def exercise_mean_square_displacement(options, n_trials):
if options.fix_random_seeds:
scitbx.random.set_random_seed(0)
# check adptbx.mean_square_displacement_difference
# against adp_restraints.rigid_bond_pair
for i in xrange(n_trials):
x1 = matrix.col(site_coord(3))
x2 = matrix.col(site_coord(3))
u1 = matrix.col(as_sym_mat3(symm_mat(u_eigenval(3))))
u2 = matrix.col(as_sym_mat3(symm_mat(u_eigenval(3))))
g = as_sym_mat3(symm_mat(g_eigenval(3)))
uc = uctbx.unit_cell(metrical_matrix=g)
hirshfeld = adptbx.mean_square_displacement(uc, x1-x2)
rigid = adp_restraints.rigid_bond_pair(x1, x2, u1, u2, uc)
del uc
assert hirshfeld.well_defined
h1 = hirshfeld(u1).value
h2 = hirshfeld(u2).value
assert approx_equal(abs(h1 - h2), rigid.delta_z(), eps=1e-12)
# check gradients with finite difference
finite_difference_computation = scitbx.math.finite_difference_computation()
best_delta = finite_difference_computation.best_delta
for i in xrange(n_trials):
z = site_coord(3)
dz = best_delta(z, site_coord(3))
z = matrix.col(z)
dz = matrix.col(dz)
u_eigen = u_eigenval(3)
du_eigen = best_delta(u_eigen, direction(3))
u = matrix.col(as_sym_mat3(symm_mat(u_eigen)))
du = matrix.col(as_sym_mat3(symm_mat(du_eigen)))
g_eigen = g_eigenval(3)
dg_eigen = best_delta(g_eigen, direction(3))
g = matrix.col(as_sym_mat3(symm_mat(g_eigen)))
dg = matrix.col(as_sym_mat3(symm_mat(dg_eigen)))
uc = uctbx.unit_cell(metrical_matrix=g)
h = adptbx.mean_square_displacement(uc, z)(u)
uc_p = uctbx.unit_cell(metrical_matrix=g+dg)
h_p = adptbx.mean_square_displacement(uc_p, z+dz)(u+du).value
uc_m = uctbx.unit_cell(metrical_matrix=g-dg)
h_m = adptbx.mean_square_displacement(uc_m, z-dz)(u-du).value
finite_diff = (h_p - h_m)/2
taylor_diff = ( matrix.col(h.grad_u).dot(du)
+ matrix.col(h.grad_z).dot(dz)
+ matrix.col(h.grad_g).dot(dg) )
assert approx_equal(taylor_diff, finite_diff,
eps=5*finite_difference_computation.precision),\
(taylor_diff, finite_diff)
def exercise_mean_square_displacement(options, n_trials):
if options.fix_random_seeds:
scitbx.random.set_random_seed(0)
# check adptbx.mean_square_displacement_difference
# against adp_restraints.rigid_bond_pair
for i in range(n_trials):
x1 = matrix.col(site_coord(3))
x2 = matrix.col(site_coord(3))
u1 = matrix.col(as_sym_mat3(symm_mat(u_eigenval(3))))
u2 = matrix.col(as_sym_mat3(symm_mat(u_eigenval(3))))
g = as_sym_mat3(symm_mat(g_eigenval(3)))
uc = uctbx.unit_cell(metrical_matrix=g)
hirshfeld = adptbx.mean_square_displacement(uc, x1 - x2)
rigid = adp_restraints.rigid_bond_pair(x1, x2, u1, u2, uc)
del uc
assert hirshfeld.well_defined
h1 = hirshfeld(u1).value
h2 = hirshfeld(u2).value
assert approx_equal(abs(h1 - h2), rigid.delta_z(), eps=1e-12)
# check gradients with finite difference
finite_difference_computation = scitbx.math.finite_difference_computation()
best_delta = finite_difference_computation.best_delta
for i in range(n_trials):
z = site_coord(3)
dz = best_delta(z, site_coord(3))
z = matrix.col(z)
dz = matrix.col(dz)
u_eigen = u_eigenval(3)
du_eigen = best_delta(u_eigen, direction(3))
u = matrix.col(as_sym_mat3(symm_mat(u_eigen)))
du = matrix.col(as_sym_mat3(symm_mat(du_eigen)))
g_eigen = g_eigenval(3)
dg_eigen = best_delta(g_eigen, direction(3))
g = matrix.col(as_sym_mat3(symm_mat(g_eigen)))
dg = matrix.col(as_sym_mat3(symm_mat(dg_eigen)))
uc = uctbx.unit_cell(metrical_matrix=g)
h = adptbx.mean_square_displacement(uc, z)(u)
uc_p = uctbx.unit_cell(metrical_matrix=g + dg)
h_p = adptbx.mean_square_displacement(uc_p, z + dz)(u + du).value
uc_m = uctbx.unit_cell(metrical_matrix=g - dg)
h_m = adptbx.mean_square_displacement(uc_m, z - dz)(u - du).value
finite_diff = (h_p - h_m) / 2
taylor_diff = (matrix.col(h.grad_u).dot(du) +
matrix.col(h.grad_z).dot(dz) +
matrix.col(h.grad_g).dot(dg))
assert approx_equal(taylor_diff, finite_diff,
eps=5*finite_difference_computation.precision),\
(taylor_diff, finite_diff)
def exercise_rigid_bond_test():
"""
Results compared with THMA11 (Ver. 20-04-91) - TLS Thermal Motion
Analysis used as a part of WinGX (WinGX - Crystallographic Program
System for Windows)
"""
ins_file = libtbx.env.find_in_repositories(
relative_path="phenix_regression/pdb/enk_11i.res", test=os.path.isfile)
if (ins_file is None):
print("Skipping exercise_rigid_bond_test(): input file not available")
return
with open(ins_file) as f:
ins_xray_structure = cctbx.xray.structure.from_shelx(file=f)
sites_frac = ins_xray_structure.sites_frac()
sites_cart = ins_xray_structure.sites_cart()
ustars = ins_xray_structure.scatterers().extract_u_star()
scatterers = ins_xray_structure.scatterers()
j = 0
for site_cart_1,site_frac_1,ustar_1,scat_1 in zip(sites_cart,sites_frac,ustars,scatterers):
for site_cart_2,site_frac_2,ustar_2, scat_2 in zip(sites_cart,sites_frac,ustars,scatterers):
d = math.sqrt(flex.sum(flex.pow2(flex.double(site_cart_1)-\
flex.double(site_cart_2))))
if(d > 1.1 and d < 1.55):
p = adp_restraints.rigid_bond_pair(site_frac_1,
site_frac_2,
ustar_1,
ustar_2,
ins_xray_structure.unit_cell())
if(0):
print("%4s %4s %7.4f %7.4f %7.4f" % \
(scat_1.label,scat_2.label,p.delta_z(),p.z_12(),p.z_21()))
r = result[j]
assert r[0] == scat_1.label
assert r[1] == scat_2.label
assert approx_equal(r[2], p.delta_z(), 1.e-4)
assert approx_equal(r[3], p.z_12(), 1.e-4)
assert approx_equal(r[4], p.z_21(), 1.e-4)
j += 1
assert j == 56
def exercise_rigid_bond_test():
"""
Results compared with THMA11 (Ver. 20-04-91) - TLS Thermal Motion
Analysis used as a part of WinGX (WinGX - Crystallographic Program
System for Windows)
"""
ins_file = libtbx.env.find_in_repositories(
relative_path="phenix_regression/pdb/enk_11i.res", test=os.path.isfile)
if (ins_file is None):
print "Skipping exercise_rigid_bond_test(): input file not available"
return
ins_xray_structure = cctbx.xray.structure.from_shelx(file=open(ins_file))
sites_frac = ins_xray_structure.sites_frac()
sites_cart = ins_xray_structure.sites_cart()
ustars = ins_xray_structure.scatterers().extract_u_star()
scatterers = ins_xray_structure.scatterers()
j = 0
for site_cart_1,site_frac_1,ustar_1,scat_1 in zip(sites_cart,sites_frac,ustars,scatterers):
for site_cart_2,site_frac_2,ustar_2, scat_2 in zip(sites_cart,sites_frac,ustars,scatterers):
d = math.sqrt(flex.sum(flex.pow2(flex.double(site_cart_1)-\
flex.double(site_cart_2))))
if(d > 1.1 and d < 1.55):
p = adp_restraints.rigid_bond_pair(site_frac_1,
site_frac_2,
ustar_1,
ustar_2,
ins_xray_structure.unit_cell())
if(0):
print "%4s %4s %7.4f %7.4f %7.4f" % \
(scat_1.label,scat_2.label,p.delta_z(),p.z_12(),p.z_21())
r = result[j]
assert r[0] == scat_1.label
assert r[1] == scat_2.label
assert approx_equal(r[2], p.delta_z(), 1.e-4)
assert approx_equal(r[3], p.z_12(), 1.e-4)
assert approx_equal(r[4], p.z_21(), 1.e-4)
j += 1
assert j == 56
def exercise_rigid_bond():
i_seqs = (1,2)
weight = 1
p = adp_restraints.rigid_bond_proxy(i_seqs=i_seqs,weight=weight)
assert p.i_seqs == i_seqs
assert p.weight == weight
sites = ((1,2,3),(2,3,4))
u_cart = ((1,2,3,4,5,6), (3,4,5,6,7,8))
expected_gradients = ((-4, -4, -4, -8, -8, -8), (4, 4, 4, 8, 8, 8))
r = adp_restraints.rigid_bond(sites=sites, u_cart=u_cart, weight=weight)
assert r.weight == weight
assert approx_equal(r.delta_z(), -6)
assert approx_equal(r.residual(), 36)
assert approx_equal(r.gradients(), expected_gradients)
sites_cart = flex.vec3_double(((1,2,3),(2,5,4),(3,4,5)))
u_cart = flex.sym_mat3_double(((1,2,3,4,5,6),
(2,3,3,5,7,7),
(3,4,5,3,7,8)))
r = adp_restraints.rigid_bond(
adp_restraint_params(sites_cart=sites_cart, u_cart=u_cart),
proxy=p)
assert approx_equal(r.weight, weight)
unit_cell = uctbx.unit_cell([15,25,30,90,90,90])
sites_frac = unit_cell.fractionalize(sites_cart=sites_cart)
u_star = flex.sym_mat3_double([
adptbx.u_cart_as_u_star(unit_cell, u_cart_i)
for u_cart_i in u_cart])
pair = adp_restraints.rigid_bond_pair(sites_frac[1],
sites_frac[2],
u_star[1],
u_star[2],
unit_cell)
assert approx_equal(pair.delta_z(), abs(r.delta_z()))
assert approx_equal(pair.z_12(), r.z_12())
assert approx_equal(pair.z_21(), r.z_21())
#
gradients_aniso_cart = flex.sym_mat3_double(sites_cart.size(), (0,0,0,0,0,0))
gradients_iso = flex.double(sites_cart.size(), 0)
proxies = adp_restraints.shared_rigid_bond_proxy([p,p])
params = adp_restraint_params(sites_cart=sites_cart, u_cart=u_cart)
residuals = adp_restraints.rigid_bond_residuals(params, proxies=proxies)
assert approx_equal(residuals, (r.residual(),r.residual()))
deltas = adp_restraints.rigid_bond_deltas(params, proxies=proxies)
assert approx_equal(deltas, (r.delta_z(),r.delta_z()))
residual_sum = adp_restraints.rigid_bond_residual_sum(
params=params,
proxies=proxies,
gradients_aniso_cart=gradients_aniso_cart)
assert approx_equal(residual_sum, 2 * r.residual())
for g,e in zip(gradients_aniso_cart[1:3], r.gradients()):
assert approx_equal(g, matrix.col(e)*2)
fd_grads_aniso, fd_grads_iso = finite_difference_gradients(
restraint_type=adp_restraints.rigid_bond,
proxy=p,
sites_cart=sites_cart,
u_cart=u_cart)
for g,e in zip(gradients_aniso_cart, fd_grads_aniso):
assert approx_equal(g, matrix.col(e)*2)
#
# check frame invariance of residual
#
u_cart_1 = matrix.sym(sym_mat3=(0.1,0.2,0.05,0.03,0.02,0.01))
u_cart_2 = matrix.sym(sym_mat3=(0.21,0.32,0.11,0.02,0.02,0.07))
u_cart = (u_cart_1.as_sym_mat3(),u_cart_2.as_sym_mat3())
site_cart_1 = matrix.col((1,2,3))
site_cart_2 = matrix.col((3,1,4.2))
sites = (tuple(site_cart_1),tuple(site_cart_2))
a = adp_restraints.rigid_bond(sites=sites, u_cart=u_cart, weight=1)
expected_residual = a.residual()
gen = flex.mersenne_twister()
for i in range(20):
R = matrix.rec(gen.random_double_r3_rotation_matrix(),(3,3))
u_cart_1_rot = R * u_cart_1 * R.transpose()
u_cart_2_rot = R * u_cart_2 * R.transpose()
u_cart = (u_cart_1_rot.as_sym_mat3(),u_cart_2_rot.as_sym_mat3())
site_cart_1_rot = R * site_cart_1
site_cart_2_rot = R * site_cart_2
sites = (tuple(site_cart_1_rot),tuple(site_cart_2_rot))
a = adp_restraints.rigid_bond(
sites=sites, u_cart=u_cart,
weight=1)
assert approx_equal(a.residual(), expected_residual)
def exercise_rigid_bond():
i_seqs = (1,2)
weight = 1
p = adp_restraints.rigid_bond_proxy(i_seqs=i_seqs,weight=weight)
assert p.i_seqs == i_seqs
assert p.weight == weight
sites = ((1,2,3),(2,3,4))
u_cart = ((1,2,3,4,5,6), (3,4,5,6,7,8))
expected_gradients = ((-4, -4, -4, -8, -8, -8), (4, 4, 4, 8, 8, 8))
r = adp_restraints.rigid_bond(sites=sites, u_cart=u_cart, weight=weight)
assert r.weight == weight
assert approx_equal(r.delta_z(), -6)
assert approx_equal(r.residual(), 36)
assert approx_equal(r.gradients(), expected_gradients)
sites_cart = flex.vec3_double(((1,2,3),(2,5,4),(3,4,5)))
u_cart = flex.sym_mat3_double(((1,2,3,4,5,6),
(2,3,3,5,7,7),
(3,4,5,3,7,8)))
r = adp_restraints.rigid_bond(
adp_restraint_params(sites_cart=sites_cart, u_cart=u_cart),
proxy=p)
assert approx_equal(r.weight, weight)
unit_cell = uctbx.unit_cell([15,25,30,90,90,90])
sites_frac = unit_cell.fractionalize(sites_cart=sites_cart)
u_star = flex.sym_mat3_double([
adptbx.u_cart_as_u_star(unit_cell, u_cart_i)
for u_cart_i in u_cart])
pair = adp_restraints.rigid_bond_pair(sites_frac[1],
sites_frac[2],
u_star[1],
u_star[2],
unit_cell)
assert approx_equal(pair.delta_z(), abs(r.delta_z()))
assert approx_equal(pair.z_12(), r.z_12())
assert approx_equal(pair.z_21(), r.z_21())
#
gradients_aniso_cart = flex.sym_mat3_double(sites_cart.size(), (0,0,0,0,0,0))
gradients_iso = flex.double(sites_cart.size(), 0)
proxies = adp_restraints.shared_rigid_bond_proxy([p,p])
params = adp_restraint_params(sites_cart=sites_cart, u_cart=u_cart)
residuals = adp_restraints.rigid_bond_residuals(params, proxies=proxies)
assert approx_equal(residuals, (r.residual(),r.residual()))
deltas = adp_restraints.rigid_bond_deltas(params, proxies=proxies)
assert approx_equal(deltas, (r.delta_z(),r.delta_z()))
residual_sum = adp_restraints.rigid_bond_residual_sum(
params=params,
proxies=proxies,
gradients_aniso_cart=gradients_aniso_cart)
assert approx_equal(residual_sum, 2 * r.residual())
for g,e in zip(gradients_aniso_cart[1:3], r.gradients()):
assert approx_equal(g, matrix.col(e)*2)
fd_grads_aniso, fd_grads_iso = finite_difference_gradients(
restraint_type=adp_restraints.rigid_bond,
proxy=p,
sites_cart=sites_cart,
u_cart=u_cart)
for g,e in zip(gradients_aniso_cart, fd_grads_aniso):
assert approx_equal(g, matrix.col(e)*2)
#
# check frame invariance of residual
#
u_cart_1 = matrix.sym(sym_mat3=(0.1,0.2,0.05,0.03,0.02,0.01))
u_cart_2 = matrix.sym(sym_mat3=(0.21,0.32,0.11,0.02,0.02,0.07))
u_cart = (u_cart_1.as_sym_mat3(),u_cart_2.as_sym_mat3())
site_cart_1 = matrix.col((1,2,3))
site_cart_2 = matrix.col((3,1,4.2))
sites = (tuple(site_cart_1),tuple(site_cart_2))
a = adp_restraints.rigid_bond(sites=sites, u_cart=u_cart, weight=1)
expected_residual = a.residual()
gen = flex.mersenne_twister()
for i in range(20):
R = matrix.rec(gen.random_double_r3_rotation_matrix(),(3,3))
u_cart_1_rot = R * u_cart_1 * R.transpose()
u_cart_2_rot = R * u_cart_2 * R.transpose()
u_cart = (u_cart_1_rot.as_sym_mat3(),u_cart_2_rot.as_sym_mat3())
site_cart_1_rot = R * site_cart_1
site_cart_2_rot = R * site_cart_2
sites = (tuple(site_cart_1_rot),tuple(site_cart_2_rot))
a = adp_restraints.rigid_bond(
sites=sites, u_cart=u_cart,
weight=1)
assert approx_equal(a.residual(), expected_residual)
