class Poly(object):
    def __init__(self,An,x):
        '''
        @author:zengwei
        parameter：多項(xiàng)式的系數(shù)，默認(rèn)從低次項(xiàng)到高次項(xiàng);list類型
        input：輸入用于計(jì)算多項(xiàng)式值的x
        '''
        self.parameter = An
        #self.__parameter = An  # 用于設(shè)置parameter為私有變量，配合set_parameter方法修改parameter
        self.input = x
    
    def set_parameter(self):
        pass
    
    def directPoly(self):
        '''用循環(huán)的方法寫多項(xiàng)式'''
        result = 0
        for k in range(len(self.parameter)):
            result = result + self.input**k*self.parameter[k]
        return result
    
    def diff_directPoly(self):
        '''directPoly()函數(shù)對(duì)應(yīng)的多項(xiàng)式求導(dǎo)'''
        result = 0
        for k in range(1,len(self.parameter)):
            result = result + self.input**(k-1)*self.parameter[k]
        return result
    
    def QinJiushao(self):
        '''用遞推的方法寫秦九韶多項(xiàng)式寫法'''
        N = len(self.parameter) - 1
        Input = self.input
        def Iterate(Input,k):
            if k == N:
                return self.parameter[k]
            return self.parameter[k]+ Iterate(Input,k+1)*Input
        
        return Iterate(self.input,0)
    
    def _QinJiushao(self):
        '''用遞推的方法寫秦九韶多項(xiàng)式寫法之二'''
        from functools import reduce 
        result = reduce(lambda a,b: a*self.input + b, self.parameter[::-1])
        return result
    
    def numpyPoly(self):
        '''用numpy內(nèi)置函數(shù)寫多項(xiàng)式'''
        import numpy as np
        P = np.poly1d(self.parameter[::-1])  # 從高次項(xiàng)到低次項(xiàng)
        return P(self.input)
    
    def BackwardPoly(self):
        '''將parameter做為多項(xiàng)式的根，反推多項(xiàng)式；循環(huán)寫法'''
        result = 1
        for k in range(len(self.parameter)):
            result = result*(self.input - self.parameter[k])
        return result
    
    def _BackwardPoly(self):
        '''將parameter做為多項(xiàng)式的根，反推多項(xiàng)式；用np.prod()函數(shù)'''
        import numpy as np
        return np.prod(self.input - np.array(self.parameter))
    
    def diff_BackwardPoly(self):
        '''對(duì)應(yīng)_BackwardPoly()函數(shù)，求其在x處的導(dǎo)數(shù)'''
        import numpy as np
        temp = self.input - np.array(self.parameter)
        P_ = np.prod(temp)
        result = 0
        for k in range(len(self.parameter)):
            result = result + P_/temp[k]
        return result
    
    def numpyBackwardPoly():
        '''將parameter做為多項(xiàng)式的根，反推多項(xiàng)式；用numpy內(nèi)部函數(shù)'''
        import numpy as np
        P = np.poly1d(self.parameter,True)
        return P(self.input)