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def sigmoid(X):
    '''Compute the sigmoid function '''
    #d = zeros(shape=(X.shape))

    den = 1.0 + e ** (-1.0 * X)

    d = 1.0 / den

    return d


def compute_cost(theta,X,y): #computes cost given predicted and actual values
    m = X.shape[0] #number of training examples
    theta = reshape(theta,(len(theta),1))

    #y = reshape(y,(len(y),1))
    
    J = (1./m) * (-transpose(y).dot(log(sigmoid(X.dot(theta)))) - transpose(1-y).dot(log(1-sigmoid(X.dot(theta)))))
    
    grad = transpose((1./m)*transpose(sigmoid(X.dot(theta)) - y).dot(X))
    #optimize.fmin expects a single value, so cannot return grad
    return J[0][0]#,grad


def compute_grad(theta, X, y):

    #print theta.shape

    theta.shape = (1, 3)

    grad = zeros(3)

    h = sigmoid(X.dot(theta.T))

    delta = h - y

    l = grad.size

    for i in range(l):
        sumdelta = delta.T.dot(X[:, i])
        grad[i] = (1.0 / m) * sumdelta * - 1

    theta.shape = (3,)

    return  grad