Module `regpy.util.functional_tests`

Functions

def test_moreaus_identity(func, u=None, tau=1.0, tolerance=1e-10)

Numerically test validity of moreaus identity for a given functional

Checks if: $u=prox_{\tau F}(u)+\tau prox_{\frac{1}{\tau}F(\frac{u}{\tau})$ .

func : Functional: The functional.
u : np.ndarray: Element in domain of func, if None it is chosen at random. Defaults to None.
tau : float, optional: Positive number tau in prox
tolerance : float, optional: The maximum allowed error in norm. Defaults to 1e-10.

def test_subgradient(func, u=None, v=None, v_length=1e-05, tolerance=1e-10)

Numerically test validity of subgradient for a given functional

Checks if: $0\geq F(u)-F(v)+\langle \grad F(u),v-u \rangle$ .

func : Functional: The functional.
u : np.ndarray, optional: Element in essential domain of func, where gradient is computed. If None it is chosen at random. Defaults to None.
v : np.ndarray, optional: Element in domain of func, where gradient is computed. If None it is chosen at random with length given by v_length. Defaults to None.
v_length : float, optional: Positive number determining the length of v if it is not given explicitly. Defaults to 1e-5.
tolerance : float, optional: The maximum allowed error. Defaults to 1e-10.

def test_young_equality(func, u=None, tolerance=1e-10)

Numerically test validity of young equality for a given functional

Checks if: $F(u)+F*(u*)=\langle u*,u \rangle$ . where u* is in the subradient of F at u.

func : Functional: The functional.
u : np.ndarray, optional: Element in essential domain of func, where gradient is computed. If None it is chosen at random. Defaults to None.
tolerance : float, optional: The maximum allowed error. Defaults to 1e-10.

def test_functional(func, u_s=None, sample_N=5, test_conj=True, u_stars=None, sample_conj_N=5, print_results=False, tolerance=1e-10)

Runs all implemented tests for a given functional. By default tests that cannot be verified because of missing implementations are ignored.

func : Functional: The functional.
u_s : list of np.ndarray, optional: List of elements in essential domain of func. If None it they chosen at random. Defaults to None.
sample_N : int, optional: If u_s i None this is the number of randomly generated elements in u_s. Defaults to 5.
test_conj : bool, optional: Determines wether the conjugate functional should be tested aswell. Defaluts to True.
u_stars : list of np.ndarray, optional: Same as u_s but for conjugate functional. Defaults to None.
sample_conj_N : int, optional: Same as sample_N but for conjugate functional. Defaults to 5.
print_results : bool, optional: If set to True, further information about test that could not be evaluated because of missing implementations are printed. Defaults to False.
tolerance : float, optional: The maximum allowed error. Defaults to 1e-10.