ml = []
ui = []
suml1 = []
suml2 = []
suml3 = []
suml4 = []
suml5 = []
L = 0
while 1:
# Step 1: run inital cases
# set up runs
ml.append(M**L*nx)
if not(os.path.exists("L"+str(L))):
os.mkdir("L"+str(L))
sums = mmc.preprocess(ml,N,L,frames,res,ui)
suml1.append(N)
suml2.append(sums[0,:])
suml3.append(sums[1,:])
suml4.append(sums[2,:])
suml5.append(sums[3,:])
# Step 2: estimate the variance using the inital number of samples
Vl = mmc.variance(suml3,suml2,suml1)
# Step 3: Calculate Optimal Nl, l=0,1,...,L
Nl = np.ceil(2*e**(-2)*np.sqrt(Vl/ml)*np.sum(np.sqrt(Vl/ml)))
# Step 4: Evaluate extra samples at each level as needed for the
# new Nl
for k in range(0,L+1):
res= 400 # plotting resolution
frames = 10
ml = []
suml1 = []
suml2 = []
suml3 = []
suml4 = []
suml5 = []
while 1:
# Step 1: run inital cases
# set up runs
ml.append(M**L*nx)
os.mkdir("L"+str(L))
sums = mmc.preprocess(ml,N,L,frames,res)
suml1.append(N)
suml2.append(sums[0,:])
suml3.append(sums[1,:])
suml4.append(sums[2,:])
suml5.append(sums[3,:])
# Step 2: estimate the variance using the inital number of samples
Vl = mmc.variance(suml3,suml2,suml1)
# Step 3: Calculate Optimal Nl, l=0,1,...,L
Nl = np.ceil(2*e**(-2)*np.sqrt(Vl/ml)*np.sum(np.sqrt(Vl/ml)))
# Step 4: Evaluate extra samples at each level as needed for the
# new Nl
for k in range(0,L+1):
L = 4
frames = 10
Pl_mean = np.zeros((L+1,res), np.float)
Pl1_mean= np.zeros((L+1,res), np.float)
Pl_sigm = np.zeros((L+1,res), np.float)
Pl1_sigm= np.zeros((L+1,res), np.float)
levels = []
uii = []
mll = []
NN = 50
for m in range(0,L+1):
mll.append(M**m*res)
sums = mmc.preprocess(mll,NN,m,frames,res,uii)
Pl_mean[m,:] = sums[2,:]/NN
Pl_sigm[m,:] = sums[3,:]/(NN-1) - (1/(NN**2-NN))*(sums[2,:])**2
Pl1_mean[m,:] = sums[0,:]/NN
Pl1_sigm[m,:] = sums[1,:]/(NN-1) - (1/(NN**2-NN))*(sums[0,:])**2
levels.append(m)
figure(2)
font = {'fontsize' : 20}
subplot(2,1,1),plot(levels,np.log(np.abs(Pl_mean[:,0]))/np.log(M),'-s',levels[1:L+1],np.log(np.abs(Pl1_mean[1:L+1,0]))/np.log(M),'-*r',linewidth=2)
legend(('$P_l$','$P_l-P_{l-1}$'),3)
xlabel('$\ell$',font)
ylabel('$log_M |mean|$',font)
font = {'fontsize' : 20}
subplot(2,1,2),plot(levels,np.log(Pl_sigm[:,0])/np.log(M),'-s',levels[1:L+1],np.log(Pl1_sigm[1:L+1,0])/np.log(M),'-*r',linewidth=2)
ml = []
ui = []
suml1 = []
suml2 = []
suml3 = []
suml4 = []
suml5 = []
while 1:
# Step 1: run inital cases
# set up runs
ml.append(M**L * nx)
if not (os.path.exists("L" + str(L))):
os.mkdir("L" + str(L))
sums = mmc.preprocess(ml, N, L, frames, ui)
suml1.append(N)
suml2.append(sums[0, :])
suml3.append(sums[1, :])
suml4.append(sums[2, :])
suml5.append(sums[3, :])
# Step 2: estimate the variance using the inital number of samples
Vl = mmc.variance(suml3, suml2, suml1)
# Step 3: Calculate Optimal Nl, l=0,1,...,L
Nl = np.ceil(2 * e**(-2) * np.sqrt(Vl / ml) * np.sum(np.sqrt(Vl / ml)))
# Step 4: Evaluate extra samples at each level as needed for the
# new Nl
for k in range(0, L + 1):
res = 400 # plotting resolution
frames = 10
ml = []
suml1 = []
suml2 = []
suml3 = []
suml4 = []
suml5 = []
while 1:
# Step 1: run inital cases
# set up runs
ml.append(M**L * nx)
os.mkdir("L" + str(L))
sums = mmc.preprocess(ml, N, L, frames, res)
suml1.append(N)
suml2.append(sums[0, :])
suml3.append(sums[1, :])
suml4.append(sums[2, :])
suml5.append(sums[3, :])
# Step 2: estimate the variance using the inital number of samples
Vl = mmc.variance(suml3, suml2, suml1)
# Step 3: Calculate Optimal Nl, l=0,1,...,L
Nl = np.ceil(2 * e**(-2) * np.sqrt(Vl / ml) * np.sum(np.sqrt(Vl / ml)))
# Step 4: Evaluate extra samples at each level as needed for the
# new Nl
for k in range(0, L + 1):
