92 lines
2.5 KiB
Python
92 lines
2.5 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:
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return li[begin].y
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q = (quoDiff(begin+1, end)-quoDiff(begin, end-1)) / \
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(li[end].x-li[begin].x)
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if begin == a:
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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:
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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:
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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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