Generating Random vectors and matrices for weights and bias

Question

I am trying to know the chance of fire based on sensors x1 and x2.

y=1 

For this, I am trying to generate random vectors and matrices for weights and bias but I get an error.

import numpy as np

np.random.seed(seed=123)
w1 = np.random.rand(4,2)
b1 = 4*1
x = np.array([0.4, 0.32])

z1 = np.dot(w1,x) + b1
a1 = 1 / (1+np.exp(-z1))

np.random.seed(seed=123)
w2 = np.random.rand(1,4)
b2 = 1*1

z2 = np.dot(w2,x) + b2
a2 = 1 /(1+np.exp(-z2))

But I get the error below:

----> 1 z2 = np.dot(w2,x) + b2
      2 a2 = np.tanh(Z1)
      3 print(a2)

ValueError: shapes (2,4) and (2,) not aligned: 4 (dim 1) != 2 (dim 0)

I am not able to figure out how to solve this.

Answer 1

The answer is in the error - you are trying to multiply the matrices w2 and x, which have invalid dimensions to be multiplied.

Matrix w2 has 1 row and 4 columns:

>>> w2 = np.random.rand(1,4)
>>> w2.shape
(1, 4)

Matrix x has 2 entries:

>>> x = np.array([0.4, 0.32])
>>> x.shape
(2,)

Therefore, you cannot multiply these matrices together - matrices can only be multiplied if and only if the number of columns in the first matrix, w2, is equal to the number of rows in the second, x. Here, as the error says, 4 (dim 1) != 2 (dim 0).

You can solve this by either giving x four rows, or w2 two columns.

Hope this helps.