85 lines
2.4 KiB
Python
85 lines
2.4 KiB
Python
''' mbinary
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#########################################################################
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# File : interplotion.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-10-02 21:14
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# Description:
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#########################################################################
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'''
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#########################################################################
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# File : interplotion.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-05-18 09:29
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# Description: 插值计算,有牛顿插值,拉格朗日插值,以及通过插值得到的多项式估计新的函数值
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#########################################################################
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import sympy
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from collections import namedtuple
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from functools import reduce
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from operator import mul
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X = sympy.Symbol ('x')
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point = namedtuple('point',['x','y'])
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class interplotion:
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def __init__(self,points):
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self.points = [point(x,y) for x,y in points]
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self.xs= [i for i,j in points]
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self.poly,self.rem = self.newton(self.points,0,len(self.points)-1)
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def newton(self,li,a,b):
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'''li:[(x,f(x))...]'''
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qs = [li[0].y]
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def quoDiff(begin,end):
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if begin == end:return li[begin].y
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q = (quoDiff(begin+1,end)-quoDiff(begin,end-1))/(li[end].x-li[begin].x)
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if begin == a:qs.append(q)
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return q
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quoDiff(a,b)
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poly ,base = 0, 1
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for i,q in enumerate(qs):
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poly += q*base
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base*= X-li[i].x
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return poly, base*qs[-1]
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def lagrange(self,points=None):
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xs = None
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if points is None:
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xs = self.xs
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points = self.points
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else: xs =[x for x,y in points]
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product = reduce(mul,[X-x for x in xs],1)
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poly = 0
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for x,y in points:
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tmp = product/(X-x)
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coef = y/(tmp.subs(X,x))
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poly+= coef *tmp
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return poly
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def predict(self,val,poly = None):
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if poly is None:poly = self.poly
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return poly.subs(X,val) # note the func subs
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if __name__ == '__main__':
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f = interplotion([(81,9),(100,10),(121,11)])
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p = f.lagrange()
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print(p.subs(X,105))
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print(p)
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intor = interplotion([(0,11),(0.02,9),(0.04,7),(0.06,10)])
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p = intor.lagrange()
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print(p)
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res = intor.predict(0.08)
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print(res)
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