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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def _matrix_grad(q, h, h_dx, t, t_prime):
    ''' Returns the gradient with respect to a single variable'''

    N = len(q)
    W = np.zeros([N, N])
    Wprime = np.zeros([N, N])
    for i in range(N):
        W[i, i] = 0.5*(h[min(i+1, N-1)] - h[max(i-1, 0)])
        Wprime[i, i] = \
            0.5*(h_dx[min(i+1, N-1)] - h_dx[max(i-1, 0)])

    tgrad = np.array([t_prime[i]*h_dx[i] for i in np.arange(N)])

    grad = 2.0*(q - t).T.dot(W).dot(-1.0*tgrad) \
            + (q - t).T.dot(Wprime).dot(q - t)

    return grad