def plot_physical_evolution(function_evolution, x, t, dW, storedTime, N, L):
vf.is_vector(x)
# vf.is_matrix(function_evolution) # function_evolution is not a numpy matrix
fig = plt.figure()
ax = fig.add_subplot(111)
plotVal = function_evolution[0, :]
axis_ceil = 1.1 * np.max(np.abs(plotVal))
line = ax.plot(x, np.real(plotVal), 'b', x, np.imag(plotVal), 'r', x,
np.abs(plotVal), 'y')
W = np.cumsum(sum(dW))
W = np.insert(W, 0, 0)
for i in range(storedTime):
index = int((i + 1) * N / storedTime)
t_val = t[index]
W_val = W[index]
plotVal = function_evolution[i + 1, :]
line[0].set_ydata(np.real(plotVal))
line[1].set_ydata(np.imag(plotVal))
line[2].set_ydata(np.abs(plotVal))
plt.legend(line, ['real(u)', 'imag(u)', 'abs(u)'])
#plt.plot(x, np.real(plotVal),'b', x, np.imag(plotVal),'r', x, np.abs(plotVal), 'y')
plt.axis([-L, L, -axis_ceil, axis_ceil])
plt.suptitle('t = {:1.4f}, W_t = {:4.4f}'.format(
t_val, W_val)) #,fontsize=20)
#plt.draw()
fig.canvas.draw()
fig.canvas.flush_events()
plt.pause(np.spacing(1))
plt.show()
def plot_norm_evolution(norm_evolution, stored_t, axis_args, norm_string,
save_title):
vf.is_vector(norm_evolution)
# vf.is_matrix(function_evolution) # function_evolution is not a numpy matrix
fig = plt.figure(figsize=(15, 15))
plt.plot(stored_t, np.real(norm_evolution))
plt.axis(axis_args)
plt.xlabel('t')
plt.ylabel(norm_string)
#plt.show()
plt.savefig(save_title)
return fig
def FD_N_star_solver(currU,firstHalfdW,FDMatSq,h,sigma): vf.is_vector(currU) # Initialize loop variables crit = True i = 1 NStar = currU # Calculate some values which don't change a = linalg.expm(1j*firstHalfdW*FDMatSq).dot(currU) while crit and i < 120: oldNStar = NStar tempNStar = a+h/2*NStar NStar = cubicU(tempNStar,sigma) crit = linalg.norm(oldNStar-NStar) > np.spacing(1); i = i+1; return NStar
def FDEulTypeSolver(currU,dW,FDMatSq,h,sigma,G): vf.is_vector(currU) # Initialize loop variables crit = True; i = 1; nextU = currU; # Calculate some values which don't change A = sparse.eye(len(currU)) + 1j*dW/2*FDMatSq B = sparse.eye(len(currU)) - 1j*dW/2*FDMatSq AcurrU = A.dot(currU) while (crit and i < 120): tempU = nextU; nextU = spla.spsolve(B,AcurrU + 1j*h*G(currU,nextU,sigma)) crit = linalg.norm(tempU-nextU) > np.spacing(1); i = i+1; return nextU
def PS_N_star_solver(currU,firstHalfdW,kSq,h,sigma): vf.is_vector(currU) # Initialize loop variables crit = True i = 1 NStar = currU # Calculate some values which don't change a = np.multiply( np.exp(-firstHalfdW*1j*kSq), currU) while crit and i < 120: oldNStar = NStar tempNStar = a + h/2*NStar NStar = fft(1j*cubicU(ifft(tempNStar),sigma)) crit = linalg.norm(oldNStar-NStar) > np.spacing(1); i = i+1; return NStar
def pseudospectral_simulation(N,h,kSq,sigma,u0,W,scheme,queries): vf.is_vector(u0) vf.is_vector(kSq) # Need to preallocate memory for query results currU = u0 queryStorage = [] queryIndex = [] for q in range(len(queries)): queryStorage.append(queries[q].preallocateQueryResult()) queryStorage[q][0,:] = queries[q].function(currU) queryIndex.append(1) for i in range(N): dW = W[:,i] # dW = np.random.randn(2,1)*(h/2) currU = scheme(currU,dW,kSq,h,sigma) for q in range(len(queries)): if (i % queries[q].periodicity) == (queries[q].periodicity - 1): queryStorage[q][queryIndex[q],:] = queries[q].function(currU) queryIndex[q] += 1 return queryStorage
def PSEulTypeSolver(currU,dW,kSq,h,sigma,G): vf.is_vector(currU) # Initialize loop variables crit = True; i = 1; nextU = currU; realSpaceCurrU = ifft(currU); realSpaceNextU = realSpaceCurrU; # Calculate some values which don't change a = np.multiply( np.divide(1 - 1j*dW/2*kSq, 1 + 1j*dW/2*kSq), currU) b = 1j*h/(1 + 1j*dW/2*kSq); while (crit and i < 120): tempU = nextU; nextU = a + np.multiply(b,fft(G(realSpaceCurrU,realSpaceNextU,sigma))); realSpaceNextU=ifft(nextU); crit = linalg.norm(tempU-nextU) > np.spacing(1); i = i+1; return nextU
def finite_difference_simulation(N,h,FDMatSq,sigma,u0,W,scheme,queries): vf.is_vector(u0) # Need to preallocate memory for query results currU = u0 queryStorage = [] queryIndex = [] for q in range(len(queries)): queryStorage.append(queries[q].preallocateQueryResult()) queryStorage[q][0,:] = queries[q].function(currU) queryIndex.append(1) for i in range(N): dW = W[:,i] # dW = np.random.randn(2,1)*(h/2) currU = scheme(currU,dW,FDMatSq,h,sigma) for q in range(len(queries)): if (i % queries[q].periodicity) == (queries[q].periodicity - 1): #print(currU) #print(type(currU)) #print(q) queryStorage[q][queryIndex[q],:] = queries[q].function(currU) queryIndex[q] += 1 return queryStorage
def H1_norm(u, dx):
vf.is_vector(u)
deriv_val = (u[1:] - u[:-1]) / dx
return L2_norm(u, dx) + L2_norm(np.append(deriv_val, deriv_val[-1]), dx)
def L2_norm(u, dx):
vf.is_vector(u)
int_val = np.power(np.abs(u), 2)
return trapezoidal_integral(int_val, dx)
def trapezoidal_integral(u, dx):
vf.is_vector(u)
return dx / 2 * np.sum(u[:-1] + u[1:])
def cubicU(currU,sigma): vf.is_vector(currU) return np.multiply(np.power(np.absolute(currU),2*sigma),currU)