def tst_dmatrix():
# expected values are the d_jmn at beta=1.0 and j=2, m=-2, -2<=n<=2
expect = [0.593133, 0.64806, 0.433605, 0.193411, 0.0528305]
eps = 1e-4
d2 = dmatrix( 2, 1.0) # dmatrix( max_L, beta )
for n in range(-2, 3):
assert abs(expect[n+2] - d2.djmn(2, -2, n) ) < eps
d4 = dmatrix( 4, 1.0)
for n in range(-2, 3):
assert abs(expect[n+2] - d4.djmn(2, -2, n) ) < eps
d7 = dmatrix( 2, 1.0)
for n in range(-2, 3):
assert abs(expect[n+2] - d7.djmn(2, -2, n) ) < eps
# check agains d(2,2,1) = -(1+cos(beta))*sin(beta)/2.0
for ii in range(10):
expt = -(1.0+smath.cos(ii))*smath.sin(ii)/2.0
assert abs( dmatrix(2,ii).djmn(2,2,1) - expt ) < eps
# check beta= multiple of pi/2
assert abs( dmatrix( 20, smath.pi ).djmn(2,2,0) )< eps
assert abs( dmatrix( 2, smath.pi*2 ).djmn(2,2,0) )< eps
assert abs( dmatrix( 20, smath.pi*0.5 ).djmn(2,2,0)-smath.sqrt(6.0)/4.0 )< eps
def tst():
M=10
xy = []
for ii in range(M):
r=10.0
phi = ii*(smath.pi*2/M)
x = r*smath.cos(phi)
y = r*smath.sin(phi)
xy.append( flex.double([x,y]) )
# build distance matrix
dmat = []
for ii in range(M):
tmp = []
for jj in range(M):
x1=xy[ii][0]
x2=xy[jj][0]
y1=xy[ii][1]
y2=xy[jj][1]
dd = smath.sqrt( (x1-x2)**2.0 +(y1-y2)**2.0 )
if jj != ii:
tmp.append( (jj,dd) )
dmat.append( tmp )
spee=classic_spe_engine( dmat, l=1.0,max_cycle=5000 )
x,s = spee.embed(2,M)
assert s<1e-4
print "OK"
def tst():
M = 10
xy = []
for ii in range(M):
r = 10.0
phi = ii * (smath.pi * 2 / M)
x = r * smath.cos(phi)
y = r * smath.sin(phi)
xy.append(flex.double([x, y]))
# build distance matrix
dmat = []
for ii in range(M):
tmp = []
for jj in range(M):
x1 = xy[ii][0]
x2 = xy[jj][0]
y1 = xy[ii][1]
y2 = xy[jj][1]
dd = smath.sqrt((x1 - x2)**2.0 + (y1 - y2)**2.0)
if jj != ii:
tmp.append((jj, dd))
dmat.append(tmp)
spee = classic_spe_engine(dmat, l=1.0, max_cycle=5000)
x, s = spee.embed(2, M)
assert s < 1e-4
print "OK"
def tst_dmatrix():
# expected values are the d_jmn at beta=1.0 and j=2, m=-2, -2<=n<=2
expect = [0.593133, 0.64806, 0.433605, 0.193411, 0.0528305]
eps = 1e-4
d2 = dmatrix(2, 1.0) # dmatrix( max_L, beta )
for n in range(-2, 3):
assert abs(expect[n + 2] - d2.djmn(2, -2, n)) < eps
d4 = dmatrix(4, 1.0)
for n in range(-2, 3):
assert abs(expect[n + 2] - d4.djmn(2, -2, n)) < eps
d7 = dmatrix(2, 1.0)
for n in range(-2, 3):
assert abs(expect[n + 2] - d7.djmn(2, -2, n)) < eps
# check agains d(2,2,1) = -(1+cos(beta))*sin(beta)/2.0
for ii in range(10):
expt = -(1.0 + smath.cos(ii)) * smath.sin(ii) / 2.0
assert abs(dmatrix(2, ii).djmn(2, 2, 1) - expt) < eps
# check beta= multiple of pi/2
assert abs(dmatrix(20, smath.pi).djmn(2, 2, 0)) < eps
assert abs(dmatrix(2, smath.pi * 2).djmn(2, 2, 0)) < eps
assert abs(
dmatrix(20, smath.pi * 0.5).djmn(2, 2, 0) -
smath.sqrt(6.0) / 4.0) < eps
def __init__(self, n):
self.n = n
self.step = 2*math.pi/self.n
self.sin_table = flex.double()
self.cos_table = flex.double()
for i in xrange(self.n):
self.sin_table.append(math.sin(i*self.step))
self.cos_table.append(math.cos(i*self.step))
def __init__(self, n):
self.n = n
self.step = 2*math.pi/self.n
self.sin_table = flex.double()
self.cos_table = flex.double()
for i in xrange(self.n):
self.sin_table.append(math.sin(i*self.step))
self.cos_table.append(math.cos(i*self.step))
def print_correlation( out_correlation, correlation, q_array, N_phi):
print >>out_correlation, "# phi, q, correlation"
two_pi = smath.pi*2.0
ii = 0
for qq in q_array:
for pp in range(N_phi):
phi = pp*two_pi/N_phi
print >>out_correlation, qq*smath.cos(phi),qq*smath.sin(phi), correlation[pp][ii][ii]
ii=ii+1
def rosca(m=9, hemisphere=True):
"""
Regular grid on the unit sphere, Rosca (2010).
"""
def truncate(x):
if(abs(x)<1.e-6): return 0
else: return x
def add(result, new):
foud = False
for s in result:
d = math.sqrt((s[0]-new[0])**2+(s[1]-new[1])**2+(s[2]-new[2])**2)
if(d<1.e-3): return
result.append(new)
return
d_l = math.sqrt(2)/m
result = flex.vec3_double()
for m_ in xrange(m+1):
if(m_==0):
add(result, [0,0,1])
else:
l_m = m_ * d_l
d_phi = math.pi/(4*m_)
assert l_m>=0 and l_m<=math.sqrt(2)
for k in xrange(m_+1):
arg1 = k*d_phi
arg2 = l_m*math.sqrt(1-l_m**2/4)
x_km = truncate(math.cos(arg1)*arg2)
y_km = truncate(math.sin(arg1)*arg2)
z_m = truncate(1.-l_m**2/2 )
add(result, [ x_km, y_km,z_m])
add(result, [ y_km, x_km,z_m])
add(result, [-y_km, x_km,z_m])
add(result, [-x_km, y_km,z_m])
add(result, [ x_km,-y_km,z_m])
add(result, [ y_km,-x_km,z_m])
add(result, [-x_km,-y_km,z_m])
add(result, [-y_km,-x_km,z_m])
if(not hemisphere):
add(result, [ x_km, y_km,-z_m])
add(result, [ y_km, x_km,-z_m])
add(result, [-y_km, x_km,-z_m])
add(result, [-x_km, y_km,-z_m])
add(result, [ x_km,-y_km,-z_m])
add(result, [ y_km,-x_km,-z_m])
add(result, [-x_km,-y_km,-z_m])
add(result, [-y_km,-x_km,-z_m])
for r in result:
assert abs(1.-math.sqrt(r[0]**2+r[1]**2+r[2]**2))<1.e-6
# XXX for debugging
if(0):
f = "HETATM%5d O HOH A%4d %8.3f%8.3f%8.3f 1.00 23.99 O "
o = open("junk.pdb", "w")
for i, r in enumerate(result):
print >> o, f%(i, i, r[0],r[1],r[2])
o.close()
return result
def euler_angles_as_matrix(angles, deg=False):
if (deg):
angles = [a * math.pi / 180 for a in angles]
c = [math.cos(a) for a in angles]
s = [math.sin(a) for a in angles]
# Based on subroutine angro7 in CONVROT.
# Urzhumtseva, L.M. & Urzhumtsev, A.G. (1997).
return matrix.sqr(
(c[0] * c[1] * c[2] - s[0] * s[2], -c[0] * c[1] * s[2] - s[0] * c[2],
c[0] * s[1], s[0] * c[1] * c[2] + c[0] * s[2],
-s[0] * c[1] * s[2] + c[0] * c[2], s[0] * s[1], -s[1] * c[2],
s[1] * s[2], c[1]))
def rotate_image(self,data,angle_deg,sigma=1.0):
# we take an image, rotate, interpolate it back onto a regular grid and return it
#
# There is however the problem that some pixels will never be seen. those pixels will be filled up by interpolation
data = data*self.mask
cost = smath.cos( angle_deg*smath.pi/180.0 )
sint = smath.sin( angle_deg*smath.pi/180.0 )
new_image = flex.double(self.grid,0)
visited = flex.bool(self.grid,False)
nx_array = flex.double()
ny_array = flex.double()
val_array = flex.double()
for ix in range(self.np):
for iy in range(self.np):
x = ix - self.ox
y = iy - self.oy
nx = cost*x - sint*y
ny = sint*x + cost*y
jx = int(nx+self.ox+0.5)
jy = int(ny+self.oy+0.5)
if jx >= self.np : jx = self.np-1
if jy >= self.np : jy = self.np-1
if jx<0: jx=0
if jy<0: jy=0
new_image[ (jx,jy) ] = data[ (ix,iy) ]
visited[ (jx,jy) ] = True
nx_array.append( nx+self.ox )
ny_array.append( ny+self.oy )
val_array.append( data[ (ix,iy) ] )
assert nx_array.size() == self.mask.size()
not_visited = ~visited
not_visited = not_visited.iselection()
# now we need to loop over all non-visited pixel values
for pixel in not_visited:
#for ix in range(self.np):
# for iy in range(self.np):
nv = 0
if self.mask[(ix,iy)]>-0.1:
nv = -9
index = n_dim_index_from_one_dim(pixel, [self.np,self.np] )
nvx = index[1]
nvy = index[0]
dx = nx_array-nvx
dy = ny_array-nvy
dd = (dx*dx+dy*dy)
ss = flex.exp( -dd/(sigma*sigma) )*self.mask
nv = flex.sum(ss*val_array)/(1e-12+flex.sum(ss))
new_image[ (ix,iy) ] = nv
new_image = new_image*self.mask
return new_image
def r3_rotation_matrix_logarithm(r):
"""
Chirikjian, G. Stochastic models, information theory, and Lie groups.
Volume 2, pp 39-40.
Applied and Numerical Harmonic Analysis, Birkhauser
"""
cos_theta = r3_rotation_cos_rotation_angle_from_matrix( r )
if cos_theta < 1.0:
theta = math.acos( cos_theta )
a1 = theta / math.sin( theta )
else:
a1 = 1.0
return 0.5 * a1 * ( r - r.transpose() )
def r3_rotation_matrix_logarithm(r):
"""
Chirikjian, G. Stochastic models, information theory, and Lie groups.
Volume 2, pp 39-40.
Applied and Numerical Harmonic Analysis, Birkhauser
"""
cos_theta = r3_rotation_cos_rotation_angle_from_matrix( r )
if cos_theta < 1.0:
theta = math.acos( cos_theta )
a1 = theta / math.sin( theta )
else:
a1 = 1.0
return 0.5 * a1 * ( r - r.transpose() )
def euler_angles_as_matrix(angles, deg=False):
if (deg):
angles = [a*math.pi/180 for a in angles]
c = [math.cos(a) for a in angles]
s = [math.sin(a) for a in angles]
# Based on subroutine angro7 in CONVROT.
# Urzhumtseva, L.M. & Urzhumtsev, A.G. (1997).
return matrix.sqr((
c[0]*c[1]*c[2]-s[0]*s[2],
-c[0]*c[1]*s[2]-s[0]*c[2],
c[0]*s[1],
s[0]*c[1]*c[2]+c[0]*s[2],
-s[0]*c[1]*s[2]+c[0]*c[2],
s[0]*s[1],
-s[1]*c[2],
s[1]*s[2],
c[1]))
def j1(x):
result = smath.sin(x) / (x * x) - smath.cos(x) / x
return result
def j2(x): result = (3.0/(x*x) -1.0)*(smath.sin(x)/x) - 3.0*smath.cos(x)/(x*x) return result
def j1(x): result = smath.sin(x)/(x*x) - smath.cos(x)/x return result
def j0(x): result = smath.sin(x)/x return result
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 compute_H_position(ih, sites_cart, hp):
r0 = matrix.col(sites_cart[hp.a0])
r1 = matrix.col(sites_cart[hp.a1])
dh = hp.dist_h
a, b, h = hp.a, hp.b, hp.h
# alg2a
if (hp.htype == 'flat_2neigbs'):
a, b = hp.a, hp.b
r2 = matrix.col(sites_cart[hp.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
length = math.sqrt(a * a + b * b + 2 * a * b * (u10).dot(u20))
if (length == 0):
raise RuntimeError(
"Denominator zero: length in generate_H_positions")
uh0 = (a * u10 + b * u20) / length
rh_calc = r0 + dh * uh0
h_distance = (rh_calc - matrix.col(sites_cart[ih])).length()
# 2 neigbs
elif (hp.htype == '2neigbs'):
a, b, h = hp.a, hp.b, hp.h
r2 = matrix.col(sites_cart[hp.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v0 = (u10.cross(u20)).normalize()
rh0 = (a * u10 + b * u20 + h * v0)
length = math.sqrt(rh0.dot(rh0))
if (length == 0):
raise RuntimeError(
"Denominator zero: length in generate_H_positions")
uh0 = rh0 / length
rh_calc = r0 + dh * uh0
h_distance = (rh_calc - matrix.col(sites_cart[ih])).length()
# 2tetrahedral
elif (hp.htype == '2tetra'):
a, b, delta = hp.a, hp.b, hp.alpha
r2 = matrix.col(sites_cart[hp.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v0 = (u10.cross(u20)).normalize()
d0 = (a * u10 + b * u20).normalize()
rh_calc = r0 + dh * (math.cos(delta) * d0 + math.sin(delta) * v0)
h_distance = (rh_calc - matrix.col(sites_cart[ih])).length()
# tetragonal alg3
elif (hp.htype == '3neigbs'):
a, b, h = hp.a, hp.b, hp.h
r2 = matrix.col(sites_cart[hp.a2])
r3 = matrix.col(sites_cart[hp.a3])
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
u30 = (r3 - r0).normalize()
rh0 = (a * u10 + b * u20 + h * u30)
length = math.sqrt(rh0.dot(rh0))
if (length == 0):
raise RuntimeError(
"Denominator zero: length in generate_H_positions")
uh0 = rh0 / length
rh_calc = r0 + dh * uh0
h_distance = (rh_calc - matrix.col(sites_cart[ih])).length()
# alg1b or alg1a or propeller group
elif (hp.htype in ['alg1b', 'alg1a', 'prop']):
rb1 = matrix.col(sites_cart[hp.a2])
n = hp.n
phi = hp.phi + n * 2 * math.pi / 3
alpha = hp.alpha
salpha = math.sin(alpha)
calpha = math.cos(alpha)
sphi = math.sin(phi)
cphi = math.cos(phi)
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u1)) * u1).normalize()
u3 = u1.cross(u2)
rh_calc = r0 + dh * (salpha * (cphi * u2 + sphi * u3) - calpha * u1)
h_distance = (rh_calc - matrix.col(sites_cart[ih])).length()
else:
rh_calc = sites_cart[ih]
return rh_calc
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 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 generate_H_positions(sites_cart, ih, para_info):
#sites_cart = xray_structure.sites_cart()
r0 = matrix.col(sites_cart[para_info.a0])
r1 = matrix.col(sites_cart[para_info.a1])
dh = para_info.dist_h
# case 2a
if (para_info.htype == 'flat_2neigbs'):
a, b = para_info.a, para_info.b
r2 = matrix.col(sites_cart[para_info.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
#uh0 = (a * u10 + b * u20).normalize()
uh0 = (a * u10 + b * u20)
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# case 2b and 3
elif (para_info.htype == '2neigbs' or para_info.htype == '3neigbs'):
a, b, h= para_info.a, para_info.b, para_info.h
r2 = matrix.col(sites_cart[para_info.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v = u10.cross(u20)
uh0 = (a * u10 + b * u20 + h * v).normalize()
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# case 1a
elif (para_info.htype == 'alg1a'):
a, b, h = para_info.a, para_info.b, para_info.h
rb1 = matrix.col(sites_cart[para_info.a2])
r2 = r0 + (r1 - rb1).normalize()
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v = u10.cross(u20)
uh0 = (a * u10 + b * u20 + h * v).normalize()
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
elif (para_info.htype == 'alg1b_flat'):
rb1 = matrix.col(sites_cart[para_info.a2])
a = para_info.a
alpha = para_info.alpha
u10 = (r1 - r0).normalize()
rb10 = rb1 - r1
v10 = a * (rb10 - ((rb10).dot(u10)) * u10).normalize()
calpha, salpha = math.cos(alpha), math.sin(alpha)
rH_gen = r0 + dh * (calpha * u10 + salpha * v10)
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# case one H atom free rotation
elif (para_info.htype == 'alg1b'):
rb1 = matrix.col(sites_cart[para_info.a2])
a, b = para_info.a, para_info.b
chi, eps = para_info.chi, para_info.eps
alpha = para_info.alpha
u10 = (r1 - r0).normalize()
rb10 = rb1 - r1
v10 = a * (rb10 - ((rb10).dot(u10)) * u10).normalize()
w10 = b * (u10.cross(v10)).normalize()
c_chi, s_chi = math.cos(abs(chi)), math.sin(abs(chi))
c1, s1 = math.cos(eps), math.sin(eps)
calpha = math.cos(alpha)
rH_gen = r0 + dh * ((calpha * u10) + (calpha * s1/c1 * v10) + (s_chi * w10))
#rH_gen = r0 + dh * ((c1 * c_chi * u10) + (s1 * c_chi * v10) + (s_chi * w10))
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
else:
deltaH, rH_gen = None, None
return group_args(
distance = deltaH,
rH_gen = rH_gen)
def j2(x):
result = (3.0 / (x * x) - 1.0) * (smath.sin(x) /
x) - 3.0 * smath.cos(x) / (x * x)
return result
def j0(x):
result = smath.sin(x) / x
return result
def generate_H_positions(sites_cart, ih, para_info):
r0 = matrix.col(sites_cart[para_info.a0])
r1 = matrix.col(sites_cart[para_info.a1])
dh = para_info.dist_h
a, b, h = para_info.a, para_info.b, para_info.h
# alg2a
if (para_info.htype == 'flat_2neigbs'):
a, b = para_info.a, para_info.b
r2 = matrix.col(sites_cart[para_info.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
length = math.sqrt(a*a + b*b + 2*a*b*(u10).dot(u20))
if(length==0):
raise RuntimeError("Denominator zero: length in generate_H_positions")
uh0 = (a * u10 + b * u20)/length
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# 2 neigbs
elif (para_info.htype == '2neigbs'):
a, b, h = para_info.a, para_info.b, para_info.h
r2 = matrix.col(sites_cart[para_info.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v0 = (u10.cross(u20)).normalize()
rh0 = (a * u10 + b * u20 + h * v0)
length = math.sqrt(rh0.dot(rh0))
if(length==0):
raise RuntimeError("Denominator zero: length in generate_H_positions")
uh0 = rh0/length
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# 2tetrahedral
elif (para_info.htype == '2tetra'):
a, b, delta = para_info.a, para_info.b, para_info.alpha
r2 = matrix.col(sites_cart[para_info.a2])
u10, u20 = (r1 - r0).normalize(), (r2 - r0).normalize()
v0 = (u10.cross(u20)).normalize()
d0 = (a * u10 + b * u20).normalize()
rH_gen = r0 + dh * (math.cos(delta) * d0 + math.sin(delta) * v0)
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# tetragonal alg3
elif (para_info.htype == '3neigbs'):
a, b, h = para_info.a, para_info.b, para_info.h
r2 = matrix.col(sites_cart[para_info.a2])
r3 = matrix.col(sites_cart[para_info.a3])
u10 = (r1 - r0).normalize()
u20 = (r2 - r0).normalize()
u30 = (r3 - r0).normalize()
rh0 = (a*u10 + b*u20 + h*u30)
length = math.sqrt(rh0.dot(rh0))
if(length==0):
raise RuntimeError("Denominator zero: length in generate_H_positions")
uh0 = rh0/length
rH_gen = r0 + dh * uh0
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
# alg1b or alg1a or propeller group
elif (para_info.htype in ['alg1b', 'alg1a', 'prop']):
rb1 = matrix.col(sites_cart[para_info.a2])
n = para_info.n
phi = para_info.phi + n*2*math.pi/3
#phi = para_info.phi
alpha = para_info.alpha
salpha = math.sin(alpha)
calpha = math.cos(alpha)
sphi = math.sin(phi)
cphi = math.cos(phi)
u1 = (r0 - r1).normalize()
rb10 = rb1 - r1
u2 = (rb10 - ((rb10).dot(u1)) * u1).normalize()
u3 = u1.cross(u2)
rH_gen = r0 + dh * (salpha*(cphi*u2 + sphi*u3) - calpha*u1)
deltaH = (rH_gen - matrix.col(sites_cart[ih])).length()
else:
deltaH, rH_gen = None, None
return group_args(
distance = deltaH,
rH_gen = rH_gen)
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