Automatic Differentiation on CoCalc

In [1]:

from ad import adnumber
from ad.admath import *  # sin(), etc.

In [2]:

import ad
ad.__version__

'1.3.2'

In [3]:

x = adnumber(1)
print(2*x + 1)

ad(3)

In [4]:

sin(2*x)

ad(0.9092974268256817)

So far, there shouldn’t be anything unexpected, but first and second derivatives can now be accessed through intuitive methods:

In [5]:

y = sin(2*x)
y.d(x)  # dy/dx at x=1

-0.8322936730942848

In [6]:

y.d2(x)  # d2y/dx2 at x=1

-3.637189707302727

In [7]:

z = adnumber(3.141592)
y2 = sin(z)
y2.d(z) # dy/dx1 at approximately pi

-0.9999999999997864

In [0]: