Module regpy.util.functional_tests
Functions
def test_moreaus_identity(func, u=None, tau=1.0, tolerance=1e-10)-
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def test_moreaus_identity(func,u=None,tau=1.0,tolerance=1e-10): r"""Numerically test validity of moreaus identity for a given functional Checks if: \[u=prox_{\tau F}(u)+\tau prox_{\frac{1}{\tau}F(\frac{u}{\tau})\]. Parameters ---------- func : regpy.functionals.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. Raises ------ AssertionError If the test fails. """ if(u is None): u=func.domain.randn() prox = func.proximal(u,tau) gram = func.h_domain.gram proxstar = func.conj.proximal(gram(u/tau),1/tau) err=np.linalg.norm(u-prox-tau*gram.inverse(proxstar)) assert err<tolerance,f'err={err}'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}).
Parameters
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.
Raises
AssertionError- If the test fails.
def test_subgradient(func, u=None, v=None, v_length=1e-05, tolerance=1e-10)-
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def test_subgradient(func,u=None,v=None,v_length=1e-5,tolerance=1e-10): r"""Numerically test validity of subgradient for a given functional Checks if: \[0\geq F(u)-F(v)+\langle \grad F(u),v-u \rangle\]. Parameters ---------- func : regpy.functionals.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. Raises ------ AssertionError If the test fails. """ if(u is None): u=func.domain.randn() if(v is None): v=func.domain.randn() v*=v_length/np.linalg.norm(v) grad_u=func.subgradient(u) err=func(u)-func(v)+np.real(np.vdot(grad_u,v-u)) assert err<tolerance,f'err={err}'Numerically test validity of subgradient for a given functional
Checks if: 0\geq F(u)-F(v)+\langle \grad F(u),v-u \rangle.
Parameters
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.
Raises
AssertionError- If the test fails.
def test_young_equality(func, u=None, tolerance=1e-10)-
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def test_young_equality(func,u=None,tolerance=1e-10): r"""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. Parameters ---------- func : regpy.functionals.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. Raises ------ AssertionError If the test fails. """ if(u is None): u=func.domain.randn() grad_u=func.subgradient(u) err=np.abs(np.real(np.vdot(u,grad_u))-func(u)-func.conj(grad_u)) assert err<tolerance,f'err={err}'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.
Parameters
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.
Raises
AssertionError- If the test fails.
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)-
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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): r"""Runs all implemented tests for a given functional. By default tests that cannot be verified because of missing implementations are ignored. Parameters ---------- func : regpy.functionals.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. Raises ------ AssertionError If the test fails. """ if(u_s is None): u_s=[func.domain.randn() for _ in range(sample_N)] if(print_results): print(type(func)) for u in u_s: try: tau=np.random.uniform(tolerance,4) test_moreaus_identity(func,u,tau=tau,tolerance=tolerance) except(NotImplementedError): if(print_results): print('Moreaus identity could not be checked because of missing implementation') try: test_subgradient(func,u,tolerance=tolerance) except(NotImplementedError): if(print_results): print('Subgradient could not be checked because of missing implementation') try: test_young_equality(func,u,tolerance=tolerance) except(NotImplementedError): if(print_results): print('Young equality could not be checked because of missing implementation') if(test_conj): test_functional(func.conj,u_s=u_stars,sample_N=sample_conj_N,test_conj=False,print_results=print_results,tolerance=tolerance)Runs all implemented tests for a given functional. By default tests that cannot be verified because of missing implementations are ignored.
Parameters
func:Functional- The functional.
u_s:listofnp.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:listofnp.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.
Raises
AssertionError- If the test fails.