37 lines
933 B
Python
37 lines
933 B
Python
# 查找根区间
|
|
def FindRootZone(fx,start,stop,step):
|
|
x = start
|
|
while x < stop:
|
|
if fx(x) * fx(x+step) < 0:
|
|
return x
|
|
x += step
|
|
return None
|
|
|
|
# 求n次方根迭代过程如下
|
|
def GetNthRoot(a,n):
|
|
if a < 0 and n % 2 == 0:
|
|
print("Cannot compute even root of negative number")
|
|
return None
|
|
fx = lambda x: x**n - a
|
|
dfx = lambda x: n * x**(n-1)
|
|
err = 1e-10
|
|
N0 = 100
|
|
x0 = 0
|
|
if a > 0:
|
|
x0 = FindRootZone(fx, 0, a, 0.01)
|
|
else:
|
|
x0 = FindRootZone(fx, a, 0, 0.01)
|
|
|
|
count = 0
|
|
x1 = x0 + 1 + err
|
|
while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
|
|
x1 = x0 - fx(x0) / dfx(x0)
|
|
count += 1
|
|
if count > N0:
|
|
return None
|
|
x0 = x1
|
|
return x1
|
|
|
|
if __name__ == "__main__":
|
|
re = GetNthRoot(30, 5) #30的5次方根###########################
|
|
print(re) |