Commit ffd56e4b authored by Mathieu RASSON's avatar Mathieu RASSON

Merge modification

parents 0f84a571 87ffc984
......@@ -476,21 +476,20 @@
"source": [
"# Energy evolution\n",
"\n",
"ener = np.zeros(crank.n_z)\n",
"for i in range(crank.n_z):\n",
" # Filled at each z\n",
" for j in range(crank.n_r):\n",
" # Term integrated along t at r added against r value\n",
" ener[i] += crank.delta_t * np.sum(np.abs(E[i,j,:])**2) * np.real(crank.r_pts[j])\n",
"# r integration step\n",
"ener *= crank.delta_r\n",
"ener = np.array([crank.delta_r*crank.delta_t*np.sum(np.abs(E[i,:,:])**2) for i in range(crank.n_z)])\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(crank.z_pts), ener)\n",
"plt.ylim(0,2e-14)\n",
"plt.plot(ener)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
......@@ -718,9 +717,9 @@
"diff_coeff = 1j*1/(2 * k)\n",
"#diff_coeff = 0\n",
"#diff_coeff = 1e-4\n",
"disp_coeff = -1j*k_2/2\n",
"#disp_coeff = -1j*k_2/2\n",
"#disp_coeff = 1j * 1e-25\n",
"#disp_coeff = 0\n",
"disp_coeff = 0\n",
"\n",
"print('diff :', diff_coeff)\n",
"print('disp :', disp_coeff)\n",
......@@ -847,29 +846,6 @@
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Energy evolution\n",
"\n",
"ener = np.zeros(crank.n_z)\n",
"for i in range(crank.n_z):\n",
" # Filled at each z\n",
" for j in range(crank.n_r):\n",
" # Term integrated along t at r added against r value\n",
" ener[i] += crank.delta_t * np.sum(np.abs(E[i,j,:])**2) * np.real(crank.r_pts[j])\n",
"# r integration step\n",
"ener *= crank.delta_r\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(crank.z_pts), ener)\n",
"plt.ylim(0,2e-14)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
......@@ -1022,18 +998,10 @@
"source": [
"# Energy evolution\n",
"\n",
"ener = np.zeros(crank.n_z)\n",
"for i in range(crank.n_z):\n",
" # Filled at each z\n",
" for j in range(crank.n_r):\n",
" # Term integrated along t at r added against r value\n",
" ener[i] += crank.delta_t * np.sum(np.abs(E[i,j,:])**2) * np.real(crank.r_pts[j])\n",
"# r integration step\n",
"ener *= crank.delta_r\n",
"ener = np.array([crank.delta_r*crank.delta_t*np.sum(np.abs(E[i,:,:])**2) for i in range(crank.n_z)])\n",
"\n",
"plt.figure()\n",
"plt.plot(np.real(crank.z_pts), ener)\n",
"plt.ylim(0,2e-5)\n",
"plt.plot(ener)\n",
"plt.show()"
]
},
......
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"DATA PRODUCTION\n",
"\n",
"We define some constants for the whole problem, as well as some functions :\n",
"\n",
"- wavevector\n",
"- potential\n",
"- initialisation of E"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'CrankNicolson'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-1-bc37d7a89e1a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mCrankNicolson\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mlambd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.7e-6\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'CrankNicolson'"
]
}
],
"source": [
"import numpy as np\n",
"import CrankNicolson\n",
"\n",
"lambd = 0.7e-6\n",
"\n",
"k = 2 * np.pi / lambd\n",
"\n",
"w0 = 1e-3\n",
"Pin = 1\n",
"\n",
"diff_coeff = 1j*1/(2 * k)\n",
"#diff_coeff = 0\n",
"#diff_coeff = 1e-4\n",
"\n",
"print('diff :', diff_coeff)\n",
"\n",
"\n",
"def potential(r):\n",
" try:\n",
" return diff_coeff / r\n",
" except ZeroDivisionError:\n",
" return 0\n",
"\n",
"\n",
"def gaussian(r, r0=0, w0=1, Pin=1):\n",
" return np.sqrt(2*Pin/(np.pi*w0**2)) * np.exp(-(r-r0)** 2/(w0**2))\n",
"\n",
"\n",
"def initial_enveloppe(r_pts, w0, Pin):\n",
" return np.array([gaussian(r_pts[i], w0=w0, Pin=Pin) for i in range(len(r_pts))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Instanciation of the CN Class"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'CrankNicolson' is not defined",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-4-4030111dc1b1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mcrank\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCrankNicolson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mcrank\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_grid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr_max\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_r\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_min\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_max\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_z\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m200\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mcrank\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_parameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdiff_coeff\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mV\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpotential\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mNameError\u001b[0m: name 'CrankNicolson' is not defined"
]
}
],
"source": [
"crank = CrankNicolson()\n",
"\n",
"crank.set_grid(r_max=1e-2, n_r=100, z_min=0, z_max=10, n_z=200)\n",
"crank.set_parameters(D=diff_coeff, V=potential)\n",
"\n",
"crank.solve(initial_enveloppe(crank.r_pts, w0, Pin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Save the result for later analysis"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"np.savetxt(\"../CN_cylindric_complex_E.dat\", np.abs(crank.E_matrix))\n",
"np.savetxt(\"../CN_cylindric_complex_r_pts.dat\", crank.r_pts)\n",
"np.savetxt(\"../CN_cylindric_complex_z_pts.dat\", crank.z_pts)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
{
"cells": [],
"metadata": {},
"nbformat": 4,
"nbformat_minor": 2
}
"""
### Adapted crank Nicholson class.
* Prepare half-step method.
* Prepare non linear term for one of the half-step.
* Use $V$ advection to add first radial derivative.
$V$ is a function of $r$
$$
V(r) = \dfrac{i}{2 k_0} \dfrac{1}{r}
$$
and $V(0) = 0$.
**Warning**: do not use $V(0)=0$ for any calculation.
**Warning**: Test scheme matrices separately.
"""
import numpy as np
import scipy.sparse
import scipy.linalg as la
class CrankNicolson:
"""A class that solves dE/dz = D*d2E/dr2 + V(r)*dE/dr"""
# Cylindrical grid
def set_grid(self, r_max, n_r, z_min, z_max, n_z):
self.r_max, self.n_r = r_max, n_r
self.z_min, self.z_max, self.n_z = z_min, z_max, n_z
self.r_pts, self.delta_r = np.linspace(0, r_max, n_r, retstep=True, endpoint=False)
self.z_pts, self.delta_z = np.linspace(z_min, z_max, n_z, retstep=True, endpoint=False)
# Parameters of the scheme
def set_parameters(self, D, V):
# V has to be vectorised
self.D, self.V = D, V
# One solving step for r dependency
def solve(self, E_init):
# Coefficient of matrices
sig = self.D * self.delta_z / 2. / self.delta_r ** 2
nu = lambda x: - self.delta_z / 4. / self.delta_r * self.V(x) # minus sign for V convention
# Empty solution matrix
self.E_matrix = np.zeros([self.n_z, self.n_r], dtype=complex)
# Sparse solver
A = self._fillA_sp(sig, nu, self.n_r)
B = self._fillB_sp(sig, nu, self.n_r)
# Set boundary conditions
# Dirichlet at infinity
A[1, -1] = 1.0
A[2, -2] = 0.0
B[-1, -1] = 0.0
B[-1, -2] = 0.0
# Neumann at r=0
A[0, 1] = -2 * sig
B[0, 1] = 2 * sig
# Propagate
E = E_init.copy()
for n in range(self.n_z):
self.E_matrix[n, :] = E
E = la.solve_banded((1, 1), A, B.dot(E), check_finite=False)
# Deep copy of results for export
# np.savetxt ?
def get_E(self):
return self.E_matrix.copy()
# Diagonal packing for banded
def _fillA_sp(self, sig, nu, n):
"""Returns a tridiagonal matrix in compact form ab[1+i-j,j]=a[i,j]"""
A = np.zeros([3, n], dtype=complex) # A has three diagonals and size n
# Superdiagonal
A[0, 1:] = -(sig - nu(self.r_pts[:-1]))
# Diagonal
A[1] = 1 + 2 * sig
# Subdiagonal
A[2, :-1] = -(sig + nu(self.r_pts[1:]))
return A
# Sparse tridiagonal storage
def _fillB_sp(self, sig, nu, n):
"""Returns a tridiagonal sparse matrix in csr-form"""
_o = np.ones(n, dtype=complex)
supdiag = (sig - nu(self.r_pts[:-1]))
diag = (1 - 2 * sig) * _o
subdiag = (sig + nu(self.r_pts[1:]))
return scipy.sparse.diags([supdiag, diag, subdiag], [1, 0, -1], (n, n), format="csr")
\ No newline at end of file
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"DATA PRODUCTION\n",
"\n",
"We define some constants for the whole problem, as well as some functions :\n",
"\n",
"- wavevector\n",
"- potential\n",
"- initialisation of E"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"diff : 5.570423008216336e-08j\n"
]
}
],
"source": [
"import numpy as np\n",
"from CCCN import CrankNicolson\n",
"\n",
"lambd = 0.7e-6\n",
"\n",
"k = 2 * np.pi / lambd\n",
"\n",
"w0 = 1e-3\n",
"Pin = 1\n",
"\n",
"diff_coeff = 1j*1/(2 * k)\n",
"#diff_coeff = 0\n",
"#diff_coeff = 1e-4\n",
"\n",
"print('diff :', diff_coeff)\n",
"\n",
"\n",
"def potential(r):\n",
" try:\n",
" return diff_coeff / r\n",
" except ZeroDivisionError:\n",
" return 0\n",
"\n",
"\n",
"def gaussian(r, r0=0, w0=1, Pin=1):\n",
" return np.sqrt(2*Pin/(np.pi*w0**2)) * np.exp(-(r-r0)** 2/(w0**2))\n",
"\n",
"\n",
"def initial_enveloppe(r_pts, w0, Pin):\n",
" return np.array([gaussian(r_pts[i], w0=w0, Pin=Pin) for i in range(len(r_pts))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Instanciation of the CN Class"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/antoine/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: RuntimeWarning: divide by zero encountered in true_divide\n",
"/home/antoine/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: RuntimeWarning: invalid value encountered in true_divide\n"
]
}
],
"source": [
"crank = CrankNicolson()\n",
"\n",
"crank.set_grid(r_max=1e-2, n_r=100, z_min=0, z_max=10, n_z=200)\n",
"crank.set_parameters(D=diff_coeff, V=potential)\n",
"\n",
"crank.solve(initial_enveloppe(crank.r_pts, w0, Pin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Save the result for later analysis"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"np.savetxt(\"../CCCN_E.dat\", np.abs(crank.E_matrix))\n",
"np.savetxt(\"../CCCN_r_pts.dat\", crank.r_pts)\n",
"np.savetxt(\"../CCCN_z_pts.dat\", crank.z_pts)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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"pygments_lexer": "ipython3",
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"nbformat": 4,
"nbformat_minor": 2
}
"""
### Adapted class
Term added with new table dimension:
$$
D_t \dfrac{\partial^2 \mathcal{E}}{\partial t^2}
$$
Matrix similar to TP4 without advection.
3D matrix format:
$$
E(z_i, r_j, t_k)
$$
**Warning**: Non linear term treated with **space half step**. Initial conditions at $z=0$ in **2D**.
Half step $\Delta z/2$ in the scheme.
"""
import numpy as np
import scipy.sparse
import scipy.linalg as la
class CrankNicolsonDisp:
"""A class that solves dE/dz = D1*d2E/dr2 + V(r)*dE/dr + D2*d2E/dt2 + f(E)"""
# Cylindrical grid with rectangular time
def set_grid(self, r_max, n_r, z_min, z_max, n_z, t_min, t_max, n_t):
self.r_max, self.n_r = r_max, n_r
self.z_min, self.z_max, self.n_z = z_min, z_max, n_z
self.t_min, self.t_max, self.n_t = t_min, t_max, n_t
self.r_pts, self.delta_r = np.linspace(0, r_max, n_r, retstep=True, endpoint=False, dtype=complex)
self.z_pts, self.delta_z = np.linspace(z_min, z_max, n_z, retstep=True, endpoint=False, dtype=complex)
self.t_pts, self.delta_t = np.linspace(t_min, t_max, n_t, retstep=True, endpoint=False, dtype=complex)
# Parameters of the scheme
# Dr for diffraction, Dt for dispersion
def set_parameters(self, Dr, Dt, V):
# V has to be vectorised
self.Dr, self.Dt, self.V = Dr, Dt, V
# One solving step for r dependency and t dependency
def solve(self, E_init):
# Coefficient of matrices
sig_r = self.Dr * (self.delta_z) / 2. / self.delta_r**2
sig_t = self.Dt * (self.delta_z) / 2. / self.delta_t**2
nu = lambda x : -self.V(x) * (self.delta_z) / 4. / self.delta_r # minus sign for V convention
# Empty solution matrix (z,r,t)
self.E_matrix = np.zeros([self.n_z, self.n_r, self.n_t], dtype=complex)
# Sparse solver
Ar = self._fillAr_sp(sig_r, nu, self.n_r)
Br = self._fillBr_sp(sig_r, nu, self.n_r)
At = self._fillAt_sp(sig_t, self.n_t) # null advection coefficient
Bt = self._fillBt_sp(sig_t, self.n_t) # null advection coefficient
# Set boundary conditions
# Spatial:
# Dirichlet at infinity
Ar[1,-1] = 1.0
Ar[2,-2] = 0.0
Br[-1,-1] = 0.0
Br[-1,-2] = 0.0
# Neumann at r=0
Ar[0,1] = -2*sig_r
Br[0,1] = 2*sig_r
# Time
# Neumann at t=t_min, t_max
for b in [0,1]:
At[1,-b] = 1.0
At[2*b,1-3*b] = 0.0
Bt[-b,-b] = 0.0
Bt[-b,1-3*b] = 0.0
# Propagate
E = E_init.copy()
E_intermediate = E_init.copy()
for n in range(self.n_z):
# General step initialisation
self.E_matrix[n,:,:] = E
# First half step
# r operator solver for each t
for i in range(self.n_t):
E_intermediate[:,i] = la.solve_banded((1,1), Ar, Br.dot(E[:,i]), \
check_finite=False)
# Second half step
# t operator solver for each r
for i in range(self.n_r):
E[i,:] = la.solve_banded((1,1), At, Bt.dot(E_intermediate[i,:]), \
check_finite=False)
# E has been updated, put into E_matrix at next step
# Deep copy of results for export
# np.savetxt ?
def get_E(self):
return self.E_matrix.copy()
# Diagonal packing for banded r
def _fillAr_sp(self, sig, nu, n):
"""Returns a tridiagonal matrix in compact form ab[1+i-j,j]=a[i,j]"""
A = np.zeros([3,n], dtype=complex) # A has three diagonals and size n
# Superdiagonal
A[0,1:] = -(sig - nu(self.r_pts[:-1]))
# Diagonal
A[1] = 1+2*sig
# Subdiagonal
A[2,:-1] = -(sig + nu(self.r_pts[1:]))
return A
# Diagonal packing for banded t
def _fillAt_sp(self, sig, n):
"""Returns a tridiagonal matrix in compact form ab[1+i-j,j]=a[i,j]"""
_o = np.ones(n, dtype=complex)
A = np.zeros([3,n], dtype=complex) # A has three diagonals and size n
# Superdiagonal
A[0,1:] = -sig
# Diagonal
A[1] = 1+2*sig
# Subdiagonal
A[2,:-1] = -sig
return A
# Sparse tridiagonal storage for r
def _fillBr_sp(self, sig, nu, n):
"""Returns a tridiagonal sparse matrix in csr-form"""
_o = np.ones(n, dtype=complex)
supdiag = (sig - nu(self.r_pts[:-1]))
diag = (1-2*sig)*_o
subdiag = (sig + nu(self.r_pts[1:]))
return scipy.sparse.diags([supdiag, diag, subdiag], [1,0,-1], (n,n), format="csr")
# Sparse tridiagonal storage for t
def _fillBt_sp(self, sig, n):
"""Returns a tridiagonal sparse matrix in csr-form"""
_o = np.ones(n, dtype=complex)
supdiag = sig*_o[:-1]
diag = (1-2*sig)*_o
subdiag = sig*_o[:-1]
return scipy.sparse.diags([supdiag, diag, subdiag], [1,0,-1], (n,n), format="csr")
\ No newline at end of file
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"diff : 5.570423008216336e-08j\n",
"disp : -1e-28j\n"
]
}
],
"source": [
"import numpy as np\n",
"from HSCN import CrankNicolsonDisp\n",
"\n",
"lambd = 0.7e-6\n",
"\n",
"k = 2 * np.pi / lambd\n",
"k_2 = 2e-28\n",
"\n",
"w0 = 1e-3\n",
"tp = 85e-15\n",
"#tp = 1\n",
"Pin = 1\n",
"\n",
"diff_coeff = 1j*1/(2 * k)\n",
"#diff_coeff = 0\n",
"#diff_coeff = 1e-4\n",
"disp_coeff = -1j*k_2/2\n",
"#disp_coeff = 1j * 1e-25\n",
"#disp_coeff = 0\n",
"\n",
"print('diff :', diff_coeff)\n",
"print('disp :', disp_coeff)\n",
"\n",
"\n",
"def potential(r):\n",
" try:\n",
" return diff_coeff / r\n",
" except ZeroDivisionError:\n",
" return 0\n",
"\n",
"\n",
"def gaussian(r, t, r0=0, w0=1, t0=0, tp=1, Pin=1):\n",
" return np.sqrt(2*Pin/(np.pi*w0**2)) * np.exp(-(r-r0)** 2/(w0**2) - (t-t0)** 2/(tp**2))\n",
"\n",
"\n",
"def initial_enveloppe(r_pts, t_pts, w0, tp, Pin):\n",
" return np.array([[gaussian(r_pts[i], t_pts[j], w0=w0, tp=tp, Pin=Pin) for j in range(len(t_pts))] \\\n",
" for i in range(len(r_pts))])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/antoine/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:27: RuntimeWarning: divide by zero encountered in true_divide\n",
"/home/antoine/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:27: RuntimeWarning: invalid value encountered in true_divide\n"
]
}
],
"source": [
"crank = CrankNicolsonDisp()\n",
"\n",