39 lines
1.1 KiB
Python
39 lines
1.1 KiB
Python
import math
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# 逐次分半梯形递推公式
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def SplitTrapezoidal(a,b,fx,err):
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count = 1
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t1 = (b-a)*(fx(a)+fx(b))/2
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print(f"t{count}={t1}")
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k = 1
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while True:
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tmp = 0
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for i in range(1, 2**(k-1)+1):
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tmp += fx(a + (b-a)*(2*i-1)/(2**k))
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t2 = t1/2+(b-a)*tmp/(2**k)
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count *= 2
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print(f"t{count}={t2}")
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if abs(t2-t1) < err:
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break
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t1 = t2
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k += 1
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return t2,k
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# 积分原函数 ##############################################################
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def fx(x):
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if x == 0:
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x = 1e-10 # Avoid division by zero #如果x能为0，注释掉这行##############
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pass
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return 1/x #把函数改成题干的形式###################
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if __name__ == "__main__":
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##############################################################################################################
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x_start = 1 # 积分下限
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x_end = 3 # 积分上限
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err = 1e-2 # 精度要求 P106
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result,k = SplitTrapezoidal(x_start, x_end, fx, err)
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print(f"Result: {result},k={k}")
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