def qDist(x, y):
d1 = 0.43
d2 = 0.85
if state(x, y) == -1:
return 0.0
elif state(x, y) == 1:
return 1.0
elif (x - 1.15)**2 + y**2 >= (2.0 * 1.15 - d1)**2:
return 0.0
elif (x - 1.15)**2 + y**2 <= d2**2:
return 1.0
else:
return 1.0 - (np.sqrt(
(x - 1.15)**2 + y**2) - d2) / (2 * 1.15 - d1 - d2)
def dqDist(x, y):
d1 = 0.43
d2 = 0.85
if state(x, y) == -1:
return 0.0, 0.0
elif state(x, y) == 1:
return 0.0, 0.0
elif (x - 1.15)**2 + y**2 >= (2.0 * 1.15 - d1)**2:
return 0.0, 0.0
elif (x - 1.15)**2 + y**2 <= d2**2:
return 0.0, 0.0
else:
return -(x - 1.15) / (
(2 * 1.15 - d1 - d2) * np.sqrt((x - 1.15)**2 + y**2)), -y / (
(2 * 1.15 - d1 - d2) * np.sqrt((x - 1.15)**2 + y**2))
def Lang(ncomm, q0, tstep, temperature, isteps):
# Define preliminary variables
q = np.empty((isteps, 2), dtype=np.float64)
q_trans = np.empty((isteps, 2), dtype=np.float64)
# Initial conditions
q[0, 0] = q0[0]
q[0, 1] = q0[1]
# Diffusion coefficient
Dt = np.sqrt(2.0 * temperature * tstep)
# Index for the transition trajectory
j = 0
for i in range(isteps - 1):
# Evaluate evolution of the system
fx, fy = force(q[i, 0], q[i, 1])
q[i + 1, 0] = q[i, 0] + fx * tstep + Dt * np.random.normal(0, 1)
q[i + 1, 1] = q[i, 1] + fy * tstep + Dt * np.random.normal(0, 1)
if state(q[i + 1, 0], q[i + 1, 1]) == 0:
q_trans[j, :] = q[i + 1, :]
j += 1
if j == 0:
out = np.empty((1, 2), dtype=np.float64)
out[0, 0] = 0.0
out[0, 1] = 0.0
return out
else:
return q_trans[:j, :]
def LangM(ncomm, q0, tstep, temperature, isteps):
# Define preliminary variables
q = np.empty((isteps, 2), dtype=np.float64)
q_trans = np.empty((isteps, 2), dtype=np.float64)
M = np.empty((isteps, ncomm, ncomm), dtype=np.float64)
dGx = np.empty(ncomm, dtype=np.float64)
dGy = np.empty(ncomm, dtype=np.float64)
# Initial conditions
q[0, 0] = q0[0]
q[0, 1] = q0[1]
# Diffusion coefficient
Dt = np.sqrt(2.0 * temperature * tstep)
# Index for the transition trajectory
j = 0
for i in range(isteps - 1):
# Evaluate evolution of the system
fx, fy = force(q[i, 0], q[i, 1])
q[i + 1, 0] = q[i, 0] + fx * tstep + Dt * np.random.normal(0, 1)
q[i + 1, 1] = q[i, 1] + fy * tstep + Dt * np.random.normal(0, 1)
if state(q[i + 1, 0], q[i + 1, 1]) == 0:
# Gradient components of the committors
for k in range(ncomm):
dGx[k], dGy[k] = ListdGuess(k, q[i + 1, 0], q[i + 1, 1])
# Evaluating M Matrix
for k in range(ncomm):
for l in range(ncomm):
M[j, k, l] = dGx[k] * dGx[l] + dGy[k] * dGy[l]
q_trans[j, :] = q[i + 1, :]
j += 1
if j == 0:
out = np.empty((1, 2), dtype=np.float64)
out[0, 0] = 0.0
out[0, 1] = 0.0
outM = np.empty((1, ncomm, ncomm), dtype=np.float64)
for k in range(ncomm):
for l in range(ncomm):
outM[i, k, l] = 0.0
return out, outM
else:
return q_trans[:j, :], M[:j, :, :]
def main():
print("Algorithm has started")
## Parameters of the run
ncomm = 0 # Number of guess committors
temperature = 1.0 # Temperature
tstep = 0.01 # time interval for MD simulations
kratchet = 150 # Force constant of the ratchet
MDsteps = 10000 # Maximum number of steps fo MD simulations
biassim = 1000 # Number of bias simulations used to sample transition region
selfsteps = 5 # Number of self consistent iterations
alpha = 0.5 # Percentage of previous iteration in self consistent step
threshold = 0.001 # Threshold for the end of the self consistent part
relax = 5 # How often do we pick a point of a biased trajectory as starting point of a MD trajectory
relaxation = False # If true, we do a relaxation after we estimate the transition probability with the biased simulations
## Limits of the plots
xlimleft = -2.0
xlimright = 2.0
ylimdown = -2.5
ylimup = 1.5
delta = 0.025
## Name of file if we want to save the evolution of the coefficients of the committor during the self consistent
savecoeff = False
namecoeff = ""
## Parameters of plots
axisticslabelfontsize = 9
axisticslabelfontsizeinset = 7
axislabelfontsize = 11
axislabelfontsizeinset = 9
legendfontsize = 7
lineswidth = 2
ncontour = 25
cmap = plt.get_cmap('RdBu')
## Name of file if we want to save the trajectories of the last run
savetraj = False
savetraj = ""
## Name of file if we want to save transition probability distribution plot
saveprob = False
nameprob = ""
with open("input", "r") as f:
for line in f:
line = re.sub("#.*$", "", line)
line = re.sub(" *$", "", line)
words = line.split()
if len(words) == 0:
continue
key = words[0]
if key == "ncomm":
ncomm = int(words[1])
elif key == "temperature":
temperature = float(words[1])
elif key == "tstep":
tstep = float(words[1])
elif key == "kratchet":
kratchet = float(words[1])
elif key == "MDsteps":
MDsteps = int(words[1])
elif key == "biassim":
biassim = int(words[1])
elif key == "selfsteps":
selfsteps = int(words[1])
elif key == "alpha":
alpha = float(words[1])
elif key == "threshold":
threshold = float(words[1])
elif key == "relaxation":
if re.match("[Tt].*", words[1]):
relaxation = True
elif key == "relax":
relax = int(words[1])
elif key == "xlimleft":
xlimleft = float(words[1])
elif key == "xlimright":
xlimright = float(words[1])
elif key == "ylimdown":
ylimdown = float(words[1])
elif key == "ylimup":
ylimup = float(words[1])
elif key == "delta":
delta = float(words[1])
elif key == "namecoeff":
savecoeff = True
namecoeff = words[1]
elif key == "nametraj":
savetraj = True
nametraj = words[1]
elif key == "nameprob":
saveprob = True
nameprob = words[1]
elif key == "axisticslabelfontsize":
axisticslabelfontsize = int(words[1])
elif key == "axisticslabelfontsizeinset":
axisticslabelfontsizeinset = int(words[1])
elif key == "axislabelfontsize":
axislabelfontsize = int(words[1])
elif key == "axislabelfontsizeinset":
axislabelfontsizeinset = int(words[1])
elif key == "legendfontsize":
legendfontsize = int(words[1])
elif key == "lineswidth":
lineswidth = float(words[1])
elif key == "ncontour":
ncontour = int(words[1])
else:
raise Exception("Unknown keyword: " + key)
if ncomm == 0:
raise Exception("Specify the number of guess committors")
print("Parameters loaded correctly")
## Prepare the contour lines for the potential and the basins
xcontour = np.arange(xlimleft, xlimright, 0.025)
ycontour = np.arange(ylimdown, ylimup, 0.025)
X, Y = np.meshgrid(xcontour, ycontour)
# Potential
CONT = X * 0
for i in range(X.shape[0]):
for j in range(X.shape[1]):
CONT[i, j] = potential(X[i, j], Y[i, j])
# Basins
BASINS = X * 0
for i in range(X.shape[0]):
for j in range(X.shape[1]):
BASINS[i, j] = state(X[i, j], Y[i, j])
levelsb = [-1.0, 0.0, 1.0]
## Prepare the grid for the plots
yplot, xplot = np.mgrid[slice(ylimdown, ylimup + delta, delta),
slice(xlimleft, xlimright + delta, delta)]
## I do the self consistent operation
print("Cycle = ", 1)
co = np.array([1.0 / ncomm for i in range(ncomm)])
print(co)
if savecoeff == True:
cprint = []
cprint.append(co)
print("Cycle = ", 2)
M = BiasRuns(ncomm, co, tstep, temperature, kratchet, MDsteps, biassim,
relaxation, relax)
print(M)
c = minimization(co, M, ncomm)
print(c)
if savecoeff == True:
cprint.append(c)
# I iterate the previous procedure many times
k = 0
while k < selfsteps - 2 and np.any(c - co > threshold):
print("Cycle = ", k + 3)
M = BiasRuns(ncomm, alpha * c + (1.0 - alpha) * co, tstep, temperature,
kratchet, MDsteps, biassim, relaxation, relax)
print(M)
cn = minimization(alpha * c + (1.0 - alpha) * co, M, ncomm)
co = np.copy(c)
c = np.copy(cn)
print(c)
k += 1
if savecoeff == True:
cprint.append(c)
## I save the coefficients of the linear combination
if savecoeff == True:
cprint = np.array(cprint)
with open(namecoeff, "w") as f:
np.savetxt(f, cprint, fmt="%10.10f")
print("Coefficients saved correctly")
## Relaxation of the last iteration
if savetraj == True or saveprob == True:
tmp = 0
for j in range(biassim):
q0 = start_pos()
biastraj = RatchetLang(c, q0, tstep, temperature, kratchet,
MDsteps)
if biastraj[0, 0] != 0.0 and biastraj[0, 1] != 0.0:
q0Lang = biastraj[1::5, :]
for i in range(q0Lang.shape[0]):
traj, M = LangM(ncomm, q0Lang[i, :], tstep, temperature,
relax) # I run the integrator
if traj[0, 0] != 0 and traj[0, 1] != 0:
if tmp == 0:
trajall = np.copy(traj)
Mall = np.copy(M)
tmp = 1
if tmp == 1:
trajall = np.concatenate((trajall, traj), axis=0)
Mall = np.concatenate((Mall, M), axis=0)
del traj, M
del biastraj
M = np.zeros((ncomm, ncomm), dtype=np.float64)
# Average all the values of M
for k in range(Mall.shape[0]):
for i in range(ncomm):
for j in range(ncomm):
M[i, j] += Mall[k, i, j]
# Average M over all the values obtained with the sampling
M /= Mall.shape[0]
## Evaluate the rate
rate = 0.0
for i in range(ncomm):
for j in range(ncomm):
rate += M[i, j] * c[i] * c[j]
rate *= np.sqrt(2.0 * temperature)
print("Rate of optimal linear combination: ", rate)
## I do the plot of the Langevin trajectories
if savetraj == True:
with PdfPages(nametraj) as pdf:
fmt1 = '%r %%'
fig = plt.figure(figsize=(4., 2.8))
plt.rc('text')
panel = fig.add_axes([
0.15, 0.15, 0.72, 0.75
]) # dimensions and location of the panel within the figure
# Potential
pcm = panel.plot(trajall[:, 0],
trajall[:, 1],
linewidth=0.5,
zorder=10)
panel.set_xlabel(
r'$x$', fontsize=axislabelfontsize, labelpad=2
) # labels and ticklabels along x with their fontsize and location, x limits and same for y below
for tick in panel.xaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_xlim(xlimleft - delta, xlimright + delta)
panel.xaxis.set_major_locator(MultipleLocator(1))
panel.xaxis.set_minor_locator(MultipleLocator(0.2))
panel.set_ylabel(r'$y$', fontsize=axislabelfontsize, labelpad=2)
for tick in panel.yaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_ylim(ylimdown - delta, ylimup + delta)
panel.yaxis.set_major_locator(MultipleLocator(1))
panel.yaxis.set_minor_locator(MultipleLocator(0.2))
CS = panel.contour(X,
Y,
CONT,
ncontour,
colors='k',
linewidths=0.5,
zorder=0)
plt.clabel(CS, fontsize=4, inline=1)
contour = panel.contour(X,
Y,
BASINS,
levels=levelsb,
colors="orange",
linewidths=0.5,
linestyles='dashed',
zorder=5)
plt.title("Trajectories") # title
pdf.savefig(fig)
print("Trajectories plotted successfully")
## I do the plot of the probability distribution in the transition region
if saveprob == True:
with PdfPages(nameprob) as pdf:
fmt1 = '%r %%'
fig = plt.figure(figsize=(4., 2.8))
plt.rc('text')
panel = fig.add_axes([
0.15, 0.15, 0.72, 0.75
]) # dimensions and location of the panel within the figure
# Borders of the plot
xedges = np.arange(xlimleft, xlimright, delta).tolist()
yedges = np.arange(ylimdown, ylimup, delta).tolist()
# Create the histogram
H, xedges, yedges = np.histogram2d(trajall[:, 0],
trajall[:, 1],
bins=(xedges, yedges),
density=True)
H = H.T # Let each row list bins with common y range.
pcm = panel.imshow(
H,
interpolation='nearest',
origin='low',
extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])
cbar = plt.colorbar(pcm, format=ticker.FuncFormatter(
fmt)) # plot colorbar and select format
cbar.ax.tick_params(labelsize=axisticslabelfontsize -
2) # dimension of the labels of the colorbar
pcm.set_cmap('RdBu')
panel.set_xlabel(
r'$x$', fontsize=axislabelfontsize, labelpad=2
) # labels and ticklabels along x with their fontsize and location, x limits and same for y below
for tick in panel.xaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_xlim(xlimleft - delta, xlimright + delta)
panel.xaxis.set_major_locator(MultipleLocator(1))
panel.xaxis.set_minor_locator(MultipleLocator(0.2))
panel.set_ylabel(r'$y$', fontsize=axislabelfontsize, labelpad=2)
for tick in panel.yaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_ylim(ylimdown - delta, ylimup + delta)
panel.yaxis.set_major_locator(MultipleLocator(1))
panel.yaxis.set_minor_locator(MultipleLocator(0.2))
# Potential
CS = panel.contour(X,
Y,
CONT,
ncontour,
colors='k',
linewidths=0.5)
plt.clabel(CS, fontsize=4, inline=1)
contour = panel.contour(X,
Y,
BASINS,
levels=levelsb,
colors="white",
linewidths=0.5,
linestyles='dashed')
plt.title("Transition probability distribution") # title
pdf.savefig(fig)
print("Transition probability distribution plotted successfully")
def RatchetLangM(c, q0, tstep, temperature, kr, isteps):
## Number of committor functions given as input
ncomm = len(c)
# Define preliminary variables
q = np.empty((isteps, 2), dtype=np.float64)
M = np.empty((isteps, ncomm, ncomm), dtype=np.float64)
dGx = np.empty(ncomm, dtype=np.float64)
dGy = np.empty(ncomm, dtype=np.float64)
# Assign initial position to the border of the reactant state
q[0, 0] = q0[0]
q[0, 1] = q0[1]
# Incremental variables in the loop
i = 0
j = 0
tmp = 0
# State of the point. If in reactant = -1, if in product = 1, otherwise = 0
s = state(q[0, 0], q[1, 1])
zmax = 0.0
# Diffusion coefficient
Dt = np.sqrt(2.0 * temperature * tstep)
while i < isteps - 1 and tmp == 0:
if s == -1:
# Restart trajectory
j = i
elif s == 1:
#Exit from loop
tmp = 1
# Evaluate evolution of the system
fx, fy = force(q[i, 0], q[i, 1])
# Evaluate z
z = 0.0
for k in range(ncomm):
z += c[k] * ListGuess(k, q[i, 0], q[i, 1])
# Gradient components of the committors
for k in range(ncomm):
dGx[k], dGy[k] = ListdGuess(k, q[i, 0], q[i, 1])
# Evaluating M Matrix
for k in range(ncomm):
for l in range(ncomm):
M[i, k, l] = dGx[k] * dGx[l] + dGy[k] * dGy[l]
# Dynamics
if z > zmax:
q[i + 1, 0] = q[i, 0] + fx * tstep + Dt * np.random.normal(0, 1)
q[i + 1, 1] = q[i, 1] + fy * tstep + Dt * np.random.normal(0, 1)
zmax = z
else:
ratchetx = 0.0
ratchety = 0.0
for k in range(ncomm):
ratchetx += c[k] * dGx[k]
ratchety += c[k] * dGy[k]
q[i + 1, 0] = q[i, 0] + fx * tstep + Dt * np.random.normal(
0, 1) + kr * ratchetx * (zmax - z) * tstep
q[i + 1, 1] = q[i, 1] + fy * tstep + Dt * np.random.normal(
0, 1) + kr * ratchety * (zmax - z) * tstep
i += 1
s = state(q[i, 0], q[i, 1])
# Output in the case we do not find a reactive coordinate, so that the function does not crash
if tmp == 0:
print('No reactive trajectory found!')
out = np.empty((1, 2), dtype=np.float64)
out[0, 0] = 0.0
out[0, 1] = 0.0
outM = np.empty((1, ncomm, ncomm), dtype=np.float64)
for k in range(ncomm):
for l in range(ncomm):
outM[i, k, l] = 0.0
return out, outM
return q[j + 1:i - 1, :], M[j + 1:i - 1, :, :]
def main():
print("Algorithm has started")
## Parameters of the run
temperature = 1.0 # Temperature
diffusion = 1.0 # diffusion coefficient
tstep = 0.01 # time interval for MD simulations
Nsim = 1000 # Number of MD simulations to determine boundary conditions
stepsim = 5000 # maximum number of steps for MD simulations
## Parameters of the grid
xlimleft = -3.0
xlimright = 3.0
nxstep = 50
ylimdown = -3.0
ylimup = 3.0
nystep = 50
## Name of file if we want to save the committor
savefile = False
namefile = ""
## Parameters if we want to save committor plot
saveplot = False
nameplot = ""
axisticslabelfontsize = 9
axisticslabelfontsizeinset = 7
axislabelfontsize = 11
axislabelfontsizeinset = 9
legendfontsize = 7
lineswidth = 2
ncontour = 25
with open("input", "r") as f:
for line in f:
line = re.sub("#.*$", "", line)
line = re.sub(" *$", "", line)
words = line.split()
if len(words) == 0:
continue
key = words[0]
if key == "temperature":
temperature = float(words[1])
elif key == "diffusion":
diffusion = float(words[1])
elif key == "tstep":
tstep = float(words[1])
elif key == "Nsim":
Nsim = int(words[1])
elif key == "stepsim":
stepsim = int(words[1])
elif key == "tstep":
tstep = float(words[1])
elif key == "xlimleft":
xlimleft = float(words[1])
elif key == "xlimright":
xlimright = float(words[1])
elif key == "nxstep":
nxstep = int(words[1])
elif key == "ylimup":
ylimup = float(words[1])
elif key == "ylimdown":
ylimdown = float(words[1])
elif key == "nystep":
nystep = int(words[1])
elif key == "namefile":
savefile = True
namefile = words[1]
elif key == "nameplot":
saveplot = True
nameplot = words[1]
elif key == "axisticslabelfontsize":
axisticslabelfontsize = int(words[1])
elif key == "axisticslabelfontsizeinset":
axisticslabelfontsizeinset = int(words[1])
elif key == "axislabelfontsize":
axislabelfontsize = int(words[1])
elif key == "axislabelfontsizeinset":
axislabelfontsizeinset = int(words[1])
elif key == "legendfontsize":
legendfontsize = int(words[1])
elif key == "lineswidth":
lineswidth = float(words[1])
elif key == "ncontour":
ncontour = int(words[1])
else:
raise Exception("Unknown keyword: " + key)
print("Parameters loaded correctly")
x = np.linspace(xlimleft, xlimright, nxstep)
y = np.linspace(ylimdown, ylimup, nystep)
beta = 1.0 / temperature # 1/k_{B}T
dx = x[1] - x[0] # step of the grid along the x direction
dy = y[1] - y[0] # step of the grid along the y direction
I = len(x) - 1 # index of the last cell along x
J = len(y) - 1 # index of the last cell along y
N = I * (
J + 1
) + J # index of the last cell in the 1D vector that contains all the I*(J+1)+J+1 = N+1 cells in the system
q = np.zeros(
shape=(N + 1)
) # vector that contains the N+1 values of the committor for each grid point
P = np.zeros(
shape=(N + 1, N + 1)
) # matrix with (N+1)*(N+1) elements, that determines the linear system to solve P*q = R
R = np.zeros(shape=(
N + 1
)) # vector with the N+1 elements of results of the backward F-P equation
bd = 0 # counter for boundary points on which the MD is finished
## Precompute some coefficients
D1 = diffusion * beta * tstep
D2 = np.sqrt(2. * diffusion * tstep)
print("Total number of boundary points = ", 2 * (nxstep + nystep) - 4)
now = time.time()
# construction of P and R
i = 0
while i < len(x):
xp = x[i]
j = 0
while j < len(y):
yp = y[j]
Fx, Fy = force(xp, yp)
n = i * (
J + 1
) + j # for each grid point i,j computes the corresponding index n in the 1D vectors and computes the coefficients A,B,C,D,E
A = diffusion / (dx**2) + (beta * diffusion * Fx) / (2 * dx)
B = 2. * diffusion / (dx**2) + 2. * diffusion / (dy**2)
C = diffusion / (dx**2) - (beta * diffusion * Fx) / (2 * dx)
D = diffusion / (dy**2) + (beta * diffusion * Fy) / (2 * dy)
E = diffusion / (dy**2) - (beta * diffusion * Fy) / (2 * dy)
if state(
xp, yp
) != 0: # if you are inside the reactant basin or the product basin impose boundary condition of q = 0 in Reactant and q = 1 in Product
P[n, n] = 1.
if xp > 0.:
R[n] = 1.
elif (
(i == 0) or (i == I)
): # if you are on the two boundaries along x, do MD simulations for each boundary point to find the committor on the edges of the grid
t = 0
nr = 0
nt = 0
while t < Nsim: # 1000 trajectories for each point
xi = x[
i] # for each trajectory in a given grid point on the edge, set as initial conditions the coordinates of that grid point
yi = y[j]
k = 0
while (
state(xi, yi) == 0 and k < stepsim
): # keep evolving the system untill you enter in Reactant or Product
Fx, Fy = force(xi, yi)
xf = xi + Fx * D1 + D2 * np.random.normal(
loc=0., scale=1.
) # evolve x and y with the equations of motion for a passive particle performing brownian motion in a potential energy landscape
yf = yi + Fy * D1 + D2 * np.random.normal(loc=0.,
scale=1.)
xi = xf
yi = yf
k += 1
if xf < 0.: # if you enter in Reactant
nr += 1
elif xf > 0.: # if you enter in Product
nt += 1
t += 1
if t != (nt + nr): # just a check
print("Something wrong occurred during MD simulation!")
bd += 1
print(
bd
) # print the index of the boundary point in which you finished the MD simulations
P[n, n] = 1.
R[n] = nt / (nt + nr) # value of the committor in that point
elif (
(i != 0) and (i != I) and ((j == 0) or (j == J))
): # if you are on the boundaries along y do MD simulation for each grid point on the boundary, except those included in the boundaries of x that are already done
t = 0
nr = 0
nt = 0
while t < Nsim:
xi = x[i]
yi = y[j]
k = 0
while (state(xi, yi) == 0 and k < stepsim):
Fx, Fy = force(xi, yi)
xf = xi + Fx * D1 + D2 * np.random.normal(loc=0.,
scale=1.)
yf = yi + Fy * D1 + D2 * np.random.normal(loc=0.,
scale=1.)
xi = xf
yi = yf
k += 1
if xf < 0.:
nr += 1
elif xf > 0.:
nt += 1
t += 1
if t != (nt + nr):
print("Something wrong occurred during MD simulation!")
bd += 1
print(bd)
P[n, n] = 1.
R[n] = nt / (nt + nr)
else: # if you are in every other point of the grid fill the P matrix according to the usual pattern
P[n, (i - 1) * (J + 1) + j] = C
P[n, i * (J + 1) + j - 1] = E
P[n, i * (J + 1) + j] = -B
P[n, i * (J + 1) + j + 1] = D
P[n, (i + 1) * (J + 1) + j] = A
j += 1
i += 1
print("System initialized")
q = scipy.linalg.solve(P, R) # solve linear system to find the committor
for el in q:
if el > 1.: # some errors in the solution of the system are inevitable, so don't mind if you get some of these errors, as long as the values of the committor are not too much larger than 1 or too much smaller than 0
print("Error! Committor larger than 1!")
elif el < 0.:
print("Error! Committor smaller than 0!")
q = np.reshape(
q, (I + 1, J + 1)) # reshape the committor from 1D vector to 2D grid
print("Simulation time ", time.time() - now)
# Save committor on a File
if savefile == True:
with open(namefile, "w") as f:
np.savetxt(f, q, fmt="%10.10f")
print("Committor saved correctly")
# Make the plot
if saveplot == True:
xplot = np.empty(shape=(
len(x) + 1
)) # set x and y coordinates for the edges of the bins in the grid
yplot = np.empty(shape=(len(y) + 1))
k = 0
for el in x:
xplot[k] = x[k] - (dx / 2.)
k += 1
xplot[len(x)] = x[len(x) - 1] + (dx / 2.)
k = 0
for el in y:
yplot[k] = y[k] - (dy / 2.)
k += 1
yplot[len(y)] = y[len(y) - 1] + (dy / 2.)
with PdfPages(nameplot) as pdf:
fmt1 = '%r %%'
fig = plt.figure(figsize=(4., 2.8), dpi=600)
plt.rc('text')
panel = fig.add_axes([
0.15, 0.15, 0.72, 0.75
]) # dimensions and location of the panel within the figure
cmap = plt.get_cmap('RdBu') # choose colormap for the committor
pcm = panel.pcolormesh(xplot,
yplot,
q.T,
cmap=cmap,
zorder=0,
vmin=0.,
vmax=1.) # plot the committor in the grid
cbar = plt.colorbar(pcm, format=ticker.FuncFormatter(
fmt)) # plot colorbar and select format
cbar.ax.tick_params(labelsize=axisticslabelfontsize -
2) # dimension of the labels of the colorbar
panel.set_xlabel(
r'$x$', fontsize=axislabelfontsize, labelpad=2
) # labels and ticklabels along x with their fontsize and location, x limits and same for y below
for tick in panel.xaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_xlim(xlimleft - 0.1, xlimright + 0.1)
panel.xaxis.set_major_locator(MultipleLocator(1))
panel.xaxis.set_minor_locator(MultipleLocator(0.2))
panel.set_ylabel(r'$y$', fontsize=axislabelfontsize, labelpad=2)
for tick in panel.yaxis.get_major_ticks():
tick.label.set_fontsize(axisticslabelfontsize)
panel.set_ylim(ylimdown - 0.1, ylimup + 0.1)
panel.yaxis.set_major_locator(MultipleLocator(1))
panel.yaxis.set_minor_locator(MultipleLocator(0.2))
# Grid for contour lines
x = np.arange(xlimleft, xlimright, 0.025)
y = np.arange(ylimdown, ylimup, 0.025)
X, Y = np.meshgrid(x, y)
# Potential contour lines
Z = X * 0
for i in range(X.shape[0]):
for j in range(X.shape[1]):
Z[i, j] = potential(X[i, j], Y[i, j])
CS = panel.contour(X, Y, Z, ncontour, colors='k', linewidths=0.5)
plt.clabel(CS, fontsize=4, inline=1)
# Basins contour lines
P = X * 0
for i in range(X.shape[0]):
for j in range(X.shape[1]):
P[i, j] = state(X[i, j], Y[i, j])
levelsb = [-1.0, 0.0, 1.0]
contour = panel.contour(X,
Y,
P,
levels=levelsb,
colors="white",
linewidths=0.5,
linestyles='dashed')
plt.title(r"$q(x,y)$") # title
pdf.savefig(fig)
print("Committor plot saved correctly")