test_fourier.py 文件源码

def test_gradE(adjcube):
    """Tests the gradient of `E` using finite difference methods.
    """
    from pydft.bases.fourier import gradE, E
    from numpy.matlib import randn
    cell = adjcube
    V = QHO(cell)

    Ns=4
    #He set the random seed; we could do the same, but the
    #implementation is probably different between numpy and matlab:
    #randn('seed', 0.2004)
    W = np.array(randn(np.prod(cell.S), Ns) + 1j*randn(np.prod(cell.S), Ns))

    # Compute intial energy and gradient
    E0 = E(V, W, cell)
    g0 = gradE(V, W, cell)

    # Choose a random direction to explore
    dW = np.array(randn(W.shape) + 1j*randn(W.shape))

    # Explore a range of step sizes decreasing by powers of ten
    steps = np.logspace(np.log10(1e-3), np.log10(1e-7), 8)
    for delta in steps:
        # Directional derivative formula
        dE = 2*np.real(np.trace(np.dot(g0.conjugate().T, delta*dW)))

        # Print ratio of actual change to expected change, along with estimate
        # of the error in this quantity due to rounding
        ratio = abs(1.-(E(V, W+delta*dW, cell)-E0)/dE)
        print(int(np.log10(ratio)), int(np.log10(delta)), ratio)
        assert abs(int(np.log10(ratio)) - int(np.log10(delta))) <= 2