def fourier3D(coordinates,L,frequencies):
# Note, that I do not perform the calculation below on the central particle
# Messes with results!
N = coordinates.shape[0]-1;
if N == 0:
return [0]
# Note. The first coordinates is the center particle.
#Translate all coordinates so the center is the origin
coordinates = coordinate_helper.pbc(coordinates[1:,:]-coordinates[0,:],L)
#-- STEP 1 - Convert to spherical coordinates
# calculate the radial distance of all the coordinates
r = np.linalg.norm(coordinates) #Radial
phi = np.arctan2(coordinates[:,1],coordinates[:,0]) +np.pi #Azimuthal
theta = np.arccos(coordinates[:,2]/r) #Inclination
#-- STEP 2: compute Ylm(theta, phi) for each theta, phi
# Using spherical harmonic function provided by scipy
#http://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.special.sph_harm.html
# scipy.special.sph_harm(m, l, azimuthal, polar) azimuthal in [0,2pi], polar in [0,pi] (n == l)
# NEED MORE WORK BELOW
# In the original smac code, for a given frequency l, loops over the n particles, and over m values from -l to +l, and then applies a "q" invarinace that combines all the m values generated for all the particles.
shape_descriptor= []
for l in frequencies:
components = np.zeros(shape=(coordinates.shape[0],2*l+1,2))
for m in range(-l,l+1):
w = 1.0
ylm = sp.sph_harm(m,l,phi,theta)
components[:,m,0] = w*ylm.real
components[:,m,1] = w*ylm.imag
# Summing over all the particles
ylm_average = np.sum(components,axis=0)/components.shape[0]
# Applying invariance
# computes the "q" invariant for a 3d fourier coefficient
sd = np.sqrt(4.0*np.pi/ylm.shape[1]*np.sum(ylm_average**2))
shape_descriptor.append(sd)
return shape_descriptor
def calculate(self, coordinates, L, N):
# Calculate RDF - Doing this Brute Force for now - no cell list
# radial position of the bin
x_i = np.array(range(self.maxbin))*self.dr
hist = np.zeros(self.maxbin)
# Convienent Lambdas
makeint = lambda x: int(x)
# Note that currently all distances are being calculated twice.
# If I change this, need to double the weight of the count in the histogram
for rollval in range(1,N):
dd = np.array(map(sub, coordinates, np.roll(coordinates,rollval,axis=0))) # Box Periodicity is not used right now
dd = coordinate_helper.pbc(dd,L)
rij = np.linalg.norm(dd, axis=1)
# DEBUGGING
mask = rij < 0.5
if sum(mask) :
print
print coordinates[mask], np.roll(coordinates,rollval,axis=0)[mask], dd[mask]
bin = map(makeint, rij/self.dr)
for b in bin:
if b < self.maxbin :
hist[b] += 1
# Calculate the array of normalization factors
delta = self.dr/2.
# density
number_density = float(N)/np.product(L)
volume_shell = 4./3.*np.pi*np.power(x_i+delta, 3) - 4./3.*np.pi*np.power(x_i-delta, 3);
# Correction for first shell
volume_shell[0] += 4./3.*np.pi*np.power(-delta, 3);
np_ideal_gas = number_density * volume_shell;
normalization = np_ideal_gas * N;
hist /= normalization;
self.x_i = x_i
self.hist = hist
return x_i,hist
def fourier3D(coordinates, L, frequencies):
# Note, that I do not perform the calculation below on the central particle
# Messes with results!
N = coordinates.shape[0] - 1
if N == 0:
return [0]
# Note. The first coordinates is the center particle.
#Translate all coordinates so the center is the origin
coordinates = coordinate_helper.pbc(coordinates[1:, :] - coordinates[0, :],
L)
#-- STEP 1 - Convert to spherical coordinates
# calculate the radial distance of all the coordinates
r = np.linalg.norm(coordinates) #Radial
phi = np.arctan2(coordinates[:, 1], coordinates[:, 0]) + np.pi #Azimuthal
theta = np.arccos(coordinates[:, 2] / r) #Inclination
#-- STEP 2: compute Ylm(theta, phi) for each theta, phi
# Using spherical harmonic function provided by scipy
#http://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.special.sph_harm.html
# scipy.special.sph_harm(m, l, azimuthal, polar) azimuthal in [0,2pi], polar in [0,pi] (n == l)
# NEED MORE WORK BELOW
# In the original smac code, for a given frequency l, loops over the n particles, and over m values from -l to +l, and then applies a "q" invarinace that combines all the m values generated for all the particles.
shape_descriptor = []
for l in frequencies:
components = np.zeros(shape=(coordinates.shape[0], 2 * l + 1, 2))
for m in range(-l, l + 1):
w = 1.0
ylm = sp.sph_harm(m, l, phi, theta)
components[:, m, 0] = w * ylm.real
components[:, m, 1] = w * ylm.imag
# Summing over all the particles
ylm_average = np.sum(components, axis=0) / components.shape[0]
# Applying invariance
# computes the "q" invariant for a 3d fourier coefficient
sd = np.sqrt(4.0 * np.pi / ylm.shape[1] * np.sum(ylm_average**2))
shape_descriptor.append(sd)
return shape_descriptor
def fourier2D(coordinates,L,frequencies):
# Note, that I do not perform the calculation below on the central particle
# Messes with results!
N = coordinates.shape[0]-1;
if N == 0:
return [0]
# Note. The first coordinates is the center particle.
#Translate all coordinates so the center is the origin
coordinates = coordinate_helper.pbc(coordinates[1:,:]-coordinates[0,:],L)
#RSQ is only calculated in SMAC to partition particles by shells.
#We are not partitioning particles by shells
#rsq = coordinate_helper.rsq(coordinates)
# calculate theta of all particles (including center)
theta = np.arctan2(coordinates[:,1],coordinates[:,0]) + np.pi
shape_descriptor = []
# For each frequency.. calculate a complex number which
# is sum [np.cos(k*theta), -np.sin(k*theta)] for each theta
# Applying weight of 1.0 to all
for k in frequencies:
components = np.zeros(shape=(coordinates.shape[0],2))
#components += [np.cos(k*theta), -np.sin(k*theta)]
# weights
w=1.0
components[:,0] += w*np.cos(k*theta)
components[:,1] += -w*np.sin(k*theta)
# c is a complex number
c= np.sum(components,axis=0)
# scale the components
c /=float(N)
#print c
# because invariant (return magnitude of complex number)
c = np.sqrt(np.sum(c*c))
shape_descriptor.append(c)
return shape_descriptor
def fourier2D(coordinates, L, frequencies):
# Note, that I do not perform the calculation below on the central particle
# Messes with results!
N = coordinates.shape[0] - 1
if N == 0:
return [0]
# Note. The first coordinates is the center particle.
#Translate all coordinates so the center is the origin
coordinates = coordinate_helper.pbc(coordinates[1:, :] - coordinates[0, :],
L)
#RSQ is only calculated in SMAC to partition particles by shells.
#We are not partitioning particles by shells
#rsq = coordinate_helper.rsq(coordinates)
# calculate theta of all particles (including center)
theta = np.arctan2(coordinates[:, 1], coordinates[:, 0]) + np.pi
shape_descriptor = []
# For each frequency.. calculate a complex number which
# is sum [np.cos(k*theta), -np.sin(k*theta)] for each theta
# Applying weight of 1.0 to all
for k in frequencies:
components = np.zeros(shape=(coordinates.shape[0], 2))
#components += [np.cos(k*theta), -np.sin(k*theta)]
# weights
w = 1.0
components[:, 0] += w * np.cos(k * theta)
components[:, 1] += -w * np.sin(k * theta)
# c is a complex number
c = np.sum(components, axis=0)
# scale the components
c /= float(N)
#print c
# because invariant (return magnitude of complex number)
c = np.sqrt(np.sum(c * c))
shape_descriptor.append(c)
return shape_descriptor
def getClusters(self,rmax):
clusters = []
for i in range(self.N):
mask_notme = [True]*(self.N)
mask_notme[i] = False
dd = self.coordinates - self.coordinates[i]
dd = coordinate_helper.pbc(dd,self.L)
rij = np.linalg.norm(dd, axis=1)
mask = (rij < rmax) & mask_notme
myparticles = self.coordinates[mask]
tmp = np.zeros(shape=(myparticles.shape[0]+1, 3))
tmp[0,:] =copy.copy(self.coordinates[i])
tmp[1:,:]= copy.copy(myparticles)
clusters.append(tmp)
return clusters
def getClusters(self, rmax):
clusters = []
for i in range(self.N):
mask_notme = [True] * (self.N)
mask_notme[i] = False
dd = self.coordinates - self.coordinates[i]
dd = coordinate_helper.pbc(dd, self.L)
rij = np.linalg.norm(dd, axis=1)
mask = (rij < rmax) & mask_notme
myparticles = self.coordinates[mask]
tmp = np.zeros(shape=(myparticles.shape[0] + 1, 3))
tmp[0, :] = copy.copy(self.coordinates[i])
tmp[1:, :] = copy.copy(myparticles)
clusters.append(tmp)
return clusters
