fminunc alternate in numpy

Looks like you have to change to scipy.

There you find all basic optimization algorithms readily implemented.

http://docs.scipy.org/doc/scipy/reference/optimize.html

I was also trying to implement logistic regression as discussed in Coursera ML course, but in python. I found scipy helpful. After trying different algorithm implementations in minimize function, I found Newton Conjugate Gradient as most helpful. Also After examining its returned value, it seems that it is equivalent to that of fminunc in Octave. I have included my implementation in python below find to optimal theta.

import numpy as np
import scipy.optimize as op

def Sigmoid(z):
    return 1/(1 + np.exp(-z));

def Gradient(theta,x,y):
    m , n = x.shape
    theta = theta.reshape((n,1));
    y = y.reshape((m,1))
    sigmoid_x_theta = Sigmoid(x.dot(theta));
    grad = ((x.T).dot(sigmoid_x_theta-y))/m;
    return grad.flatten();

def CostFunc(theta,x,y):
    m,n = x.shape; 
    theta = theta.reshape((n,1));
    y = y.reshape((m,1));
    term1 = np.log(Sigmoid(x.dot(theta)));
    term2 = np.log(1-Sigmoid(x.dot(theta)));
    term1 = term1.reshape((m,1))
    term2 = term2.reshape((m,1))
    term = y * term1 + (1 - y) * term2;
    J = -((np.sum(term))/m);
    return J;

# intialize X and y
X = np.array([[1,2,3],[1,3,4]]);
y = np.array([[1],[0]]);

m , n = X.shape;
initial_theta = np.zeros(n);
Result = op.minimize(fun = CostFunc, 
                                 x0 = initial_theta, 
                                 args = (X, y),
                                 method = 'TNC',
                                 jac = Gradient);
optimal_theta = Result.x;

There is more information about the functions of interest here: http://docs.scipy.org/doc/scipy-0.10.0/reference/tutorial/optimize.html

Also, it looks like you are doing the Coursera Machine Learning course, but in Python. You might check out http://aimotion.blogspot.com/2011/11/machine-learning-with-python-logistic.html; this guy's doing the same thing.