# Evaluate the gradient of function at xdef dC(x): ##### To be Updated ##### # 1. Compute and return the gradient return <fill> #########################
Question
Evaluate the gradient of function at xdef dC(x): ##### To be Updated ##### # 1. Compute and return the gradient return <fill>
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Solution
It seems like you want to compute the gradient of a function at a given point x. However, you haven't provided the function for which you want to compute the gradient. The gradient is a vector that points in the direction of the greatest rate of increase of the function, and its magnitude is the rate of increase in that direction.
Here is a general way to compute the gradient of a function in Python:
import numpy as np
def f(x):
# Your function here
pass
def gradient(f, x):
h = 1e-7 # This is a small number for numerical differentiation
grad = np.zeros_like(x) # Initialize a gradient array with the same shape as x
for idx in range(x.size):
tmp_val = x[idx]
# Compute f(x+h)
x[idx] = tmp_val + h
fxh1 = f(x)
# Compute f(x-h)
x[idx] = tmp_val - h
fxh2 = f(x)
grad[idx] = (fxh1 - fxh2) / (2*h)
x[idx] = tmp_val # Restore the value
return grad
You can use the gradient function to compute the gradient of your function at a given point. Just replace f with your function.
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