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functions.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"id": "f3038a60",
"metadata": {
"editable": true
},
"source": [
"<!-- File automatically generated using DocOnce (https://github.com/doconce/doconce/):\n",
"doconce format ipynb functions.do.txt -->\n",
"\n",
"# Demo - Working with Functions\n",
"**Mikael Mortensen** (email: `mikaem@math.uio.no`), Department of Mathematics, University of Oslo.\n",
"\n",
"Date: **August 7, 2020**\n",
"\n",
"**Summary.** This is a demonstration of how the Python module [shenfun](https://github.com/spectralDNS/shenfun) can be used to work with\n",
"global spectral functions in one and several dimensions."
]
},
{
"cell_type": "markdown",
"id": "be63430d",
"metadata": {
"editable": true
},
"source": [
"## Construction\n",
"\n",
"A global spectral function $u(x)$ can be represented on the real line as"
]
},
{
"cell_type": "markdown",
"id": "75869282",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"u(x) = \\sum_{k=0}^{N-1} \\hat{u}_k \\psi_k(x), \\quad x \\in \\Omega = [a, b],\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "174c39e0",
"metadata": {
"editable": true
},
"source": [
"where the domain $\\Omega$ has to be defined such that $b > a$.\n",
"The array $\\{\\hat{u}_k\\}_{k=0}^{N-1}$ contains the\n",
"expansion coefficient for the series, often referred to as the\n",
"degrees of freedom. There is one degree of freedom per basis function and\n",
"$\\psi_k(x)$ is the $k$'th basis function.\n",
"We can use any number of basis functions,\n",
"and the span of the chosen basis is then a function space. Also part of the\n",
"function space is the domain, which is\n",
"specified when a function space is created. To create a function space\n",
"$T=\\text{span}\\{T_k\\}_{k=0}^{N-1}$ for\n",
"the first N Chebyshev polynomials of the first kind on the default domain $[-1, 1]$,\n",
"do"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f17eb498",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:15.796356Z",
"iopub.status.busy": "2024-09-06T11:44:15.796262Z",
"iopub.status.idle": "2024-09-06T11:44:16.160133Z",
"shell.execute_reply": "2024-09-06T11:44:16.159862Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [],
"source": [
"from shenfun import *\n",
"N = 8\n",
"T = FunctionSpace(N, 'Chebyshev', domain=(-1, 1))"
]
},
{
"cell_type": "markdown",
"id": "51d18e17",
"metadata": {
"editable": true
},
"source": [
"The function $u(x)$ can now be created with all N coefficients\n",
"equal to zero as"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b77b3fc9",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.161726Z",
"iopub.status.busy": "2024-09-06T11:44:16.161577Z",
"iopub.status.idle": "2024-09-06T11:44:16.163303Z",
"shell.execute_reply": "2024-09-06T11:44:16.163079Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [],
"source": [
"u = Function(T)"
]
},
{
"cell_type": "markdown",
"id": "791e8067",
"metadata": {
"editable": true
},
"source": [
"When using Chebyshev polynomials the computational domain is always\n",
"$[-1, 1]$. However, we can still use a different physical domain,\n",
"like"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "8ec4daad",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.164604Z",
"iopub.status.busy": "2024-09-06T11:44:16.164530Z",
"iopub.status.idle": "2024-09-06T11:44:16.166423Z",
"shell.execute_reply": "2024-09-06T11:44:16.166199Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [],
"source": [
"T = FunctionSpace(N, 'Chebyshev', domain=(0, 1))"
]
},
{
"cell_type": "markdown",
"id": "c08835aa",
"metadata": {
"editable": true
},
"source": [
"and under the hood shenfun will then map this domain to the reference\n",
"domain through"
]
},
{
"cell_type": "markdown",
"id": "ab3b7822",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"u(x) = \\sum_{k=0}^{N-1} \\hat{u}_k \\psi_k(2(x-0.5))\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ca3cb4d4",
"metadata": {
"editable": true
},
"source": [
"## Approximating analytical functions\n",
"\n",
"The `u` function above was created with only zero\n",
"valued coefficients, which is the default. Alternatively,\n",
"a [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) may be initialized using a constant\n",
"value"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "761f5f53",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.167676Z",
"iopub.status.busy": "2024-09-06T11:44:16.167607Z",
"iopub.status.idle": "2024-09-06T11:44:16.169492Z",
"shell.execute_reply": "2024-09-06T11:44:16.169264Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [],
"source": [
"T = FunctionSpace(N, 'Chebyshev', domain=(-1, 1))\n",
"u = Function(T, val=1)"
]
},
{
"cell_type": "markdown",
"id": "36f77fe7",
"metadata": {
"editable": true
},
"source": [
"but that is not very useful. A third method to initialize\n",
"a [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) is to interpolate using an analytical\n",
"Sympy function."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b9ad36a9",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.170743Z",
"iopub.status.busy": "2024-09-06T11:44:16.170670Z",
"iopub.status.idle": "2024-09-06T11:44:16.176352Z",
"shell.execute_reply": "2024-09-06T11:44:16.176135Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-8.32667268e-17 -5.47405982e-17 2.38204300e-17 1.00000000e+00\n",
" 0.00000000e+00 -3.20040096e-16 1.60078838e-16 -2.93881977e-16]\n"
]
}
],
"source": [
"import sympy as sp\n",
"x = sp.Symbol('x', real=True)\n",
"u = Function(T, buffer=4*x**3-3*x)\n",
"print(u)"
]
},
{
"cell_type": "markdown",
"id": "4a9048d9",
"metadata": {
"editable": true
},
"source": [
"Here the analytical Sympy function will first be evaluated\n",
"on the entire quadrature mesh of the `T` function space,\n",
"and then forward transformed to get the coefficients. This\n",
"corresponds to a finite-dimensional projection to `T`.\n",
"The projection is\n",
"\n",
"Find $u_h \\in T$, such that"
]
},
{
"cell_type": "markdown",
"id": "27a6add1",
"metadata": {
"editable": true
},
"source": [
"<!-- Equation labels as ordinary links -->\n",
"<a id=\"eq:proj1\"></a>\n",
"\n",
"$$\n",
"(u_h - u, v)^{N}_w = 0 \\quad \\forall v \\in T, \\label{eq:proj1} \\tag{1} \n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "e76306fe",
"metadata": {
"editable": true
},
"source": [
"where $v$ is a test function and\n",
"$u_h=\\sum_{k=0}^{N-1} \\hat{u}_k T_k$ is a trial function. The\n",
"notation $(\\cdot, \\cdot)^N_w$ represents a discrete version of\n",
"the weighted inner product $(u, v)_w$ defined as"
]
},
{
"cell_type": "markdown",
"id": "3ed95d25",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"(u, v)_{\\omega} = \\int_{\\Omega} u \\overline{v} \\omega d\\Omega,\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a26f170f",
"metadata": {
"editable": true
},
"source": [
"where $\\omega(x)$ is a weight functions and $\\overline{v}$ is the\n",
"complex conjugate of $v$. If $v$ is\n",
"a real function, then $\\overline{v}=v$.\n",
"With quadrature we approximate the integral such that"
]
},
{
"cell_type": "markdown",
"id": "b801c1d1",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"(u, v)_{\\omega} \\approx (u, v)^N_{\\omega} = \\sum_{j\\in\\mathcal{I}^N} u(x_j) v(x_j) w_j.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "c2a63677",
"metadata": {
"editable": true
},
"source": [
"where the index set $\\mathcal{I}^N = \\{0, 1, \\ldots, N-1\\}$ and $\\{x_j\\}_{j\\in \\mathcal{I}^N}$ and $\\{w_j\\}_{j\\in \\mathcal{I}^N}$\n",
"are the quadrature points and weights.\n",
"\n",
"A linear system of equations arise when inserting for the chosen\n",
"basis functions in Eq. ([1](#eq:proj1)). We get"
]
},
{
"cell_type": "markdown",
"id": "aee62172",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\sum_{k\\in \\mathcal{I}^N} \\left( T_k, T_i\\right)^N_{\\omega} \\hat{u}_k =\n",
"\\left(u, T_i\\right)^N_{\\omega}\\, \\forall \\, i \\in \\mathcal{I}^N,\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "0b6dffc4",
"metadata": {
"editable": true
},
"source": [
"In matrix notation the solution becomes"
]
},
{
"cell_type": "markdown",
"id": "35773a2f",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\boldsymbol{\\hat{u}} = A^{-1} \\boldsymbol{\\tilde{u}},\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "09d7d46b",
"metadata": {
"editable": true
},
"source": [
"where we use two column vectors $\\boldsymbol{\\hat{u}}=(\\hat{u}_i)^T_{i\\in \\mathcal{I}^N}$,\n",
"$\\boldsymbol{\\tilde{u}}=\\left(\\tilde{u}_i\\right)^T_{i \\in \\mathcal{I}^N}$,\n",
"$\\tilde{u}_i = (u, T_i)^N_{\\omega}$ and the matrix\n",
"$A=(a_{ik}) \\in \\mathbb{R}^{N \\times N}$, that is diagonal with\n",
"$a_{ik}=\\left( T_k, T_i\\right)^N_{\\omega}$. For the default\n",
"Gauss-Chebyshev quadrature this matrix is $a_{ik} = c_i \\pi/2 \\delta_{ik}$,\n",
"where $c_0=2$ and $c_i=1$ for $i>0$."
]
},
{
"cell_type": "markdown",
"id": "a93601a6",
"metadata": {
"editable": true
},
"source": [
"## Adaptive function size\n",
"\n",
"The number of basis functions can also be left open during creation\n",
"of the function space, through"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6b3431b4",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.177947Z",
"iopub.status.busy": "2024-09-06T11:44:16.177876Z",
"iopub.status.idle": "2024-09-06T11:44:16.179509Z",
"shell.execute_reply": "2024-09-06T11:44:16.179310Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [],
"source": [
"T = FunctionSpace(0, 'Chebyshev', domain=(-1, 1))"
]
},
{
"cell_type": "markdown",
"id": "b919c637",
"metadata": {
"editable": true
},
"source": [
"This is useful if you want to approximate a function and\n",
"are uncertain how many basis functions that are required.\n",
"For example, you may want to approximate the function $\\cos(20 x)$.\n",
"You can then find the required [Function](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.Function) using"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9a55e6d5",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.180685Z",
"iopub.status.busy": "2024-09-06T11:44:16.180607Z",
"iopub.status.idle": "2024-09-06T11:44:16.207604Z",
"shell.execute_reply": "2024-09-06T11:44:16.207388Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45\n"
]
}
],
"source": [
"u = Function(T, buffer=sp.cos(20*x))\n",
"print(len(u))"
]
},
{
"cell_type": "markdown",
"id": "07d341ea",
"metadata": {
"editable": true
},
"source": [
"We see that $N=45$ is required to resolve this function. This agrees\n",
"well with what is reported also by [Chebfun](https://www.chebfun.org/docs/guide/guide01.html).\n",
"Note that in this process a new [FunctionSpace()](https://shenfun.readthedocs.io/en/latest/shenfun.forms.html#shenfun.forms.arguments.FunctionSpace) has been\n",
"created under the hood. The function space of `u` can be\n",
"extracted using"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d6cdcdb9",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.208793Z",
"iopub.status.busy": "2024-09-06T11:44:16.208726Z",
"iopub.status.idle": "2024-09-06T11:44:16.210336Z",
"shell.execute_reply": "2024-09-06T11:44:16.210132Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45\n"
]
}
],
"source": [
"Tu = u.function_space()\n",
"print(Tu.N)"
]
},
{
"cell_type": "markdown",
"id": "cd42b044",
"metadata": {
"editable": true
},
"source": [
"To further show that shenfun is compatible with Chebfun we can also\n",
"approximate the Bessel function"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f3f6e277",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.211475Z",
"iopub.status.busy": "2024-09-06T11:44:16.211404Z",
"iopub.status.idle": "2024-09-06T11:44:16.238539Z",
"shell.execute_reply": "2024-09-06T11:44:16.238309Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"83\n"
]
}
],
"source": [
"T1 = FunctionSpace(0, 'Chebyshev', domain=(0, 100))\n",
"u = Function(T1, buffer=sp.besselj(0, x))\n",
"print(len(u))"
]
},
{
"cell_type": "markdown",
"id": "527bcff6",
"metadata": {
"editable": true
},
"source": [
"which gives 83 basis functions, in close agreement with Chebfun (89).\n",
"The difference lies only in the cut-off criteria. We cut frequencies\n",
"with a relative tolerance of 1e-12 by default, but if we make this criteria\n",
"a little bit stronger, then we will also arrive at a slightly higher number:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f909dbb0",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.239721Z",
"iopub.status.busy": "2024-09-06T11:44:16.239652Z",
"iopub.status.idle": "2024-09-06T11:44:16.248557Z",
"shell.execute_reply": "2024-09-06T11:44:16.248191Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"87\n"
]
}
],
"source": [
"u = Function(T1, buffer=sp.besselj(0, x), reltol=1e-14)\n",
"print(len(u))"
]
},
{
"cell_type": "markdown",
"id": "631b5bda",
"metadata": {
"editable": true
},
"source": [
"Plotting the function on its quadrature points looks\n",
"a bit ragged, though:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "24ce622f",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.250065Z",
"iopub.status.busy": "2024-09-06T11:44:16.249968Z",
"iopub.status.idle": "2024-09-06T11:44:16.438812Z",
"shell.execute_reply": "2024-09-06T11:44:16.438569Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import matplotlib.pyplot as plt\n",
"Tu = u.function_space()\n",
"plt.plot(Tu.mesh(), u.backward());"
]
},
{
"cell_type": "markdown",
"id": "0c9b4803",
"metadata": {
"editable": true
},
"source": [
"To improve the quality of this plot we can instead evaluate the\n",
"function on more points"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "aa3f4008",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.440234Z",
"iopub.status.busy": "2024-09-06T11:44:16.440073Z",
"iopub.status.idle": "2024-09-06T11:44:16.481370Z",
"shell.execute_reply": "2024-09-06T11:44:16.481128Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xj = np.linspace(0, 100, 1000)\n",
"plt.plot(xj, u(xj));"
]
},
{
"cell_type": "markdown",
"id": "f56c9597",
"metadata": {
"editable": true
},
"source": [
"Alternatively, we can refine the function, which simply\n",
"pads zeros to $\\hat{u}$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "39cb107e",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.482709Z",
"iopub.status.busy": "2024-09-06T11:44:16.482632Z",
"iopub.status.idle": "2024-09-06T11:44:16.642002Z",
"shell.execute_reply": "2024-09-06T11:44:16.641781Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"up = u.refine(200)\n",
"Tp = up.function_space()\n",
"plt.plot(Tp.mesh(), up.backward());"
]
},
{
"cell_type": "markdown",
"id": "df254f80",
"metadata": {
"editable": true
},
"source": [
"The padded expansion coefficients are now given as"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "760bd263",
"metadata": {
"editable": true,
"execution": {
"iopub.execute_input": "2024-09-06T11:44:16.643378Z",
"iopub.status.busy": "2024-09-06T11:44:16.643295Z",
"iopub.status.idle": "2024-09-06T11:44:16.645661Z",
"shell.execute_reply": "2024-09-06T11:44:16.645462Z"
},
"tags": [
"thebe-init"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 6.43655435e-02 -1.37262942e-01 1.26593632e-01 -1.31630372e-01\n",
" 1.19810309e-01 -1.19499576e-01 1.07387826e-01 -9.95196201e-02\n",
" 8.81197795e-02 -7.07299943e-02 6.13974837e-02 -3.40222966e-02\n",
" 2.84578300e-02 6.05886310e-03 -6.23468323e-03 4.01956708e-02\n",
" -3.44202241e-02 5.58353154e-02 -4.58848577e-02 4.33923041e-02\n",
" -3.39778387e-02 6.26445963e-03 -3.37831264e-03 -3.27304442e-02\n",
" 2.63630973e-02 -4.12313235e-02 3.07429560e-02 -7.73458857e-03\n",
" 4.10441868e-03 3.29922472e-02 -2.47812478e-02 2.71654360e-02\n",
" -1.81421444e-02 -2.02112290e-02 1.53660102e-02 -3.02943723e-02\n",
" 1.97324599e-02 1.94051084e-02 -1.41460820e-02 2.47321146e-02\n",
" -1.49668436e-02 -3.02763148e-02 1.98156190e-02 -2.08517347e-03\n",
" -6.91643640e-05 3.13799203e-02 -1.81924272e-02 -3.77110141e-02\n",
" 2.23051599e-02 2.82766986e-02 -1.67226896e-02 -1.59965877e-02\n",
" 9.40673776e-03 7.34392211e-03 -4.28398348e-03 -2.84497604e-03\n",
" 1.64428109e-03 9.53197714e-04 -5.45450869e-04 -2.80998822e-04\n",
" 1.59136941e-04 7.38240716e-05 -4.13664358e-05 -1.74579288e-05\n",
" 9.67744748e-06 3.74610168e-06 -2.05413769e-06 -7.34256601e-07\n",
" 3.98257402e-07 1.32202237e-07 -7.09282453e-08 -2.19709846e-08\n",
" 1.16601214e-08 3.38459233e-09 -1.77684429e-09 -4.85085275e-10\n",
" 2.51925718e-10 6.48957767e-11 -3.33432388e-11 -8.12795878e-12\n",
" 4.13189925e-12 9.55535215e-13 -4.80638850e-13 -1.05625737e-13\n",
" 5.24914276e-14 1.10219183e-14 -6.06441767e-15 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n"
]
}
],
"source": [
"print(up)"
]
},
{
"cell_type": "markdown",
"id": "2773efbb",
"metadata": {
"editable": true
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"## More features\n",
"\n",
"Since we have used a regular Chebyshev basis above, there\n",
"are many more features that could be explored simply by going through\n",
"[Numpy's Chebyshev module](https://numpy.org/doc/stable/reference/routines.polynomials.chebyshev.html).\n",
"For example, we can create a Chebyshev series like"
]
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"source": [
"import numpy.polynomial.chebyshev as cheb\n",
"c = cheb.Chebyshev(u, domain=(0, 100))"
]
},
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"The Chebyshev series in Numpy has a wide range of possibilities,\n",
"see [here](https://numpy.org/doc/stable/reference/generated/numpy.polynomial.chebyshev.Chebyshev.html#numpy.polynomial.chebyshev.Chebyshev).\n",
"However, we may also work directly with the Chebyshev\n",
"coefficients already in `u`. To find the roots of the\n",
"polynomial that approximates the Bessel function on\n",
"domain $[0, 100]$, we can do"
]
},
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"source": [
"z = Tu.map_true_domain(cheb.chebroots(u))"
]
},
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"Note that the roots are found on the reference domain $[-1, 1]$\n",
"and as such we need to move the result to the physical domain using\n",
"`map_true_domain`. The resulting roots `z` are both real and imaginary,\n",
"so to extract the real roots we need to filter a little bit"
]
},
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"text": [
"[ 2.40482556 5.52007811 8.65372791 11.79153444 14.93091771]\n"
]
}
],
"source": [
"z2 = z[np.where((z.imag == 0)*(z.real > 0)*(z.real < 100))].real\n",
"print(z2[:5])"
]
},
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"Here `np.where` returns the indices where the condition is true. The condition\n",
"is that the imaginary part is zero, whereas the real part is within the\n",
"true domain $[0, 100]$.\n",
"\n",
":::{note}\n",
"Using directly `cheb.chebroots(c)` does not seem to work (even though the\n",
"series has been generated with the non-standard domain) because\n",
"Numpy only looks for roots in the reference domain $[-1, 1]$.\n",
":::\n",
"\n",
"We could also use a function space with boundary conditions built\n",
"in, like"
]
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{
"name": "stdout",
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"text": [
"82\n"
]
}
],
"source": [
"Td = FunctionSpace(0, 'C', bc=(sp.besselj(0, 0), sp.besselj(0, 100)), domain=(0, 100))\n",
"ud = Function(Td, buffer=sp.besselj(0, x))\n",