def TwoGaussianImmuneResponse2D(strength, x, y, Ra):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz))/numerix.sqrt(2*numerix.pi*2*dz))
return ((strength) * numerix.exp(-((x + 0.6)**2 + (y - 0.3)**2) /
(2 * Ra)) +
(strength) * numerix.exp(-((x - 0.6)**2 + (y - 0.2)**2) /
(2 * Ra))) / (numerix.sqrt(
2 * numerix.pi * Ra))
def loopGaussianKernel(z, dz):
n = z.shape[0]
m = z.shape[0]
kern = sp.lil_matrix((n, m), dtype=np.float64)
# kern = numerix.zeros((n,m))
# eps = 1e-10
eps = dz**2
digits = len(str(n - 1))
delete = "\b" * (digits + 1)
for i in range(n):
#if i>0:
# for j in range(m):
# if j>0:
# kern[i, j] = numerix.exp((-(2*z[i] - z[j])**2)/(2*eps))
kern[i] = numerix.exp((-(2 * z[i] - z)**2) / (2 * eps))
# kern = kern + sp.coo_matrix((np.array([numerix.exp((-(2*z[i] - z[j])**2)/(2*eps))]), (np.array([i]), np.array([j]))), shape=(n, m))
# kern.tocsc()
#/numerix.sqrt(2*numerix.pi*eps)
# print "{0}{1:{2}}".format(delete, i, digits),
# level = int((np.float(i)/np.float(n))*100)
# print "{0}%\r".format((np.float(i)/np.float(n)*100))
# print "#"*(level+1),
return kern / numerix.sqrt(2 * numerix.pi * eps)
def gaussianKernel(z, dz):
Z = np.ones((z.shape[0], 1)) * np.array([z])
eps = dz**2
kern = np.exp(-(2 * Z.T - Z) * (2 * Z.T - Z) / (2 * eps))
return kern / numerix.sqrt(2 * numerix.pi * eps)
def GaussianKernel2D(strength, x, y, Ra):
return strength * numerix.exp(-(
(x**2) + (y**2)) / (2 * Ra)) / (numerix.sqrt(2 * numerix.pi * Ra))
def GaussianKernel(strength, x, Ra):
return strength * numerix.exp(-(x**2) / (2 * Ra)) / (numerix.sqrt(
2 * numerix.pi * Ra))
def SigmaF1D(x, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
# return 0.00001*numerix.exp(-((x)**2)/(2*Rs))/(numerix.sqrt(2*numerix.pi*Rs))
return 10.*numerix.exp(-((x)**2)/(2*Rs))/(numerix.sqrt(2*numerix.pi*Rs))
def AxiSymmetricSigmaF(r, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return 10*numerix.exp(-((r)**2)/(2*Rs))/(numerix.sqrt(2*numerix.pi*Rs))
def AxiSymmetricGaussianGammaF(r, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return 0.03 * numerix.exp(-(r**2) /
(2 * Rs)) / (numerix.sqrt(2 * numerix.pi * Rs))
def SigmaF2D(amp, x,y, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return amp*numerix.exp(-(x**2 + y**2)/(2*Rs))/(numerix.sqrt(2*numerix.pi*Rs))
def GaussianConversionRate(r, mean, Rp):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return 0.3*numerix.exp(-(r-mean)**2/(2*Rp))/(numerix.sqrt(2*numerix.pi*Rp))
def gaussianGammaF(x, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return 0.3 * numerix.exp(-(x**2) /
(2 * Rs)) / (numerix.sqrt(2 * numerix.pi * Rs))
def GaussianConversionRate2D(amp, x,y, mean, Rp):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return amp*numerix.exp(-((x-mean)**2 + (y-mean)**2)/(2*Rp))/(numerix.sqrt(2*numerix.pi*Rp))
def gaussianDivisionRate(z, mean, sigma):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz))/numerix.sqrt(2*numerix.pi*2*dz))
return numerix.exp(-(z - mean)**2 /
(2 * sigma**2)) / (sigma * numerix.sqrt(2 * numerix.pi))
def AxiSymetricGaussianImmuneResponse(r, Ra):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz))/numerix.sqrt(2*numerix.pi*2*dz))
return 22 * numerix.exp(-r**2 /
(2 * Ra)) / (numerix.sqrt(2 * numerix.pi * Ra))
elif (problem == "b"):
print "Creating mesh for problem b"
mesh = fp.Grid2D(nx=N, ny=N, dx=200.0/float(N), dy=200.0/float(N))
elif (problem == "c"):
print "Creating mesh for problem c"
# mesh = fp.Grid2D(dx=0.5, dy=0.5, nx=40, ny=200) + (fp.Grid2D(dx=0.5, dy=0.5, nx=200, ny=40) + [[-40],[100]])
mesh = fp.Grid2D(Lx=20., Ly=100.0, nx=N / 5, ny=N) + (fp.Grid2D(Ly=20.0, Lx=100.0, nx=N, ny=N / 5) + [[-40],[100]])
elif (problem == "d"):
print "Creating mesh for problem da"
r = float(sys.argv[2])
numCellsDesired = int(sys.argv[3])
epsilon = 0.05
cellSize = 16 * np.pi * r**2 / (nmx.sqrt(3.) * numCellsDesired)
cellSize = nmx.sqrt(cellSize)
substring1 = '''
radius = {0};
cellSize = {1};
'''.format(r, round(cellSize, 6))
mesh = fp.Gmsh2DIn3DSpace(substring1 + '''
// create inner 1/8 shell
Point(1) = {0, 0, 0, cellSize};
Point(2) = {-radius, 0, 0, cellSize};
Point(3) = {0, radius, 0, cellSize};
Point(4) = {0, 0, radius, cellSize};
Circle(1) = {2, 1, 3};
def TwoSigmaF2D(x,y, Rs):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz**2))/(numerix.sqrt(dz**2)*numerix.sqrt(2*numerix.pi)))
return ((200e-3+0.)*numerix.exp(-((x+0.6)**2 + (y-0.3)**2)/(2*Rs))
+(300e-3+0.)*numerix.exp(-((x-0.6)**2 + (y-0.2)**2)/(2*Rs)))/(numerix.sqrt(2*numerix.pi*Rs))
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np
import fipy as fp
from fipy import numerix as nmx
r = 100
numCellsDesired = 2500
epsilon = 0.05
cellSize = 16 * np.pi * r**2 / (nmx.sqrt(3.) * numCellsDesired)
cellSize = nmx.sqrt(cellSize)
substring1 = '''
radius = {0};
cellSize = {1};
'''.format(r, round(cellSize, 6))
mesh = fp.Gmsh2DIn3DSpace(substring1 + '''
// create inner 1/8 shell
Point(1) = {0, 0, 0, cellSize};
Point(2) = {-radius, 0, 0, cellSize};
Point(3) = {0, radius, 0, cellSize};
Point(4) = {0, 0, radius, cellSize};
Circle(1) = {2, 1, 3};
Circle(2) = {4, 1, 2};
Circle(3) = {4, 1, 3};
Line Loop(1) = {1, -3, 2};
Ruled Surface(1) = {1};
def GaussianImmuneResponse2D(strength, x, y, Ra):
#Test : plt.plot(r,10*numerix.exp(-r**2/(2*dz))/numerix.sqrt(2*numerix.pi*2*dz))
return strength * numerix.exp(-(
(x**2) + (y**2)) / (2 * Ra)) / (numerix.sqrt(2 * numerix.pi * Ra))