def test_objective_matches_sym():
    sigma = 1.
    lmbda = 1.
    Z = np.random.randn(100, 2)
    
    alpha = np.random.randn(len(Z))
    
    J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha)
    J = gaussian.objective(Z, Z, sigma, lmbda, alpha)
    
    print type(J)
    print type(J_sym)
    assert_equal(J, J_sym)
def test_objective_matches_sym():
    sigma = 1.
    lmbda = 1.
    Z = np.random.randn(100, 2)

    alpha = np.random.randn(len(Z))

    J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha)
    J = gaussian.objective(Z, Z, sigma, lmbda, alpha)

    print type(J)
    print type(J_sym)
    assert_equal(J, J_sym)
def test_objective_matches_sym_precomputed_KbC():
    sigma = 1.
    lmbda = 1.
    Z = np.random.randn(100, 2)
    K = gaussian_kernel(Z, sigma=sigma)

    alpha = np.random.randn(len(Z))
    C = develop_gaussian.compute_C_sym(Z, K, sigma)
    b = develop_gaussian.compute_b_sym(Z, K, sigma)

    K = gaussian_kernel(Z, sigma=sigma)
    J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
    J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)

    assert_equal(J, J_sym)
def test_objective_matches_sym_precomputed_KbC():
    sigma = 1.
    lmbda = 1.
    Z = np.random.randn(100, 2)
    K = gaussian_kernel(Z, sigma=sigma)
    
    alpha = np.random.randn(len(Z))
    C = develop_gaussian.compute_C_sym(Z, K, sigma)
    b = develop_gaussian.compute_b_sym(Z, K, sigma)
    
    K = gaussian_kernel(Z, sigma=sigma)
    J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
    J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)
    
    assert_equal(J, J_sym)
def test_objective_matches_full():
    sigma = 1.
    lmbda = 1.
    X = np.random.randn(100, 2)
    Y = np.random.randn(10, 2)
    low_rank_dim = int(len(X) * 0.9)
    
    kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
    alpha = np.random.randn(len(X))
    
    K_XY = kernel(X, Y)
    C = gaussian.compute_C(X, Y, K_XY, sigma)
    b = gaussian.compute_b(X, Y, K_XY, sigma)
    J_full = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY, b=b, C=C)
    
    temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
    I, R, nu = (temp["I"], temp["R"], temp["nu"])
    R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
    b = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
    J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T, b)
    
    assert_close(J, J_full, decimal=1)
def test_objective_matches_full():
    sigma = 1.
    lmbda = 1.
    X = np.random.randn(100, 2)
    Y = np.random.randn(10, 2)
    low_rank_dim = int(len(X) * 0.9)

    kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
    alpha = np.random.randn(len(X))

    K_XY = kernel(X, Y)
    C = gaussian.compute_C(X, Y, K_XY, sigma)
    b = gaussian.compute_b(X, Y, K_XY, sigma)
    J_full = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY, b=b, C=C)

    temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
    I, R, nu = (temp["I"], temp["R"], temp["nu"])
    R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
    b = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
    J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T,
                                    b)

    assert_close(J, J_full, decimal=1)
def test_objective_against_naive():
    sigma = 1.
    D = 2
    NX = 10
    NY = 20
    X = np.random.randn(NX, D)
    Y = np.random.randn(NY, D)

    K_XY = gaussian_kernel(X, Y, sigma=sigma)

    num_trials = 10
    for _ in range(num_trials):
        alpha = np.random.randn(NX)

        J_naive_a = 0
        for d in range(D):
            for i in range(NX):
                for j in range(NY):
                    J_naive_a += alpha[i] * K_XY[i, j] * \
                                (-1 + 2. / sigma * ((X[i][d] - Y[j][d]) ** 2))
        J_naive_a *= (2. / (NX * sigma))

        J_naive_b = 0
        for d in range(D):
            for i in range(NY):
                temp = 0
                for j in range(NX):
                    temp += alpha[j] * (X[j, d] - Y[i, d]) * K_XY[j, i]
                J_naive_b += (temp**2)
        J_naive_b *= (2. / (NX * (sigma**2)))

        J_naive = J_naive_a + J_naive_b

        # compare to unregularised objective
        lmbda = 0.
        J = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY)
        assert_close(J_naive, J)
def test_objective_against_naive():
    sigma = 1.
    D = 2
    NX = 10
    NY = 20
    X = np.random.randn(NX, D)
    Y = np.random.randn(NY, D)
    
    K_XY = gaussian_kernel(X, Y, sigma=sigma)
    
    num_trials = 10
    for _ in range(num_trials):
        alpha = np.random.randn(NX)
        
        J_naive_a = 0
        for d in range(D):
            for i in range(NX):
                for j in range(NY):
                    J_naive_a += alpha[i] * K_XY[i, j] * \
                                (-1 + 2. / sigma * ((X[i][d] - Y[j][d]) ** 2))
        J_naive_a *= (2. / (NX * sigma))
        
        J_naive_b = 0
        for d in range(D):
            for i in range(NY):
                temp = 0
                for j in range(NX):
                    temp += alpha[j] * (X[j, d] - Y[i, d]) * K_XY[j, i]
                J_naive_b += (temp ** 2)
        J_naive_b *= (2. / (NX * (sigma ** 2)))
        
        J_naive = J_naive_a + J_naive_b
        
        # compare to unregularised objective
        lmbda = 0.
        J = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY)
        assert_close(J_naive, J)