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Fix tanh(x) example + README #636

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Aug 28, 2024
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Fix tanh(x) example + README #636

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10 changes: 4 additions & 6 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -25,13 +25,13 @@ Example use:
>>> from autograd import grad # The only autograd function you may ever need
>>>
>>> def tanh(x): # Define a function
... return (1.0 - np.exp(-x)) / (1.0 + np.exp(-x))
... return (1.0 - np.exp((-2 * x))) / (1.0 + np.exp(-(2 * x)))
...
>>> grad_tanh = grad(tanh) # Obtain its gradient function
>>> grad_tanh(1.0) # Evaluate the gradient at x = 1.0
np.float64(0.39322386648296376)
np.float64(0.419974341614026)
>>> (tanh(1.0001) - tanh(0.9999)) / 0.0002 # Compare to finite differences
np.float64(0.39322386636453377)
np.float64(0.41997434264973155)
```

We can continue to differentiate as many times as we like, and use numpy's
Expand All @@ -40,14 +40,12 @@ vectorization of scalar-valued functions across many different input values:
```python
>>> from autograd import elementwise_grad as egrad # for functions that vectorize over inputs
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-7, 7, 200)
>>> x = np.linspace(-7, 7, 700)
>>> plt.plot(x, tanh(x),
... x, egrad(tanh)(x), # first derivative
... x, egrad(egrad(tanh))(x), # second derivative
... x, egrad(egrad(egrad(tanh)))(x), # third derivative
... x, egrad(egrad(egrad(egrad(tanh))))(x), # fourth derivative
... x, egrad(egrad(egrad(egrad(egrad(tanh)))))(x), # fifth derivative
... x, egrad(egrad(egrad(egrad(egrad(egrad(tanh))))))(x)) # sixth derivative
>>> plt.show()
```

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39 changes: 18 additions & 21 deletions examples/tanh.py
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@@ -1,5 +1,6 @@
import autograd.numpy as np
import matplotlib.pyplot as plt

import autograd.numpy as np
from autograd import elementwise_grad as egrad

"""
Expand All @@ -19,27 +20,23 @@


def tanh(x):
return (1.0 - np.exp(-x)) / (1.0 + np.exp(-x))

return (1.0 - np.exp((-2 * x))) / (1.0 + np.exp(-(2 * x)))

x = np.linspace(-7, 7, 200)
plt.plot(
x,
tanh(x),
x,
egrad(tanh)(x), # first derivative
x,
egrad(egrad(tanh))(x), # second derivative
x,
egrad(egrad(egrad(tanh)))(x), # third derivative
x,
egrad(egrad(egrad(egrad(tanh))))(x), # fourth derivative
x,
egrad(egrad(egrad(egrad(egrad(tanh)))))(x), # fifth derivative
x,
egrad(egrad(egrad(egrad(egrad(egrad(tanh))))))(x),
) # sixth derivative

plt.axis("off")
### Plotting
plt.figure(figsize=(12, 8))
x = np.linspace(-7, 7, 700)
plt.plot(x, tanh(x), label='tanh(x)')
plt.plot(x, egrad(tanh)(x), label="1st derivative")
plt.plot(x, egrad(egrad(tanh))(x), label="2nd derivative")
plt.plot(x, egrad(egrad(egrad(tanh)))(x), label="3rd derivative")
plt.plot(x, egrad(egrad(egrad(egrad(tanh))))(x), label="4th derivative")
plt.xlabel('x')
plt.ylabel('y')
plt.ylim(-5, 5)
plt.yticks(np.arange(-5, 6, 1))
plt.legend()
plt.grid(True)
plt.title("tanh(x) and its derivatives")
plt.savefig("tanh.png")
plt.show()