def fpt_poisson_inverselapl (x, t, α, D, σ, fpt): mpmath.mp.dps = 30 x = np.atleast_1d(x) t = np.atleast_1d(t) P = np.zeros((len(x),len(t))) sqrt2 = mpmath.sqrt(2) if fpt: ret_psr_lp = lambda psr,s: 1 - s*psr # p(tf) = - d/dt psr else: ret_psr_lp = lambda psr,s: psr for i in range(len(x)): if σ == 0: def ps0_lp (κ, s): return (1 - mpmath.exp(-κ * x[i])) / s else: b = x[i] / σ def ps0_lp (κ, s): k = σ * κ return (1 - mpmath.exp(k**2/2)/2 * ( mpmath.exp(+κ*x[i]) * mpmath.erfc((b+k)/sqrt2) + mpmath.exp(-κ*x[i]) * (1+mpmath.erf((b-k)/sqrt2)) ) ) / s def psr_lp (s): κ = mpmath.sqrt( (α+s) / D ) ps0 = ps0_lp(κ, s=α+s) psr = ps0 / (1 - α*ps0) return ret_psr_lp(psr, s) for j in range(len(t)): if x[i] < 0: P[i,j] = 0 else: P[i,j] = mpmath.invertlaplace(psr_lp, t[j], method='talbot', degree=20) return np.squeeze(P)
def linear_ramp_inv(self, t):
inv_lap_func=lambda s: 1/(s**2*(s**(-self.nd_param.nd_param_dict["psi"])+self.nd_param.nd_param_dict["tau"]))
inv_lap_val=mpmath.invertlaplace(inv_lap_func,t,method='talbot')
if t<self.dim_dict["tr"]:
return self.nd_param.nd_param_dict["Cdl"]*inv_lap_val
else:
return -self.nd_param.nd_param_dict["Cdl"]*inv_lap_val
def B(self, t):
inv_lap_func = lambda s: 1 / (s * (self.nd_param.nd_param_dict[
"tau"] + s**-self.nd_param.nd_param_dict["psi"]))
inv_lap_val = mpmath.invertlaplace(inv_lap_func, t, method='talbot')
return inv_lap_val
# -*- coding: utf-8 -*-
"""
Created on Wed Feb 6 11:36:46 2019
@author: CatOnTour
"""
import mpmath as mp
import numpy as np
import matplotlib.pyplot as plt
def f(s):
return 1 / (s - 1)
t = np.linspace(0.01, 10, 20)
G = []
for i in t:
G.append(mp.invertlaplace(f, i, method='dehoog', dps=10, degree=18))
plt.plot(t, G)
plt.show()
x_RLC_func = lambdify(s, x_RLC[0])
x_RCL_func = lambdify(s, x_RCL[0])
#t = np.linspace(0.01,20,20)
t = np.linspace(0.01,20,50)
X_CLR = []
X_LCR = []
X_CRL = []
X_LRC = []
X_RLC = []
X_RCL = []
for i in t:
X_CRL.append(mp.invertlaplace(x_CRL_func, i, method = 'dehoog', dps = 10, degree = 18))
X_CLR.append(mp.invertlaplace(x_CLR_func, i, method = 'dehoog', dps = 10, degree = 18))
X_LCR.append(mp.invertlaplace(x_LCR_func, i, method = 'dehoog', dps = 10, degree = 18))
X_LRC.append(mp.invertlaplace(x_LRC_func, i, method = 'dehoog', dps = 10, degree = 18))
X_RLC.append(mp.invertlaplace(x_RLC_func, i, method = 'dehoog', dps = 10, degree = 18))
X_RCL.append(mp.invertlaplace(x_RCL_func, i, method = 'dehoog', dps = 10, degree = 18))
U2_func = lambdify(s,U_2)
U2_time = []
for i in t:
U2_time.append(mp.invertlaplace(U2_func, i, method = 'dehoog', dps = 10, degree = 18))
plt.plot(t, U2_time, "k", label = "U2")
x_P_func = lambdify(s, x_P[0])
x_B_func = lambdify(s, x_B[0])
#t = np.linspace(0.01,20,20)
t = np.linspace(0.01, 20, 50)
X_A = []
X_Z = []
X_Y = []
X_H = []
X_P = []
X_B = []
for i in t:
X_A.append(
mp.invertlaplace(x_A_func, i, method='dehoog', dps=10, degree=18))
X_Z.append(
mp.invertlaplace(x_Z_func, i, method='dehoog', dps=10, degree=18))
X_Y.append(
mp.invertlaplace(x_Y_func, i, method='dehoog', dps=10, degree=18))
X_H.append(
mp.invertlaplace(x_H_func, i, method='dehoog', dps=10, degree=18))
X_P.append(
mp.invertlaplace(x_P_func, i, method='dehoog', dps=10, degree=18))
X_B.append(
mp.invertlaplace(x_B_func, i, method='dehoog', dps=10, degree=18))
x_21_func = lambdify(s, x_21)
x_21_time = []
for i in t:
x_21_time.append(
def G(y, x_0, tau, b, a, beta):
return float(
invertlaplace(lambda s: Laplace_Transform_G(y, x_0, s, b, a, beta),
tau,
method='dehoog',
dps=10))
def F(s):
a = 1
b = 2
return 1 / (s * (s * s + a * s + b))
start = 0.01
end = 20
step = 0.1
no = (end - start) / step
t = np.linspace(start, end, int(no))
y = []
for i in range(0, len(t)):
y.append(mp.invertlaplace(F, t[i], method='dehoog'))
#print(t)
#print(y)
fig_reg1, axs_reg1 = plt.subplots()
axs_reg1.plot(t, y, color='black', alpha=0.7)
axs_reg1.set_xlabel(r'$t$', fontsize=30)
axs_reg1.set_ylabel(r'$y$', fontsize=30)
axs_reg1.grid(True)
plt.show()
def visco_template(self, method_class, model_class, region):
# region.plot()
# plt.show()
data = region.all_points
model = model_class(region=region)
method = method_class(model=model, basis=quadratic_2d)
# cache_path = "result.npy"
# if os.path.exists(cache_path):
# result = np.load(cache_path)
# else:
# result = method.solve()
# np.save(cache_path, result)
result = method.solve()
print("result", result)
def nearest_indices(t):
print(".", end="")
return np.abs(model.s - t).argmin()
fts = np.array([[
mp.invertlaplace(lambda t: result[nearest_indices(t)][i][0],
x,
method='stehfest',
degree=model.iterations)
for x in range(1, model.time + 1)
] for i in range(result.shape[1])],
dtype=np.float64)
for point_index, point in enumerate(data):
analytical_x = num.Function(model.analytical[0],
name="analytical ux(%s)").eval(
point)[::model.iterations].ravel()
analytical_y = num.Function(model.analytical[1],
name="analytical uy(%s)").eval(
point)[::model.iterations].ravel()
calculated_x = fts[2 * point_index].ravel()
calculated_y = fts[2 * point_index + 1].ravel()
print('point', point)
print('calculated_x, point diff, analytical', [
calculated_x,
np.diff(calculated_x),
analytical_x,
])
print('calculated_y', calculated_y)
plt.plot(point[0], point[1], "r^-")
plt.plot(point[0] + np.diff(calculated_x),
point[1] + np.diff(calculated_y), "b^-")
plt.plot(point[0] + analytical_x, point[1] + analytical_y, "gs-")
region.plot()
plt.show()
for point_index, point in enumerate(data):
analytical_x = num.Function(model.analytical[0],
name="analytical ux(%s)").eval(
point)[::model.iterations].ravel()
calculated_x = fts[2 * point_index].ravel()
print(point)
t = np.arange(0.5, calculated_x.size - 1)
# plt.plot(t, 1.5*np.diff(np.diff(calculated_x))[0]+np.diff(calculated_x), "b^-")
plt.plot(calculated_x, "r^-")
# plt.plot(np.diff(calculated_x), "b^-")
plt.plot(analytical_x, "gs-")
plt.show()
