,x):
        return self.fi[self.xi.index(x)]

    def _fr(self,l):
        if len(l) == 1 :
            return self._f(l[0])
        rev = ( self._fr(l[1:]) - self._fr(l[:-1]) )
        self.ls += [mpf(rev)]
        return rev 
    
    def calc(self):
        '''calculate p(x) function.'''
        self._fr(self.xi)
        fc = [self._f(self.xi[0])] + self.ls[ -(len(self.xi) - 1) :]
        n = len(fc)
        h = abs(self.xi[1] - self.xi[0])
        xi =[]
        xi += self.xi
        px = lambda x: sum( fc[i] * \
                            DifferForward_Newton_Func._C((x - xi[0]) / h, i) for i in range(n) )        
        return px