如何在python中停止十进制值和e格式化值的舍入

Question

我正在键入代码以通过梯形方法和辛普森规则以及给定输入“n”的情况下这些值的绝对差来生成积分值。如果 i 在 (1, 19) 范围内，则“n”输入本身就是 n = 2 ** i 的函数。

我的代码输出的表格如下

     n    Trapezoidal    Simpson    Absolute Difference
------  -------------  ---------  ---------------------
     2      -0.929894  -0.68338             0.246515
     4      -0.687139  -0.606221            0.0809183
     8      -0.614581  -0.590396            0.024186
    16      -0.594187  -0.587389            0.00679814
    32      -0.588796  -0.587               0.00179688
    64      -0.587422  -0.586964            0.000458234
   128      -0.587076  -0.586961            0.000115222
   256      -0.58699   -0.586961            2.88492e-05
   512      -0.586968  -0.586961            7.21507e-06
  1024      -0.586962  -0.586961            1.80394e-06
  2048      -0.586961  -0.586961            4.50996e-07
  4096      -0.586961  -0.586961            1.1275e-07
  8192      -0.586961  -0.586961            2.81874e-08
 16384      -0.586961  -0.586961            7.04687e-09
 32768      -0.586961  -0.586961            1.7617e-09
 65536      -0.586961  -0.586961            4.40314e-10
131072      -0.586961  -0.586961            1.10276e-10
262144      -0.586961  -0.586961            2.76881e-11
524288      -0.586961  -0.586961            7.86082e-12

但是，我希望表中的值全部四舍五入为 7 个十进制值，并且不使用 e/E 进行格式化，以便我的表如下所示：

n Trapezoidal Simpson Absolute Difference
------------------------------------------------------------------------
2 -0.9298943 -0.6833796 0.2465147
4 -0.6871394 -0.6062211 0.0809183
8 -0.6145815 -0.5903955 0.0241860
16 -0.5941871 -0.5873889 0.0067981
32 -0.5887964 -0.5869996 0.0017969
64 -0.5874217 -0.5869635 0.0004582
128 -0.5870761 -0.5869609 0.0001152
256 -0.5869895 -0.5869607 0.0000288
512 -0.5869679 -0.5869607 0.0000072
1024 -0.5869625 -0.5869607 0.0000018
2048 -0.5869611 -0.5869607 0.0000005
4096 -0.5869608 -0.5869607 0.0000001
8192 -0.5869607 -0.5869607 0.0000000
16384 -0.5869607 -0.5869607 0.0000000
32768 -0.5869607 -0.5869607 0.0000000
65536 -0.5869607 -0.5869607 0.0000000
131072 -0.5869607 -0.5869607 0.0000000
262144 -0.5869607 -0.5869607 0.0000000
524288 -0.5869607 -0.5869607 0.0000000

下面是我用来获取表格的代码

from numpy import arange
import numpy as np
from numpy import subtract
from tabulate import tabulate
from math import cos, sin

def trapezoidal(f, n, a, b):
    
    h = (b-a)/ n
    x = a + arange(n + 1) * h
    
    integral_approx = 0.5 * h * (f(x[0]) + f(x[n]))
    
    for i in arange(1, n):
        
        integral_approx = integral_approx + h * f(x[i])
        
    return integral_approx


def simpson(f, n, a, b):
    
    if n % 2 is not 0:
        return None
    
    h = (b - a)/n
    first = f(a)
    last = f(b)
    
    x = a
    summ = 0
    
    for i in range(n - 1):
        
        x += h
        value = f(x)
        
        if i % 2 == 0:
            
            summ += 4 * value
            
        else:
            
            summ += 2 * value
            
    integral_approx = (h/3) * (first + summ + last)
    
    return integral_approx
    
       
a = 0.1

b = pi/2

f = lambda x: (cos(x)*np.log(sin(x)))/((sin(x)**2) + 1)

d = []

for i in range(1, 20):
    
    n = 2**i
    
    absdiff = abs(subtract(trapezoidal(f, n, a, b), simpson(f, n, a, b)))
      
    d.append([n, trapezoidal(f, n, a, b), simpson(f, n, a, b), absdiff])

print(tabulate(d, headers = ["n", "Trapezoidal", "Simpson", "Absolute Difference"]))

由于我格式化函数的方式，我不确定是否存在差异。如果可以的话，请帮忙。

Answer 1

def truncate(n, decimals=0):
    multiplier = 10 ** decimals
    return int(n * multiplier) / multiplier
print(truncate(0.123456789,7))

输出：0.1234567

希望这个功能有帮助

Answer 2

from tabulate import tabulate

默认情况下，浮点数使用g 格式，这意味着它将根据值大小在. 和e-notation 表示之间进行选择。您可以传递 floatfmt 其他格式说明符。考虑以下示例

from tabulate import tabulate
data = [[0.1],[0.01],[0.001],[0.0001],[0.00001]]
print(tabulate(data, headers=['value'], floatfmt='.5f'))

输出

  value
-------
0.10000
0.01000
0.00100
0.00010
0.00001

Answer 3

我建议使用表格的构建方式来格式化数字（另见this article）：

print(tabulate(d, headers=["n", "Trapezoidal", "Simpson", "Absolute Difference"], floatfmt=".2f"))

使用它，您的输出将如下所示：

  n    Trapezoidal    Simpson    Absolute Difference
------  -------------  ---------  ---------------------
2          -0.93      -0.68                   0.25
4          -0.69      -0.61                   0.08
8          -0.61      -0.59                   0.02
16         -0.59      -0.59                   0.01
32         -0.59      -0.59                   0.00
64         -0.59      -0.59                   0.00
128        -0.59      -0.59                   0.00
256        -0.59      -0.59                   0.00
512        -0.59      -0.59                   0.00
1024       -0.59      -0.59                   0.00
2048       -0.59      -0.59                   0.00
4096       -0.59      -0.59                   0.00
8192       -0.59      -0.59                   0.00
16384      -0.59      -0.59                   0.00
32768      -0.59      -0.59                   0.00
65536      -0.59      -0.59                   0.00
131072     -0.59      -0.59                   0.00
262144     -0.59      -0.59                   0.00
524288     -0.59      -0.59                   0.00

当然，如果需要，您可以指定小数位数。