Problem Description

I have written Python code to compute the following function, for fixed y_i and fixed z_i.

In practice, I will have many different vectors x at which I will want to evaluate this. Rather than going through a loop, I wanted to take full advantage of NumPy’s vectorization and broadcasting abilities.

Aim: Write a Python function that takes as input a matrix X of shape (M, p) where each row is a different vector x and compute the expression above for each of these rows, thus obtaining an output of shape (M, p).

Single Function

def single_function(x):
    """Assumes y is a vector (n,) and Z is a matrix (n, p). These are fixed."""
    return x / (sigma**2) - gamma*np.sum((np.exp(-np.logaddexp(0.0, y*np.matmul(Z, x))) * y)[:, None] * Z, axis=0)

Vectorised Function

My attempt is wrong, but I cannot tell where I am going wrong.

def vectorised(X):
    return X / (sigma**2) - gamma*np.matmul(np.exp(-np.logaddexp(0.0, y[None, :] * X.dot(Z.T))) * y[None, :], Z)