def test_likelihood_aniso():
u_star = [0, 0, 0, 0, 0, 0]
d_star_sq = flex.double(2, 0.25)
f_obs = flex.double(2, 1.0)
centric_array = flex.bool(2, True)
sigma_f_obs = f_obs / 10.0
sigma_sq = flex.double(2, 1.0)
epsilon = flex.double(2, 1.0)
gamma = flex.double(2, 0.0)
unit_cell = uctbx.unit_cell('20, 30, 40, 90.0, 90.0, 90.0')
mi = flex.miller_index(((1, 2, 3), (1, 2, 3)))
xs = crystal.symmetry((20, 30, 40), "P 2 2 2")
ms = miller.set(xs, mi)
nll_centric_aniso = scaling.wilson_single_nll_aniso(
ms.indices()[0], f_obs[0], sigma_f_obs[0], epsilon[0], sigma_sq[0],
gamma[0], centric_array[0], 0.0, unit_cell, u_star)
assert approx_equal(nll_centric_aniso, 1.07239) ## from Mathematica
nll_acentric_aniso = scaling.wilson_single_nll_aniso(
ms.indices()[0], f_obs[0], sigma_f_obs[0], epsilon[0], sigma_sq[0],
gamma[0], centric_array[0], 0.0, unit_cell, u_star)
centric_array = flex.bool(2, False)
nll_acentric_aniso = scaling.wilson_single_nll_aniso(
ms.indices()[0], f_obs[0], sigma_f_obs[0], epsilon[0], sigma_sq[0],
gamma[0], centric_array[0], 0.0, unit_cell, u_star)
assert approx_equal(nll_acentric_aniso, 0.306902) ## from Mathematica
centric_array = flex.bool(2, True)
u_star = [1, 1, 1, 0, 0, 0]
nll_centric_aniso = scaling.wilson_single_nll_aniso(
ms.indices()[0], f_obs[0], sigma_f_obs[0], epsilon[0], sigma_sq[0],
gamma[0], centric_array[0], 0.0, unit_cell, u_star)
assert approx_equal(nll_centric_aniso, 1.535008) ## from Mathematica
centric_array = flex.bool(2, False)
nll_acentric_aniso = scaling.wilson_single_nll_aniso(
ms.indices()[0], f_obs[0], sigma_f_obs[0], epsilon[0], sigma_sq[0],
gamma[0], centric_array[0], 0.0, unit_cell, u_star)
assert approx_equal(nll_acentric_aniso, 0.900003) ## from Mathematica
centric_array[1] = True
nll_total_aniso = scaling.wilson_total_nll_aniso(ms.indices(), f_obs,
sigma_f_obs, epsilon,
sigma_sq, gamma,
centric_array, 0.0,
unit_cell, u_star)
assert approx_equal(nll_total_aniso, 2.435011)
def test_likelihood_aniso():
u_star = [0,0,0,0,0,0]
d_star_sq = flex.double(2,0.25)
f_obs = flex.double(2,1.0)
centric_array = flex.bool(2,True)
sigma_f_obs = f_obs/10.0
sigma_sq = flex.double(2,1.0)
epsilon = flex.double(2,1.0)
gamma =flex.double(2,0.0)
unit_cell = uctbx.unit_cell('20, 30, 40, 90.0, 90.0, 90.0')
mi = flex.miller_index(((1,2,3), (1,2,3)))
xs = crystal.symmetry((20,30,40), "P 2 2 2")
ms = miller.set(xs, mi)
nll_centric_aniso = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
0.0,
unit_cell,
u_star)
assert approx_equal(nll_centric_aniso, 1.07239 ) ## from Mathematica
nll_acentric_aniso = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
0.0,
unit_cell,
u_star)
centric_array = flex.bool(2,False)
nll_acentric_aniso = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
0.0,
unit_cell,
u_star)
assert approx_equal(nll_acentric_aniso,0.306902 ) ## from Mathematica
centric_array = flex.bool(2,True)
u_star = [1,1,1,0,0,0]
nll_centric_aniso = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
0.0,
unit_cell,
u_star)
assert approx_equal(nll_centric_aniso, 1.535008 ) ## from Mathematica
centric_array = flex.bool(2,False)
nll_acentric_aniso = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
0.0,
unit_cell,
u_star)
assert approx_equal(nll_acentric_aniso, 0.900003 ) ## from Mathematica
centric_array[1]=True
nll_total_aniso = scaling.wilson_total_nll_aniso(ms.indices(),
f_obs,
sigma_f_obs,
epsilon,
sigma_sq,
gamma,
centric_array,
0.0,
unit_cell,
u_star)
assert approx_equal(nll_total_aniso, 2.435011)
def finite_diffs_aniso(p_scale, u_star, centric=False, h=0.0001):
d_star_sq = flex.double(2, 0.25)
f_obs = flex.double(2, 1.0)
centric_array = flex.bool(2, centric)
sigma_f_obs = f_obs / 10.0
sigma_sq = flex.double(2, 1.0)
epsilon = flex.double(2, 1.0)
gamma = flex.double(2, 0.0)
unit_cell = uctbx.unit_cell('20, 30, 40, 90.0, 90.0, 90.0')
mi = flex.miller_index(((1, 2, 3), (1, 2, 3)))
xs = crystal.symmetry((20, 30, 40), "P 2 2 2")
ms = miller.set(xs, mi)
nll_norm = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
nll_scale = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale + h,
unit_cell, u_star)
u_star[0] += h
nll_u11 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
u_star[0] -= h
u_star[1] += h
nll_u22 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
u_star[1] -= h
u_star[2] += h
nll_u33 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
u_star[2] -= h
u_star[3] += h
nll_u12 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
u_star[3] -= h
u_star[4] += h
nll_u13 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
u_star[4] -= h
u_star[5] += h
nll_u23 = scaling.wilson_single_nll_aniso(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
g = scaling.wilson_single_nll_aniso_gradient(ms.indices()[0], f_obs[0],
sigma_f_obs[0], epsilon[0],
sigma_sq[0], gamma[0],
centric_array[0], p_scale,
unit_cell, u_star)
g2 = scaling.wilson_total_nll_aniso_gradient(ms.indices(), f_obs,
sigma_f_obs, epsilon,
sigma_sq, gamma,
centric_array, p_scale,
unit_cell, u_star)
ds = (nll_norm - nll_scale) / -h
du11 = (nll_norm - nll_u11) / -h
du22 = (nll_norm - nll_u22) / -h
du33 = (nll_norm - nll_u33) / -h
du12 = (nll_norm - nll_u12) / -h
du13 = (nll_norm - nll_u13) / -h
du23 = (nll_norm - nll_u23) / -h
assert approx_equal(ds, g[0]), (ds, g[0])
assert approx_equal(du11, g[1]), (du11, g[1])
assert approx_equal(du22, g[2])
assert approx_equal(du33, g[3])
assert approx_equal(du12, g[4])
assert approx_equal(du13, g[5])
assert approx_equal(du23, g[6])
assert approx_equal(ds, g2[0] / 2.0)
assert approx_equal(du11, g2[1] / 2.0)
assert approx_equal(du22, g2[2] / 2.0)
assert approx_equal(du33, g2[3] / 2.0)
assert approx_equal(du12, g2[4] / 2.0)
assert approx_equal(du13, g2[5] / 2.0)
assert approx_equal(du23, g2[6] / 2.0)
def finite_diffs_aniso(p_scale,
u_star,
centric=False,
h=0.0001):
d_star_sq = flex.double(2,0.25)
f_obs = flex.double(2,1.0)
centric_array = flex.bool(2,centric)
sigma_f_obs = f_obs/10.0
sigma_sq = flex.double(2,1.0)
epsilon = flex.double(2,1.0)
gamma =flex.double(2,0.0)
unit_cell = uctbx.unit_cell('20, 30, 40, 90.0, 90.0, 90.0')
mi = flex.miller_index(((1,2,3), (1,2,3)))
xs = crystal.symmetry((20,30,40), "P 2 2 2")
ms = miller.set(xs, mi)
nll_norm = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
nll_scale = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale+h,
unit_cell,
u_star)
u_star[0]+=h
nll_u11 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
u_star[0]-=h
u_star[1]+=h
nll_u22 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
u_star[1]-=h
u_star[2]+=h
nll_u33 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
u_star[2]-=h
u_star[3]+=h
nll_u12 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
u_star[3]-=h
u_star[4]+=h
nll_u13 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
u_star[4]-=h
u_star[5]+=h
nll_u23 = scaling.wilson_single_nll_aniso(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
g = scaling.wilson_single_nll_aniso_gradient(ms.indices()[0],
f_obs[0],
sigma_f_obs[0],
epsilon[0],
sigma_sq[0],
gamma[0],
centric_array[0],
p_scale,
unit_cell,
u_star)
g2 = scaling.wilson_total_nll_aniso_gradient(ms.indices(),
f_obs,
sigma_f_obs,
epsilon,
sigma_sq,
gamma,
centric_array,
p_scale,
unit_cell,
u_star)
ds=(nll_norm-nll_scale)/-h
du11=(nll_norm-nll_u11)/-h
du22=(nll_norm-nll_u22)/-h
du33=(nll_norm-nll_u33)/-h
du12=(nll_norm-nll_u12)/-h
du13=(nll_norm-nll_u13)/-h
du23=(nll_norm-nll_u23)/-h
assert approx_equal(ds,g[0]), (ds,g[0])
assert approx_equal(du11,g[1]), (du11,g[1])
assert approx_equal(du22,g[2])
assert approx_equal(du33,g[3])
assert approx_equal(du12,g[4])
assert approx_equal(du13,g[5])
assert approx_equal(du23,g[6])
assert approx_equal(ds,g2[0]/2.0)
assert approx_equal(du11,g2[1]/2.0)
assert approx_equal(du22,g2[2]/2.0)
assert approx_equal(du33,g2[3]/2.0)
assert approx_equal(du12,g2[4]/2.0)
assert approx_equal(du13,g2[5]/2.0)
assert approx_equal(du23,g2[6]/2.0)
