def test_ExpressionParameterFunctional_for_2d_array():
dict_of_d_mus_2d = {'mu': [['10', '20'], ['1', '2']], 'nu': 'cos(nu)'}
epf2d = ExpressionParameterFunctional(
'10 * mu[(0,0)] + 20 * mu[(0,1)] \
+ 1 * mu[(1,0)] + 2 * mu[(1,1)] \
+ sin(nu)', {
'mu': (2, 2),
'nu': ()
}, 'functional_with_derivative', dict_of_d_mus_2d)
derivative_to_11_mu_index = epf2d.d_mu('mu', (0, 0))
derivative_to_12_mu_index = epf2d.d_mu('mu', (0, 1))
derivative_to_21_mu_index = epf2d.d_mu('mu', (1, 0))
derivative_to_22_mu_index = epf2d.d_mu('mu', (1, 1))
derivative_to_nu_index = epf2d.d_mu('nu')
mu = {'mu': (1, 2, 3, 4), 'nu': 0}
der_mu_11 = derivative_to_11_mu_index.evaluate(mu)
der_mu_12 = derivative_to_12_mu_index.evaluate(mu)
der_mu_21 = derivative_to_21_mu_index.evaluate(mu)
der_mu_22 = derivative_to_22_mu_index.evaluate(mu)
der_nu = derivative_to_nu_index.evaluate(mu)
assert epf2d.evaluate(mu) == 1 * 10 + 2 * 20 + 3 * 1 + 4 * 2 + 0
assert der_mu_11 == 10
assert der_mu_12 == 20
assert der_mu_21 == 1
assert der_mu_22 == 2
assert der_nu == 1
def test_LincombParameterFunctional():
dict_of_d_mus = {'mu': ['200 * mu[0]', '2 * mu[0]'], 'nu': ['cos(nu[0])']}
epf = ExpressionParameterFunctional('100 * mu[0]**2 + 2 * mu[1] * mu[0] + sin(nu[0])',
{'mu': 2, 'nu': 1},
'functional_with_derivative_and_second_derivative',
dict_of_d_mus)
pf = ProjectionParameterFunctional('mu', 2, 0)
mu = Mu({'mu': [10,2], 'nu': [3]})
zero = pf - pf
two_pf = pf + pf
three_pf = pf + 2*pf
pf_plus_one = pf + 1
sum_ = epf + pf
pf_squared = (pf + 2*epf) * (pf - 2*epf) + 4 * epf * epf
assert zero(mu) == 0
assert two_pf(mu) == 2 * pf(mu)
assert three_pf(mu) == 3 * pf(mu)
assert pf_plus_one(mu) == pf(mu) + 1
assert sum_(mu) == epf(mu) + pf(mu)
assert pf_squared(mu) == pf(mu) * pf(mu)
assert sum_.d_mu('mu', 0)(mu) == epf.d_mu('mu', 0)(mu) + pf.d_mu('mu', 0)(mu)
assert sum_.d_mu('mu', 1)(mu) == epf.d_mu('mu', 1)(mu) + pf.d_mu('mu', 1)(mu)
assert sum_.d_mu('nu', 0)(mu) == epf.d_mu('nu', 0)(mu) + pf.d_mu('nu', 0)(mu)
def test_LincombParameterFunctional():
dict_of_d_mus = {'mu': ['200 * mu[0]', '2 * mu[0]'], 'nu': ['cos(nu[0])']}
epf = ExpressionParameterFunctional('100 * mu[0]**2 + 2 * mu[1] * mu[0] + sin(nu[0])',
{'mu': 2, 'nu': 1},
'functional_with_derivative_and_second_derivative',
dict_of_d_mus)
pf = ProjectionParameterFunctional('mu', 2, 0)
mu = Mu({'mu': [10,2], 'nu': [3]})
zero = pf - pf
two_pf = pf + pf
two_pf_named = two_pf.with_(name='some_interesting_quantity')
three_pf = pf + 2*pf
three_pf_ = pf + two_pf
three_pf_named = pf + two_pf_named
pf_plus_one = pf + 1
pf_plus_one_ = 1 + pf
sum_ = epf + pf + 1 - 3
pf_squared_ = pf * pf
pf_squared_named = pf_squared_.with_(name='some_interesting_quantity')
pf_times_pf_squared = pf * pf_squared_
pf_times_pf_squared_named = pf * pf_squared_named
pf_squared = 4 * epf * epf * 1 + (pf + 2*epf) * (pf - 2*epf)
assert zero(mu) == 0
assert two_pf(mu) == 2 * pf(mu)
assert three_pf(mu) == 3 * pf(mu)
assert three_pf_(mu) == 3 * pf(mu)
assert pf_plus_one(mu) == pf(mu) + 1
assert pf_plus_one_(mu) == pf(mu) + 1
assert sum_(mu) == epf(mu) + pf(mu) + 1 - 3
assert pf_squared_(mu) == pf(mu) * pf(mu)
assert pf_squared(mu) == pf(mu) * pf(mu)
assert pf_times_pf_squared(mu) == pf(mu) * pf(mu) * pf(mu)
# derivatives are linear
assert sum_.d_mu('mu', 0)(mu) == epf.d_mu('mu', 0)(mu) + pf.d_mu('mu', 0)(mu)
assert sum_.d_mu('mu', 1)(mu) == epf.d_mu('mu', 1)(mu) + pf.d_mu('mu', 1)(mu)
assert sum_.d_mu('nu', 0)(mu) == epf.d_mu('nu', 0)(mu) + pf.d_mu('nu', 0)(mu)
# sums and products are not nested
assert len(sum_.coefficients) == 4
assert len(pf_squared.functionals[0].factors) == 4
# named functions will not be merged and still be nested
assert three_pf_named(mu) == three_pf_(mu)
assert len(three_pf_named.coefficients) != len(three_pf_.coefficients)
assert pf_times_pf_squared_named(mu) == pf_times_pf_squared(mu)
assert len(pf_times_pf_squared_named.factors) != len(pf_times_pf_squared.factors)
def test_ExpressionParameterFunctional():
dict_of_d_mus = {'mu': ['100', '2'], 'nu': 'cos(nu)'}
epf = ExpressionParameterFunctional('100 * mu[0] + 2 * mu[1] + sin(nu)', {
'mu': (2, ),
'nu': ()
}, 'functional_with_derivative', dict_of_d_mus)
mu = {'mu': (10, 2), 'nu': 0}
derivative_to_first_mu_index = epf.d_mu('mu', 0)
derivative_to_second_mu_index = epf.d_mu('mu', 1)
derivative_to_nu_index = epf.d_mu('nu', ())
der_mu_1 = derivative_to_first_mu_index.evaluate(mu)
der_mu_2 = derivative_to_second_mu_index.evaluate(mu)
der_nu = derivative_to_nu_index.evaluate(mu)
assert epf.evaluate(mu) == 100 * 10 + 2 * 2 + 0
assert der_mu_1 == 100
assert der_mu_2 == 2
assert der_nu == 1
def test_ExpressionParameterFunctional():
dict_of_d_mus = {'mu': ['200 * mu[0]', '2 * mu[0]'], 'nu': 'cos(nu)'}
dict_of_second_derivative = {
'mu': [{
'mu': ['200', '2'],
'nu': '0'
}, {
'mu': ['2', '0'],
'nu': '0'
}],
'nu': {
'mu': ['0', '0'],
'nu': '-sin(nu)'
}
}
epf = ExpressionParameterFunctional(
'100 * mu[0]**2 + 2 * mu[1] * mu[0] + sin(nu)', {
'mu': (2, ),
'nu': ()
}, 'functional_with_derivative_and_second_derivative', dict_of_d_mus,
dict_of_second_derivative)
mu = {'mu': (10, 2), 'nu': 0}
derivative_to_first_mu_index = epf.d_mu('mu', 0)
derivative_to_second_mu_index = epf.d_mu('mu', 1)
derivative_to_nu_index = epf.d_mu('nu', ())
der_mu_1 = derivative_to_first_mu_index.evaluate(mu)
der_mu_2 = derivative_to_second_mu_index.evaluate(mu)
der_nu = derivative_to_nu_index.evaluate(mu)
second_derivative_first_mu_first_mu = epf.d_mu('mu', 0).d_mu('mu', 0)
second_derivative_first_mu_second_mu = epf.d_mu('mu', 0).d_mu('mu', 1)
second_derivative_first_mu_nu = epf.d_mu('mu', 0).d_mu('nu')
second_derivative_second_mu_first_mu = epf.d_mu('mu', 1).d_mu('mu', 0)
second_derivative_second_mu_second_mu = epf.d_mu('mu', 1).d_mu('mu', 1)
second_derivative_second_mu_nu = epf.d_mu('mu', 1).d_mu('nu')
second_derivative_nu_first_mu = epf.d_mu('nu').d_mu('mu', 0)
second_derivative_nu_second_mu = epf.d_mu('nu').d_mu('mu', 1)
second_derivative_nu_nu = epf.d_mu('nu').d_mu('nu')
hes_mu_1_mu_1 = second_derivative_first_mu_first_mu.evaluate(mu)
hes_mu_1_mu_2 = second_derivative_first_mu_second_mu.evaluate(mu)
hes_mu_1_nu = second_derivative_first_mu_nu.evaluate(mu)
hes_mu_2_mu_1 = second_derivative_second_mu_first_mu.evaluate(mu)
hes_mu_2_mu_2 = second_derivative_second_mu_second_mu.evaluate(mu)
hes_mu_2_nu = second_derivative_second_mu_nu.evaluate(mu)
hes_nu_mu_1 = second_derivative_nu_first_mu.evaluate(mu)
hes_nu_mu_2 = second_derivative_nu_second_mu.evaluate(mu)
hes_nu_nu = second_derivative_nu_nu.evaluate(mu)
assert epf.evaluate(mu) == 100 * 10**2 + 2 * 2 * 10 + 0
assert der_mu_1 == 200 * 10
assert der_mu_2 == 2 * 10
assert der_nu == 1
assert hes_mu_1_mu_1 == 200
assert hes_mu_1_mu_2 == 2
assert hes_mu_1_nu == 0
assert hes_mu_2_mu_1 == 2
assert hes_mu_2_mu_2 == 0
assert hes_mu_2_nu == 0
assert hes_nu_mu_1 == 0
assert hes_nu_mu_2 == 0
assert hes_nu_nu == -0
