def get_coefficients_alg3(rh, a0, a1, a2, a3, idealize, sites_cart):
r0 = matrix.col(sites_cart[a0.iseq])
r1 = matrix.col(sites_cart[a1.iseq])
r2 = matrix.col(sites_cart[a2.iseq])
r3 = matrix.col(sites_cart[a3.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
u30 = (r3 - r0).normalize()
if idealize:
alpha0 = math.radians(a1.angle_ideal)
alpha1 = math.radians(a2.angle_ideal)
alpha2 = math.radians(a3.angle_ideal)
c1, c2, c3 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
omega0 = math.radians(a0.angle_ideal[0])
omega1 = math.radians(a0.angle_ideal[1])
omega2 = math.radians(a0.angle_ideal[2])
w12, w23, w13 = math.cos(omega0), math.cos(omega1), math.cos(omega2)
else:
c1 = (uh0).dot(u10)
c2 = (uh0).dot(u20)
c3 = (uh0).dot(u30)
w12 = (u10).dot(u20)
w23 = (u20).dot(u30)
w13 = (u10).dot(u30)
matrix_d = matrix.sqr([
1, w12, w13,
w12, 1, w23,
w13, w23, 1 ])
#
matrix_x = matrix.sqr([
c1, w12, w13,
c2, 1, w23,
c3, w23, 1 ])
#
matrix_y = matrix.sqr([
1, c1, w13,
w12, c2, w23,
w13, c3, 1 ])
#
matrix_z = matrix.sqr([
1, w12, c1,
w12, 1, c2,
w13, w23, c3 ])
if(matrix_d.determinant()==0):
raise RuntimeError(
"Denominator zero: matrix_d in get_h_parameterization.")
a = matrix_x.determinant()/matrix_d.determinant()
b = matrix_y.determinant()/matrix_d.determinant()
c = matrix_z.determinant()/matrix_d.determinant()
return a, b, c
def get_coefficients_alg3(self, ih):
neighbors = self.h_connectivity[ih]
i_a0 = neighbors.a0['iseq']
i_a1 = neighbors.a1['iseq']
i_a2 = neighbors.a2['iseq']
i_a3 = neighbors.a3['iseq']
rh = matrix.col(self.sites_cart[ih])
r0 = matrix.col(self.sites_cart[i_a0])
r1 = matrix.col(self.sites_cart[i_a1])
r2 = matrix.col(self.sites_cart[i_a2])
r3 = matrix.col(self.sites_cart[i_a3])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
u30 = (r3 - r0).normalize()
if self.use_ideal_bonds_angles:
alpha0 = math.radians(neighbors.a1['angle_ideal'])
alpha1 = math.radians(neighbors.a2['angle_ideal'])
alpha2 = math.radians(neighbors.a3['angle_ideal'])
c1, c2, c3 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
omega0 = math.radians(neighbors.a0['angle_a1a0a2'])
omega1 = math.radians(neighbors.a0['angle_a2a0a3'])
omega2 = math.radians(neighbors.a0['angle_a3a0a1'])
w12, w23, w13 = math.cos(omega0), math.cos(omega1), math.cos(
omega2)
else:
c1 = (uh0).dot(u10)
c2 = (uh0).dot(u20)
c3 = (uh0).dot(u30)
w12 = (u10).dot(u20)
w23 = (u20).dot(u30)
w13 = (u10).dot(u30)
matrix_d = matrix.sqr([1, w12, w13, w12, 1, w23, w13, w23, 1])
#
matrix_x = matrix.sqr([c1, w12, w13, c2, 1, w23, c3, w23, 1])
#
matrix_y = matrix.sqr([1, c1, w13, w12, c2, w23, w13, c3, 1])
#
matrix_z = matrix.sqr([1, w12, c1, w12, 1, c2, w13, w23, c3])
if (matrix_d.determinant() == 0):
raise RuntimeError(
"Denominator zero: matrix_d in get_h_parameterization.")
a = matrix_x.determinant() / matrix_d.determinant()
b = matrix_y.determinant() / matrix_d.determinant()
c = matrix_z.determinant() / matrix_d.determinant()
return a, b, c
def get_coefficients_alg3(rh, a0, a1, a2, a3, use_ideal_bonds_angles,
sites_cart):
r0 = matrix.col(sites_cart[a0.iseq])
r1 = matrix.col(sites_cart[a1.iseq])
r2 = matrix.col(sites_cart[a2.iseq])
r3 = matrix.col(sites_cart[a3.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
u30 = (r3 - r0).normalize()
if use_ideal_bonds_angles:
alpha0 = math.radians(a1.angle_ideal)
alpha1 = math.radians(a2.angle_ideal)
alpha2 = math.radians(a3.angle_ideal)
c1, c2, c3 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
omega0 = math.radians(a0.angle_ideal[0])
omega1 = math.radians(a0.angle_ideal[1])
omega2 = math.radians(a0.angle_ideal[2])
w12, w23, w13 = math.cos(omega0), math.cos(omega1), math.cos(omega2)
else:
c1 = (uh0).dot(u10)
c2 = (uh0).dot(u20)
c3 = (uh0).dot(u30)
w12 = (u10).dot(u20)
w23 = (u20).dot(u30)
w13 = (u10).dot(u30)
matrix_d = matrix.sqr([1, w12, w13, w12, 1, w23, w13, w23, 1])
#
matrix_x = matrix.sqr([c1, w12, w13, c2, 1, w23, c3, w23, 1])
#
matrix_y = matrix.sqr([1, c1, w13, w12, c2, w23, w13, c3, 1])
#
matrix_z = matrix.sqr([1, w12, c1, w12, 1, c2, w13, w23, c3])
if (matrix_d.determinant() == 0):
raise RuntimeError(
"Denominator zero: matrix_d in get_h_parameterization.")
a = matrix_x.determinant() / matrix_d.determinant()
b = matrix_y.determinant() / matrix_d.determinant()
c = matrix_z.determinant() / matrix_d.determinant()
return a, b, c
def process_1_neighbor(self, neighbors):
ih = neighbors.ih
i_a0 = neighbors.a0['iseq']
rh = matrix.col(self.sites_cart[ih])
r0 = matrix.col(self.sites_cart[i_a0])
if self.use_ideal_bonds_angles:
disth = neighbors.a0['dist_ideal']
else:
disth = (r0 - rh).length()
i_a1 = neighbors.a1['iseq']
i_b1 = neighbors.b1['iseq']
r1 = matrix.col(self.sites_cart[i_a1])
rb1 = matrix.col(self.sites_cart[i_b1])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
dihedral = dihedral_angle(sites=[
self.sites_cart[ih], self.sites_cart[i_a0], self.sites_cart[i_a1],
self.sites_cart[i_b1]
])
if self.use_ideal_bonds_angles:
alpha = math.radians(neighbors.a1['angle_ideal'])
#allow for rotation even for idealize = True
#phi = math.radians(b1.dihedral_ideal)
phi = dihedral
else:
alpha = (u10).angle(uh0)
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u1)) * u1).normalize()
u3 = u1.cross(u2)
if (neighbors.number_h_neighbors == 0):
self.h_parameterization[ih] = riding_coefficients(htype='alg1b',
ih=ih,
a0=i_a0,
a1=i_a1,
a2=i_b1,
a3=0,
a=alpha,
b=phi,
h=0,
n=0,
disth=disth)
if (neighbors.number_h_neighbors == 2):
i_h1, i_h2 = neighbors.h1['iseq'], neighbors.h2['iseq']
i_h1, i_h2 = self.check_propeller_order(i_a0=i_a0,
i_a1=i_a1,
ih=ih,
i_h1=i_h1,
i_h2=i_h2)
for nprop, hprop in zip([0, 1, 2], [ih, i_h1, i_h2]):
self.h_parameterization[hprop] = riding_coefficients(
htype='prop',
ih=hprop,
a0=i_a0,
a1=i_a1,
a2=i_b1,
a3=0,
a=alpha,
n=nprop,
b=phi,
h=0,
disth=disth)
def get_coefficients(self, ih):
neighbors = self.h_connectivity[ih]
if (neighbors.number_h_neighbors == 1):
i_h1 = neighbors.h1['iseq']
else:
i_h1 = None
i_a0 = neighbors.a0['iseq']
i_a1 = neighbors.a1['iseq']
i_a2 = neighbors.a2['iseq']
rh = matrix.col(self.sites_cart[ih])
r0 = matrix.col(self.sites_cart[i_a0])
r1 = matrix.col(self.sites_cart[i_a1])
r2 = matrix.col(self.sites_cart[i_a2])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
if self.use_ideal_bonds_angles:
alpha0 = math.radians(neighbors.a0['angle_a1a0a2'])
alpha1 = math.radians(neighbors.a1['angle_ideal'])
alpha2 = math.radians(neighbors.a2['angle_ideal'])
c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
else:
alpha0 = (u10).angle(u20)
alpha0 = math.acos(u10.dot(u20))
alpha1 = (u10).angle(uh0)
alpha2 = (uh0).angle(u20)
c0 = (u10).dot(u20)
c1 = (u10).dot(uh0)
c2 = (uh0).dot(u20)
sumang = alpha0 + alpha1 + alpha2
denom = (1.0 - c0**2)
if (denom == 0):
raise RuntimeError(
"Denominator zero: (1-c0*c0) in get_h_parameterization.")
a = (c1 - c0 * c2) / (1 - c0 * c0)
b = (c2 - c0 * c1) / (1 - c0 * c0)
root = None
# # check if H, A0, A1, A2 are in a plane
if (sumang < (2 * math.pi + 0.05) and (sumang > 2 * math.pi - 0.05)):
h = None
elif (sumang > (2 * math.pi + 0.05)
and 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2 < 0):
root = 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2
h = None
return sumang, a, b, h, root
else:
# two tetragonal geometry: e.g. CH2 group
if (i_h1 is not None):
rh2 = matrix.col(self.sites_cart[neighbors.h1['iseq']])
uh02 = (rh2 - r0).normalize()
if self.use_ideal_bonds_angles:
h = math.radians(neighbors.h1['angle_ideal']) * 0.5
else:
h = (uh0).angle(uh02) * 0.5
#test if vector v points to same 'side' as uh0
if ((u10.cross(u20)).dot(uh0) < 0):
h = -h
else:
# if H is out of plane, but not in tetrahedral geometry
root = 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2
if (root < 0):
raise RuntimeError(
"Expression in square root < 0 in get_h_parameterization."
)
denom = math.sin(alpha0)
if (denom == 0):
raise RuntimeError(
"Denominator zero: sin(alpha0)in get_h_parameterization."
)
cz = (math.sqrt(1 - c1 * c1 - c2 * c2 - c0 * c0 +
2 * c0 * c1 * c2)) / math.sin(alpha0)
h = cz
#test if vector v points to same 'side' as uh0
if ((u10.cross(u20)).dot(uh0) < 0):
h = -h
return sumang, a, b, h, root
def process_1_neighbor_type_arg(self, neighbors):
ih = neighbors.ih
i_h1 = neighbors.h1['iseq']
i_a0 = neighbors.a0['iseq']
rh = matrix.col(self.sites_cart[ih])
r0 = matrix.col(self.sites_cart[i_a0])
if self.use_ideal_bonds_angles:
disth = neighbors.a0['dist_ideal']
else:
disth = (r0 - rh).length()
i_a1 = neighbors.a1['iseq']
r1 = matrix.col(self.sites_cart[i_a1])
if ('dihedral_ideal' in neighbors.b1):
ih_dihedral = ih
ih_no_dihedral = i_h1
else:
if ('dihedral_ideal' in self.h_connectivity[i_h1].b1):
ih_dihedral = i_h1
ih_no_dihedral = ih
else:
self.unk_list.append(ih)
return
i_b1 = self.h_connectivity[ih_dihedral].b1['iseq']
rb1 = matrix.col(self.sites_cart[i_b1])
# check if angle is typical for propeller
# catches case of missing propeller atom
if (neighbors.h1['angle_ideal'] > 107
and neighbors.h1['angle_ideal'] < 111):
self.unk_list.append(ih)
else:
dihedral = dihedral_angle(sites=[
self.sites_cart[i_b1], self.sites_cart[i_a1],
self.sites_cart[i_a0], self.sites_cart[ih_dihedral]
])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
if self.use_ideal_bonds_angles:
alpha = math.radians(neighbors.a1['angle_ideal'])
phi = math.radians(
self.h_connectivity[ih_dihedral].b1['dihedral_ideal'])
else:
alpha = (u10).angle(uh0)
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u10)) * u10).normalize()
u3 = u1.cross(u2)
for ih_alg1a, phi_alg1a in zip([ih_dihedral, ih_no_dihedral],
[phi, phi + math.pi]):
if self.h_parameterization[ih_alg1a] is None:
self.h_parameterization[ih_alg1a] = riding_coefficients(
htype='alg1a',
ih=ih_alg1a,
a0=i_a0,
a1=i_a1,
a2=i_b1,
a3=0,
a=alpha,
b=phi_alg1a,
n=0,
h=0,
disth=disth)
def get_h_parameterization(
connectivity, sites_cart, idealize):
#connectivity, xray_structure, names, atoms_list, idealize):
#sites_cart = xray_structure.sites_cart()
h_parameterization = {}
for ih in connectivity.keys():
a0 = connectivity[ih][0]
count_H, reduced_neighbs = a0.count_H, a0.reduced_neighbs
n_red_neigbs = len(reduced_neighbs)
rh = matrix.col(sites_cart[ih])
r0 = matrix.col(sites_cart[a0.iseq])
if idealize:
dist_h = a0.dist_ideal
else:
dist_h = (r0 - rh).length()
# case 2a and 2b, case 3
if(n_red_neigbs == 2 or
(n_red_neigbs == 3 and count_H == 0)):
a1, a2 = reduced_neighbs[0], reduced_neighbs[1]
r1 = matrix.col(sites_cart[a1.iseq])
r2 = matrix.col(sites_cart[a2.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
if idealize:
alpha0 = math.radians(a0.angle_ideal)
alpha1 = math.radians(a1.angle_ideal)
alpha2 = math.radians(a2.angle_ideal)
c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
else:
alpha0 = (u10).angle(u20)
alpha1 = (u10).angle(uh0)
alpha2 = (uh0).angle(u20)
c0 = (u10).dot(u20)
c1 = (u10).dot(uh0)
c2 = (uh0).dot(u20)
#sumang = math.degrees(alpha0) + math.degrees(alpha1) + math.degrees(alpha2)
#c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
sumang = alpha0 + alpha1 + alpha2
denom = (1.0-c0**2)
if(denom==0):
raise RuntimeError(
"Denominator zero: (1-c0*c0) in get_h_parameterization.")
a, b = (c1-c0*c2)/(1-c0*c0), (c2-c0*c1)/(1-c0*c0)
h_parameterization[ih] = parameterization_info(
a0 = a0.iseq,
a1 = a1.iseq,
a2 = a2.iseq,
a = a,
b = b,
dist_h = dist_h)
#if ((sumang < 361 and sumang > 359) and idealize == True ):
#if (0):
#if (sumang < 361 and sumang > 359):
if (sumang < (2*math.pi + 0.01) and (sumang > 2*math.pi - 0.01)):
h_parameterization[ih].htype = 'flat_2neigbs'
else:
root = 1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2
if(root < 0):
raise RuntimeError(
"Expression in square root < 0 in get_h_parameterization.")
denom = math.sin(alpha0)
if(denom==0):
raise RuntimeError(
"Denominator zero: sin(alpha0)in get_h_parameterization.")
cz = (math.sqrt(1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2))/math.sin(alpha0)
h = cz/math.sin(alpha0)
#test if vector v points to same 'side' as uh0
if((u10.cross(u20)).dot(uh0) < 0):
h = -h
h_parameterization[ih].h = h
if (n_red_neigbs == 2): # case 2b
h_parameterization[ih].htype = '2neigbs'
elif (n_red_neigbs == 3): # case 3
h_parameterization[ih].htype = '3neigbs'
# case 1a
elif(n_red_neigbs == 1 and count_H == 1):
neigbs_14 = connectivity[ih][2]
a1 = reduced_neighbs[0]
b1, b2 = neigbs_14[0], neigbs_14[1]
r1 = matrix.col(sites_cart[a1.iseq])
rb1 = matrix.col(sites_cart[b1.iseq])
rb2 = matrix.col(sites_cart[b2.iseq])
# chose 1-4 neighbor which is closer - important!
if((rh-rb2).length() < (rh-rb1).length()):
neigbs_14[0], neigbs_14[1] = neigbs_14[1], neigbs_14[0]
rb1 = matrix.col(sites_cart[neigbs_14[0].iseq])
r2 = r0 + (r1 - rb1).normalize()
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
alpha0 = (u10).angle(u20)
alpha1 = (u10).angle(uh0)
alpha2 = (uh0).angle(u20)
c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
denom = (1-c0*c0)
if(denom==0):
raise RuntimeError(
"Denominator zero: (1-c0*c0) in get_h_parameterization.")
a, b = (c1-c0*c2)/(1-c0*c0), (c2-c0*c1)/(1-c0*c0)
root = 1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2
if(root < 0):
raise RuntimeError(
"Expression in square root < 0 in get_h_parameterization.")
denom = math.sin(alpha0)
if(denom==0):
raise RuntimeError(
"Denominator zero: sin(alpha0)in get_h_parameterization.")
cz = (math.sqrt(1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2))/math.sin(alpha0)
h = cz/math.sin(alpha0)
# test if vector v points to same 'side' as uh0
if((u10.cross(u20)).dot(uh0) < 0):
h = -h
h_parameterization[ih] = parameterization_info(
htype = 'alg1a',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = neigbs_14[0].iseq,
a = a,
b = b,
h = h,
dist_h = dist_h)
# case 1b
elif(n_red_neigbs == 1 and (count_H == 0 or count_H ==2)):
a1 = reduced_neighbs[0]
a, b = 1, 1
sec_neigbs = connectivity[ih][2]
b1 = sec_neigbs[0]
r1 = matrix.col(sites_cart[a1.iseq])
rb1 = matrix.col(sites_cart[b1.iseq])
#dh = a0.dist_ideal
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
if idealize:
alpha = math.radians(a1.angle_ideal)
else:
alpha = (u10).angle(uh0)
rb10 = rb1 - r1
v10 = (rb10 - ((rb10).dot(u10)) * u10).normalize()
if(v10.dot(uh0) < 0):
v10 = -v10
a = -1
#if(abs((u10.cross(v10)).dot(uh0)) < 0.001):
# h_parameterization[ih] = parameterization_info(
# htype = 'alg1b_flat',
# a0 = a0.iseq,
# a1 = a1.iseq,
# a2 = b1.iseq,
# a = a,
# alpha = alpha,
# dist_h = dist_h)
#else:
# w10 = (u10.cross(v10)).normalize()
# if(w10.dot(uh0) < 0):
# w10 = -w10
# b = -1
# chi = math.asin((uh0).dot(w10))
# c_chi, s_chi = math.cos(abs(chi)), math.sin(abs(chi))
# rp = rh - dh * s_chi * w10
# rp0 = rp - r0
# eps = (rp0).angle(u10)
# h_parameterization[ih] = parameterization_info(
# htype = 'alg1b',
# a0 = a0.iseq,
# a1 = a1.iseq,
# a2 = b1.iseq,
# a = a,
# b = b,
# chi = chi,
# eps = eps,
# alpha = alpha,
# dist_h = dist_h)
w10 = (u10.cross(v10)).normalize()
if(w10.dot(uh0) < 0):
w10 = -w10
b = -1
chi = math.asin((uh0).dot(w10))
c_chi, s_chi = math.cos(abs(chi)), math.sin(abs(chi))
rp = rh - dist_h * s_chi * w10
rp0 = rp - r0
eps = (rp0).angle(u10)
h_parameterization[ih] = parameterization_info(
htype = 'alg1b',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
a = a,
b = b,
chi = chi,
eps = eps,
alpha = alpha,
dist_h = dist_h)
else:
h_parameterization[ih] = parameterization_info(
htype = 'unk',
a0 = a0.iseq,
a1 = a1.iseq)
return h_parameterization
def get_coefficients(ih, a0, a1, a2, ih2, idealize, sites_cart, typeh):
rh = matrix.col(sites_cart[ih])
r0 = matrix.col(sites_cart[a0.iseq])
r1 = matrix.col(sites_cart[a1.iseq])
r2 = matrix.col(sites_cart[a2.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
if idealize:
alpha0 = math.radians(a0.angle_ideal)
alpha1 = math.radians(a1.angle_ideal)
alpha2 = math.radians(a2.angle_ideal)
c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
else:
alpha0 = (u10).angle(u20)
alpha1 = (u10).angle(uh0)
alpha2 = (uh0).angle(u20)
c0 = (u10).dot(u20)
c1 = (u10).dot(uh0)
c2 = (uh0).dot(u20)
sumang = alpha0 + alpha1 + alpha2
denom = (1.0-c0**2)
if(denom==0):
raise RuntimeError(
"Denominator zero: (1-c0*c0) in get_h_parameterization.")
a = (c1-c0*c2)/(1-c0*c0)
b = (c2-c0*c1)/(1-c0*c0)
root = None
# check if H, A0, A1, A2 are in a plane
if (sumang < (2*math.pi + 0.05) and (sumang > 2*math.pi - 0.05)):
h = None
elif (sumang > (2*math.pi + 0.05) and 1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2 < 0):
root = 1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2
h = None
return sumang, a, b, h, root
else:
# two tetragonal geometry: e.g. CH2 group
if (ih2 is not None):
rh2 = matrix.col(sites_cart[ih2.iseq])
uh02 = (rh2 - r0).normalize()
if idealize:
h = math.radians(ih2.angle_ideal) * 0.5
else:
h = (uh0).angle(uh02) * 0.5
#test if vector v points to same 'side' as uh0
if((u10.cross(u20)).dot(uh0) < 0):
h = -h
else:
# if H is out of plane, but not in tetrahedral geometry
root = 1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2
if(root < 0):
raise RuntimeError(
"Expression in square root < 0 in get_h_parameterization.")
denom = math.sin(alpha0)
if(denom==0):
raise RuntimeError(
"Denominator zero: sin(alpha0)in get_h_parameterization.")
cz = (math.sqrt(1-c1*c1-c2*c2-c0*c0+2*c0*c1*c2))/math.sin(alpha0)
h = cz
#test if vector v points to same 'side' as uh0
if((u10.cross(u20)).dot(uh0) < 0):
h = -h
return sumang, a, b, h, root
def get_h_parameterization(connectivity, sites_cart, idealize):
h_parameterization = {}
for ih in connectivity.keys():
#for debugging
#print 'atom:', names[ih]+' ('+str(ih)+ ') residue:', \
# atoms_list[ih].resseq, 'chain', atoms_list[ih].chain_id
# if entry exists already, skip it
if ih in h_parameterization:
continue
a0 = connectivity[ih][0]
count_H = a0.count_H
reduced_neighbs = connectivity[ih][1]
n_red_neigbs = len(reduced_neighbs)
rh = matrix.col(sites_cart[ih])
r0 = matrix.col(sites_cart[a0.iseq])
if idealize:
dist_h = a0.dist_ideal
else:
dist_h = (r0 - rh).length()
# alg2a, 2tetra, 2neigbs
if(n_red_neigbs == 2):
a1, a2 = reduced_neighbs[0], reduced_neighbs[1]
# if H is second neighbor, gets its index
if (count_H == 1):
hlist = connectivity[ih][2]
if hlist:
ih2 = (hlist[0])
i_h2 = (hlist[0]).iseq
else:
ih2 = None
sumang, a, b, h, root = get_coefficients(
ih = ih,
a0 = a0,
a1 = a1,
a2 = a2,
ih2 = ih2,
idealize = idealize,
sites_cart = sites_cart,
typeh = 'alg2')
h_parameterization[ih] = parameterization_info(
a0 = a0.iseq,
a1 = a1.iseq,
a2 = a2.iseq,
a = a,
b = b,
dist_h = dist_h)
# alg2a
if (sumang > (2*math.pi + 0.05) and root < 0):
h_parameterization[ih].htype = 'unk_ideal'
elif (sumang < (2*math.pi + 0.05) and (sumang > 2*math.pi - 0.05)):
h_parameterization[ih].htype = 'flat_2neigbs'
else:
if (count_H == 1):
# 2 tetragonal geometry
h_parameterization[ih].htype = '2tetra'
h_parameterization[ih].alpha = h
h_parameterization[i_h2] = parameterization_info(
a0 = a0.iseq,
a1 = a1.iseq,
a2 = a2.iseq,
a = a,
b = b,
alpha = -h,
dist_h = dist_h,
htype = '2tetra')
else:
# 2neigbs
h_parameterization[ih].h = h
h_parameterization[ih].htype = '2neigbs'
# tetragonal geometry: 3neigbs
elif (n_red_neigbs == 3 and count_H == 0):
a1, a2, a3 = reduced_neighbs[0], reduced_neighbs[1], reduced_neighbs[2]
a, b, h = get_coefficients_alg3(
rh = rh,
a0 = a0,
a1 = a1,
a2 = a2,
a3 = a3,
idealize = idealize,
sites_cart = sites_cart)
h_parameterization[ih] = parameterization_info(
a0 = a0.iseq,
a1 = a1.iseq,
a2 = a2.iseq,
a3 = a3.iseq,
a = a,
b = b,
h = h,
dist_h = dist_h,
htype = '3neigbs')
# alg1a: X-H2 planar groups, such as in ARG, ASN, GLN
# requires that dihedral angle restraint exists
elif(n_red_neigbs == 1 and count_H == 1 and len(connectivity[ih])==4):
a1 = reduced_neighbs[0]
r1 = matrix.col(sites_cart[a1.iseq])
hlist = connectivity[ih][2]
ih_2 = hlist[0].iseq
#if(len(connectivity[ih])!=4):
# continue
b1 = (connectivity[ih][3])[0]
if (b1.dihedral_ideal == None):
continue
#iseq_b1 = b1.iseq
dihedral = dihedral_angle(
sites=[sites_cart[b1.iseq], sites_cart[a1.iseq],
sites_cart[a0.iseq],sites_cart[ih]])
#print 'dihedrals', a0.dihedral, dihedral, a0.dihedral_ideal
rb1 = matrix.col(sites_cart[b1.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
if idealize:
alpha = math.radians(a1.angle_ideal)
phi = math.radians(b1.dihedral_ideal)
#phi = dihedral
else:
alpha = (u10).angle(uh0)
#phi = a0.dihedral
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u10)) * u10).normalize()
u3 = u1.cross(u2)
h_parameterization[ih] = parameterization_info(
htype = 'alg1a',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
phi = phi,
n = 0,
alpha = alpha,
dist_h = dist_h)
h_parameterization[ih_2] = parameterization_info(
htype = 'alg1a',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
phi = phi+math.pi,
n = 0,
alpha = alpha,
dist_h = dist_h)
# case 1b
# a0.dihedral = dihedral angle between angle ideal and actual position
elif(n_red_neigbs == 1 and (count_H == 0 or count_H ==2)):
#if(count_H == 0 and len(connectivity[ih])!=4):
# print 'the culprit is ', ih, names[ih], atoms_list[ih].resseq
if (len(connectivity[ih])!=4):
continue
a1 = reduced_neighbs[0]
b1 = (connectivity[ih][3])[0]
r1 = matrix.col(sites_cart[a1.iseq])
rb1 = matrix.col(sites_cart[b1.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
dihedral = dihedral_angle(
sites=[sites_cart[ih], sites_cart[a0.iseq],
sites_cart[a1.iseq],sites_cart[b1.iseq]])
if idealize:
alpha = math.radians(a1.angle_ideal)
#phi = math.radians(b1.dihedral_ideal)
#allow for rotation even for idealize = True
phi = dihedral
else:
alpha = (u10).angle(uh0)
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u1)) * u1).normalize()
u3 = u1.cross(u2)
h_parameterization[ih] = parameterization_info(
htype = 'alg1b',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
phi = phi,
n = 0,
alpha = alpha,
dist_h = dist_h)
if (count_H == 2):
h_parameterization[ih].htype = 'prop'
hlist = connectivity[ih][2]
# TO DO: Can the order be reversed? To be kept in mind!!
ih_2, ih_3 = hlist[0].iseq, hlist[1].iseq
h_parameterization[ih_2] = parameterization_info(
htype = 'prop',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
phi = phi,
n = 1,
alpha = alpha,
dist_h = dist_h)
ih_2_coord = generate_H_positions(
sites_cart = sites_cart,
ih = ih_2,
para_info = h_parameterization[ih_2]).rH_gen
h_parameterization[ih_3] = parameterization_info(
htype = 'prop',
a0 = a0.iseq,
a1 = a1.iseq,
a2 = b1.iseq,
phi = phi,
n = 2,
alpha = alpha,
dist_h = dist_h)
if ((ih_2_coord - matrix.col(sites_cart[ih_3])).length() <
(ih_2_coord - matrix.col(sites_cart[ih_2])).length() ):
h_parameterization[ih_2].n = 2
h_parameterization[ih_3].n = 1
else:
a1 = reduced_neighbs[0]
h_parameterization[ih] = parameterization_info(
htype = 'unk',
a0 = a0.iseq,
a1 = a1.iseq)
return h_parameterization
def get_coefficients(ih, a0, a1, a2, ih2, use_ideal_bonds_angles, sites_cart,
typeh):
rh = matrix.col(sites_cart[ih])
r0 = matrix.col(sites_cart[a0.iseq])
r1 = matrix.col(sites_cart[a1.iseq])
r2 = matrix.col(sites_cart[a2.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
if use_ideal_bonds_angles:
alpha0 = math.radians(a0.angle_ideal[0])
alpha1 = math.radians(a1.angle_ideal)
alpha2 = math.radians(a2.angle_ideal)
c0, c1, c2 = math.cos(alpha0), math.cos(alpha1), math.cos(alpha2)
else:
alpha0 = (u10).angle(u20)
alpha0 = math.acos(u10.dot(u20))
alpha1 = (u10).angle(uh0)
alpha2 = (uh0).angle(u20)
c0 = (u10).dot(u20)
c1 = (u10).dot(uh0)
c2 = (uh0).dot(u20)
sumang = alpha0 + alpha1 + alpha2
denom = (1.0 - c0**2)
if (denom == 0):
raise RuntimeError(
"Denominator zero: (1-c0*c0) in get_h_parameterization.")
a = (c1 - c0 * c2) / (1 - c0 * c0)
b = (c2 - c0 * c1) / (1 - c0 * c0)
root = None
# check if H, A0, A1, A2 are in a plane
if (sumang < (2 * math.pi + 0.05) and (sumang > 2 * math.pi - 0.05)):
h = None
elif (sumang > (2 * math.pi + 0.05)
and 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2 < 0):
root = 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2
h = None
return sumang, a, b, h, root
else:
# two tetragonal geometry: e.g. CH2 group
if (ih2 is not None):
rh2 = matrix.col(sites_cart[ih2.iseq])
uh02 = (rh2 - r0).normalize()
if use_ideal_bonds_angles:
h = math.radians(ih2.angle_ideal) * 0.5
else:
h = (uh0).angle(uh02) * 0.5
#test if vector v points to same 'side' as uh0
if ((u10.cross(u20)).dot(uh0) < 0):
h = -h
else:
# if H is out of plane, but not in tetrahedral geometry
root = 1 - c1 * c1 - c2 * c2 - c0 * c0 + 2 * c0 * c1 * c2
if (root < 0):
raise RuntimeError(
"Expression in square root < 0 in get_h_parameterization.")
denom = math.sin(alpha0)
if (denom == 0):
raise RuntimeError(
"Denominator zero: sin(alpha0)in get_h_parameterization.")
cz = (math.sqrt(1 - c1 * c1 - c2 * c2 - c0 * c0 +
2 * c0 * c1 * c2)) / math.sin(alpha0)
h = cz
#test if vector v points to same 'side' as uh0
if ((u10.cross(u20)).dot(uh0) < 0):
h = -h
return sumang, a, b, h, root
def get_h_parameterization(h_connectivity, sites_cart, use_ideal_bonds_angles):
h_parameterization = {}
n_atoms = len(sites_cart)
for ih in h_connectivity.keys():
#if (ih != 22):
# continue
#for debugging
#print 'atom:', names[ih]+' ('+str(ih)+ ') residue:', \
# atoms_list[ih].resseq, 'chain', atoms_list[ih].chain_id
# if entry exists already, skip it
if ih in h_parameterization.keys():
continue
a0 = h_connectivity[ih][0]
count_H = a0.count_H
reduced_neighbs = h_connectivity[ih][1]
n_red_neigbs = len(reduced_neighbs)
rh = matrix.col(sites_cart[ih])
r0 = matrix.col(sites_cart[a0.iseq])
if use_ideal_bonds_angles:
dist_h = a0.dist_ideal
else:
dist_h = (r0 - rh).length()
# alg2a, 2tetra, 2neigbs
if (n_red_neigbs == 2):
a1, a2 = reduced_neighbs[0], reduced_neighbs[1]
# if H is second neighbor, gets its index
if (count_H == 1):
hlist = h_connectivity[ih][2]
if hlist:
ih2 = (hlist[0])
i_h2 = (hlist[0]).iseq
else:
ih2 = None
sumang, a, b, h, root = get_coefficients(
ih=ih,
a0=a0,
a1=a1,
a2=a2,
ih2=ih2,
use_ideal_bonds_angles=use_ideal_bonds_angles,
sites_cart=sites_cart,
typeh='alg2')
h_parameterization[ih] = parameterization_info(a0=a0.iseq,
a1=a1.iseq,
a2=a2.iseq,
a=a,
b=b,
dist_h=dist_h)
# alg2a
if (sumang > (2 * math.pi + 0.05) and root < 0):
h_parameterization[ih].htype = 'unk_ideal'
elif (sumang < (2 * math.pi + 0.05)
and (sumang > 2 * math.pi - 0.05)):
h_parameterization[ih].htype = 'flat_2neigbs'
else:
if (count_H == 1):
# 2 tetragonal geometry
h_parameterization[ih].htype = '2tetra'
h_parameterization[ih].alpha = h
h_parameterization[i_h2] = parameterization_info(
a0=a0.iseq,
a1=a1.iseq,
a2=a2.iseq,
a=a,
b=b,
alpha=-h,
dist_h=dist_h,
htype='2tetra')
else:
# 2neigbs
h_parameterization[ih].h = h
h_parameterization[ih].htype = '2neigbs'
# tetragonal geometry: 3neigbs
elif (n_red_neigbs == 3 and count_H == 0):
a1, a2, a3 = reduced_neighbs[0], reduced_neighbs[
1], reduced_neighbs[2]
a, b, h = get_coefficients_alg3(
rh=rh,
a0=a0,
a1=a1,
a2=a2,
a3=a3,
use_ideal_bonds_angles=use_ideal_bonds_angles,
sites_cart=sites_cart)
h_parameterization[ih] = parameterization_info(a0=a0.iseq,
a1=a1.iseq,
a2=a2.iseq,
a3=a3.iseq,
a=a,
b=b,
h=h,
dist_h=dist_h,
htype='3neigbs')
# alg1a: X-H2 planar groups, such as in ARG, ASN, GLN
# requires that dihedral angle restraint exists for at least one H atom
elif (n_red_neigbs == 1 and count_H == 1
and len(h_connectivity[ih]) == 4):
b1 = None
a1 = reduced_neighbs[0]
r1 = matrix.col(sites_cart[a1.iseq])
hlist = h_connectivity[ih][2]
ih_2 = hlist[0].iseq
for b1_test in h_connectivity[ih][3]:
if (b1_test.dihedral_ideal is None):
continue
else:
b1 = b1_test
if (b1 == None):
for b1_test in h_connectivity[ih_2][3]:
if (b1_test.dihedral_ideal is None):
continue
else:
b1 = b1_test
ih, ih_2 = ih_2, ih
if (b1 == None):
h_parameterization[ih] = parameterization_info(htype='unk',
a0=a0.iseq)
continue
# check if angle is typical for propeller
# catches case of missing propeller atom
if (hlist[0].angle_ideal > 107 and hlist[0].angle_ideal < 111):
h_parameterization[ih] = parameterization_info(htype='unk',
a0=a0.iseq)
h_parameterization[ih_2] = parameterization_info(htype='unk',
a0=a0.iseq)
continue
dihedral = dihedral_angle(sites=[
sites_cart[b1.iseq], sites_cart[a1.iseq], sites_cart[a0.iseq],
sites_cart[ih]
])
#print 'dihedrals', a0.dihedral, dihedral, a0.dihedral_ideal
rb1 = matrix.col(sites_cart[b1.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
if use_ideal_bonds_angles:
alpha = math.radians(a1.angle_ideal)
phi = math.radians(b1.dihedral_ideal)
#phi = dihedral
else:
alpha = (u10).angle(uh0)
#phi = a0.dihedral
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u10)) * u10).normalize()
u3 = u1.cross(u2)
#print names[ih], names[b1.iseq], names[a1.iseq]
if ih not in h_parameterization:
h_parameterization[ih] = parameterization_info(htype='alg1a',
a0=a0.iseq,
a1=a1.iseq,
a2=b1.iseq,
phi=phi,
n=0,
alpha=alpha,
dist_h=dist_h)
if ih_2 not in h_parameterization:
h_parameterization[ih_2] = parameterization_info(htype='alg1a',
a0=a0.iseq,
a1=a1.iseq,
a2=b1.iseq,
phi=phi +
math.pi,
n=0,
alpha=alpha,
dist_h=dist_h)
# case 1b
# a0.dihedral = dihedral angle between angle ideal and actual position
elif (n_red_neigbs == 1 and (count_H == 0 or count_H == 2)):
if (len(h_connectivity[ih]) != 4):
continue
a1 = reduced_neighbs[0]
b1 = (h_connectivity[ih][3])[0]
r1 = matrix.col(sites_cart[a1.iseq])
rb1 = matrix.col(sites_cart[b1.iseq])
uh0 = (rh - r0).normalize()
u10 = (r1 - r0).normalize()
dihedral = dihedral_angle(sites=[
sites_cart[ih], sites_cart[a0.iseq], sites_cart[a1.iseq],
sites_cart[b1.iseq]
])
if use_ideal_bonds_angles:
alpha = math.radians(a1.angle_ideal)
#phi = math.radians(b1.dihedral_ideal)
#allow for rotation even for idealize = True
phi = dihedral
else:
alpha = (u10).angle(uh0)
phi = dihedral
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u1)) * u1).normalize()
u3 = u1.cross(u2)
h_parameterization[ih] = parameterization_info(htype='alg1b',
a0=a0.iseq,
a1=a1.iseq,
a2=b1.iseq,
phi=phi,
n=0,
alpha=alpha,
dist_h=dist_h)
if (count_H == 2):
h_parameterization[ih].htype = 'prop'
hlist = h_connectivity[ih][2]
ih_2, ih_3 = hlist[0].iseq, hlist[1].iseq
h_parameterization[ih_2] = parameterization_info(htype='prop',
a0=a0.iseq,
a1=a1.iseq,
a2=b1.iseq,
phi=phi,
n=1,
alpha=alpha,
dist_h=dist_h)
# check if order is reversed
ih_2_coord = compute_H_position(sites_cart=sites_cart,
ih=ih_2,
hp=h_parameterization[ih_2])
h_parameterization[ih_3] = parameterization_info(htype='prop',
a0=a0.iseq,
a1=a1.iseq,
a2=b1.iseq,
phi=phi,
n=2,
alpha=alpha,
dist_h=dist_h)
if ((ih_2_coord - matrix.col(sites_cart[ih_3])).length() <
(ih_2_coord - matrix.col(sites_cart[ih_2])).length()):
h_parameterization[ih_2].n = 2
h_parameterization[ih_3].n = 1
else:
h_parameterization[ih] = parameterization_info(htype='unk',
a0=a0.iseq)
return h_parameterization