With the help of scipy.integrate.romberg() method, we can get the romberg integration of a callable function from limit a to b by using scipy.integrate.romberg() method.
Syntax :
scipy.integrate.romberg(func, a, b)
Return : Return the romberg integrated value of a callable function.
Example #1 :
In this example we can see that by using scipy.integrate.romberg() method, we are able to get the romberg integration of a callable function from limit a to b by using scipy.integrate.romberg() method.
# 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) |
Output :
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.
Example #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) |
Output :
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.
