def test_matrix_norm(fn, exponent):
xarr, x = _vectors(fn)
sparse_mat = _sparse_matrix(fn)
sparse_mat_as_dense = np.asarray(sparse_mat.todense())
dense_mat = _dense_matrix(fn)
# Compute true matrix-weighted norm
if exponent == 1.0: # ||x||_{A,1} = ||Ax||_1
true_norm_sparse = np.linalg.norm(np.dot(sparse_mat_as_dense, xarr),
ord=exponent)
true_norm_dense = np.linalg.norm(np.dot(dense_mat, xarr),
ord=exponent)
elif exponent == 2.0: # ||x||_{A,2} = sqrt(<x, Ax>)
true_norm_sparse = np.sqrt(
np.vdot(xarr, np.dot(sparse_mat_as_dense, xarr)))
true_norm_dense = np.sqrt(np.vdot(xarr, np.dot(dense_mat, xarr)))
elif exponent == float('inf'): # ||x||_{A,inf} = ||Ax||_inf
true_norm_sparse = np.linalg.norm(sparse_mat_as_dense.dot(xarr),
ord=exponent)
true_norm_dense = np.linalg.norm(dense_mat.dot(xarr), ord=exponent)
else: # ||x||_{A,p} = ||A^{1/p} x||_p
# Calculate matrix power
eigval, eigvec = sp.linalg.eigh(dense_mat)
eigval **= 1.0 / exponent
mat_pow = (eigval * eigvec).dot(eigvec.conj().T)
true_norm_dense = np.linalg.norm(np.dot(mat_pow, xarr), ord=exponent)
# Test weighting
if exponent in (1.0, 2.0, float('inf')):
w_sparse = FnMatrixWeighting(sparse_mat, exponent=exponent)
assert almost_equal(w_sparse.norm(x), true_norm_sparse)
w_dense = FnMatrixWeighting(dense_mat, exponent=exponent)
assert almost_equal(w_dense.norm(x), true_norm_dense)
# With free functions
if exponent not in (1.0, 2.0, float('inf')):
with pytest.raises(NotImplementedError):
weighted_norm(sparse_mat, exponent=exponent)
else:
w_sparse_norm = weighted_norm(sparse_mat, exponent=exponent)
assert almost_equal(w_sparse_norm(x), true_norm_sparse)
w_dense_norm = weighted_norm(dense_mat, exponent=exponent)
assert almost_equal(w_dense_norm(x), true_norm_dense)
def test_matrix_norm(fn, exponent):
xarr, x = example_vectors(fn)
sparse_mat = _sparse_matrix(fn)
sparse_mat_as_dense = np.asarray(sparse_mat.todense())
dense_mat = _dense_matrix(fn)
# Compute true matrix-weighted norm
if exponent == 1.0: # ||x||_{A,1} = ||Ax||_1
true_norm_sparse = np.linalg.norm(np.dot(sparse_mat_as_dense, xarr),
ord=exponent)
true_norm_dense = np.linalg.norm(np.dot(dense_mat, xarr), ord=exponent)
elif exponent == 2.0: # ||x||_{A,2} = sqrt(<x, Ax>)
true_norm_sparse = np.sqrt(
np.vdot(xarr, np.dot(sparse_mat_as_dense, xarr)))
true_norm_dense = np.sqrt(np.vdot(xarr, np.dot(dense_mat, xarr)))
elif exponent == float('inf'): # ||x||_{A,inf} = ||Ax||_inf
true_norm_sparse = np.linalg.norm(sparse_mat_as_dense.dot(xarr),
ord=exponent)
true_norm_dense = np.linalg.norm(dense_mat.dot(xarr), ord=exponent)
else: # ||x||_{A,p} = ||A^{1/p} x||_p
# Calculate matrix power
eigval, eigvec = sp.linalg.eigh(dense_mat)
eigval **= 1.0 / exponent
mat_pow = (eigval * eigvec).dot(eigvec.conj().T)
true_norm_dense = np.linalg.norm(np.dot(mat_pow, xarr), ord=exponent)
# Test weighting
if exponent in (1.0, 2.0, float('inf')):
w_sparse = FnMatrixWeighting(sparse_mat, exponent=exponent)
assert almost_equal(w_sparse.norm(x), true_norm_sparse)
w_dense = FnMatrixWeighting(dense_mat, exponent=exponent)
assert almost_equal(w_dense.norm(x), true_norm_dense)
# With free functions
if exponent not in (1.0, 2.0, float('inf')):
with pytest.raises(NotImplementedError):
weighted_norm(sparse_mat, exponent=exponent)
else:
w_sparse_norm = weighted_norm(sparse_mat, exponent=exponent)
assert almost_equal(w_sparse_norm(x), true_norm_sparse)
w_dense_norm = weighted_norm(dense_mat, exponent=exponent)
assert almost_equal(w_dense_norm(x), true_norm_dense)
def test_constant_norm(fn, exponent):
xarr, x = _vectors(fn)
constant = 1.5
if exponent == float('inf'):
factor = constant
else:
factor = constant ** (1 / exponent)
true_norm = factor * np.linalg.norm(xarr, ord=exponent)
w_const = FnConstWeighting(constant, exponent=exponent)
assert almost_equal(w_const.norm(x), true_norm)
# With free function
w_const_norm = weighted_norm(constant, exponent=exponent)
assert almost_equal(w_const_norm(x), true_norm)
def test_constant_norm(fn, exponent):
xarr, x = example_vectors(fn)
constant = 1.5
if exponent == float('inf'):
factor = constant
else:
factor = constant**(1 / exponent)
true_norm = factor * np.linalg.norm(xarr, ord=exponent)
w_const = FnConstWeighting(constant, exponent=exponent)
assert almost_equal(w_const.norm(x), true_norm)
# With free function
w_const_norm = weighted_norm(constant, exponent=exponent)
assert almost_equal(w_const_norm(x), true_norm)
def test_vector_norm(fn, exponent):
xarr, x = _vectors(fn)
weight_vec = _pos_array(fn)
weighting_vec = FnVectorWeighting(weight_vec, exponent=exponent)
if exponent == float('inf'):
true_norm = np.linalg.norm(weight_vec * xarr, ord=float('inf'))
else:
true_norm = np.linalg.norm(weight_vec ** (1 / exponent) * xarr,
ord=exponent)
assert almost_equal(weighting_vec.norm(x), true_norm)
# With free function
pnorm_vec = weighted_norm(weight_vec, exponent=exponent)
assert almost_equal(pnorm_vec(x), true_norm)
def test_vector_norm(fn, exponent):
xarr, x = example_vectors(fn)
weight_vec = _pos_array(fn)
weighting_vec = FnVectorWeighting(weight_vec, exponent=exponent)
if exponent == float('inf'):
true_norm = np.linalg.norm(weight_vec * xarr, ord=float('inf'))
else:
true_norm = np.linalg.norm(weight_vec**(1 / exponent) * xarr,
ord=exponent)
assert almost_equal(weighting_vec.norm(x), true_norm)
# With free function
pnorm_vec = weighted_norm(weight_vec, exponent=exponent)
assert almost_equal(pnorm_vec(x), true_norm)