def vec_dt(A, E):
#Constants
de, ae, ke, ea = 1., 1., 1., 10.
dx = 1.
return ea * (1. - A) * E, de * discreteLaplacian.Lap2DMt(
E, dx**2) - ke * E + ae * A * (1. - A)
def vec_dt(A, E, D, N):
#Constants
de, ae, ke, ea = 1., 1., 1., 10.
kn, dn, dc, kd, ad = 1., 0.25, 0.25, 1., 1.
#sum of D in neighboring cells
D_upper = np.roll(D, 1, axis=0)
D_upper[0, :] = 0
D_lower = np.roll(D, -1, axis=0)
D_lower[-1, :] = 0
D_left = np.roll(D, 1, axis=1)
D_left[0, :] = 0
D_right = np.roll(D, -1, axis=1)
D_right[-1, :] = 0
D_nei = D_upper + D_lower + D_left + D_right
#EGF mutant
Emut = np.ones(E.shape)
Emut[5:20, 5:20] = 0
dx = 1. #val of dx = dy for calculation of laplacian
# Calc. max{E - N, 0} by clip(min, max)
return ea * (1. - A) * (E - N).clip(0, None), \
de * discreteLaplacian.Lap2DMt(E, dx**2) - ke * E + ae * A * (1. - A) * Emut, \
-kd * D + ad * A * (1. - A),\
-kn * N + dn * D_nei - dc * D
def dvdt_dwdt(v, w, Ie):
#Constants
d, a, b, c = 1., 0.7, 0.8, 10.
dx = 1.
dx2 = dx * dx
return c * (-v**3 / 3. + v - w + Ie) + d * discreteLaplacian.Lap2DMt(
v, dx2), (v - b * w + a) / c
def heartbeat2D(matVW, t):
# reshape V, W
n = int(len(matVW) / 2)
x_max = int(np.sqrt(n))
v1, w1 = matVW[:n].reshape(x_max, x_max), matVW[n:].reshape(x_max, x_max)
#Initialize params
i = np.zeros((x_max, x_max))
i[49:51, 49:51] = 1.
d, a, b, c = 1., 0.7, 0.8, 10.
dx = 1.
dx2 = dx * dx
#PDEs
dvdt = c * (-v1**3 / 3. + v1 - w1 + i) + d * discreteLaplacian.Lap2DMt(
v1, dx2)
dwdt = (v1 - b * w1 + a) / c
return np.hstack((dvdt.ravel(), dwdt.ravel()))
A = np.zeros((Xmax, Xmax, Tmax))
I = np.zeros((Xmax, Xmax, Tmax))
#Initial conc. distributions
A[47:52, 47:52, 0] = 1.
#Production rate of A
c = np.zeros((Xmax, Xmax))
c[47:52, 47:52] = 1.
starttime = time.time() #start timing
#Solve PDEs
for T in range(Tmax - 1):
A[:, :, T + 1] = dt * (da * discreteLaplacian.Lap2DMt(A[:, :, T], dx2) +
aa * A[:, :, T] + ia * I[:, :, T] + c) + A[:, :, T]
I[:, :, T + 1] = dt * (di * discreteLaplacian.Lap2DMt(I[:, :, T], dx2) +
ai * A[:, :, T] + ii * I[:, :, T]) + I[:, :, T]
#Apply maximum and minimum values
A[:, :, T + 1] = A[:, :, T + 1].clip(0., Amax)
I[:, :, T + 1] = I[:, :, T + 1].clip(0., Imax)
elapsedtime = time.time() - starttime
print('Time elapsed (sec): {}'.format(elapsedtime))
#Plot results
len_T = len(str(Tmax)) #the number of digits in Tmax
for time in range(Tmax):
fig, axs = plt.subplots(1, 2, figsize=(6.4, 2.4))
heatmapB = axs[0].pcolor(A[:, :, time], vmin=0.0, vmax=2.0, cmap='YlOrRd')
#Initialize params
Tmax, dt = 5000, 0.02
Xmax, dx = 100, 1.
dx2 = dx*dx
V = np.zeros((Xmax, Xmax, Tmax))
W = np.zeros((Xmax, Xmax, Tmax))
I = np.zeros((Xmax, Xmax))
I[49:51, 49:51] = 1.
a, b, c = 0.7, 0.8, 10.
d = np.ones((100, 100))
d[40:50, 40:80] = 0.
#Solve ODEs
for T in range(Tmax-1):
V[:, :, T + 1] = V[:, :, T] + dt * (c * (-V[:, :, T]**3 / 3. + V[:, :, T] - W[:, :, T] + I) + d * discreteLaplacian.Lap2DMt(V[:, :, T], dx2))
W[:, :, T + 1] = W[:, :, T] + dt * (V[:, :, T] - b * W[:, :, T] + a) / c
#Reduce size of matrices by slicing
STEP = 100
Vr = V[:, :, ::STEP]
Wr = W[:, :, ::STEP]
#Plot results
len_T = len(str(Vr.shape[2])) #the number of digits
for time in range(Vr.shape[2]):
fig, axs = plt.subplots(1, 2, figsize=(6.4, 2.4))
heatmapV = axs[0].pcolor(Vr[:, :, time], vmin=0.0, vmax=np.ceil(V.max()), cmap='YlOrRd')
fig.colorbar(heatmapV, ax=axs[0])
heatmapW = axs[1].pcolor(Wr[:, :, time], vmin=0.0, vmax=np.ceil(W.max()), cmap='YlOrRd')
fig.colorbar(heatmapW, ax=axs[1])
Xmax, Tmax = 100, 500
dt, dx = 0.1, 1.
d, k, a = 1., 0.1, 1.
dx2 = dx * dx
S = np.zeros((Xmax, Xmax, Tmax))
B = np.zeros((Xmax, Xmax, Tmax))
c = np.zeros((Xmax, Xmax))
#Initial conc. distribution of Dpp
c[:, 47:53] = 0.5
starttime = time.time() #start timing
#Solve. PDEs
for T in range(Tmax - 1):
B[:, :, T + 1] = dt * (d * discreteLaplacian.Lap2DMt(B[:, :, T], dx2) -
k * B[:, :, T] + c) + B[:, :, T]
S[:, :, T + 1] = dt * (a * B[:, :, T] - k * S[:, :, T]) + S[:, :, T]
elapsedtime = time.time() - starttime
print('Time elapsed (sec): {}'.format(elapsedtime))
#Plot results
len_T = len(str(Tmax)) #the number of digits in Tmax
for time in range(Tmax):
fig, axs = plt.subplots(1, 2)
heatmapB = axs[0].pcolor(B[:, :, time], vmin=0.0, vmax=1.0, cmap='YlOrRd')
fig.colorbar(heatmapB, ax=axs[0])
heatmapS = axs[1].pcolor(S[:, :, time], vmin=0.0, vmax=1.0, cmap='YlOrRd')
fig.colorbar(heatmapS, ax=axs[1])
s = str(time).zfill(len_T)
Tmax, dt = 5000, 0.02
Xmax, dx = 100, 1.
dx2 = dx * dx
V = np.zeros((Xmax, Xmax, Tmax))
W = np.zeros((Xmax, Xmax, Tmax))
I = np.zeros((Xmax, Xmax))
I[49:51, 49:51] = 1.
d, a, b, c = 1., 0.7, 0.8, 10.
#Solve ODEs
for T in range(Tmax - 1):
V[:, :, T +
1] = V[:, :,
T] + dt * (c *
(-V[:, :, T]**3 / 3. + V[:, :, T] - W[:, :, T] + I) +
d * discreteLaplacian.Lap2DMt(V[:, :, T], dx2))
W[:, :, T + 1] = W[:, :, T] + dt * (V[:, :, T] - b * W[:, :, T] + a) / c
#Reduce size of matrices by slicing
STEP = 100
Vr = V[:, :, ::STEP]
Wr = W[:, :, ::STEP]
#Plot results
len_T = len(str(Vr.shape[2])) #the number of digits
for time in range(Vr.shape[2]):
fig, axs = plt.subplots(1, 2, figsize=(6.4, 2.4))
heatmapV = axs[0].pcolor(Vr[:, :, time],
vmin=0.0,
vmax=np.ceil(V.max()),
cmap='YlOrRd')
#init.
Xmax, Tmax = 100, 100
dt, d, dx = 0.1, 1.0, 1.0
dx2 = dx * dx
E = np.zeros((Xmax, Xmax, Tmax))
E[0:20, 40:60, 0] = np.random.randn(E[0:20, 40:60, 0].shape[0],
E[0:20, 40:60,
0].shape[1]) #Initial conc. distribution
starttime = time.time() #start timing
#Solve PDE
for T in range(Tmax - 1):
E[:, :,
T + 1] = dt * d * discreteLaplacian.Lap2DMt(E[:, :, T], dx2) + E[:, :, T]
elapsedtime = time.time() - starttime
print('Time elapsed (sec): {}'.format(elapsedtime))
#Plot results
len_T = len(str(Tmax)) #the number of digits in Tmax
for time in range(Tmax):
fig, ax = plt.subplots()
heatmap = ax.pcolor(E[:, :, time], vmin=0.0, vmax=1.0, cmap='YlOrRd')
fig.colorbar(heatmap, ax=ax)
s = str(time).zfill(len_T)
fig.savefig("GIF\\{}.png".format(s)) #Save image for each loop
plt.clf()
plt.cla()
plt.close()
A = np.zeros((Xmax, Xmax, Tmax))
I = np.zeros((Xmax, Xmax, Tmax))
#Initial conc. distributions
A[47:52, 47:52, 0] = 1.
#Production rate of A
c = np.zeros((Xmax, Xmax))
c[47:52, 47:52] = 1.
starttime = time.time() #start timing
#Solve PDEs
for T in range(Tmax - 1):
A[:, :, T + 1] = dt * (da * discreteLaplacian.Lap2DMt(A[:, :, T], dx2) + aa * A[:, :, T] + ia * I[:, :, T] + c) + A[:, :, T]
I[:, :, T + 1] = dt * (di * discreteLaplacian.Lap2DMt(I[:, :, T], dx2) + ai * A[:, :, T] + ii * I[:, :, T]) + I[:, :, T]
#Apply maximum and minimum values
A[:, :, T + 1] = A[:, :, T + 1] * ((A[:, :, T + 1] > 0.).astype(int) * (A[:, :, T + 1] < Amax).astype(int)) + Amax * (A[:, :, T + 1] >= Amax).astype(int)
I[:, :, T + 1] = I[:, :, T + 1] * ((I[:, :, T + 1] > 0.).astype(int) * (I[:, :, T + 1] < Imax).astype(int)) + Imax * (I[:, :, T + 1] >= Imax).astype(int)
elapsedtime = time.time() - starttime
print('Time elapsed (sec): {}'.format(elapsedtime))
#Plot results
len_T = len(str(Tmax)) #the number of digits in Tmax
for time in range(Tmax):
fig, axs = plt.subplots(1, 2, figsize=(6.4, 2.4))
heatmapB = axs[0].pcolor(A[:, :, time], vmin=0.0, vmax=2.0, cmap='YlOrRd')
fig.colorbar(heatmapB, ax=axs[0])
heatmapW = axs[1].pcolor(I[:, :, time], vmin=0.0, vmax=2.0, cmap='YlOrRd')