Python Scipy integrate.romberg()用法及代碼示例

借助scipy.integrate.romberg()方法，我們可以將可調用函數的romberg積分從a限製為bscipy.integrate.romberg()方法。

用法： scipy.integrate.romberg(func, a, b)

返回：Return the romberg integrated value of a callable function.

範例1：
在這個例子中，我們可以通過使用scipy.integrate.romberg()方法，我們可以通過使用來將可調用函數的romberg積分從a限製到bscipy.integrate.romberg()方法。

# import numpy and scipy.integrate 
import numpy as np 
from scipy import integrate 
gfg = lambda x:np.exp(-x**2) 
  
# using scipy.integrate.romberg() 
geek = integrate.romberg(gfg, 0, 3, show = True) 
  
print(geek)

輸出：

Romberg integration of <function vectorize1..vfunc at 0x00000209C3641EA0> from [0, 3]

 Steps  StepSize   Results
     1  3.000000  1.500185
     2  1.500000  0.908191  0.710860
     4  0.750000  0.886180  0.878843  0.890042
     8  0.375000  0.886199  0.886206  0.886696  0.886643
    16  0.187500  0.886205  0.886207  0.886207  0.886200  0.886198
    32  0.093750  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207
    64  0.046875  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207
   128  0.023438  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207

The final result is 0.8862073482595311 after 129 function evaluations.

範例2：

# import numpy and scipy.integrate 
import numpy as np 
from scipy import integrate 
gfg = lambda x:np.exp(-x**2) + 1 / np.sqrt(np.pi) 
  
# using scipy.integrate.romberg() 
geek = integrate.romberg(gfg, 1, 2, show = True) 
  
print(geek)

輸出：

Romberg integration of <function vectorize1..vfunc at 0x00000209E1605400> from [1, 2]

 Steps  StepSize   Results
     1  1.000000  0.757287
     2  0.500000  0.713438  0.698822
     4  0.250000  0.702909  0.699400  0.699438
     8  0.125000  0.700310  0.699444  0.699447  0.699447
    16  0.062500  0.699663  0.699447  0.699447  0.699447  0.699447
    32  0.031250  0.699501  0.699447  0.699447  0.699447  0.699447  0.699447

The final result is 0.6994468414978009 after 33 function evaluations.