def test_matrix_dist(fn, exponent): [xarr, yarr], [x, y] = noise_elements(fn, n=2) sparse_mat = _sparse_matrix(fn) sparse_mat_as_dense = np.asarray(sparse_mat.todense()) dense_mat = _dense_matrix(fn) if exponent == 1.0: # d(x, y)_{A,1} = ||A(x-y)||_1 true_dist_sparse = np.linalg.norm(np.dot(sparse_mat_as_dense, xarr - yarr), ord=exponent) true_dist_dense = np.linalg.norm(np.dot(dense_mat, xarr - yarr), ord=exponent) elif exponent == 2.0: # d(x, y)_{A,2} = sqrt(<x-y, A(x-y)>) true_dist_sparse = np.sqrt( np.vdot(xarr - yarr, np.dot(sparse_mat_as_dense, xarr - yarr))) true_dist_dense = np.sqrt( np.vdot(xarr - yarr, np.dot(dense_mat, xarr - yarr))) elif exponent == float('inf'): # d(x, y)_{A,inf} = ||A(x-y)||_inf true_dist_sparse = np.linalg.norm(sparse_mat_as_dense.dot(xarr - yarr), ord=exponent) true_dist_dense = np.linalg.norm(dense_mat.dot(xarr - yarr), ord=exponent) else: # d(x, y)_{A,p} = ||A^{1/p} (x-y)||_p # Calculate matrix power eigval, eigvec = scipy.linalg.eigh(dense_mat) eigval **= 1.0 / exponent mat_pow = (eigval * eigvec).dot(eigvec.conj().T) true_dist_dense = np.linalg.norm(np.dot(mat_pow, xarr - yarr), ord=exponent) if exponent in (1.0, 2.0, float('inf')): w_sparse = NumpyFnMatrixWeighting(sparse_mat, exponent=exponent) assert almost_equal(w_sparse.dist(x, y), true_dist_sparse) w_dense = NumpyFnMatrixWeighting(dense_mat, exponent=exponent) assert almost_equal(w_dense.dist(x, y), true_dist_dense) # With free functions if exponent in (1.0, 2.0, float('inf')): w_sparse_dist = npy_weighted_dist(sparse_mat, exponent=exponent) assert almost_equal(w_sparse_dist(x, y), true_dist_sparse) w_dense_dist = npy_weighted_dist(dense_mat, exponent=exponent) assert almost_equal(w_dense_dist(x, y), true_dist_dense)
def test_constant_dist(fn, exponent): [xarr, yarr], [x, y] = noise_elements(fn, 2) constant = 1.5 if exponent == float('inf'): factor = constant else: factor = constant**(1 / exponent) true_dist = factor * np.linalg.norm(xarr - yarr, ord=exponent) w_const = NumpyFnConstWeighting(constant, exponent=exponent) assert almost_equal(w_const.dist(x, y), true_dist) # With free function w_const_dist = npy_weighted_dist(constant, exponent=exponent) assert almost_equal(w_const_dist(x, y), true_dist)
def test_const_dist_using_inner(fn): [xarr, yarr], [x, y] = noise_elements(fn, 2) constant = 1.5 w = NumpyFnConstWeighting(constant) true_dist = np.sqrt(constant) * np.linalg.norm(xarr - yarr) # Using 3 places (single precision default) since the result is always # double even if the underlying computation was only single precision assert almost_equal(w.dist(x, y), true_dist, places=3) # Only possible for exponent=2 with pytest.raises(ValueError): NumpyFnConstWeighting(constant, exponent=1, dist_using_inner=True) # With free function w_dist = npy_weighted_dist(constant, use_inner=True) assert almost_equal(w_dist(x, y), true_dist, places=3)
def test_array_dist(fn, exponent): [xarr, yarr], [x, y] = noise_elements(fn, n=2) weight_arr = _pos_array(fn) weighting_arr = NumpyFnArrayWeighting(weight_arr, exponent=exponent) if exponent == float('inf'): true_dist = np.linalg.norm(weight_arr * (xarr - yarr), ord=float('inf')) else: true_dist = np.linalg.norm(weight_arr**(1 / exponent) * (xarr - yarr), ord=exponent) assert almost_equal(weighting_arr.dist(x, y), true_dist) # With free function pdist_vec = npy_weighted_dist(weight_arr, exponent=exponent) assert almost_equal(pdist_vec(x, y), true_dist)
def test_matrix_dist_using_inner(fn): [xarr, yarr], [x, y] = noise_elements(fn, 2) mat = _dense_matrix(fn) w = NumpyFnMatrixWeighting(mat, dist_using_inner=True) true_dist = np.sqrt(np.vdot(xarr - yarr, np.dot(mat, xarr - yarr))) # Using 3 places (single precision default) since the result is always # double even if the underlying computation was only single precision assert almost_equal(w.dist(x, y), true_dist, places=3) # Only possible for exponent=2 with pytest.raises(ValueError): NumpyFnMatrixWeighting(mat, exponent=1, dist_using_inner=True) # With free function w_dist = npy_weighted_dist(mat, use_inner=True) assert almost_equal(w_dist(x, y), true_dist)