mc_harmonic 0

Query

import numpy as np

def run_mc(n_steps, T, k):
    """
    This function performs metropolis monte carlo sampling of a harmonic potential at temperature T
    and returns the trajectory
    """
    [insert]
    return traj

Output

import numpy as np

def run_mc(n_steps, T, k):
    """
    This function performs metropolis monte carlo sampling of a harmonic potential at temperature T
    and returns the trajectory
    """
    traj = np.zeros(n_steps)
    traj[0] = np.random.uniform(-1, 1)
    for i in range(1, n_steps):
        x_new = np.random.uniform(-1, 1)
        dE = 0.5*k*(x_new**2 - traj[i-1]**2)
        if dE < 0:
            traj[i] = x_new
        else:
            if np.random.uniform(0, 1) < np.exp(-dE/T):
                traj[i] = x_new
            else:
                traj[i] = traj[i-1]

    return traj

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