用python实现二次函数的求导求梯度求模

Posted 2020-11-13 "sanctuary

建立一个Function类，构造函数的参数是一个函数

其中part的功能是求偏导，var_index表示是第几个变量，val表示这些变量的值

diff的功能是方便一元函数求导

为方便梯度进行线性代数运算，在定义grad函数时，返回值转化成了numpy.array类型

#求导所得为近似结果

from numpy import *

#定义Function类
class Function:
    def __init__(self, _f):
        self.fun = _f

    def value(self, val):
        return self.fun(val)

    #求偏导
    def part(self, var_index, val):
        a = self.fun(val)
        b = a + 1
        i = 0
        e = 1
        e1 = 0.1
        while e > 10 ** (-6) or e > e1:
            e1 = e
            a = b
            val_ = list(val)
            val_[var_index] += 10 ** i
            m = self.fun(val_)
            n = self.fun(val)
            b = (m - n) / 10 ** i
            i -= 2
            e = abs(b - a)
        return a

    #一元函数求导
    def diff(self, val):
        a = self.fun(val)
        b = a + 1
        i = 0
        e = 1
        e1 = 0.1
        while e > 10 ** (-6) or e > e1:
            e1 = e
            a = b
            val_ = val + 10 ** i
            m = self.fun(val_)
            n = self.fun(val)
            b = (m - n) / 10 ** i
            i -= 2
            e = abs(b - a)
        return a

    #求梯度
    def grad(self, val):
        g = array(val)
        for i in range(0, g.size):
            g[i] = self.part(i, val)
        return array(g)

    #求模
    def norm(self, val):
        s = 0
        for x in self.grad(val):
            s += x ** 2
        return sqrt(s)