diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..5d58ef5 --- /dev/null +++ b/.gitignore @@ -0,0 +1,8 @@ +*.ipynb_* +*.swp +*.vscode +*.h5 +*.dat +*.pyc +*w11/swe/output/frames/* +*_old \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..85b2489 --- /dev/null +++ b/README.md @@ -0,0 +1,11 @@ +# Mathematische Modellierung in der Klimaforschung + + + + +---- + +## .gitignore + +`.gitignore` contains files which are to be ignored by git. + diff --git a/w0/Try/file.txt b/w0/Try/file.txt new file mode 100644 index 0000000..e69de29 diff --git a/w0/hello_world.ipynb b/w0/hello_world.ipynb new file mode 100644 index 0000000..4602860 --- /dev/null +++ b/w0/hello_world.ipynb @@ -0,0 +1,59 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "57178893-d689-4d3d-b699-e49917a47a7f", + "metadata": {}, + "source": [ + "# Tutorial 1\n", + "## Exercise 1: Hello world!\n", + "This exercise is to help us get started with *git* and our Python setup.\n", + "\n", + "1. Pull this notebook and open it with jupyter lab.\n", + "2. Run the cell below. Does it print \"Hello world!\"?\n", + "3. Familiarise yourself with the jupyer lab interface." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "c70e0481-afe1-4c8e-b8b3-7fae045e2a01", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello World!\n" + ] + } + ], + "source": [ + "print(\"Hello World!\")" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + }, + "kernelspec": { + "display_name": "Python 3.9.5 64-bit", + "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": "3.9.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w0/notes.pdf b/w0/notes.pdf new file mode 100644 index 0000000..605946c Binary files /dev/null and b/w0/notes.pdf differ diff --git a/w1/functions_and_lists.ipynb b/w1/functions_and_lists.ipynb new file mode 100644 index 0000000..e5abd3b --- /dev/null +++ b/w1/functions_and_lists.ipynb @@ -0,0 +1,206 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a8d5e426-5dff-42d2-b819-b68fdbf63f9f", + "metadata": {}, + "source": [ + "# Introduction to Python - 1\n", + "\n", + "---\n", + "\n", + "## Functions\n", + "\n", + "Functions are self-contained reusable code that does a specific task. Functions may take one or more arguments, and functions may return a result. The code snippet below demonstrates the function of a function." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5139ac13-2bc3-42c8-b048-95ca3cf15884", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a36cf1cf-83b6-4559-b5e9-56b90dcba828", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "15\n", + "-5\n", + "(6+1j)\n" + ] + } + ], + "source": [ + "# In Python, comments start with a hashtag\n", + "# And the keyword ``def`` introduces a function definition.\n", + "\n", + "# Let's make a function called `sum_func` that takes two values `a` and `b` as inputs, i.e. arguments:\n", + "def sum_func(a,b):\n", + " # All code belonging to a function must be indented\n", + " \n", + " # Let's calculate the sum of `a` and `b`, and store it in `c`:\n", + " c = a + b\n", + " \n", + " # finally, we want to return the result of sum:\n", + " return c\n", + "\n", + "# Then now we can reuse this code snippet by calling the function with any values of `a` and `b`:\n", + "print(sum_func(5,10))\n", + "print(sum_func(-8,3))\n", + "\n", + "# Because the Python `+` operator supports addition of complex numbers, the function also works with complex inputs\n", + "print(sum_func(5+3j,1-2j))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8b6d4766-f28f-4465-8d24-3d7a889163f5", + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "sum_func() missing 1 required positional argument: 'b'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Finally, recall that positional arguments are mandatory.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;31m# Let's see what happens if we only input `a` but not `b`:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msum_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\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[0;31mTypeError\u001b[0m: sum_func() missing 1 required positional argument: 'b'" + ] + } + ], + "source": [ + "# Finally, recall that positional arguments are mandatory.\n", + "# Let's see what happens if we only input `a` but not `b`:\n", + "print(sum_func(5,))" + ] + }, + { + "cell_type": "markdown", + "id": "3f45138c-cf4b-4bc1-9055-a63747a10d54", + "metadata": {}, + "source": [ + "### Questions:\n", + "1. Can you create a function that takes both positional and keyword arguments?\n", + "2. What happens if you change the order of the keyword arguments?\n", + "\n", + "----" + ] + }, + { + "cell_type": "markdown", + "id": "61a037f2-6e54-4b6f-a648-598200f85a6f", + "metadata": {}, + "source": [ + "## Lists\n", + "\n", + "Lists in Python store a collection of items in a single variable, for example
\n", + "``a=[1,2,3,4,5]``
\n", + "stores the values 1 to 5 in the variable `a`.\n", + "\n", + "Lists are pretty flexible in Python, see the code snippet below." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3847780c-1b0b-42f2-971d-5145453aa3b2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1, 2, 3, 'a', 'dog', 'item', 10.0, 55.5, 1e-06]\n", + "[1, 2, 3, 'a', 'dog', 'item', 10.0, 55.5, 1e-06, ]\n", + "[1, 2, 3, 'a', 'dog', 'item', 10.0, 55.5, 1e-06, , array([[ 0, 1, 2, 3, 4],\n", + " [ 5, 6, 7, 8, 9],\n", + " [10, 11, 12, 13, 14],\n", + " [15, 16, 17, 18, 19],\n", + " [20, 21, 22, 23, 24]])]\n" + ] + } + ], + "source": [ + "# A list can store a collection (floating point) numbers, integers, and strings, etc.\n", + "lst = [1,2,3,'a','dog','item',10.0,55.5,1e-6]\n", + "\n", + "# Now, when we print `lst`, we get the collection of items we defined above.\n", + "print(lst)\n", + "\n", + "# We can even store a function (and other objects) in a list.\n", + "# Let's add the `sum_func` function into the list:\n", + "lst_func = lst + [sum_func]\n", + "print(lst_func)\n", + "\n", + "# Or a 2D array:\n", + "array = np.arange(25).reshape(5,5)\n", + "lst_func += [array]\n", + "print(lst_func)" + ] + }, + { + "cell_type": "markdown", + "id": "c206297a-03fd-4d41-be33-157bd12c5267", + "metadata": {}, + "source": [ + "----\n", + "\n", + "## Additional reading:\n", + "There are many ways to store data in Python, and `list` is just one them. Here are some other examples of [*data structures*](https://en.wikipedia.org/wiki/Data_structure): \n", + "\n", + "* In pure Python, i.e. Python without any additional libraries, bells, and whistles, we have *dictionaries* and *lists*. \n", + "* In the `numpy` library, we have [*numpy arrays*](https://numpy.org/doc/stable/reference/generated/numpy.array.html),\n", + "* while for data analysis, there are [*pandas dataframes*](https://pandas.pydata.org/docs/user_guide/dsintro.html#dataframe) and [*xarrays*](http://xarray.pydata.org/en/stable/).\n", + "* For larger-than-memory arrays, Python has the dask library with its [*dask arrays*](https://docs.dask.org/en/latest/array.html).\n", + "\n", + "These are a just a few more-popular examples of the types of data structures that Python and its libraries offers. In this course, we will stick to the [KISS principle](https://en.wikipedia.org/wiki/KISS_principle), and we will only use the standard Python lists and dictionaries. We will also be using [classes](https://docs.python.org/3/tutorial/classes.html) to create our own data containers. The most 'advanced' arrays that we will be using will be numpy arrays.\n", + "\n", + "Numpy array, dictionaries and classes will be introduced in later tutorial sessions.\n", + "\n", + "### Question: \n", + "1. What is a *list*, an *array*, a *matrix*, and a *tuple*? What are their similarities and differences?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "87d65e32-2724-4451-bc03-493fb7c03e3b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w1/oscillator.ipynb b/w1/oscillator.ipynb new file mode 100644 index 0000000..f2d3819 --- /dev/null +++ b/w1/oscillator.ipynb @@ -0,0 +1,222 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e841e005-3209-4f72-a570-a1db723c1b81", + "metadata": {}, + "source": [ + "# Tutorial 2\n", + "## Exercise 2: ``import``, ``odeint`` and functions\n", + "\n", + "Let's first import the libraries that we will be using.\n", + "\n", + "Notice the following:\n", + "1. We are importing the ``numpy`` library and from now on, we call it ``np``.\n", + "2. From the ``scipy`` library, we are importing the ``odeint`` module from the ``integrate`` package.\n", + "3. From ``matplotlib``, we are importing the ``pyplot`` package as ``plt``. \n", + "\n", + "Pay attention to how these libraries, packages, and modules are called in the code below." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a1ff50d3-c72a-4de3-bff9-74f921fe9b8f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "19562495-8c0e-4430-86a5-e12f59b9fb6e", + "metadata": {}, + "source": [ + "``odeint`` is a Python module that allows us to integrate a system of ordinary differential equations (ODEs).\n", + "\n", + "A good starting point for everything is to read the documentation:
\n", + "\n", + "\n", + "Notice that we have to provide three **mandatory** *positional arguments*: \n", + "1. a function ``func``\n", + "2. a set of initial conditions `y0`\n", + "3. the duration for which we want to solve the ODEs `t`\n", + "\n", + "The rest of the arguments are optional *keyword arguments*." + ] + }, + { + "cell_type": "markdown", + "id": "71a78032-9451-4389-b68b-50d29accf5b5", + "metadata": {}, + "source": [ + "## Exercise 3: Our first problem\n", + "We want to solve the harmonic oscillator problem on page 17 of the lecture notes by Klein et al. (2011), i.e.\n", + "\n", + "$$m \\ddot{x} = - cx - k \\dot{x} + F_D(t),$$\n", + "\n", + "which is best explained by the following illustration from the lecture notes...\n", + "\n", + "
\n", + "\n", + "The analytical solutions are already given in the lecture notes and we want solve the problem computationally.\n", + "\n", + "Say as a first step, we want to solve a simple spring-mass system without any damping and without any forcing, i.e. $k=0$, $F_D \\equiv 0$. We then want to reproduce Figure 4 in the lecture notes.\n", + "\n", + "How do you suggest we start tackling this problem?" + ] + }, + { + "cell_type": "markdown", + "id": "05ebc743-e50c-4da8-8d32-44205b8b2c8d", + "metadata": {}, + "source": [ + "### Hints:" + ] + }, + { + "cell_type": "markdown", + "id": "2f609fef-429e-466e-8be3-f458cb069018", + "metadata": { + "tags": [] + }, + "source": [ + "1. Recall that we need three inputs: a function, an initial condition, and a duration.\n", + "2. What should be our function here?\n", + "3. Our problem is a second-order ODE, where $\\ddot{x}$ is is the second-order derivative with respect to time $t$. On the other hand, `odeint` solves a (system of) first-oder ODE(s). What must we do to make the function work with `odeint`?" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "d56e80eb-9b13-4f6b-a3ee-ece6c0eef206", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Try out your solution here:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "58f14da5-ac64-4075-b740-09e8634a2790", + "metadata": {}, + "outputs": [], + "source": [ + "# Here are some code to help you plot the solution.\n", + "\n", + "# plt.plot(t, sol[:, 0], label='undamped')\n", + "# plt.legend(loc='best')\n", + "# plt.xlabel('t')\n", + "# plt.grid()\n", + "# plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ad3027ff-500a-4c7a-aba2-c6a7bf4afc0e", + "metadata": {}, + "source": [ + "## Exercise 4: Reproduce Figure 5" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "e1d94d81-cd5c-499f-8172-e0efc9e355b4", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Try out your solution here:\n", + "# D < 0, under-damped\n", + "\n", + "\n", + "# D = 0, critically damped\n", + "\n", + "\n", + "# D > 0, over-damped\n", + "\n", + "\n", + "# Let's plot the solutions\n", + "# plt.plot(t, undr_damped[:, 0], label='under-damped')\n", + "# plt.plot(t, crit_damped[:, 0], label='critically damped')\n", + "# plt.plot(t, over_damped[:, 0], label='over-damped')\n", + "# plt.legend(loc='best')\n", + "# plt.xlabel('t')\n", + "# plt.grid()\n", + "# plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "31b36525-90f0-4b8f-9eff-32a03b8bdbb6", + "metadata": {}, + "source": [ + "## Exercise 5:\n", + "1. Reproduce the graphs in Figure 6 (you don't have to reproduce them *exactly*).\n", + "2. In the process, develop an intuition for the harmonic oscillator." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "d8a127f9-f2ce-4106-acef-e83642f4e6ef", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Try out your solution here:\n", + "\n", + "# ...\n", + "\n", + "# Let's plot the solutions\n", + "# plt.plot(t, superposition[:, 0], label='superposition')\n", + "# plt.plot(t, external_forcing[:, 0], label='external forcing')\n", + "# plt.plot(t, resonance[:, 0], label='resonance')\n", + "# plt.legend(loc='best')\n", + "# plt.xlabel('t')\n", + "# plt.grid()\n", + "# plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "56a85a2a-a00e-43af-985f-10d2d1b02e88", + "metadata": {}, + "source": [ + "# Reference\n", + "Klein, Rupert, et al. \"Multiple scales methods in meteorology.\" Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances. 2010. 127-196." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.3 64-bit ('anaconda3': virtualenv)", + "language": "python", + "name": "python37364bitanaconda3virtualenv7a28dc8db0264e168ad4f93d8f9f620c" + }, + "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": 5 +} diff --git a/w1/soln/ex3.png b/w1/soln/ex3.png new file mode 100644 index 0000000..02d14b5 Binary files /dev/null and b/w1/soln/ex3.png differ diff --git a/w1/soln/ex4.png b/w1/soln/ex4.png new file mode 100644 index 0000000..77206c2 Binary files /dev/null and b/w1/soln/ex4.png differ diff --git a/w1/soln/ex5.png b/w1/soln/ex5.png new file mode 100644 index 0000000..e180b89 Binary files /dev/null and b/w1/soln/ex5.png differ diff --git a/w1/w1.pdf b/w1/w1.pdf new file mode 100644 index 0000000..d7a4e04 Binary files /dev/null and b/w1/w1.pdf differ diff --git a/w10/swe.zip b/w10/swe.zip new file mode 100644 index 0000000..e27e396 Binary files /dev/null and b/w10/swe.zip differ diff --git a/w10/swe/data/__input__.py b/w10/swe/data/__input__.py new file mode 100644 index 0000000..e69de29 diff --git a/w10/swe/data/grid.py b/w10/swe/data/grid.py new file mode 100644 index 0000000..c5fda5d --- /dev/null +++ b/w10/swe/data/grid.py @@ -0,0 +1,35 @@ +import numpy as np + +class sGrid(object): + def __init__(self, ud): + self.Nx = ud.Nx + self.xmin = ud.xmin + self.xmax = ud.xmax + + self.x = np.linspace(self.xmin, self.xmax, self.Nx).reshape(-1,1) + self.dx = np.diff(self.x.flatten())[0] + + if ud.Ny > 1: + self.Ny = ud.Ny + self.ymin = ud.ymin + self.ymax = ud.ymax + + self.y = np.linspace(self.ymin, self.ymax, self.Ny).reshape(1,-1) + self.dy = np.diff(self.y.flatten())[0] + else: + self.y = 0.0 + self.dy = np.nan + + self.dxy = (self.dx, self.dy) + self.xg, self.yg = np.meshgrid(self.x, self.y) + + +class tGrid(object): + def __init__(self, ud): + self.T = ud.T + self.dt = ud.dt + self.t = np.arange(0.0, self.T+self.dt, self.dt) + + + + diff --git a/w10/swe/data/io.py b/w10/swe/data/io.py new file mode 100644 index 0000000..85a4dfb --- /dev/null +++ b/w10/swe/data/io.py @@ -0,0 +1,68 @@ +import argparse +import os +import h5py +import numpy as np + +class writer(object): + def __init__(self, folder='./output/', filename='output.h5'): + self.OUTPUT_FOLDER = folder + self.OUTPUT_FILENAME = filename + self.FILE_PATH = self.OUTPUT_FOLDER + '/' + self.OUTPUT_FILENAME + + # If directory does not exist, create it. + if not os.path.exists(self.OUTPUT_FOLDER): + os.mkdir(self.OUTPUT_FOLDER) + + # If file exists, rename it with old. + if os.path.exists(self.FILE_PATH): + os.rename(self.FILE_PATH, self.FILE_PATH+'_old') + + file = h5py.File(self.FILE_PATH, 'a') + file.close() + + def f(self): + file = h5py.File(self.FILE_PATH, 'r+') + return file + + def write(self, time, name, data): + time = np.around(time, 4) + file = self.f() + file.create_dataset(str(time) + '/' + str(name), data=data, chunks=True, compression='gzip', compression_opts=4) + file.close() + + def write_attr(self,obj): + file = self.f() + for key, value in vars(obj).items(): + try: + file.attrs.create(key,value) + except: + file.attrs.create(key,repr(value),dtype='max_wind)] = max_wind + u[np.where(u<-max_wind)] = -max_wind + v[np.where(v>max_wind)] = max_wind + v[np.where(v<-max_wind)] = -max_wind + + # this creates the solution container + sol = Variables(sg) + sol.h[...] = height.T + sol.u[...] = u.T + sol.v[...] = v.T + sol.F = F.T + + return sol \ No newline at end of file diff --git a/w10/swe/input/block.py b/w10/swe/input/block.py new file mode 100644 index 0000000..48c3bdc --- /dev/null +++ b/w10/swe/input/block.py @@ -0,0 +1,22 @@ +import numpy as np +from data.vars import Variables + +class UserData(object): + def __init__(self): + + self.xmin = -4.0 + self.xmax = +4.0 + self.Nx = 81 + + self.ymin = -4.0 + self.ymax = +4.0 + self.Ny = 81 + + self.dt = 0.001 + self.T = 1.0 + + +def sol_init(sg): + sol = Variables(sg) + sol.u[20:60] = 1.0 + return sol \ No newline at end of file diff --git a/w10/swe/input/gw.py b/w10/swe/input/gw.py new file mode 100644 index 0000000..cedb615 --- /dev/null +++ b/w10/swe/input/gw.py @@ -0,0 +1,31 @@ +import numpy as np +from data.vars import Variables + +class UserData(object): + def __init__(self): + + self.xmin = 0.0 # [m] + self.xmax = 25400000.0 - 100000 # [m] + self.Nx = 254 + + self.ymin = 0.0 # [m] + self.ymax = 5000000.0 - 100000 # [m] + self.Ny = 50 + + self.dt = 60.0 # [s] + self.T = 4.0 * 24.0 * 3600.0 # [s] + + self.g = 9.81 # [m/s^2] + self.f = 0.0 # [s^(-1)] + + +def sol_init(sg): + std_blob = 8.0*sg.dy; # Standard deviation of blob (m) + height = 9750. + 1000.*np.exp(-((sg.xg-0.25*np.mean(sg.x))**2.+(sg.yg-np.mean(sg.y))**2.)/(2.* \ + std_blob**2.)) + + # this creates the solution container + sol = Variables(sg) + sol.h[...] = height + + return sol \ No newline at end of file diff --git a/w10/swe/input/random.py b/w10/swe/input/random.py new file mode 100644 index 0000000..e69de29 diff --git a/w10/swe/input/user_data.py b/w10/swe/input/user_data.py new file mode 100644 index 0000000..a5d671f --- /dev/null +++ b/w10/swe/input/user_data.py @@ -0,0 +1,18 @@ +class UserDataInit(object): + """ + Loads user defined initial conditions. Specifically, all attributes of the class object defined in the initial condition is loaded. + + Attributes + ---------- + **kwargs: class object + + """ + + def __init__(self,**kwargs): + for key, value in kwargs.items(): + setattr(self, key, value) + + + def update_ud(self, rewrite): + for key, value in rewrite.items(): + setattr(self, key, value) \ No newline at end of file diff --git a/w10/swe/main.py b/w10/swe/main.py new file mode 100644 index 0000000..e4a0293 --- /dev/null +++ b/w10/swe/main.py @@ -0,0 +1,36 @@ +from data.grid import sGrid, tGrid +from numerics.lax_wendroff import lax_wendroff +from numerics.bc import set_boundary +from data import io + + +if __name__ == '__main__': + user_data, sol_init = io.get_args() + ud = user_data() + + writer = io.writer() + + sg = sGrid(ud) + tg = tGrid(ud) + writer.write_attr(sg) + writer.write_attr(tg) + + sol = sol_init(sg,ud) + + for nn, t in enumerate(tg.t): + + if nn % 60 == 0: + writer.write(nn, "h", sol.h) + writer.write(nn, "u", sol.u) + writer.write(nn, "v", sol.v) + print("time-step %.2f" %nn) + + lax_wendroff(sol, tg, sg, ud) + set_boundary(sol) + + + + + + + diff --git a/w10/swe/numerics/__init__.py b/w10/swe/numerics/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/w10/swe/numerics/bc.py b/w10/swe/numerics/bc.py new file mode 100644 index 0000000..071e83d --- /dev/null +++ b/w10/swe/numerics/bc.py @@ -0,0 +1,25 @@ +import numpy as np + +def set_boundary(sol): + # we set periodic BC in the x-direction + sol.h[:,0] = sol.h[:,-2] + sol.h[:,-1] = sol.h[:,1] + + sol.u[:,0] = sol.u[:,-2] + sol.u[:,-1] = sol.u[:,1] + + sol.v[:,0] = sol.v[:,-2] + sol.v[:,-1] = sol.v[:,1] + + # we set no-flux BC in the y-direction + sol.v[[0,-1],:] = 0.0 + + # sol.h[0,:] = sol.h[-2,:] + # sol.h[-1,:] = sol.h[1,:] + + # sol.u[0,:] = sol.u[-2,:] + # sol.u[-1,:] = sol.u[1,:] + + # sol.v[0,:] = sol.v[-2,:] + # sol.v[-1,:] = sol.v[1,:] + diff --git a/w10/swe/numerics/lax_wendroff.py b/w10/swe/numerics/lax_wendroff.py new file mode 100644 index 0000000..892213e --- /dev/null +++ b/w10/swe/numerics/lax_wendroff.py @@ -0,0 +1,68 @@ +import numpy as np + + +def lax_wendroff(sol, tg, sg, ud): + # We want the quantities that we are updating with the RLW method + h = sol.h + hu = sol.h * sol.u + hv = sol.h * sol.v + + # Now we need the to specify how we index our arrays. + + # we take the values on the right in the x direction + r_i = (..., slice(1,None)) + # we take the values on the left in the x direction + l_i = (..., slice(0,-1)) + # we take the values on the right in the y direction + r_j = (slice(1,None),) + # we take the values on the left in the y direction + l_j = (slice(0,-1),) + + # define the inner domain, i.e. without the ghost cells, + i1 = (slice(1,-1), slice(1,-1)) + in_i = (slice(1,-1),) + in_j = (..., slice(1,-1)) + + # Get values defined by the user in the initial conditions file + g = ud.g + f = sol.F[i1] + + + # implement substep (2) + h_ih_nph = 0.5 * (h[r_i] + h[l_i]) - tg.dt / (2.0 * sg.dx) * (hu[r_i] - hu[l_i]) + + h_jh_nph = 0.5 * (h[r_j] + h[l_j]) - tg.dt / (2.0 * sg.dy) * (hv[r_j] - hv[l_j]) + + hu_flx_i = (hu) * sol.u + g / 2.0 * h**2 + hu_ih_nph = 0.5 * (hu[r_i] + hu[l_i]) - tg.dt / (2.0 * sg.dx) * (hu_flx_i[r_i] - hu_flx_i[l_i]) + + hu_flx_j = hv * sol.u + hu_jh_nph = 0.5 * (hu[r_j] + hu[l_j]) - tg.dt / (2.0 * sg.dy) * (hu_flx_j[r_j] - hu_flx_j[l_j]) + + hv_flx_i = hu * sol.v + hv_ih_nph = 0.5 * (hv[r_i] + hv[l_i]) - tg.dt / (2.0 * sg.dx) * (hv_flx_i[r_i] - hv_flx_i[l_i]) + + hv_flx_j = (hv) * sol.v + g / 2.0 * h**2 + hv_jh_nph = 0.5 * (hv[r_j] + hv[l_j]) - tg.dt / (2.0 * sg.dy) * (hv_flx_j[r_j] - hv_flx_j[l_j]) + + + # implement substep (3) + h_np1 = h[i1] - tg.dt / sg.dx * (hu_ih_nph[r_i][in_i] - hu_ih_nph[l_i][in_i]) - tg.dt / sg.dy * (hv_jh_nph[r_j][in_j] - hv_jh_nph[l_j][in_j]) + + # implement source term for Coriolis parameter + fvh = f * sol.v[i1] * (h_np1 + h[i1]) / 2.0 + hu_flx_x = hu_ih_nph**2 / h_ih_nph + g / 2.0 * h_ih_nph**2 + hu_flx_y = hu_jh_nph * hv_jh_nph / h_jh_nph + hu_np1 = hu[i1] - tg.dt / sg.dx * (hu_flx_x[r_i][in_i] - hu_flx_x[l_i][in_i]) - tg.dt / sg.dy * (hu_flx_y[r_j][in_j] - hu_flx_y[l_j][in_j]) + tg.dt * fvh + + fuh = -f * sol.u[i1] * (h_np1 + h[i1]) / 2.0 + hv_flx_x = hu_ih_nph * hv_ih_nph / h_ih_nph + hv_flx_y = hv_jh_nph**2 / h_jh_nph + g / 2.0 * h_jh_nph**2 + hv_np1 = hv[i1] - tg.dt / sg.dx * (hv_flx_x[r_i][in_i] - hv_flx_x[l_i][in_i]) - tg.dt / sg.dy * (hv_flx_y[r_j][in_j] - hv_flx_y[l_j][in_j]) + tg.dt * fuh + + u_np1 = hu_np1 / h_np1 + v_np1 = hv_np1 / h_np1 + + sol.h[i1] = h_np1 + sol.u[i1] = u_np1 + sol.v[i1] = v_np1 \ No newline at end of file diff --git a/w10/swe/output/visualise.ipynb b/w10/swe/output/visualise.ipynb new file mode 100644 index 0000000..6ed51b4 --- /dev/null +++ b/w10/swe/output/visualise.ipynb @@ -0,0 +1,1217 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 33, + "id": "01e48b90-fc9b-4e60-afd0-c608742cd321", + "metadata": {}, + "outputs": [], + "source": [ + "# This script animates the height field and the vorticity produced by\n", + "# a shallow water model.\n", + "# All credit goes to Robin Hogan and Paul Connolly\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import animation, rc\n", + "import h5py\n", + "from IPython.display import HTML\n", + "\n", + "rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n", + "rc('text', usetex=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "6ab0433f-3b56-4b3e-bfb6-82496d73ad59", + "metadata": {}, + "outputs": [], + "source": [ + "# Set this to \"True\" to save each frame as a png file\n", + "plot_frames = True;\n", + "\n", + "# Specify the range of heights to plot in metres\n", + "plot_height_range = np.array([9500., 10500.])" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "a9033d9d-39e4-41b9-9a1a-985fa403a691", + "metadata": {}, + "outputs": [], + "source": [ + "file = h5py.File('./output.h5', 'r')\n", + "tt = file.attrs.get('t') / 60\n", + "Nx, Ny = file.attrs.get('Nx'), file.attrs.get('Ny')\n", + "x, y = file.attrs.get('x').flatten(), file.attrs.get('y').flatten()\n", + "dx, dy = file.attrs.get('dx'), file.attrs.get('dy')\n", + "\n", + "tout = []\n", + "for t in tt:\n", + " if t % 60 == 0:\n", + " tout.append(t)\n", + "\n", + "noutput = len(tout)\n", + "# H = file['0/H'][:].T\n", + "h_save = np.zeros((Nx,Ny,noutput))\n", + "u_save = np.zeros((Nx,Ny,noutput))\n", + "v_save = np.zeros((Nx,Ny,noutput))\n", + "t_save = np.array(tout) * 60.0\n", + "\n", + "H = np.zeros_like(h_save)[:,:,0]\n", + "\n", + "for it in range(noutput):\n", + " h_save[:,:,it] = file['%i/h' %tout[it]][:].T\n", + " u_save[:,:,it] = file['%i/u' %tout[it]][:].T\n", + " v_save[:,:,it] = file['%i/v' %tout[it]][:].T\n", + " \n", + "file.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "a785bcdf-5c9e-4221-8d46-fc0382a941c6", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "from matplotlib.animation import FFMpegWriter\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "d14d40f8-62cf-44d9-8aa0-f05906a1d3e0", + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. 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rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "\n", + "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", + "// prettier-ignore\n", + "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.on(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/97 [00:00 1000:\n", + " height_scale = 0.001;\n", + " height_title = 'Height (km)';\n", + "else:\n", + " height_scale = 1;\n", + " height_title = 'Height (m)';\n", + "\n", + "print('Maximum orography height = %f m' % np.max(H[:]));\n", + "u = np.squeeze(u_save[:,:,0]);\n", + "vorticity = np.zeros(np.shape(u));\n", + "\n", + "writer = FFMpegWriter(fps=5)\n", + "\n", + "# Loop through the frames of the animation\n", + "with writer.saving(f, \"animation.mp4\", 240):\n", + " for it in tqdm(range(0,noutput)):\n", + " # Extract the height and velocity components for this frame\n", + " h = np.squeeze(h_save[:,:,it])\n", + " u = np.squeeze(u_save[:,:,it])\n", + " v = np.squeeze(v_save[:,:,it])\n", + "\n", + " # Compute the vorticity\n", + " vorticity[1:-1,1:-1] = (1./dy)*(u[1:-1,0:-2]-u[1:-1,2:]) \\\n", + " + (1./dx)*(v[2:,1:-1]-v[0:-2,1:-1])\n", + "\n", + " # First plot the height field\n", + " if it==0:\n", + " # Plot the height field\n", + " im=ax1.imshow(np.transpose(h+H)*height_scale, \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb1=f.colorbar(im,ax=ax1)\n", + " cb1.set_label('height (km)')\n", + " # Contour the terrain:\n", + " cs=ax1.contour(x_1000km,y_1000km,np.transpose(H),levels=range(1,11001,1000),colors='k')\n", + "\n", + " # Plot the velocity vectors\n", + " Q = ax1.quiver(x_1000km[2::interval],y_1000km[2::interval], \\\n", + " np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]), scale=5e2,scale_units='xy',pivot='mid')\n", + " ax1.set_ylabel('Y distance (1000s of km)')\n", + " ax1.set_xlabel('X distance (1000s of km)')\n", + " ax1.set_title(height_title)\n", + " tx1=ax1.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + "\n", + " # Now plot the vorticity\n", + " im2=ax2.imshow(np.transpose(vorticity), \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb2=f.colorbar(im2,ax=ax2)\n", + " cb2.set_label('vorticity (s$^{-1}$)')\n", + " ax2.set_xlabel('X distance (1000s of km)')\n", + " ax2.set_ylabel('Y distance (1000s of km)')\n", + " ax2.set_title('Relative vorticity (s$^{-1}$)')\n", + " tx2=ax2.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " else:\n", + " # top plot:\n", + " im.set_data(np.transpose(H+h)*height_scale)\n", + " cs.set_array(np.transpose(h))\n", + " Q.set_UVC(np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]))\n", + " tx1.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " # bottom plot:\n", + " im2.set_data(np.transpose(vorticity))\n", + " tx2.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " im.set_clim((plot_height_range*height_scale));\n", + " im2.set_clim((-3e-4,3e-4))\n", + " ax1.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + " ax2.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + "\n", + " # To make an animation we can save the frames as a \n", + " # sequence of images\n", + " if plot_frames:\n", + " plt.savefig('frames/frame%03d.pdf' % it,format='pdf') \n", + "\n", + " writer.grab_frame()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "552c0405-47db-46d8-8037-8b6c85511f49", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w10/w10.pdf b/w10/w10.pdf new file mode 100644 index 0000000..35bf7a1 Binary files /dev/null and b/w10/w10.pdf differ diff --git a/w11/swe/data/__init__.py b/w11/swe/data/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/w11/swe/data/grid.py b/w11/swe/data/grid.py new file mode 100644 index 0000000..c5fda5d --- /dev/null +++ b/w11/swe/data/grid.py @@ -0,0 +1,35 @@ +import numpy as np + +class sGrid(object): + def __init__(self, ud): + self.Nx = ud.Nx + self.xmin = ud.xmin + self.xmax = ud.xmax + + self.x = np.linspace(self.xmin, self.xmax, self.Nx).reshape(-1,1) + self.dx = np.diff(self.x.flatten())[0] + + if ud.Ny > 1: + self.Ny = ud.Ny + self.ymin = ud.ymin + self.ymax = ud.ymax + + self.y = np.linspace(self.ymin, self.ymax, self.Ny).reshape(1,-1) + self.dy = np.diff(self.y.flatten())[0] + else: + self.y = 0.0 + self.dy = np.nan + + self.dxy = (self.dx, self.dy) + self.xg, self.yg = np.meshgrid(self.x, self.y) + + +class tGrid(object): + def __init__(self, ud): + self.T = ud.T + self.dt = ud.dt + self.t = np.arange(0.0, self.T+self.dt, self.dt) + + + + diff --git a/w11/swe/data/io.py b/w11/swe/data/io.py new file mode 100644 index 0000000..dc04095 --- /dev/null +++ b/w11/swe/data/io.py @@ -0,0 +1,66 @@ +import argparse +import os +import h5py +import numpy as np + +class writer(object): + def __init__(self, folder='./output/', filename='swe.h5'): + self.OUTPUT_FOLDER = folder + self.OUTPUT_FILENAME = filename + self.FILE_PATH = self.OUTPUT_FOLDER + '/' + self.OUTPUT_FILENAME + + # If directory does not exist, create it. + if not os.path.exists(self.OUTPUT_FOLDER): + os.mkdir(self.OUTPUT_FOLDER) + + # If file exists, rename it with old. + if os.path.exists(self.FILE_PATH): + os.rename(self.FILE_PATH, self.FILE_PATH+'_old') + + file = h5py.File(self.FILE_PATH, 'a') + file.close() + + def f(self): + file = h5py.File(self.FILE_PATH, 'r+') + return file + + def write(self, time, name, data): + time = np.around(time, 4) + file = self.f() + file.create_dataset(str(time) + '/' + str(name), data=data, chunks=True, compression='gzip', compression_opts=4) + file.close() + + def write_attr(self,obj): + file = self.f() + for key, value in vars(obj).items(): + try: + file.attrs.create(key,value) + except: + file.attrs.create(key,repr(value),dtype='max_wind)] = max_wind + u[np.where(u<-max_wind)] = -max_wind + v[np.where(v>max_wind)] = max_wind + v[np.where(v<-max_wind)] = -max_wind + + sol.u[...] = u.T + sol.v[...] = v.T + + sol.H = np.zeros_like(height.T) + sol.F = F.T + + return sol \ No newline at end of file diff --git a/w11/swe/input/gravity_wave.py b/w11/swe/input/gravity_wave.py new file mode 100644 index 0000000..e1059a8 --- /dev/null +++ b/w11/swe/input/gravity_wave.py @@ -0,0 +1,37 @@ +import numpy as np +from data.vars import Variables + +class UserData(object): + def __init__(self): + + self.xmin = 0.0 + self.xmax = 25400000.0 - 100000 + self.Nx = 254+0 + + self.ymin = 0.0 + self.ymax = 5000000.0 - 100000 + self.Ny = 50+0 + + self.dt = 60.0 + self.T = 4*24.0*60*60 + + self.g = 9.81 + self.f = 0.0 + + self.fn = 'gravity_wave' + self.output_interval = 60*60 + + +def sol_init(sg, ud): + std_blob = 8.0*sg.dy + height = 9750. + 1000.*np.exp(-((sg.xg-0.25*np.mean(sg.x))**2.+(sg.yg-np.mean(sg.y))**2.)/(2.*std_blob**2.)) + + sol = Variables(sg) + sol.h[...] = height + sol.u[...] = 0.0 + sol.v[...] = 0.0 + + sol.H = np.zeros_like(sol.h) + sol.F = np.zeros_like(sol.h) + + return sol \ No newline at end of file diff --git a/w11/swe/input/user_data.py b/w11/swe/input/user_data.py new file mode 100644 index 0000000..a5d671f --- /dev/null +++ b/w11/swe/input/user_data.py @@ -0,0 +1,18 @@ +class UserDataInit(object): + """ + Loads user defined initial conditions. Specifically, all attributes of the class object defined in the initial condition is loaded. + + Attributes + ---------- + **kwargs: class object + + """ + + def __init__(self,**kwargs): + for key, value in kwargs.items(): + setattr(self, key, value) + + + def update_ud(self, rewrite): + for key, value in rewrite.items(): + setattr(self, key, value) \ No newline at end of file diff --git a/w11/swe/main.py b/w11/swe/main.py new file mode 100644 index 0000000..43dedd5 --- /dev/null +++ b/w11/swe/main.py @@ -0,0 +1,42 @@ +from data.grid import sGrid, tGrid +from numerics.lax_wendroff import lax_wendroff +from numerics.bc import set_boundary +from data import io + +import numpy as np + +if __name__ == '__main__': + user_data, sol_init = io.get_args() + ud = user_data() + + writer = io.writer(filename=ud.fn) + + sg = sGrid(ud) + tg = tGrid(ud) + writer.write_attr(ud) + writer.write_attr(sg) + writer.write_attr(tg) + + sol = sol_init(sg, ud) + writer.write(0, 'H', sol.H) + writer.write(0, 'F', sol.F) + + for nn, tt in enumerate(tg.t): + + if tt % ud.output_interval == 0: + max_u = np.sqrt(np.max(sol.u**2 + sol.v**2)) + print("Time = %f hours (max %f); max(|u|) = %f" % ((tt)/3600., tg.t[-1] / 3600, max_u) ) + writer.write(nn, 'h', sol.h) + writer.write(nn, 'u', sol.u) + writer.write(nn, 'v', sol.v) + + lax_wendroff(sol, tg, sg, ud) + set_boundary(sol) + + + + + + + + diff --git a/w11/swe/numerics/__init__.py b/w11/swe/numerics/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/w11/swe/numerics/bc.py b/w11/swe/numerics/bc.py new file mode 100644 index 0000000..566d34e --- /dev/null +++ b/w11/swe/numerics/bc.py @@ -0,0 +1,28 @@ +import numpy as np + +def set_boundary(sol): + i1i = (..., slice(1,-1)) + i1j = (slice(1,-1),...) + # sol.h[...] = np.pad(sol.h[i1i], (get_ghost(sol.h, 1)), mode='wrap') + # sol.u[...] = np.pad(sol.u[i1i], (get_ghost(sol.u, 1)), mode='wrap') + # sol.v[...] = np.pad(sol.v[i1i], (get_ghost(sol.v, 1)), mode='wrap') + + + # sol.h[...] = np.pad(sol.h[i1j], (get_ghost(sol.h, 0)), mode='symmetric') + # sol.u[...] = np.pad(sol.u[i1j], (get_ghost(sol.u, 0)), mode='symmetric') + # sol.v[...] = np.pad(sol.v[i1j], (get_ghost(sol.v, 0)), mode='symmetric') + + sol.h[:,-1] = sol.h[:,1] + sol.u[:,-1] = sol.u[:,1] + sol.v[:,-1] = sol.v[:,1] + + sol.h[:,0] = sol.h[:,-2] + sol.u[:,0] = sol.u[:,-2] + sol.v[:,0] = sol.v[:,-2] + + sol.v[[0,-1],:] = 0.0 + +def get_ghost(u, idx): + ghost_cells = [(0,0)]*u.ndim + ghost_cells[idx] = (1,1) + return ghost_cells diff --git a/w11/swe/numerics/lax_wendroff.py b/w11/swe/numerics/lax_wendroff.py new file mode 100644 index 0000000..9c90c9a --- /dev/null +++ b/w11/swe/numerics/lax_wendroff.py @@ -0,0 +1,47 @@ +import numpy as np + +from copy import deepcopy + +def lax_wendroff(sol, tg, sg, ud): + li, ri = (...,slice(0,-1)), (...,slice(1,None)) + lj, rj = (slice(0,-1),), (slice(1,None),) + i1, i1i, i1j = (slice(1,-1),slice(1,-1)), (...,slice(1,-1)), (slice(1,-1),) + + hu = sol.h * sol.u + hv = sol.h * sol.v + + ##### + + hi_nph = 0.5 * (sol.h[li] + sol.h[ri]) - tg.dt / (2.0 * sg.dx) * (hu[ri] - hu[li]) + hj_nph = 0.5 * (sol.h[lj] + sol.h[rj]) - tg.dt / (2.0 * sg.dy) * (hv[rj] - hv[lj]) + + hui_flx = hu*sol.u + ud.g / 2.0 * sol.h**2 + hui_nph = 0.5 * (hu[li] + hu[ri]) - tg.dt / (2.0 * sg.dx) * (hui_flx[ri] - hui_flx[li]) + + huj_flx = hu*sol.v + huj_nph = 0.5 * (hu[lj] + hu[rj]) - tg.dt / (2.0 * sg.dy) * (huj_flx[rj] - huj_flx[lj]) + + hvi_flx = hu*sol.v + hvi_nph = 0.5 * (hv[li] + hv[ri]) - tg.dt / (2.0 * sg.dx) * (hvi_flx[ri] - hvi_flx[li]) + + hvj_flx = hv*sol.v + ud.g / 2.0 * sol.h**2 + hvj_nph = 0.5 * (hv[lj] + hv[rj]) - tg.dt / (2.0 * sg.dy) * (hvj_flx[rj] - hvj_flx[lj]) + + ##### + + uF = sol.F[i1] * sol.v[i1] + vF = -sol.F[i1] * sol.u[i1] + + h_np1 = sol.h[i1] - (tg.dt / sg.dx) * (hui_nph[ri][i1j] - hui_nph[li][i1j]) - (tg.dt / sg.dy) * (hvj_nph[rj][i1i] - hvj_nph[lj][i1i]) + + hui_flx_nph = hui_nph**2 / hi_nph + ud.g / 2.0 * hi_nph**2 + huj_flx_nph = huj_nph * hvj_nph / hj_nph + hu_np1 = hu[i1] - (tg.dt / sg.dx) * (hui_flx_nph[ri][i1j] - hui_flx_nph[li][i1j]) - (tg.dt / sg.dy) * (huj_flx_nph[rj][i1i] - huj_flx_nph[lj][i1i]) + tg.dt * uF * (sol.h[i1] + h_np1) / 2.0 + + hvi_flx_nph = hui_nph * hvi_nph / hi_nph + hvj_flx_nph = hvj_nph**2 / hj_nph + ud.g / 2.0 * hj_nph**2 + hv_np1 = hv[i1] - (tg.dt / sg.dx) * (hvi_flx_nph[ri][i1j] - hvi_flx_nph[li][i1j]) - (tg.dt / sg.dy) * (hvj_flx_nph[rj][i1i] - hvj_flx_nph[lj][i1i]) + tg.dt * vF * (sol.h[i1] + h_np1) / 2.0 + + sol.h[i1] = h_np1 + sol.u[i1] = hu_np1 / h_np1 + sol.v[i1] = hv_np1 / h_np1 \ No newline at end of file diff --git a/w11/swe/output/animation.mp4 b/w11/swe/output/animation.mp4 new file mode 100644 index 0000000..30d745a Binary files /dev/null and b/w11/swe/output/animation.mp4 differ diff --git a/w11/swe/output/animation_gw_nf.mp4 b/w11/swe/output/animation_gw_nf.mp4 new file mode 100644 index 0000000..f27af94 Binary files /dev/null and b/w11/swe/output/animation_gw_nf.mp4 differ diff --git a/w11/swe/output/baroclinic_instability b/w11/swe/output/baroclinic_instability new file mode 100644 index 0000000..f8ccf1e Binary files /dev/null and b/w11/swe/output/baroclinic_instability differ diff --git a/w11/swe/output/gravity_wave b/w11/swe/output/gravity_wave new file mode 100644 index 0000000..ceb0c95 Binary files /dev/null and b/w11/swe/output/gravity_wave differ diff --git a/w11/swe/output/visualise.ipynb b/w11/swe/output/visualise.ipynb new file mode 100644 index 0000000..ae1f2fc --- /dev/null +++ b/w11/swe/output/visualise.ipynb @@ -0,0 +1,1215 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "01e48b90-fc9b-4e60-afd0-c608742cd321", + "metadata": {}, + "outputs": [], + "source": [ + "# This script animates the height field and the vorticity produced by\n", + "# a shallow water model.\n", + "# All credit goes to Robin Hogan and Paul Connolly\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import animation, rc\n", + "import h5py\n", + "from IPython.display import HTML\n", + "\n", + "rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n", + "rc('text', usetex=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6ab0433f-3b56-4b3e-bfb6-82496d73ad59", + "metadata": {}, + "outputs": [], + "source": [ + "# Set this to \"True\" to save each frame as a png file\n", + "plot_frames = True;\n", + "\n", + "# Specify the range of heights to plot in metres\n", + "plot_height_range = np.array([9500., 10500.])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a9033d9d-39e4-41b9-9a1a-985fa403a691", + "metadata": {}, + "outputs": [], + "source": [ + "file = h5py.File('./gravity_wave', 'r')\n", + "tt = file.attrs.get('t') / 60\n", + "Nx, Ny = file.attrs.get('Nx'), file.attrs.get('Ny')\n", + "x, y = file.attrs.get('x').flatten(), file.attrs.get('y').flatten()\n", + "dx, dy = file.attrs.get('dx'), file.attrs.get('dy')\n", + "\n", + "tout = []\n", + "for t in tt:\n", + " if t % 60 == 0:\n", + " tout.append(t)\n", + "\n", + "noutput = len(tout)\n", + "H = file['0/H'][:].T\n", + "h_save = np.zeros((Nx,Ny,noutput))\n", + "u_save = np.zeros((Nx,Ny,noutput))\n", + "v_save = np.zeros((Nx,Ny,noutput))\n", + "t_save = np.array(tout) * 60.0\n", + "\n", + "for it in range(noutput):\n", + " h_save[:,:,it] = file['%i/h' %tout[it]][:].T\n", + " u_save[:,:,it] = file['%i/u' %tout[it]][:].T\n", + " v_save[:,:,it] = file['%i/v' %tout[it]][:].T\n", + " \n", + "file.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a785bcdf-5c9e-4221-8d46-fc0382a941c6", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "from matplotlib.animation import FFMpegWriter\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d14d40f8-62cf-44d9-8aa0-f05906a1d3e0", + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. 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button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "\n", + "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", + "// prettier-ignore\n", + "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.on(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/97 [00:00 1000:\n", + " height_scale = 0.001;\n", + " height_title = 'Height (km)';\n", + "else:\n", + " height_scale = 1;\n", + " height_title = 'Height (m)';\n", + "\n", + "print('Maximum orography height = %f m' % np.max(H[:]));\n", + "u = np.squeeze(u_save[:,:,0]);\n", + "vorticity = np.zeros(np.shape(u));\n", + "\n", + "writer = FFMpegWriter(fps=5)\n", + "\n", + "# Loop through the frames of the animation\n", + "with writer.saving(f, \"animation.mp4\", 240):\n", + " for it in tqdm(range(0,noutput)):\n", + " # Extract the height and velocity components for this frame\n", + " h = np.squeeze(h_save[:,:,it])\n", + " u = np.squeeze(u_save[:,:,it])\n", + " v = np.squeeze(v_save[:,:,it])\n", + "\n", + " # Compute the vorticity\n", + " vorticity[1:-1,1:-1] = (1./dy)*(u[1:-1,0:-2]-u[1:-1,2:]) \\\n", + " + (1./dx)*(v[2:,1:-1]-v[0:-2,1:-1])\n", + "\n", + " # First plot the height field\n", + " if it==0:\n", + " # Plot the height field\n", + " im=ax1.imshow(np.transpose(h+H)*height_scale, \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb1=f.colorbar(im,ax=ax1)\n", + " cb1.set_label('height (km)')\n", + " # Contour the terrain:\n", + " cs=ax1.contour(x_1000km,y_1000km,np.transpose(H),levels=range(1,11001,1000),colors='k')\n", + "\n", + " # Plot the velocity vectors\n", + " Q = ax1.quiver(x_1000km[2::interval],y_1000km[2::interval], \\\n", + " np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]), scale=5e2,scale_units='xy',pivot='mid')\n", + " ax1.set_ylabel('Y distance (1000s of km)')\n", + " ax1.set_xlabel('X distance (1000s of km)')\n", + " ax1.set_title(height_title)\n", + " tx1=ax1.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + "\n", + " # Now plot the vorticity\n", + " im2=ax2.imshow(np.transpose(vorticity), \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb2=f.colorbar(im2,ax=ax2)\n", + " cb2.set_label('vorticity (s$^{-1}$)')\n", + " ax2.set_xlabel('X distance (1000s of km)')\n", + " ax2.set_ylabel('Y distance (1000s of km)')\n", + " ax2.set_title('Relative vorticity (s$^{-1}$)')\n", + " tx2=ax2.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " else:\n", + " # top plot:\n", + " im.set_data(np.transpose(H+h)*height_scale)\n", + " cs.set_array(np.transpose(h))\n", + " Q.set_UVC(np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]))\n", + " tx1.set_text('Time = %.1f hours' % (t_save[it]/3600.))pr\n", + "\n", + " # bottom plot:\n", + " im2.set_data(np.transpose(vorticity))\n", + " tx2.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " im.set_clim((plot_height_range*height_scale));\n", + " im2.set_clim((-3e-4,3e-4))\n", + " ax1.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + " ax2.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + "\n", + " # To make an animation we can save the frames as a \n", + " # sequence of images\n", + " if plot_frames:\n", + " plt.savefig('frames/frame%03d.pdf' % it,format='pdf') \n", + "\n", + " writer.grab_frame()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "552c0405-47db-46d8-8037-8b6c85511f49", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w11/w11_bc_src.pdf b/w11/w11_bc_src.pdf new file mode 100644 index 0000000..63ad9be Binary files /dev/null and b/w11/w11_bc_src.pdf differ diff --git a/w11/wip_code/lax_wendroff.py b/w11/wip_code/lax_wendroff.py new file mode 100644 index 0000000..857092b --- /dev/null +++ b/w11/wip_code/lax_wendroff.py @@ -0,0 +1,41 @@ +import numpy as np + + +def lax_wendroff(sol, tg, sg, ud): + # We want the quantities that we are updating with the RLW method + h = sol.h + hu = sol.h * sol.u + hv = sol.h * sol.v + + # Get values defined by the user in the initial conditions file + g = ud.g + + # Now we need the to specify how we index our arrays. + + # we take the values on the right in the x direction + r_i = (..., slice(1,None)) + # we take the values on the left in the x direction + l_i = (..., slice(0,-1)) + # we take the values on the right in the y direction + r_j = (slice(1,None), ...) + # we take the values on the left in the y direction + l_j = (slice(0,-1), ...) + + + # implement substep (2) + h_ih_nph = 0.5 * (h[r_i] + h[l_i]) - tg.dt / (2.0 * sg.dx) * (hu[r_i] - hu[l_i]) + + h_jh_nph = 0.5 * (h[r_j] + h[l_j]) - tg.dt / (2.0 * sg.dy) * (hv[r_j] - hv[l_j]) + + hu_flx_i = (hu)**2 / h + g / 2.0 * h**2 + hu_ih_nph = 0.5 * (hu[r_i] + hu[l_i]) - tg.dt / (2.0 * sg.dx) * (hu_flx_i[r_i] - hu_flx_i[l_i]) + + hu_flx_j = hv * hu / h + hu_jh_nph = 0.5 * (hu[r_j] + hu[l_j]) - tg.dt / (2.0 * sg.dy) * (hu_flx_j[r_j] - hu_flx_j[l_j]) + + hv_flx_i = hu * hv / h + hv_ih_nph = 0.5 * (hv[r_i] + hv[l_i]) - tg.dt / (2.0 * sg.dx) * (hv_flx_i[r_i] - hv_flx_i[l_i]) + + hv_flx_j = (hv)**2 / h + g / 2.0 * h**2 + hv_jh_nph = 0.5 * (hv[r_j] + hv[l_j]) - tg.dt / (2.0 * sg.dy) * (hv_flx_j[r_j] - hv_flx_j[l_j]) + diff --git a/w11/wip_code/visualise.ipynb b/w11/wip_code/visualise.ipynb new file mode 100644 index 0000000..a131ae4 --- /dev/null +++ b/w11/wip_code/visualise.ipynb @@ -0,0 +1,1215 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "01e48b90-fc9b-4e60-afd0-c608742cd321", + "metadata": {}, + "outputs": [], + "source": [ + "# This script animates the height field and the vorticity produced by\n", + "# a shallow water model.\n", + "# All credit goes to Robin Hogan and Paul Connolly\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import animation, rc\n", + "import h5py\n", + "from IPython.display import HTML\n", + "\n", + "rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n", + "rc('text', usetex=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6ab0433f-3b56-4b3e-bfb6-82496d73ad59", + "metadata": {}, + "outputs": [], + "source": [ + "# Set this to \"True\" to save each frame as a png file\n", + "plot_frames = True;\n", + "\n", + "# Specify the range of heights to plot in metres\n", + "plot_height_range = np.array([9500., 10500.])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a9033d9d-39e4-41b9-9a1a-985fa403a691", + "metadata": {}, + "outputs": [], + "source": [ + "file = h5py.File('./gravity_wave', 'r')\n", + "tt = file.attrs.get('t') / 60\n", + "Nx, Ny = file.attrs.get('Nx'), file.attrs.get('Ny')\n", + "x, y = file.attrs.get('x').flatten(), file.attrs.get('y').flatten()\n", + "dx, dy = file.attrs.get('dx'), file.attrs.get('dy')\n", + "\n", + "tout = []\n", + "for t in tt:\n", + " if t % 60 == 0:\n", + " tout.append(t)\n", + "\n", + "noutput = len(tout)\n", + "H = file['0/H'][:].T\n", + "h_save = np.zeros((Nx,Ny,noutput))\n", + "u_save = np.zeros((Nx,Ny,noutput))\n", + "v_save = np.zeros((Nx,Ny,noutput))\n", + "t_save = np.array(tout) * 60.0\n", + "\n", + "for it in range(noutput):\n", + " h_save[:,:,it] = file['%i/h' %tout[it]][:].T\n", + " u_save[:,:,it] = file['%i/u' %tout[it]][:].T\n", + " v_save[:,:,it] = file['%i/v' %tout[it]][:].T\n", + " \n", + "file.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a785bcdf-5c9e-4221-8d46-fc0382a941c6", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "from matplotlib.animation import FFMpegWriter\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d14d40f8-62cf-44d9-8aa0-f05906a1d3e0", + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", + "\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById('mpl-warnings');\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", + "\n", + " parent_element.appendChild(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", + " }\n", + " fig.send_message('refresh', {});\n", + " };\n", + "\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function () {\n", + " fig.ws.close();\n", + " };\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "};\n", + "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._init_canvas = function () {\n", + " var fig = this;\n", + "\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", + "\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", + " }\n", + "\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", + "\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", + "\n", + " this.context = canvas.getContext('2d');\n", + "\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", + "\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", + "\n", + " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", + " if (this.ResizeObserver === undefined) {\n", + " if (window.ResizeObserver !== undefined) {\n", + " this.ResizeObserver = window.ResizeObserver;\n", + " } else {\n", + " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", + " this.ResizeObserver = obs.ResizeObserver;\n", + " }\n", + " }\n", + "\n", + " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", + " });\n", + " this.resizeObserverInstance.observe(canvas_div);\n", + "\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", + " }\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "\n", + "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", + "// prettier-ignore\n", + "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.on(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/97 [00:00 1000:\n", + " height_scale = 0.001;\n", + " height_title = 'Height (km)';\n", + "else:\n", + " height_scale = 1;\n", + " height_title = 'Height (m)';\n", + "\n", + "print('Maximum orography height = %f m' % np.max(H[:]));\n", + "u = np.squeeze(u_save[:,:,0]);\n", + "vorticity = np.zeros(np.shape(u));\n", + "\n", + "writer = FFMpegWriter(fps=5)\n", + "\n", + "# Loop through the frames of the animation\n", + "with writer.saving(f, \"animation.mp4\", 240):\n", + " for it in tqdm(range(0,noutput)):\n", + " # Extract the height and velocity components for this frame\n", + " h = np.squeeze(h_save[:,:,it])\n", + " u = np.squeeze(u_save[:,:,it])\n", + " v = np.squeeze(v_save[:,:,it])\n", + "\n", + " # Compute the vorticity\n", + " vorticity[1:-1,1:-1] = (1./dy)*(u[1:-1,0:-2]-u[1:-1,2:]) \\\n", + " + (1./dx)*(v[2:,1:-1]-v[0:-2,1:-1])\n", + "\n", + " # First plot the height field\n", + " if it==0:\n", + " # Plot the height field\n", + " im=ax1.imshow(np.transpose(h+H)*height_scale, \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb1=f.colorbar(im,ax=ax1)\n", + " cb1.set_label('height (km)')\n", + " # Contour the terrain:\n", + " cs=ax1.contour(x_1000km,y_1000km,np.transpose(H),levels=range(1,11001,1000),colors='k')\n", + "\n", + " # Plot the velocity vectors\n", + " Q = ax1.quiver(x_1000km[2::interval],y_1000km[2::interval], \\\n", + " np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]), scale=5e2,scale_units='xy',pivot='mid')\n", + " ax1.set_ylabel('Y distance (1000s of km)')\n", + " ax1.set_xlabel('X distance (1000s of km)')\n", + " ax1.set_title(height_title)\n", + " tx1=ax1.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + "\n", + " # Now plot the vorticity\n", + " im2=ax2.imshow(np.transpose(vorticity), \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb2=f.colorbar(im2,ax=ax2)\n", + " cb2.set_label('vorticity (s$^{-1}$)')\n", + " ax2.set_xlabel('X distance (1000s of km)')\n", + " ax2.set_ylabel('Y distance (1000s of km)')\n", + " ax2.set_title('Relative vorticity (s$^{-1}$)')\n", + " tx2=ax2.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " else:\n", + " # top plot:\n", + " im.set_data(np.transpose(H+h)*height_scale)\n", + " cs.set_array(np.transpose(h))\n", + " Q.set_UVC(np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]))\n", + " tx1.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " # bottom plot:\n", + " im2.set_data(np.transpose(vorticity))\n", + " tx2.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " im.set_clim((plot_height_range*height_scale));\n", + " im2.set_clim((-3e-4,3e-4))\n", + " ax1.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + " ax2.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + "\n", + " # To make an animation we can save the frames as a \n", + " # sequence of images\n", + " if plot_frames:\n", + " plt.savefig('frames/frame%03d.pdf' % it,format='pdf') \n", + "\n", + " writer.grab_frame()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "552c0405-47db-46d8-8037-8b6c85511f49", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w12/swe/data/__init__.py b/w12/swe/data/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/w12/swe/data/grid.py b/w12/swe/data/grid.py new file mode 100644 index 0000000..c5fda5d --- /dev/null +++ b/w12/swe/data/grid.py @@ -0,0 +1,35 @@ +import numpy as np + +class sGrid(object): + def __init__(self, ud): + self.Nx = ud.Nx + self.xmin = ud.xmin + self.xmax = ud.xmax + + self.x = np.linspace(self.xmin, self.xmax, self.Nx).reshape(-1,1) + self.dx = np.diff(self.x.flatten())[0] + + if ud.Ny > 1: + self.Ny = ud.Ny + self.ymin = ud.ymin + self.ymax = ud.ymax + + self.y = np.linspace(self.ymin, self.ymax, self.Ny).reshape(1,-1) + self.dy = np.diff(self.y.flatten())[0] + else: + self.y = 0.0 + self.dy = np.nan + + self.dxy = (self.dx, self.dy) + self.xg, self.yg = np.meshgrid(self.x, self.y) + + +class tGrid(object): + def __init__(self, ud): + self.T = ud.T + self.dt = ud.dt + self.t = np.arange(0.0, self.T+self.dt, self.dt) + + + + diff --git a/w12/swe/data/io.py b/w12/swe/data/io.py new file mode 100644 index 0000000..85a4dfb --- /dev/null +++ b/w12/swe/data/io.py @@ -0,0 +1,68 @@ +import argparse +import os +import h5py +import numpy as np + +class writer(object): + def __init__(self, folder='./output/', filename='output.h5'): + self.OUTPUT_FOLDER = folder + self.OUTPUT_FILENAME = filename + self.FILE_PATH = self.OUTPUT_FOLDER + '/' + self.OUTPUT_FILENAME + + # If directory does not exist, create it. + if not os.path.exists(self.OUTPUT_FOLDER): + os.mkdir(self.OUTPUT_FOLDER) + + # If file exists, rename it with old. + if os.path.exists(self.FILE_PATH): + os.rename(self.FILE_PATH, self.FILE_PATH+'_old') + + file = h5py.File(self.FILE_PATH, 'a') + file.close() + + def f(self): + file = h5py.File(self.FILE_PATH, 'r+') + return file + + def write(self, time, name, data): + time = np.around(time, 4) + file = self.f() + file.create_dataset(str(time) + '/' + str(name), data=data, chunks=True, compression='gzip', compression_opts=4) + file.close() + + def write_attr(self,obj): + file = self.f() + for key, value in vars(obj).items(): + try: + file.attrs.create(key,value) + except: + file.attrs.create(key,repr(value),dtype='max_wind)] = max_wind + u[np.where(u<-max_wind)] = -max_wind + v[np.where(v>max_wind)] = max_wind + v[np.where(v<-max_wind)] = -max_wind + + # this creates the solution container + sol = Variables(sg) + sol.h[...] = height.T + sol.u[...] = u.T + sol.v[...] = v.T + sol.F = F.T + + return sol \ No newline at end of file diff --git a/w12/swe/input/block.py b/w12/swe/input/block.py new file mode 100644 index 0000000..48c3bdc --- /dev/null +++ b/w12/swe/input/block.py @@ -0,0 +1,22 @@ +import numpy as np +from data.vars import Variables + +class UserData(object): + def __init__(self): + + self.xmin = -4.0 + self.xmax = +4.0 + self.Nx = 81 + + self.ymin = -4.0 + self.ymax = +4.0 + self.Ny = 81 + + self.dt = 0.001 + self.T = 1.0 + + +def sol_init(sg): + sol = Variables(sg) + sol.u[20:60] = 1.0 + return sol \ No newline at end of file diff --git a/w12/swe/input/gw.py b/w12/swe/input/gw.py new file mode 100644 index 0000000..cedb615 --- /dev/null +++ b/w12/swe/input/gw.py @@ -0,0 +1,31 @@ +import numpy as np +from data.vars import Variables + +class UserData(object): + def __init__(self): + + self.xmin = 0.0 # [m] + self.xmax = 25400000.0 - 100000 # [m] + self.Nx = 254 + + self.ymin = 0.0 # [m] + self.ymax = 5000000.0 - 100000 # [m] + self.Ny = 50 + + self.dt = 60.0 # [s] + self.T = 4.0 * 24.0 * 3600.0 # [s] + + self.g = 9.81 # [m/s^2] + self.f = 0.0 # [s^(-1)] + + +def sol_init(sg): + std_blob = 8.0*sg.dy; # Standard deviation of blob (m) + height = 9750. + 1000.*np.exp(-((sg.xg-0.25*np.mean(sg.x))**2.+(sg.yg-np.mean(sg.y))**2.)/(2.* \ + std_blob**2.)) + + # this creates the solution container + sol = Variables(sg) + sol.h[...] = height + + return sol \ No newline at end of file diff --git a/w12/swe/input/random.py b/w12/swe/input/random.py new file mode 100644 index 0000000..e69de29 diff --git a/w12/swe/input/user_data.py b/w12/swe/input/user_data.py new file mode 100644 index 0000000..a5d671f --- /dev/null +++ b/w12/swe/input/user_data.py @@ -0,0 +1,18 @@ +class UserDataInit(object): + """ + Loads user defined initial conditions. Specifically, all attributes of the class object defined in the initial condition is loaded. + + Attributes + ---------- + **kwargs: class object + + """ + + def __init__(self,**kwargs): + for key, value in kwargs.items(): + setattr(self, key, value) + + + def update_ud(self, rewrite): + for key, value in rewrite.items(): + setattr(self, key, value) \ No newline at end of file diff --git a/w12/swe/main.py b/w12/swe/main.py new file mode 100644 index 0000000..e4a0293 --- /dev/null +++ b/w12/swe/main.py @@ -0,0 +1,36 @@ +from data.grid import sGrid, tGrid +from numerics.lax_wendroff import lax_wendroff +from numerics.bc import set_boundary +from data import io + + +if __name__ == '__main__': + user_data, sol_init = io.get_args() + ud = user_data() + + writer = io.writer() + + sg = sGrid(ud) + tg = tGrid(ud) + writer.write_attr(sg) + writer.write_attr(tg) + + sol = sol_init(sg,ud) + + for nn, t in enumerate(tg.t): + + if nn % 60 == 0: + writer.write(nn, "h", sol.h) + writer.write(nn, "u", sol.u) + writer.write(nn, "v", sol.v) + print("time-step %.2f" %nn) + + lax_wendroff(sol, tg, sg, ud) + set_boundary(sol) + + + + + + + diff --git a/w12/swe/numerics/__init__.py b/w12/swe/numerics/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/w12/swe/numerics/bc.py b/w12/swe/numerics/bc.py new file mode 100644 index 0000000..071e83d --- /dev/null +++ b/w12/swe/numerics/bc.py @@ -0,0 +1,25 @@ +import numpy as np + +def set_boundary(sol): + # we set periodic BC in the x-direction + sol.h[:,0] = sol.h[:,-2] + sol.h[:,-1] = sol.h[:,1] + + sol.u[:,0] = sol.u[:,-2] + sol.u[:,-1] = sol.u[:,1] + + sol.v[:,0] = sol.v[:,-2] + sol.v[:,-1] = sol.v[:,1] + + # we set no-flux BC in the y-direction + sol.v[[0,-1],:] = 0.0 + + # sol.h[0,:] = sol.h[-2,:] + # sol.h[-1,:] = sol.h[1,:] + + # sol.u[0,:] = sol.u[-2,:] + # sol.u[-1,:] = sol.u[1,:] + + # sol.v[0,:] = sol.v[-2,:] + # sol.v[-1,:] = sol.v[1,:] + diff --git a/w12/swe/numerics/lax_wendroff.py b/w12/swe/numerics/lax_wendroff.py new file mode 100644 index 0000000..892213e --- /dev/null +++ b/w12/swe/numerics/lax_wendroff.py @@ -0,0 +1,68 @@ +import numpy as np + + +def lax_wendroff(sol, tg, sg, ud): + # We want the quantities that we are updating with the RLW method + h = sol.h + hu = sol.h * sol.u + hv = sol.h * sol.v + + # Now we need the to specify how we index our arrays. + + # we take the values on the right in the x direction + r_i = (..., slice(1,None)) + # we take the values on the left in the x direction + l_i = (..., slice(0,-1)) + # we take the values on the right in the y direction + r_j = (slice(1,None),) + # we take the values on the left in the y direction + l_j = (slice(0,-1),) + + # define the inner domain, i.e. without the ghost cells, + i1 = (slice(1,-1), slice(1,-1)) + in_i = (slice(1,-1),) + in_j = (..., slice(1,-1)) + + # Get values defined by the user in the initial conditions file + g = ud.g + f = sol.F[i1] + + + # implement substep (2) + h_ih_nph = 0.5 * (h[r_i] + h[l_i]) - tg.dt / (2.0 * sg.dx) * (hu[r_i] - hu[l_i]) + + h_jh_nph = 0.5 * (h[r_j] + h[l_j]) - tg.dt / (2.0 * sg.dy) * (hv[r_j] - hv[l_j]) + + hu_flx_i = (hu) * sol.u + g / 2.0 * h**2 + hu_ih_nph = 0.5 * (hu[r_i] + hu[l_i]) - tg.dt / (2.0 * sg.dx) * (hu_flx_i[r_i] - hu_flx_i[l_i]) + + hu_flx_j = hv * sol.u + hu_jh_nph = 0.5 * (hu[r_j] + hu[l_j]) - tg.dt / (2.0 * sg.dy) * (hu_flx_j[r_j] - hu_flx_j[l_j]) + + hv_flx_i = hu * sol.v + hv_ih_nph = 0.5 * (hv[r_i] + hv[l_i]) - tg.dt / (2.0 * sg.dx) * (hv_flx_i[r_i] - hv_flx_i[l_i]) + + hv_flx_j = (hv) * sol.v + g / 2.0 * h**2 + hv_jh_nph = 0.5 * (hv[r_j] + hv[l_j]) - tg.dt / (2.0 * sg.dy) * (hv_flx_j[r_j] - hv_flx_j[l_j]) + + + # implement substep (3) + h_np1 = h[i1] - tg.dt / sg.dx * (hu_ih_nph[r_i][in_i] - hu_ih_nph[l_i][in_i]) - tg.dt / sg.dy * (hv_jh_nph[r_j][in_j] - hv_jh_nph[l_j][in_j]) + + # implement source term for Coriolis parameter + fvh = f * sol.v[i1] * (h_np1 + h[i1]) / 2.0 + hu_flx_x = hu_ih_nph**2 / h_ih_nph + g / 2.0 * h_ih_nph**2 + hu_flx_y = hu_jh_nph * hv_jh_nph / h_jh_nph + hu_np1 = hu[i1] - tg.dt / sg.dx * (hu_flx_x[r_i][in_i] - hu_flx_x[l_i][in_i]) - tg.dt / sg.dy * (hu_flx_y[r_j][in_j] - hu_flx_y[l_j][in_j]) + tg.dt * fvh + + fuh = -f * sol.u[i1] * (h_np1 + h[i1]) / 2.0 + hv_flx_x = hu_ih_nph * hv_ih_nph / h_ih_nph + hv_flx_y = hv_jh_nph**2 / h_jh_nph + g / 2.0 * h_jh_nph**2 + hv_np1 = hv[i1] - tg.dt / sg.dx * (hv_flx_x[r_i][in_i] - hv_flx_x[l_i][in_i]) - tg.dt / sg.dy * (hv_flx_y[r_j][in_j] - hv_flx_y[l_j][in_j]) + tg.dt * fuh + + u_np1 = hu_np1 / h_np1 + v_np1 = hv_np1 / h_np1 + + sol.h[i1] = h_np1 + sol.u[i1] = u_np1 + sol.v[i1] = v_np1 \ No newline at end of file diff --git a/w12/swe/output/visualise.ipynb b/w12/swe/output/visualise.ipynb new file mode 100644 index 0000000..6ed51b4 --- /dev/null +++ b/w12/swe/output/visualise.ipynb @@ -0,0 +1,1217 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 33, + "id": "01e48b90-fc9b-4e60-afd0-c608742cd321", + "metadata": {}, + "outputs": [], + "source": [ + "# This script animates the height field and the vorticity produced by\n", + "# a shallow water model.\n", + "# All credit goes to Robin Hogan and Paul Connolly\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import animation, rc\n", + "import h5py\n", + "from IPython.display import HTML\n", + "\n", + "rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n", + "rc('text', usetex=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "6ab0433f-3b56-4b3e-bfb6-82496d73ad59", + "metadata": {}, + "outputs": [], + "source": [ + "# Set this to \"True\" to save each frame as a png file\n", + "plot_frames = True;\n", + "\n", + "# Specify the range of heights to plot in metres\n", + "plot_height_range = np.array([9500., 10500.])" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "a9033d9d-39e4-41b9-9a1a-985fa403a691", + "metadata": {}, + "outputs": [], + "source": [ + "file = h5py.File('./output.h5', 'r')\n", + "tt = file.attrs.get('t') / 60\n", + "Nx, Ny = file.attrs.get('Nx'), file.attrs.get('Ny')\n", + "x, y = file.attrs.get('x').flatten(), file.attrs.get('y').flatten()\n", + "dx, dy = file.attrs.get('dx'), file.attrs.get('dy')\n", + "\n", + "tout = []\n", + "for t in tt:\n", + " if t % 60 == 0:\n", + " tout.append(t)\n", + "\n", + "noutput = len(tout)\n", + "# H = file['0/H'][:].T\n", + "h_save = np.zeros((Nx,Ny,noutput))\n", + "u_save = np.zeros((Nx,Ny,noutput))\n", + "v_save = np.zeros((Nx,Ny,noutput))\n", + "t_save = np.array(tout) * 60.0\n", + "\n", + "H = np.zeros_like(h_save)[:,:,0]\n", + "\n", + "for it in range(noutput):\n", + " h_save[:,:,it] = file['%i/h' %tout[it]][:].T\n", + " u_save[:,:,it] = file['%i/u' %tout[it]][:].T\n", + " v_save[:,:,it] = file['%i/v' %tout[it]][:].T\n", + " \n", + "file.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "a785bcdf-5c9e-4221-8d46-fc0382a941c6", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "from matplotlib.animation import FFMpegWriter\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "d14d40f8-62cf-44d9-8aa0-f05906a1d3e0", + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. 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button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "\n", + "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", + "// prettier-ignore\n", + "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.on(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/97 [00:00 1000:\n", + " height_scale = 0.001;\n", + " height_title = 'Height (km)';\n", + "else:\n", + " height_scale = 1;\n", + " height_title = 'Height (m)';\n", + "\n", + "print('Maximum orography height = %f m' % np.max(H[:]));\n", + "u = np.squeeze(u_save[:,:,0]);\n", + "vorticity = np.zeros(np.shape(u));\n", + "\n", + "writer = FFMpegWriter(fps=5)\n", + "\n", + "# Loop through the frames of the animation\n", + "with writer.saving(f, \"animation.mp4\", 240):\n", + " for it in tqdm(range(0,noutput)):\n", + " # Extract the height and velocity components for this frame\n", + " h = np.squeeze(h_save[:,:,it])\n", + " u = np.squeeze(u_save[:,:,it])\n", + " v = np.squeeze(v_save[:,:,it])\n", + "\n", + " # Compute the vorticity\n", + " vorticity[1:-1,1:-1] = (1./dy)*(u[1:-1,0:-2]-u[1:-1,2:]) \\\n", + " + (1./dx)*(v[2:,1:-1]-v[0:-2,1:-1])\n", + "\n", + " # First plot the height field\n", + " if it==0:\n", + " # Plot the height field\n", + " im=ax1.imshow(np.transpose(h+H)*height_scale, \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb1=f.colorbar(im,ax=ax1)\n", + " cb1.set_label('height (km)')\n", + " # Contour the terrain:\n", + " cs=ax1.contour(x_1000km,y_1000km,np.transpose(H),levels=range(1,11001,1000),colors='k')\n", + "\n", + " # Plot the velocity vectors\n", + " Q = ax1.quiver(x_1000km[2::interval],y_1000km[2::interval], \\\n", + " np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]), scale=5e2,scale_units='xy',pivot='mid')\n", + " ax1.set_ylabel('Y distance (1000s of km)')\n", + " ax1.set_xlabel('X distance (1000s of km)')\n", + " ax1.set_title(height_title)\n", + " tx1=ax1.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + "\n", + " # Now plot the vorticity\n", + " im2=ax2.imshow(np.transpose(vorticity), \\\n", + " extent=[np.min(x_1000km),np.max(x_1000km),np.min(y_1000km),np.max(y_1000km)], \\\n", + " cmap='jet',origin='lower')\n", + " # Set other axes properties and plot a colorbar\n", + " cb2=f.colorbar(im2,ax=ax2)\n", + " cb2.set_label('vorticity (s$^{-1}$)')\n", + " ax2.set_xlabel('X distance (1000s of km)')\n", + " ax2.set_ylabel('Y distance (1000s of km)')\n", + " ax2.set_title('Relative vorticity (s$^{-1}$)')\n", + " tx2=ax2.text(0, np.max(y_1000km)+0.1, 'Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " else:\n", + " # top plot:\n", + " im.set_data(np.transpose(H+h)*height_scale)\n", + " cs.set_array(np.transpose(h))\n", + " Q.set_UVC(np.transpose(u[2::interval,2::interval]), \\\n", + " np.transpose(v[2::interval,2::interval]))\n", + " tx1.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " # bottom plot:\n", + " im2.set_data(np.transpose(vorticity))\n", + " tx2.set_text('Time = %.1f hours' % (t_save[it]/3600.))\n", + "\n", + " im.set_clim((plot_height_range*height_scale));\n", + " im2.set_clim((-3e-4,3e-4))\n", + " ax1.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + " ax2.axis((0., np.max(x_1000km), 0., np.max(y_1000km)))\n", + "\n", + " # To make an animation we can save the frames as a \n", + " # sequence of images\n", + " if plot_frames:\n", + " plt.savefig('frames/frame%03d.pdf' % it,format='pdf') \n", + "\n", + " writer.grab_frame()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "552c0405-47db-46d8-8037-8b6c85511f49", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w2/discrete_oscillator.ipynb b/w2/discrete_oscillator.ipynb new file mode 100644 index 0000000..2657824 --- /dev/null +++ b/w2/discrete_oscillator.ipynb @@ -0,0 +1,340 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ada769df-0827-4614-a16a-5cb7ff34b0db", + "metadata": {}, + "source": [ + "# Tutorial 3\n", + "Before we start, let's import our libraries." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "319505e0-e5f9-4ef9-8a76-3c683d64b89b", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "09c32f0c-1395-4678-b057-f7d13577b61a", + "metadata": {}, + "source": [ + "## Finite differencing and the explicit Euler method\n", + "\n", + "Today we want to solve the oscillator problem (again). But this time, we do not rely on a fancy ODE solver like the `odeint`. Instead, we want to solve the problem with a [finite difference](https://en.wikipedia.org/wiki/Finite_difference_method) method.\n", + "\n", + "The finite difference method is a numerical method to solve differential equations. The broad idea behind the method is to approximate the differential with a discrete difference. For example, in our oscillator problem, we have the time derivative of $x$. This can be *discretised* as \n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} \\approx \\frac{x(t+\\Delta t) - x(t)}{\\Delta t}\\tag{1}.\n", + "\\end{equation}\n", + "\n", + "The process of approximating a continuous quantity with its discrete form is called *discretisation*.\n", + "\n", + "Say now we have an ODE\n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} = F(t,x(t))\\tag{2},\n", + "\\label{eq:differential}\n", + "\\end{equation}\n", + "\n", + "discretising this yields\n", + "\\begin{equation}\n", + "x(t+\\Delta t) = x(t) + \\Delta t \\, F(t,x(t)) \\tag{3} \\label{eq:discretised}\n", + "\\end{equation}\n", + "\n", + "Generally, we write equation \\eqref{eq:discretised} as \n", + "\\begin{equation}\n", + "x^{n+1} = x^n + \\Delta t \\, F(t^n,x^n), \\tag{4}\\label{eq:euler_method}\n", + "\\end{equation}\n", + "\n", + "where $n$ indexes the time-step at time $t$ and $n+1$ indexes the time-step at $t+\\Delta t$. Note that the notion of a \"time-step\" now makes sense, as we are integrating the problem discretely in time.\n", + "\n", + "Given a time-step size of $\\Delta t$, if we have the solution $(t^n,x^n)$ at time $n$, then we can evaluate the right-hand side of \\eqref{eq:euler_method}, and this gives us the solution of $x$ at the new time $n+1$.\n", + "\n", + "The method of numerically integrating an ODE with \\eqref{eq:euler_method} is also known as the [explicit Euler method](https://en.wikipedia.org/wiki/Euler_method).\n", + "\n", + "Now that we have some idea on a finite difference method, let's apply it..." + ] + }, + { + "cell_type": "markdown", + "id": "5f600fad-cdd7-4075-914e-24991adf7f37", + "metadata": {}, + "source": [ + "## Setting up the harmonic oscillator problem\n", + "\n", + "We want to use the simple harmonic oscillator problem without damping and without forcing as an exercise to get an intuition of the finite difference numerical methods:\n", + "$$m \\ddot{x} = -c x, \\qquad m,c > 0. \\tag{5}$$\n", + "\n", + "The analytical solution to this free oscillation scenario is on page 20, equation (75) of the lecture notes,\n", + "\n", + "$$x(t) = a \\cos(\\omega t) + b \\sin(\\omega t), \\tag{6}$$\n", + "\n", + "where $\\omega=\\sqrt{c/m}$.\n", + "\n", + "We can make our lives much easier by choosing the constants $c,m=1$, the initial position $x(t=0)=0$, and the initial velocity $\\dot{x}(t=0)=1$. This gives us the following analytical solutions:\n", + "$$\\begin{align}\n", + "x &= \\sin(t), \\tag{7a}\\\\\n", + "\\dot{x} &= \\cos(t), \\tag{7b}\\\\\n", + "\\ddot{x} &= -x. \\tag{7c}\n", + "\\end{align}$$\n", + "This is equivalent to\n", + "$$\\begin{align}\n", + "\\frac{dx}{dt} &= \\dot{x}, \\tag{8a}\\\\\n", + "\\frac{d\\dot{x}}{dt} &= -x. \\tag{8b}\n", + "\\end{align}$$\n", + "\n", + "Discretising this with the explicit Euler method,\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{9a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^n. \\tag{9b}\n", + "\\label{eq:ee_discretised}\n", + "\\end{align}$$\n", + "\n", + "Please go through the working above on your own to verify that it makes sense!" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "24bdebe0-9f71-4659-973e-2097c12b791a", + "metadata": {}, + "outputs": [], + "source": [ + "# Some helper functions for plots\n", + "def xt_plot(t, x, xth=None, title=\"\", ylabel=\"x\"):\n", + " plt.plot(t, x, label='num. x')\n", + " if xth is not None:\n", + " plt.plot(t, xth, '--', label='theo. x')\n", + " plt.legend(loc='best')\n", + " plt.xlabel('t')\n", + " plt.ylabel(ylabel)\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.grid()\n", + " plt.show()\n", + "\n", + "def vx_plot(x, v, xth, vth, title=\"\"):\n", + " plt.plot(x,v, label=\"num. sol.\")\n", + " plt.plot(xth,vth, '--', label=\"theo. sol.\")\n", + " plt.legend()\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"v\")\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ec7d32a-b82e-4c32-800d-406b72f8cf07", + "metadata": {}, + "source": [ + "## Exercise 1: The explicit Euler method \n", + "1. Implement equation ([9](#mjx-eqn-eq:ee_discretised)). How would you do it?\n", + "2. Compare the result for various step-sizes, e.g. `dt=0.1` and `dt=0.01`.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and the analytical solution. What do you see?\n", + "4. We know that the potential energy in a spring is given by $PE=\\frac{1}{2}kx^2$ while the kinetic energy of the spring is $KE=\\frac{1}{2}mv^2$. Compute and compare the energy of the numerical solution with the theoretical energy. What happens with the energy?" + ] + }, + { + "cell_type": "markdown", + "id": "40b00eb7-5e8c-41bb-b5e7-165eaa4a4365", + "metadata": {}, + "source": [ + "### Hints:" + ] + }, + { + "cell_type": "markdown", + "id": "95cad889-d746-4c5a-9590-af0763d51a75", + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [] + }, + "source": [ + "1. We will need a *for-loop*. A short introduction to the features of the for-loop in Python is provided in the supplementary materials.\n", + "2. What are we looping over?\n", + "3. What do we have to do in each step of the loop?" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "11b3fc8b-eeb5-4649-a55c-5ac7696d68a5", + "metadata": {}, + "outputs": [], + "source": [ + "# Here are some helper code to get you started.\n", + "\n", + "# Let's specify the number of time-steps\n", + "Nt = 10000\n", + "# and a time-step size\n", + "dt = 0.01\n", + "\n", + "# What are numpy.arange and numpy.zeros?\n", + "# Why do we need to initialise these arrays?\n", + "t = np.arange(Nt+1)*dt\n", + "x = np.zeros((Nt+1))\n", + "v = np.zeros((Nt+1))\n", + "\n", + "# Since we know the analytical solution,\n", + "# let's compare our numerical solution against them.\n", + "xth = np.sin(t)\n", + "vth = np.cos(t)\n", + "\n", + "# Fill in the rest of the code here:\n", + "# ...\n", + "\n", + "# xt_plot(t,x,xth, title=\"explicit Euler\")\n", + "# vx_plot(x,v,xth,vth, title=\"explicit Euler\")" + ] + }, + { + "cell_type": "markdown", + "id": "67d02d8f-e732-4e45-86c8-98e56d0bf80c", + "metadata": {}, + "source": [ + "## Exercise 2: Euler-A and Euler-B methods\n", + "Notice that our discretisation of equation ([2](#mjx-eqn-eq:differential)) is not unique, and there are actually many ways to discretise a differential. For example, we can write equation ([4](#mjx-eqn-eq:euler_method)) as\n", + "\n", + "$$x^{n+1} = x^n - \\Delta t \\, F(t^{n+1},x^{n+1}), \\tag{10} \\label{eq:implicit_euler} $$\n", + "\n", + "which would give us the [implicit Euler method](https://en.wikipedia.org/wiki/Backward_Euler_method).\n", + "\n", + "For the system of equations we are solving in ([9](#mjx-eqn-eq:ee_discretised)), we can apply the [semi-implicit Euler method](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method). This is given by the following updates:\n", + "\n", + "a. For the Euler-A method:\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{11a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n+1}. \\tag{11b}\n", + "\\label{eq:euler_a}\n", + "\\end{align}$$\n", + "b. For the Euler-B method:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n}, \\tag{12a}\\\\\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1}. \\tag{12b}\n", + "\\label{eq:euler_b}\n", + "\\end{align}$$\n", + "\n", + "Now on to the tasks:\n", + "1. Implement equations ([11](#mjx-eqn-eq:euler_a)) and ([12](#mjx-eqn-eq:euler_b)).\n", + "2. Again, try around with different number of time-steps and time-step sizes.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "4. Can you explain your observation?\n", + "5. Again, let's compare the energy of the numerical solution with the theoretical energy." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d65c9086-f241-48d0-9118-875b37727c90", + "metadata": {}, + "outputs": [], + "source": [ + "# Fill in the code here:\n", + "# ...\n", + "\n", + "# xt_plot(t, xb, xth, title=\"Euler B\")\n", + "# vx_plot(xb,vb,xth,vth, title=\"Euler B\")" + ] + }, + { + "cell_type": "markdown", + "id": "c1a4f16a-f625-4359-a538-d32355fecd0d", + "metadata": {}, + "source": [ + "## Exercise 3: The Störmer-Verlet method\n", + "The explicit Euler and the semi-implicit Euler methods are [*first-order methods*](https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)#Local_truncation_error). We now turn our attention to the [Störmer-Verlet method](https://en.wikipedia.org/wiki/Verlet_integration), which is a second-order numerical integrator.\n", + "\n", + "The discretised equations are:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1/2} &= \\dot{x}^n - \\frac{\\Delta t}{2} \\, x^n, \\label{eq:sv1} \\tag{13a}\\\\\n", + " x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1/2}, \\label{eq:sv2} \\tag{13b}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^{n+1/2} - \\frac{\\Delta t}{2} \\, x^{n+1}. \\label{eq:sv3} \\tag{13c}\\\\\n", + "\\end{align}$$\n", + "\n", + "Notice that ([13a](#mjx-eqn-eq:sv1)) is akin to an explicit Euler update, ([13b](#mjx-eqn-eq:sv2)) is a [midpoint method](https://en.wikipedia.org/wiki/Midpoint_method), and ([13c](#mjx-eqn-eq:sv3)) is an implicit update.\n", + "\n", + "Now, for the tasks:\n", + "1. Implement equation ([13](#mjx-eqn-eq:sv3)).\n", + "2. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "3. Plot $v$ and $x$ and the energy. Are these results in line with your expectations?\n", + "4. Plot the intermediate time steps in ([13a](#mjx-eqn-eq:sv1)). What do you observe?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "50f9f65b-56fe-43f8-abb5-9292accefb27", + "metadata": {}, + "outputs": [], + "source": [ + "# Fill in the code here:\n", + "# ...\n", + " \n", + "# xt_plot(t,x,xth, title=\"Störmer-Verlet\")\n", + "# vx_plot(v,x,xth,vth, title=\"Stömer-Verlet\")" + ] + }, + { + "cell_type": "markdown", + "id": "4f5a9ed8-3b39-4e15-8d9b-3f0776d14c02", + "metadata": {}, + "source": [ + "## Further reading\n", + "\n", + "The implicit and explicit Euler methods are part of a family of numerical integrators called the [*Runge-Kutta*](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) methods. The generalised Runge-Kutta method allows us to build higher-order integrators, and Wikipedia has such [a list](https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods). You will come across the Runge-Kutta methods frequently, especially as time integrators. We will go more in detail when we move on to numerical solution of PDEs later in this tutorial." + ] + }, + { + "cell_type": "markdown", + "id": "7f7281e0-ac5a-408b-9ff1-e40bfc4f2201", + "metadata": {}, + "source": [ + "## References\n", + "[1] Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2005.\n", + "\n", + "[2] Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations; 2nd ed. Springer, Dordrecht, 2006." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a26ff85-eb87-4cb1-93a4-a754844859d5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.3 64-bit ('anaconda3': virtualenv)", + "language": "python", + "name": "python37364bitanaconda3virtualenv7a28dc8db0264e168ad4f93d8f9f620c" + }, + "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": 5 +} diff --git a/w2/discrete_oscillator_soln.ipynb b/w2/discrete_oscillator_soln.ipynb new file mode 100644 index 0000000..25b0998 --- /dev/null +++ b/w2/discrete_oscillator_soln.ipynb @@ -0,0 +1,799 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ada769df-0827-4614-a16a-5cb7ff34b0db", + "metadata": {}, + "source": [ + "# Tutorial 3\n", + "Before we start, let's import our libraries." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "319505e0-e5f9-4ef9-8a76-3c683d64b89b", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "09c32f0c-1395-4678-b057-f7d13577b61a", + "metadata": {}, + "source": [ + "## Finite differencing and the explicit Euler method\n", + "\n", + "Today we want to solve the oscillator problem (again). But this time, we do not rely on a fancy ODE solver like the `odeint`. Instead, we want to solve the problem with a [finite difference](https://en.wikipedia.org/wiki/Finite_difference_method) method.\n", + "\n", + "The finite difference method is a numerical method to solve differential equations. The broad idea behind the method is to approximate the differential with a discrete difference. For example, in our oscillator problem, we have the time derivative of $x$. This can be *discretised* as \n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} \\approx \\frac{x(t+\\Delta t) - x(t)}{\\Delta t}\\tag{1}.\n", + "\\end{equation}\n", + "\n", + "The process of approximating a continuous quantity with its discrete form is called *discretisation*.\n", + "\n", + "Say now we have an ODE\n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} = F(t,x(t))\\tag{2},\n", + "\\label{eq:differential}\n", + "\\end{equation}\n", + "\n", + "discretising this yields\n", + "\\begin{equation}\n", + "x(t+\\Delta t) = x(t) + \\Delta t \\, F(t,x(t)) \\tag{3} \\label{eq:discretised}\n", + "\\end{equation}\n", + "\n", + "Generally, we write equation \\eqref{eq:discretised} as \n", + "\\begin{equation}\n", + "x^{n+1} = x^n + \\Delta t \\, F(t^n,x^n), \\tag{4}\\label{eq:euler_method}\n", + "\\end{equation}\n", + "\n", + "where $n$ indexes the time-step at time $t$ and $n+1$ indexes the time-step at $t+\\Delta t$. Note that the notion of a \"time-step\" now makes sense, as we are integrating the problem discretely in time.\n", + "\n", + "Given a time-step size of $\\Delta t$, if we have the solution $(t^n,x^n)$ at time $n$, then we can evaluate the right-hand side of \\eqref{eq:euler_method}, and this gives us the solution of $x$ at the new time $n+1$.\n", + "\n", + "The method of numerically integrating an ODE with \\eqref{eq:euler_method} is also known as the [explicit Euler method](https://en.wikipedia.org/wiki/Euler_method).\n", + "\n", + "Now that we have some idea on a finite difference method, let's apply it..." + ] + }, + { + "cell_type": "markdown", + "id": "5f600fad-cdd7-4075-914e-24991adf7f37", + "metadata": {}, + "source": [ + "## Setting up the harmonic oscillator problem\n", + "\n", + "We want to use the simple harmonic oscillator problem without damping and without forcing as an exercise to get an intuition of the finite difference numerical methods:\n", + "$$m \\ddot{x} = -c x, \\qquad m,c > 0. \\tag{5}$$\n", + "\n", + "The analytical solution to this free oscillation scenario is on page 20, equation (75) of the lecture notes,\n", + "\n", + "$$x(t) = a \\cos(\\omega t) + b \\sin(\\omega t), \\tag{6}$$\n", + "\n", + "where $\\omega=\\sqrt{c/m}$.\n", + "\n", + "We can make our lives much easier by choosing the constants $c,m=1$, the initial position $x(t=0)=0$, and the initial velocity $\\dot{x}(t=0)=1$. This gives us the following analytical solutions:\n", + "$$\\begin{align}\n", + "x &= \\sin(t), \\tag{7a}\\\\\n", + "\\dot{x} &= \\cos(t), \\tag{7b}\\\\\n", + "\\ddot{x} &= -x. \\tag{7c}\n", + "\\end{align}$$\n", + "This is equivalent to\n", + "$$\\begin{align}\n", + "\\frac{dx}{dt} &= \\dot{x}, \\tag{8a}\\\\\n", + "\\frac{d\\dot{x}}{dt} &= -x. \\tag{8b}\n", + "\\end{align}$$\n", + "\n", + "Discretising this with the explicit Euler method,\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{9a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^n. \\tag{9b}\n", + "\\label{eq:ee_discretised}\n", + "\\end{align}$$\n", + "\n", + "Please go through the working above on your own to verify that it makes sense!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "24bdebe0-9f71-4659-973e-2097c12b791a", + "metadata": {}, + "outputs": [], + "source": [ + "# Some helper functions for plots\n", + "def xt_plot(t, x, xth=None, title=\"\", ylabel=\"x\"):\n", + " plt.plot(t, x, label='num. x')\n", + " if xth is not None:\n", + " plt.plot(t, xth, '--', label='theo. x')\n", + " plt.legend(loc='best')\n", + " plt.xlabel('t')\n", + " plt.ylabel(ylabel)\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.grid()\n", + " plt.show()\n", + "\n", + "def vx_plot(x, v, xth, vth, title=\"\"):\n", + " plt.plot(x,v, label=\"num. sol.\")\n", + " plt.plot(xth,vth, '--', label=\"theo. sol.\")\n", + " plt.legend()\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"v\")\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ec7d32a-b82e-4c32-800d-406b72f8cf07", + "metadata": {}, + "source": [ + "## Exercise 1: The explicit Euler method \n", + "1. Implement equation ([9](#mjx-eqn-eq:ee_discretised)). How would you do it?\n", + "2. Compare the result for various step-sizes, e.g. `dt=0.1` and `dt=0.01`.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and the analytical solution. What do you see?\n", + "4. We know that the potential energy in a spring is given by $PE=\\frac{1}{2}kx^2$ while the kinetic energy of the spring is $KE=\\frac{1}{2}mv^2$. Compute and compare the energy of the numerical solution with the theoretical energy. What happens with the energy?" + ] + }, + { + "cell_type": "markdown", + "id": "40b00eb7-5e8c-41bb-b5e7-165eaa4a4365", + "metadata": {}, + "source": [ + "### Hints:" + ] + }, + { + "cell_type": "markdown", + "id": "95cad889-d746-4c5a-9590-af0763d51a75", + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [] + }, + "source": [ + "1. We will need a *for-loop*. A short introduction to the features of the for-loop in Python is provided in the supplementary materials.\n", + "2. What are we looping over?\n", + "3. What do we have to do in each step of the loop?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "11b3fc8b-eeb5-4649-a55c-5ac7696d68a5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Here are some helper code to get you started.\n", + "\n", + "# Let's specify the number of time-steps\n", + "Nt = 10000\n", + "# and a time-step size\n", + "dt = 0.01\n", + "\n", + "# What are numpy.arange and numpy.zeros?\n", + "# Why do we need to initialise these arrays?\n", + "t = np.arange(Nt+1)*dt\n", + "x = np.zeros((Nt+1))\n", + "v = np.zeros((Nt+1))\n", + "\n", + "# Since we know the analytical solution,\n", + "# let's compare our numerical solution against them.\n", + "xth = np.sin(t)\n", + "vth = np.cos(t)\n", + "\n", + "v[0] = 1.0\n", + "\n", + "for idx in range(Nt):\n", + " x[idx+1] = x[idx] + dt * v[idx]\n", + " v[idx+1] = v[idx] - dt * x[idx]\n", + " \n", + "x = np.array(x)\n", + "v = np.array(v)\n", + "energy = 0.5 * x**2 + 0.5 * v**2\n", + "th_e = 0.5 * xth**2 + 0.5 * vth**2\n", + "\n", + "xt_plot(t,x,xth, title=\"explicit Euler\")\n", + "xt_plot(t,energy,xth=th_e, title=\"explicit Euler (energy)\")\n", + "vx_plot(x,v,xth,vth, title=\"explicit Euler\")" + ] + }, + { + "cell_type": "markdown", + "id": "67d02d8f-e732-4e45-86c8-98e56d0bf80c", + "metadata": {}, + "source": [ + "## Exercise 2: Euler-A and Euler-B methods\n", + "Notice that our discretisation of equation ([2](#mjx-eqn-eq:differential)) is not unique, and there are actually many ways to discretise a differential. For example, we can write equation ([4](#mjx-eqn-eq:euler_method)) as\n", + "\n", + "$$x^{n+1} = x^n - \\Delta t \\, F(t^{n+1},x^{n+1}), \\tag{10} \\label{eq:implicit_euler} $$\n", + "\n", + "which would give us the [implicit Euler method](https://en.wikipedia.org/wiki/Backward_Euler_method).\n", + "\n", + "For the system of equations we are solving in ([9](#mjx-eqn-eq:ee_discretised)), we can apply the [semi-implicit Euler method](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method). This is given by the following updates:\n", + "\n", + "a. For the Euler-A method:\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{11a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n+1}. \\tag{11b}\n", + "\\label{eq:euler_a}\n", + "\\end{align}$$\n", + "b. For the Euler-B method:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n}, \\tag{12a}\\\\\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1}. \\tag{12b}\n", + "\\label{eq:euler_b}\n", + "\\end{align}$$\n", + "\n", + "Now on to the tasks:\n", + "1. Implement equations ([11](#mjx-eqn-eq:euler_a)) and ([12](#mjx-eqn-eq:euler_b)).\n", + "2. Again, try around with different number of time-steps and time-step sizes.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "4. Can you explain your observation?\n", + "5. Again, let's compare the energy of the numerical solution with the theoretical energy." + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "d65c9086-f241-48d0-9118-875b37727c90", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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BiSQOGMDrm45QV9+gO47hhiwWRfjuFzntE0m/C36mO06bhYV14fOBD3Nb0U/JL63WHUcbnQVkK5AgIvEiEkBjkVhx9kIiEgZMAZY3mdZZREK/ew3MBNy2u8w9K58nTCrocuFvdEdpt1tSQnii+o/sWvWq7iiGG9q6bRMpDbs4Neh6hw1T6yjnz7qKI6o7b317RHcUbbQVEKVUPXA7sArIBN5TSmWIyGIRWdxk0cuAL5RSFU2mRQEbRGQXsAX4VCnllreHNjRY6JX1Fgf9E+g7YpruOO02cdggevkWE7LTjB9ttF/JuheowZ8Bs3701afL6xvZmYXxZYzYdAc15WdaX8EDab0PRCm1Uik1UCnVXyn1V+u055RSzzVZ5lWl1DVnrZejlBphfSR9t647Slv/MfHqGOXDf+byV580x8fXl+OJCxlUn8m+bWt0xzHcSE5BOb8+PZeVSf8hoIvrXrZ+LvNG9GQ6m9m38lndUbQwd6Jr9r8DnXjK93qGzLhRdxSbJc25lVKCKf/6Sd1RDDfy+jdHqPHtzKRZV+uOYrPksVPY4zuEqH2voRq8b9RCU0A0yiko57OcOtSEu/AP6qw7js06h4azN2oeI0q/5nSe954PNtqurLKaydvv5Hf9jtI91H0vARcRiobdRE9LPgc3fag7jtOZAqLRnk+e5hK/zVwzto/uKB0WO/MO/lq/gKUZxbqjGG5g8xdLuEC2MXOA+99zM/qi6zlBJPXfPK87itOZAqJJRUU55x9+kl+Eb3Prv8C+07t/EgfiFvD6jkIsFu++O9c4N6UUoelvUOgTQdykn+iO02GdOwWxvfdNrCwbwJnyGt1xnMoUEE12f/EGEVJG0IRbdEexmwWjezKxdCW7vjGjthktS8/cS0rddk7EX+F2l+62JGHOXfy3bh5Ld3rXaJ2mgGjSee87nJAoEs5z3Y7j2uvCIT24x/9d1CbzZbrRshOp/8NXFPEzf6k7it0k9gxlTO/O5G56F9VQpzuO05gCosGhrHSG1+3iePwViI+v7jh2ExgUzP6elzC8fKP5Mt1oVnlNPZ+cDGdd5NV0juqvO45d3dn3KA9VPcLBjd7zZbopIBqkbk8nU/Wh/4xFuqPYXcz0xfiJhewvvO8LRaN1H+/KY0VtCiHzHtUdxe5GTb+afNWV2i2v6I7iNKaAOFltvYUnsyL5b8KrdI2O1x3H7vokDCc9IJk+R97H0mD6xzJ+6OD690nprhjZO1x3FLvr3CmIjKhLSCzbTNmpw7rjOIUpIE62YfsuqipKuXqM6w1Xay/VwxdwqiGE7Xv3645iuJD9B3P4Q+lfeajr54gb9rrQFtFTf4GvKHK+eK71hT2An+4A3iY09U98GZRN9IBM3VEcJmnGTYzZ2peLMusYM0x3GsNVHFnzEonSQJ8Zi1tf2E0NGjyMHX4j8TmySXcUpzBHIE50Mu8oyZXfcDJmOr6+nvtP3ynQjznDotmQnk1FeZnuOIYLqKtvoN/x5eQEDaFL76G64ziMiJAx8Qnml/2erHzP/9333E8xF5S9+hX8pYGYab/QHcXhFgyo5Wu5hcyvXtMdxXABOzavYwDHqE1y336v2mpWyiB8fXxYuuOY7igOZwqIkyil6HFoOQf9EohJGKk7jsMNGz6K0z6RdMp8T3cUwwUcSfuKGvzpP+0G3VEcrntoIH+I3skNmy/FUlPR+gpuzBQQJ8nam8ZAy0GKEi7THcUpxMeHo73nkVSzi/yjB3THMTQqqazjTycm8cTw5fiHROqO4xRDBw8hmgKy172rO4pDmQLiJO/mBDCv7hESLrxZdxSn6Tvt5wAcWvOy5iSGTp/uzqO23sKssUm6ozjNqMlzOaEiaUhbojuKQ2ktICIyS0T2i0i2iNzTzPypIlIiImnWxwNtXdeV1DdYWLH7BD0HjSEsMkp3HKeJjU8kPWA4vY58hLJYdMcxNIlJ/RXPhb7EsNgw3VGcJijAn8weFzOwfAuVZ3J1x3EYbQVERHyBp4HZwBDgWhEZ0syi65VSydbHw+1c1yXs+fYLfl/1BD8ZHKA7itPljb2PhdW/Zk9eqe4ohgbHTuRzXtU6YrtHeOy9Hy2JnHBD4z0hq1/VHcVhdB6BjAWyrcPT1gJLgHlOWNfpara8zsV+W5iY5Hl3nrdm3ITpHPXpxYq0PN1RDA32rX6DIKmj5/k36o7idMNGjOE5v+tYctpz/9/rvJEwFmh6nVsuMK6Z5caLyC4gD/itUiqjHesiIouARQBRUVGkpqbaFLa8vNymdWtrqhlfvIadQeOo37zdpn3rYmubz3ZZeA6Dt77ImuDb8PFx7XtX7dVmd+KoNiulCM9eynHpSdbJOsi3/z5s5ayfc3qPeaw8VMfYVWvpEqj3CMwRbdb5v7m5f82zRyLaAfRVSpWLyMXAR0BCG9dtnKjUC8ALACkpKWrq1Kk2hU1NTcWWdbd88hKhUkW3yTczaKJt+9bF1jafLaTyEClb1rA34EaGTHLZA0XAfm12J45q8/7sAySovWQMuIWp06bZffsd4ayfc89BpeQ98RIhNZFMvUjvJcyOaLPOU1i5QNMOoXrReJTxPaVUqVKq3Pp6JeAvIt3asq6r8N27lNOEM3DcxbqjaJM05SrKVScqtnv2JY3GD322t5DHG66kz5QbdUfRZlDPLtwfvJRBux4B5XkjdeosIFuBBBGJF5EA4BpgRdMFRKSnWL95E5GxNOYtbMu6rqCkso6tZRFkxF6Nj59rn7pxpE6dQ9gbNpnEorXUVlfpjmM4gVKK9/dWsaf/IsJ6D9YdR6sz/S4lpuE4BQc2645id9oKiFKqHrgdWAVkAu8ppTJEZLGIfNfb2pVAuvU7kP8C16hGza7r/Fac26qMkzxSdw1dZ9+nO4p2ASOvpguVZK73nsF2vNmezH0MLf2aeUO948bBc0mY8lNqlS8nNrypO4rdaf2z2HpaauVZ055r8vop4Km2rutqdm7bSHxEN6+6/r0lSZMuJf3r/qQdOskI3WEMh8vf8BrPBzxLeW/P77qkNX16xbI5cDT9jn8GFgv4eM79257TEhdTWHCSh0/eyl8jVnrd9e/N8fcP4O0Rr/HIsaFU1tbrjmM4UINF0Sfvc3IChxDS07OGrbVVRcJ8/BuqOJazV3cUuzIFxEEOfP0O/tJA9LjLdUdxGZcMj6G2rpaNaft0RzEcaNfOLSRyiKpB83VHcRmDp1/H2NpnWXYkUHcUuzIFxEE6H1hOrk80cUkTdEdxGWPjI1gZdD/dv/6D7iiGA53Z/A4WJfSfcp3uKC4jOiKM5LgefJx23KOuxjIFxAFOnTxGUk0aebGzEQ8639lRvj7CmW4pDC7fTFVZse44hgPUNVjodGonBzuPICgiVnccl7KgXyUvlCwid8fnuqPYjfl0c4Cs1CX4iiJ64k91R3E5IaOvIlDq2L/OjBPiiTbnnGFB9e84NuN53VFczvhRI4mSYoq2es7vvikgDvBk0Th+3/lv9E5M0R3F5QwZO4NTRMDe5bqjGA7w6Z4TdA7wY8LQBN1RXE6PyAjSOo2jd/5qaPCMC0lMAbGzU6XVbD5aRuzImWCuvvoRX19fsrtdYE5jeaD6BgtX7F7E/0WlEuTvqzuOS6oZeAnhqoTju1frjmIXpoDYWebqN/id7xLmDOmqO4rLCpq4mBvrfs/aQ+W6oxh2tCdtCynsJTEmQncUlzV48pVUqkAKt3jGaSxTQOys6763uTRgKwOizR24LRkxIoWs4JF8mn5KdxTDjs5sfQ+LEuInm+/+WtKzWwTvhS7kgzLPGJ3RFBA7Kiw4wZDqNPKizemrc/H1Ea4d0MDoff+iqqxIdxzDDhosij4nvySn01A6RfbSHcelNZx3K6+fTuTQ6QrdUTrMFBA7yvr6PfzEQvdxV+uO4vJm9lHc5PMJ+zeYvrE8wZ5d20jgKDUDL9EdxeXNHtqTvnKSPV8v1R2lw0wBsaNO2R9zQnoQN9TcPNiawWMu5DRhqL0f645i2MGarCLessyk3+RrdEdxeTHhnfh7lw+ZlH5/Y99YbswUEDspKq8hpyKInJhLzc2DbeDn709WxFQSS7+htsr9D+W9mcWieDfbh3UJf6BTt76647iF6v5ziFBF5Geu1x2lQ8wnnZ18mXmKX9X9krCLH9AdxW0EDZ9PsNSwf5O5J8SdpWdlEVu2h9lJUbqjuI2E86+kRvmRv/l93VE6xBQQO9m0O5NeXTuRFNNFdxS3MWT8xRxTPcg+mK07itEBpza8wdLAh5je0wwW1la9o6PY5Z9M1PEv3bpvLK0FRERmich+EckWkXuamb9ARHZbH5tEZESTeYdFZI+IpInINucm/6HyshIeOfpT/tL1c9N1ezsEBgbxWOIS/pI/ngaL+/4n8mZKKXoc/5Ij/v0IjRmoO45bKY2fRUR9AYXH9uuOYjNtBUREfIGngdnAEOBaERly1mKHgClKqeHAX4AXzpo/TSmVrJTS2mfIvvXLCJI6eg6bqjOGW7poWAxnKmrZdvCE7iiGDbJyDjK0YR8lfWfpjuJ2+ky+ntE1z/JZXifdUWym8whkLJCtlMpRStUCS4B5TRdQSm1SSn13o8C3gEteYK4yV1BEFwaOmaE7ituZktCNFYH347vqXt1RDBsc2/QBPqLoNfEnuqO4nYReUUR2i2JVxkndUWymc0jbWOBYk/e5wLhzLP9z4LMm7xXwhYgo4Hml1NlHJwCIyCJgEUBUVBSpqak2hS0vL2923bq6WsaVfsPOoHGoDRtt2raraqnN9ubn34PBBWtYs+YrfHy0jrLstDa7ko60OSDnS3KlJ9mHi+CIbdvQwVV+zhcGHWDGkZdIXX4HhDn272OHtFkppeUBXAX8r8n764EnW1h2GpAJRDaZFmN97gHsAia3ts/Ro0crW61du7bZ6TvXvK/Ug13UrtXv2LxtV9VSm+3t2xUvKvVgF3Vgyyqn7O9cnNVmV2Jrmw8VlKsBf/hIvbfKtvV1cpWfc3rmXqUe7KL2LHnA4fvqSJuBbaqZz1Sdp7Bygd5N3vcC8s5eSESGA/8D5imlCr+brpTKsz6fApbReErM6ZadiuZedTuJE8wduLYaNOlyapQfxTuW6Y5itMOqjJPU4cf4MVr+63mEwQMHkSEJhOR81vrCLkhnAdkKJIhIvIgEANcAK5ouICJ9gKXA9UqpA02mdxaR0O9eAzOBdKclt6pvsPDxgUoqBl1JYFBnZ+/eY4R1jWBvp1HEnlzt1pc0epvobx/mvog19OoarDuK2/LxEfKiLySuZj9Vp4/ojtNu2gqIUqoeuB1YRePpqfeUUhkislhEFlsXewCIBJ4563LdKGCDiOwCtgCfKqWcPk7k3p2bmF+9nDkDQ5y9a49zKulmHqm5iuz8Ut1RjDY4VXiGGZUrGRdWojuK24scfTkAhzZ+oDlJ+2n9xlIptRJYeda055q8vhm4uZn1coARZ093tootb3KP3/vUJjysO4rbG3b+pdyyMYTB+04zoGeY7jhGKzI3rmCK1NJ19BW6o7i9YckprPh4CoUFAZx9H4OrM3ei20hZLPQpWMO+4FGEdDED6HRUTHgnpkfXULf9dd1RjDbw2f8pZXSmV/J03VHcnr+vD6mDH+aJvETqG9yrc0VTQGyUs3cbsSqfmv7mBip7+VnXXdxZ9jgFxw60vrChTVllFUPLv+Fw5PmIX4DuOB5hZlIUqrKI3Xt26Y7SLqaA2Ch/y4eNo69Nukp3FI8Re96VABzZ6BnDfXqqTRk5bLIMJjDZnL6yl8kJ3VgZ+EeCUh/SHaVdTAGxUXH+YfYFDKFbzz66o3iMuIShHPTpS+dDq3RHMc7h0+xaHgj4Pf0nmj+e7CU40J8DXcYTV/wtqrZSd5w2MwXEBrlFldxacgMbJ7ysO4pHERFO9JzOwOo9lBaavrFcUW1dA/v3p3Ph4Ch8fUzHofbkM3guwVRzdLv73BNiCogNvsxo/HC7cFjvVpY02iti9GUohIyta3VHMZqRvnMjq7id67rs0B3F4wydOIdSFUzpTvcZH8cUEBuMXH8LT4W+Rnw3c/OgvSUmT2Km30u8dWaQ7ihGM4p3fIRFCQljzcUj9hYZFsquTuPoXZAKlgbdcdrEFJB2KjlziqTqHXTrbuMa9xkAACAASURBVEZfcwRfXx/GDB7A1/sLqK13r0saPZ1Sitj8NeR0SiIovKfuOB7pxIg7mFf9IMeKa3RHaRNTQNrpwIal+EsDEda7Rw37mxuneMHyEAfWu/dwn55m374MEtUhKvuZow9HGTvmPI6onnyVma87SpuYAtJOPvs/5TThDEierDuKxxozNJEkn8PU7HGfc8He4MSWpQD0nXCl5iSeK65bZ66IOETMpgfcol84U0DaobqqkkHlW8iJmIyPr6/uOB4rKCiIzJDziD+zHtVQrzuOYfVc4Uj+E/5HwnoN1h3Fo13Uo4SLKlZQeszp/cO2mykg7bAlO5//1l+G7+jrdEfxeCrxYiIo5eBOczWWKzhaWMmWUz6Ejjb3fjhazLjG0+PHvnH9zhVNAWmHz7LKedN3PkPHXag7iscbOOlyapUvRTs+0h3FANI3LGeh7ypmJnbVHcXjDUkcRIYMINgNbqg1BaSNLJYGGjI+4qIBwQT6mdNXjhYREclnIZeTWtxddxQDiMh8kzsDVtCnm+kp2dF8fITcHtOIr86kpui47jjnZApIG5WdyOLRhsf4abjrn5f0FAXn/ZGnz4zhaKH7dO3giYpKyhhatY3c7lPBx3xkOEPXkfM5aIkmfW+G7ijnZH4b2ijoxLfUKx8SJpoO5JxlxpAoulDO1q2bdEfxahkbPyFEqglNvlR3FK8xfNR5XMLjfHgqWneUc9JaQERklojsF5FsEbmnmfkiIv+1zt8tIqPauq69JZRvZX/gUMIizQ2EztI3sjNLOv+L4dvv0x3Fq1n2fUolQcSlzNYdxWsEBfgxZWB31mYcx1LnujcVaisgIuILPA3MBoYA14rI2QNyzQYSrI9FwLPtWNducg9m0I9cyuJmOmoXRgsKY6aRULePklNHdUfxStV1DVSVnCI7bAI+AZ10x/Eql/WuYFXdzzjiwldjtVpAmvtgFpGpdtj3WCBbKZWjlKoFlgDzzlpmHvC6avQtEC4i0W1c124ObWkcdbfPeHMJo7N1Gz0fgBw3HC/aE2w6eJpbau7izKxndEfxOmNHp9CAD5W7V+iO0qK2jIn+noi8ATwKBFmfU4DxHdx3LHCsyftcYFwblolt47oAiMgiGo9eiIqKIjU1td1BP6kYzov+/+KmIyc5cORku9d3V+Xl5Tb9e9mTxWIhVPXAkrGC1K6jWl+hg1yhzc52rja/vqeKIF+oO7GP1Pz9zg3mQO7yc67zG8W40+v5es1XKJ+2fFy3zBFtbkuiccA/gE1AKPAWMNEO+25uMIGz791vaZm2rNs4UakXgBcAUlJS1NSpU9sRsdHUqZCamoot67ozV2nzhr1TGVOwDMaOIjC4i0P35SptdqaW2myxKKJSR3GsxzhmXPCc84M5kLv8nL86k02X3etIjLTQc8TUDm3LEW1uy3cgdUAV0InGI5BDSil7dJOaCzQdUKMXkNfGZdqyruEhfMbfyqzaR/jmWLXuKF4lc+8uBpNDz1gz6qYuiePnUaP8Ob1tme4ozWpLAdlKYwEZA0yi8Qtre5yQ3gokiEi8iAQA1wBnn+xbAdxgvRrrPKBEKXWijesaHmLU8OHk+/fiy73u0UOpp8jf2th5YtwE892fLr2ju/N08GLermz2DL12bSkgP1dKPaCUqlNKnVRKzQM63E2qUqoeuB1YBWQC7ymlMkRksYgsti62EsgBsoEXgVvPtW5HMxmuKcjfl4W9Cxi35wEs9XW643iNbrlfcdQvni4xCbqjeDVL8vUsyetOUUWt7ig/0moBUUpta2baG/bYuVJqpVJqoFKqv1Lqr9ZpzymlnrO+Vkqp26zzhzXN0ty6huea3LOOSy1ryNnxle4oXuHosaMk1e/lTG/T75tuM4ZEMYZM0te53mkscye64RYGTZpPjfKneKfpXNEZUg8U8lj9T4iasEB3FK83LDaMPwW9S5+0x3RH+RFTQAy30LVrBOlBI+l1co1bDLTj7j7JqmZt9wVEJ4zUHcXr+fgIeVHT6FtzgOpC17qh1hQQw21U9buInuoUeQd+dFbVsKMzxSV0P7aSixNDdUcxrLqOvgyAI5tc64ZaU0AMtxE/4UoOWqLZlZmlO4pH27txBU/7/5dLuubqjmJYjRg5lkMqGp/9K3VH+QFTQAy3Eds7jtsiXuCV/HjdUTya2vcp5QQTl2L6fnMVgX6+ZEVMoWt5lkt1rmgKiOFWZg6JIu3wKc4Ul+iO4pGqqmsZUrqRnPAJiF+g7jhGE3UTfs246ifZmec64+OYAmK4lVnxfmwJ+CWHv/SsrjVcxZ7NXxAppQQkXaI7inGWSUP7IT5+LnVDrSkghlsZPKAfJT7hBOV8rjuKRypKX0MdvvSfOF93FOMsYZ38ubNnBldsvQbqXeM0likghlsREY52n0pC5S6qSs/ojuNRGiyKewtn8dd+b+IfHK47jtGMIX2jSLAcIi/tC91RAFNADDcUmjwPf2kge+NS3VE8yvYjRZyprCMlOVl3FKMFQyZeQoUKpGi7a9yVbgqI4XaGjJlOAeFYMj/WHcWjnFn7JP8KeJ4pAyJ0RzFaENOtK2mBo4nOXwsWe3SK3jGmgBhuJ8Dfj09i7uI/ZdOpb9D/n8gTKKXom/sxyUH5hAYH6Y5jnEN5/CwiLGc4c2CT7iimgBjuKWr8taRW9WfbkSLdUTzCwYMHGGzJoixuhu4oRiviJ1zGsoaJfHOsSncUU0AM9zRlYHfG+mWTu/5N3VE8wrFN7wPQe8JPNCcxWpPQpzePd/kd7x4L0x3FFBDDPXUO9OPXYWuZfugxVEO97jhur+vRVeT69iYybpjuKEYrRISLknqSf3AXZaf1djdjCojhtiyJc+lKKYd2rtEdxa0VVDSwpbo3x+LNyIPuYk4/H1b5/5bc1c9rzaGlgIhIhIh8KSJZ1ueuzSzTW0TWikimiGSIyF1N5j0kIsdFJM36uNi5LTBcQeKky6hR/hRtN5fzdsSOAgt/q19AzOzf6o5itNGwgQPZLQMJ1nxDra4jkHuA1UqpBGC19f3Z6oHfKKUGA+cBt4nIkCbz/6OUSrY+XKuLSsMpIiMiSQ8aSWz+ajNGSAcUnDjMkKhg+kZ21h3FaCMfH+F4z+mNY4ScPqIvh6b9zgNes75+DfhRvwlKqRNKqR3W12U0jn0e67SEhluo6DeLTg3l5B4xXbzb4vSZMzxVfS9/DjFHce4mcvQVABzZ+J62DKI0/OUmIsVKqfAm74uUUj86jdVkfhywDhiqlCoVkYeAG4FSYBuNRyrNXs8pIouARQBRUVGjlyxZYlPm8vJyQkJCbFrXXblDmwvLq/nDhhouT+zExfEBHd6eO7TZnk5lrufq/MdYlfBnAmO95w50T/g511sUfb++nZqArpye+H+tLt+RNk+bNm27UirlRzOUUg55AF8B6c085gHFZy1bdI7thADbgcubTIsCfGk8gvor8HJbMo0ePVrZau3atTav667cpc0XP7FOzX9qvV225S5ttpdNj16mih6MUZb6Wt1RnMpTfs5/f+UDdf6fl6m6+oZWl+1Im4FtqpnPVIedwlJKXaiUGtrMYzmQLyLRANbnU81tQ0T8gQ+Bt5RSS5tsO18p1aCUsgAvAmMd1Q7D9f2sdz7/yv85BYfSdUdxK2UVFSSVf8PeoBTE1193HMMGw0dP4GilP1sP67mhVtd3ICuAhdbXC4HlZy8gIgK8BGQqpf591rzoJm8vo/HIxvBSo0eMoJ/PSY5ttO30pLdK3/AxXaSSsugJuqMYNpqa2J1rAtZjWXWflv3rKiCPADNEJAuYYX2PiMSIyHdXVE0ErgcuaOZy3UdFZI+I7AamAb9ycn7DhcT3S2CvbyLhRz7THcWtvJEfzx2+9xPQa6TuKIaNggP8uKBrIWNPvY+l0vlHIVoKiFKqUCk1XSmVYH0+Y52ep5S62Pp6g1JKlFLD1VmX6yqlrldKDbPOu1QpdUJHOwzXUdDrIvrVZVOUe0B3FLdQWVvPmqwzdB0+C/Ht+MUHhj5BIy7Dn3qOfPOh0/dt7kQ3PEL0+KsBOLzhXc1J3MOuTV9wl3qLuQmm5113N3L8dE6oCGr3/OibAIczBcTwCAmJQ3nb7zJWnemhO4pbqE9bwo1+XzCqX0/dUYwOCu0USHqXKcQVf4OqLnXqvk0BMTyCiHBk1B946XhvSqrqdMdxadU1tQwuSiU7bDx+Qe59L4TRyHfYZWxrGMj+nENO3a8pIIbHmDW0J7GWPLZ/s1p3FJeW/u0XdJMSfIdepjuKYSejJs1mYcOfWH400Kn7NQXE8BgjeoXzctDjxG75q+4oLq1y11Kq8SdhoikgniI8OIDx/SPZtHs/qq7aafs1BcTwGD4+wrHoi0io2kNZwVHdcVxSbb2FI2eqSA+bhn+w/gGJDPv5ae8zLK1YSO7mj5y2T1NADI/S/bxr8BHFwa/f0R3FJW3MPs391ddRMusp3VEMOxt73mSKCaVi5/tO26cpIIZHGTwshWzpS3DWCt1RXNLqHZl0CfLj/ITuuqMYdhbZpTM7QybTt3A9qqbcKfs0BcTwKCLC8ZiLiKveR+mZZrtY81rVNbXctf8Gnor8gAA/81/fE8nQy+lEDcecdBrL/BYZHidy2m2k1DzDF4dqdUdxKenffE53KabboIm6oxgOMvr8izmlwqly0mksU0AMj5PUvy9dunbn0915uqO4lOq096kikIRJV+iOYjhIeEgnXo26l/sqr/1u6AuHMgXE8Dgiws/ji7n10O2UnnTujVWuqrqmhsFFqRwIm4h/p1DdcQwHih87h20loezKLXH4vkwBMTzS+KR+jPHZT87Xb+qO4hL2bPiYSCklYMSVuqMYDjYzqScz/XZS9PnfHb4vU0AMj5Q4ZAT7fAbQJdv5Hcy5oiV5PXjQ53YSJszXHcVwsLBO/lwZkcPE4//DUlns0H2ZAmJ4JBHhZJ+59KvLovCwd483Vllbz8oDlTQMvwa/oM664xhOEDDiSgKo58jG9xy6Hy0FREQiRORLEcmyPndtYbnD1oGj0kRkW3vXN7xb3ynXYVHCka9f1x1Fq+3rPuVayyfMS4rUHcVwkpSJMziiorDscuzwBrqOQO4BViulEoDV1vctmWYdTCrFxvUNLxUfn8CKoEtZfTpcdxStAna8xB3+yxkd1013FMNJQoL82dttFvHl26krPu6w/egqIPOA16yvXwPae2K2o+sbXqJg4kM8XTCCQ6crdEfRorCwgBEVmzgUNRMffzPyoDcJG/dTDlpiSEvPcNg+xBnXCv9opyLFSqnwJu+LlFI/Og0lIoeAIkABzyulXmjP+tZ5i4BFAFFRUaOXLFliU+by8nJCQrxr7ARPaPOZagsPpxZwY+9TJCcNa3V5T2hzU4Xpq7ji9DN8nvgIQdGDm13G09rcFt7Q5nqL4u61FSRF+vHL5KAOtXnatGnbzzoLBIBfh1O2QES+Apob7uy+dmxmolIqT0R6AF+KyD6l1Lr25LAWnRcAUlJS1NSpU9uz+vdSU1OxdV135Sltjkmbw8DT6XQ9/yDie+5feU9p83d2bXyQPJ9oZl2zGESaXcbT2twW3tLmy0rTWb79ICkjx7Bt5x67t9lhp7CUUhcqpYY281gO5ItINID1udlOi5RSedbnU8AyYKx1VpvWNwyAusGXE6GKObz1M91RnOpQfjFl1XXk9b20xeJheLbLh4bztc+tHPvkEYdsX9d3ICuAhdbXC4EfXawvIp1FJPS718BMIL2t6xvGd4ZPu5oy1YnSLd51U+HyPae4vv4+es37s+4ohibJ/WPJ8h1At5zl4ICvK3QVkEeAGSKSBcywvkdEYkRkpXWZKGCDiOwCtgCfKqU+P9f6htGcsC6hpIVNZ+CZtdRWOL57B1eglGLNjkzG94ukZ3gn3XEMTUSE0/3mc7wuhMqKIrtv32HfgZyLUqoQmN7M9DzgYuvrHGBEe9Y3jJYEjbmeTqs/YefGjxk58zrdcRxub9q3LK24kW8H/wc4T3ccQ6OBM27m0gODWVxl/497cye64RVGjp/BPN+nefbkIN1RnKJow0tYEJInzdYdxdBsQFQoO+6fwfDupoAYhk38/HwZN3o0a/adorC8Rncch6qsqmTI6c/JDDufkK5RuuMYLiDI39ch2zUFxPAaVyRH87jvExxe6tlfKu9a/S4RUkbQmIWtL2wYHWAKiOE1EmPCiQmqpffh98Bi0R3HYQL2vE2BRDJwwqW6oxgezhQQw6uUD76aHpYCDm//vPWF3dCRwgruKLmOjcP+2upNk4bRUaaAGF5l+IULKFGdKdv0su4oDvHB9lxOSjfGTTfdwxmOZwqI4VXCu3RhZ9dZJBatpaooX3ccu2posJDw7b38once0WHm3g/D8UwBMbxO18m38Fz9XL7I9KwecHZv+JRLLauZ3btOdxTDS5gCYnid4SPHsiLiJl7ZWao7il3Vb36BEkIYcqG5+spwDlNADK8jIlw3NpZux1eTndauzp1d1vGjOSRXbCQrZh4BncywtYZzmAJieKXLhvfkUf8XqF77mO4odpGz6hn8pYE+F92uO4rhRUwBMbxSWJcQdnWby6Di9VScPqY7TodU1zWwJs+PdV3m0KPvEN1xDC9iCojhtXpMuwU/sZD1+TO6o3TIZ+kneKXqfOSSJ3RHMbyMKSCG1xqSlMw2/9H0PvgOqq5adxybpX+9lIGR/kzs3013FMPLmAJieC0RoTplMZUNfmzduUN3HJtk7dnC/cX385fojfj4mFEHDecyBcTwamMvuIKfBD7Nf3c7prdSRyv88t9UqQAGz/6l7iiGF9LSWY6IRADvAnHAYeBqpVTRWcskWpf5Tj/gAaXU4yLyEPALoMA6749KqZXYoK6ujtzcXKqrz30KIywsjMzMTFt24ZaCgoIQLxhHO8Dfl+sm9ueJz/eQlbVfd5x2yTuWw6iSL9jVYz5jInvqjmN4IV29rd0DrFZKPSIi91jf/6HpAkqp/UAygIj4AseBZU0W+Y9SqsPXYObm5hIaGkpcXNw5PzDLysoIDQ3t6O7cglKKwsJCOnf2jvsJfjqmN9PWXk7D8p6Q8kfdcdrs0CePEYWFPnN/rzuK4aV0ncKaB7xmff0a0FrPb9OBg0qpI/YOUl1dTWRkpFf8td1WIkJkZCS+vu55Wqe9wjsHkhczk0Hlm2k4c1h3nDYpqajF7+ROdneZSlRf7xhl0XA9opRy/k5FipVS4U3eFymlup5j+ZeBHUqpp6zvHwJuBEqBbcBvzj4F1mTdRcAigKioqNFLliz5wfywsDAGDBjQauaGhgav+UD9TlZWFqWlntXdR0uKiouZvfNmtgVNoH78r3XHadUnB2v5IKuWv42DmK4hHdpWeXk5ISEd24a7MW1un2nTpm1XSqWcPd1hBUREvgKaOzF7H/BaWwuIiAQAeUCSUirfOi0KOA0o4C9AtFLqptYypaSkqG3btv1gWmZmJoMHD261Pd50Cus7O3fuZOTIkbpjOM3a/9zIpOIVVN2ymS4xCbrjtKimpprZ//yc2Oho3vj5uA5vLzU1lalTp3Y8mBsxbW4fEWm2gDjsFJZS6kKl1NBmHsuBfBGJtgaLBs7VLepsGo8+vu97WymVr5RqUEpZgBeBsY5qh+E9el3yRyz4sPvz/+mOck47lj/Nirpb+FWyOe1q6KXrO5AVwHddhi4Elp9j2WuBd5pO+K74WF0GpNs1neGVEgYM5Hehj7L4yDSKK2t1x2lWdVUF/fY+TV5AHCNH/ugPQsNwKl1XYT0CvCciPweOAlcBiEgM8D+l1MXW98HADOCWs9Z/VESSaTyFdbiZ+Tb588cZ7M1r/py/rd+BDInpwoOXJLU4//Dhw8yePZtJkyaxadMmYmNjWb58OZ06dWLq1Kk89thjpKSkcPr0aVJSUjh8+DCvvvoqH330EQ0NDaSnp/Ob3/yG2tpa3njjDQIDA1m5ciUREREt7vPf//436enpvPzyy+zZs4drr72WLVu2EBwc3O72eZoxiXGs2FjFa6l7ueviZN1xfmTH0v8wgULOTH0c8TG3cRl6afkNVEoVKqWmK6USrM9nrNPzvise1veVSqlIpVTJWetfr5QappQarpS6VCl1wtltsKesrCxuu+02MjIyCA8P58MPP2x1nfT0dN5++222bNnCfffdR3BwMDt37mT8+PG8/vrr51z37rvvJjs7m2XLlvGzn/2M559/3hQPq96hPtwTn8NNm2dRkuta94WUl5WQmPUCewNHMHjipbrjGIa2IxCXdK4jBUd+iR4fH09ycuNfu6NHj+bw4cOtrjNt2jRCQ0MJDQ0lLCyMSy65BIBhw4axe/fuc67r4+PDq6++yvDhw7nllluYOHFih9vgSS68cDb+r/+Z7I8eIuz2d1pfwUnWr3yH2ZRQOOMB3VEMAzBdmbiEwMDA71/7+vpSX18PgJ+fHxaLBeBHd8o3XcfHx+f79z4+Pt+vfy5ZWVmEhISQl5fX4fyeZkD/AWyIuIKhp1eSn7lJdxwASirr+ENmPH/s9RoDUy7UHccwAFNAXFpcXBzbt28H4IMPPrDbdktKSrjrrrtYt24dhYWFdt22pxhyzV8oUGFULP8taLhX6mwvfraJspp6rrv4At1RDON7poC4sN/+9rc8++yzTJgwgdOnT7d7/eeee47nnnvuR9N/9atfceuttzJw4EBeeukl7rnnHk6dOteV1N4nJqoHOwfeSVzVXtK3rNGa5WD6Zu7YfTmPDDzAkJguWrMYRlNa7kTXxdxI2D7ediMh/PBmq6qaOn7xrzc503kAH98xCV8N3aUri4XMv59PdN0RfO7YRpgDOk00N9V5B7e6kdAw3F2nQH+umXsRe0+UsmL9di0Ztn38HEPq0ske9huHFA/D6AhTQAzjHOYMi+aeqC3MXTuTggPfOnXfpcWnid/5Dw74DWT0/Dudum/DaAtTQAzjHESEOVcv4ozqQu17N2OpqXTavt/+cBmdVBUy99/4eFlHnoZ7MAXEMFrROzaWjDGPEFt/jMy3fuuUfS7dkcsjWTG8ed6nJCSf75R9GkZ7mQJiGG0wbc5PWB06j6Sjb3F8x+cO3Vdu1m42fvQCY+MiuPki09+V4bpMATGMNhARhv3scQ7Qh1e+2klZdZ1D9lNbXUXNkhu53+clHp8fp+XKL8NoK1NANCsuLuaZZ575/n1qaipz587VmMhoSY+ICPJ/8jmvFI/gtrd3UlffYNftW+rryXhmAf0bDpI9/lFieka3vpJhaGQKiGZnFxDDtZ0/OJa/zh9KePZyDj5+Maq+xi7bVRYLO5+/mZGlq1nf9w5SLlpgl+0ahiOZzhTP9sqcH09Lmg+Dr4HaSnjrqh/PT/4pjFwAFYXw3g0/nPezT8+5u3vuuYeDBw+SnJzMjBkzmDNnDuXl5Vx55ZWkp6czevRo3nzzTUSE7du38+tf/5ry8nK6devGq6++SnR0NGlpaSxevJjKykr69+/Pyy+/TNeuLY4QbLpz76Brxvahy4FuDMr+lv3PXcfAxW8ifoGtr3gOy1e8z/yCZazvcR2TbvyLnZIahmOZIxDNHnnkEfr3709aWhr//Oc/gcY7wB9//HH27t1LTk4OGzdupK6ujjvuuIMPPviA7du3c9NNN3HfffcBcMMNN/CPf/yD3bt3M2zYMP785z+fc5+mO/eOm73gbj7ucQuJp7/g0H9mUFtaYNN2LA0WHv/qAHd/G8J/+zzOxFueRMR872G4B3MEcraWjhjKyiAg+NxHFJ0jWz3iaIuxY8fSq1cvAJKTkzl8+DDh4eGkp6czY8YMoHGAq+joaEpKSiguLmbKlCkALFy4kKuuauYoqQnTnXvHiQhzFv+DT96OZUbWXzjzxPkE3raBrhHd2ryN4hOHOPnq9awvvZzLR17AL6+cjY+v+ZvOcB9afltF5CoRyRARi4i0eJ2iiMwSkf0iki0i9zSZHiEiX4pIlvW55fM1bqi57t2VUiQlJZGWlkZaWhp79uzhiy++sHkfpjv3jvPxEeZedxffTn6Vd2rPZ/Zzu3h781HqKkvOuV5DTQUZKx6H58+nV3UWd46P4F9Xj8DfFA/Dzej6jU0HLgfWtbSAiPgCTwOzgSHAtSIyxDr7HmC1UioBWG1975ZCQ0MpKytrdbnExEQKCgr45ptvAKirqyMjI4OwsDC6du3K+vXrAXjjjTe+PxppienO3b6mTJ/LBYv+SXR4EO9+tIzaRxPJfOU2jm54h9rTh6Ghjrr6Bo4UVrDl3Uco/3siSTseJM+nJ8evWsmUS280p60Mt6TlFJZSKhNo7T/NWCBbKZVjXXYJMA/Ya32eal3uNSAV+INj0jpWZGQkEydOZOjQocyePZs5c5r5Eh8ICAjggw8+4M4776SkpIT6+nruvvtukpKSeO21177/Er1fv3688sorAN935b548eIfbOvs7tynTZvG5MmT6dGjh2Mb68FG9A5n6S8n8M1Wf3Z8OYrzDr+D/5E34avG+ZNqniZfdWWhbx6Wzkmo825jzOQ5+PmZLkoM96W1O3cRSQV+q5Ta1sy8K4FZSqmbre+vB8YppW4XkWKlVHiTZYuUUs2exhKRRcAigKioqNFLliz5wfywsDAGDBjQataGhgZ8vaw/oqysLEpLS3XHcKry8nJCQkI6tA2lFAXlNVQVHCagOIvA2mK2hc+iU0g4vUKEuDBflzrisEeb3Y1pc/tMmzat2e7cHXYEIiJfAc31P32fUmp5WzbRzLR2Vzul1AvAC9A4HsjZ/eFnZma2aZwPbxwPRETMmAl2crndt2g/ZmwM7+CINjusgCilOjpwcy7Qu8n7XsB33/jmi0i0UuqEiEQDZjg9wzAMJ3Plyz62AgkiEi8iAcA1wArrvBXAQuvrhUBbjmha5E2jMraV+TcxDKM1ui7jvUxEcoHxwKcisso6PUZEVgIopeqB24FVQCbwnlIqw7qJR4AZIpIFzLC+ybf+XQAABK1JREFUt0lQUBCFhYXmA7MJpRSFhYU0NNi3ryfDMDyLrquwlgHLmpmeB1zc5P1KYGUzyxUC0+2RpVevXuTm5lJQcO47iaurqwkKCrLHLt1CUFAQFRUVumMYhuHCvP5OdH9/f+Lj41tdLjU1lZEjRzohkes4cuSI7giGYbgwV/4OxDAMw3BhpoAYhmEYNjEFxDAMw7CJ1jvRnU1ECgBbT+x3A07bMY47MG32DqbN3qEjbe6rlOp+9kSvKiAdISLbmruV35OZNnsH02bv4Ig2m1NYhmEYhk1MATEMwzBsYgpI272gO4AGps3ewbTZO9i9zeY7EMMwDMMm5gjEMAzDsIkpIIZhGIZNTAFpAxGZJSL7RSRbRNx2/PW2EpHeIrJWRDJFJENE7tKdyRlExFdEdorIJ7qzOIOIhIvIByKyz/qzHq87k6OJyK+sv9PpIvKOiHhcD6ki8rKInBKR9CbTIkTkSxHJsj43O4Jre5kC0goR8QWeBmYDQ4BrRWSI3lQOVw/8Rik1GDgPuM0L2gxwF41DB3iLJ4DPlVKDgBF4eNtFJBa4E0hRSg0FfGkcZ8jTvArMOmvaPcBqpVQCsNr6vsNMAWndWCBbKZWjlKoFlgDzNGdyKKXUCaXUDuvrMho/WGL1pnIsEekFzAH+pzuLM4hIF2Ay8BKAUqpWKVWsN5VT+AGdRMQPCOb/j3LqMZRS64AzZ02eB7xmff0aMN8e+zIFpHWxwLEm73Px8A/TpkQkDhgJbNabxOEeB34PWHQHcZJ+QAHwyv9r7+5BpLriMIw/LyQW0YCFJCQouASx1kpiI1nLoJWdsgS7ECFt0tgKEds0wSoihM2CkiYp7CxE/AC/uhg2G9YYLJJgZeBvca8gITB6mTsnO/v8mpm9xZ0XduC959wz5/bTdt8k2do61Jiq6jfgLLAKrAN/VtVPbVPNzLtVtQ7dBSLwzjROaoFMlv84tinWPifZBnwPfF5Vf7XOM5YkHwOPq+pG6ywz9AawH/i6qvYBT5nStMb/VT/vfxRYAN4HtiY53jbVxmaBTLYG7Hrp753M4bD335K8SVceF6pqpXWekR0EjiT5hW6K8qMk37aNNLo1YK2qXowsl+kKZZ4dBh5W1R9V9QxYAT5snGlWfk/yHkD/+ngaJ7VAJrsO7EmykGQL3U23y40zjSpJ6ObGH1TVudZ5xlZVX1TVzqraTff/vVJVc31lWlWPgF+T7O0PLQL3G0aahVXgQJK3+u/4InO+cOAll4Gl/v0ScGkaJ930j7SdpKr+SfIZ8CPdqo3zVXWvcayxHQROAHeS3O6Pfdk/o17z4xRwob8w+hn4pHGeUVXVtSTLwE26lYa3mMMtTZJcBA4BO5KsAaeBM8B3SU7SFemxqXyWW5lIkoZwCkuSNIgFIkkaxAKRJA1igUiSBrFAJEmDWCBSY/2uuJ+2ziG9LgtEam87YIFow7FApPbOAB8kuZ3kq9ZhpFflDwmlxvodj3/on1EhbRiOQCRJg1ggkqRBLBCpvb+Bt1uHkF6XBSI1VlVPgKtJ7noTXRuJN9ElSYM4ApEkDWKBSJIGsUAkSYNYIJKkQSwQSdIgFogkaRALRJI0yHN0+lz77H5g+gAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Nt = 100\n", + "dt = 0.1\n", + "t = np.arange(Nt+1)*dt\n", + "\n", + "xth = np.sin(t)\n", + "vth = np.cos(t)\n", + "\n", + "# Euler-A\n", + "xa = np.zeros((Nt+1))\n", + "va = np.zeros((Nt+1))\n", + "\n", + "va[0] = 1.0\n", + "\n", + "for idx in range(Nt):\n", + " xa[idx+1] = xa[idx] + dt * va[idx]\n", + " va[idx+1] = va[idx] - dt * xa[idx+1]\n", + " \n", + "xt_plot(t, xa, xth, title=\"Euler A\")\n", + "vx_plot(xa,va,xth,vth, title=\"Euler A\")\n", + "\n", + "# Euler-B\n", + "xb = np.zeros((Nt+1))\n", + "vb = np.zeros((Nt+1))\n", + "\n", + "vb[0] = 1.0\n", + "\n", + "def euler_b(xb,vb,dt,Nt):\n", + " for idx in range(Nt):\n", + " vb[idx+1] = vb[idx] - dt * xb[idx]\n", + " xb[idx+1] = xb[idx] + dt * vb[idx+1]\n", + " \n", + " energy = 0.5 * xb**2 + 0.5 * vb**2\n", + " return xb, vb, energy \n", + "\n", + "xb, vb, energy = euler_b(xb, vb, dt,Nt)\n", + "\n", + "\n", + "def euler_c(xc,vc,dt,Nt):\n", + " for idx in range(Nt):\n", + " xc[idx+1] = xc[idx] + 0.5 *dt * vc[idx]\n", + " vc[idx+1] = vc[idx] - 1.0 * dt * xc[idx+1]\n", + " xc[idx+1] = xc[idx] + 0.5* dt * vc[idx+1]\n", + " \n", + " energy = 0.5 * xb**2 + 0.5 * vb**2\n", + " return xb, vb, energy \n", + "\n", + "xb, vb, energy = euler_b(xb, vb, dt,Nt)\n", + "\n", + "eth = 0.5 * xth**2 + 0.5 * vth**2\n", + "e_a = 0.5 * xa**2 + 0.5 * va**2\n", + "\n", + "xt_plot(t, xb, xth, title=\"Euler B\")\n", + "vx_plot(xb,vb,xth,vth, title=\"Euler B\")\n", + "\n", + "xt_plot(t, e_a, eth, title=\"Euler A energy\")\n", + "xt_plot(t, energy, eth, title=\"Euler B energy\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9acf8ef-dcc2-4f98-b71a-fd07cb923fb7", + "metadata": {}, + "outputs": [], + "source": [ + "def euler_c(x,v,dt,Nt):\n", + " for idx in range(Nt):\n", + " x[idx+1] = x[idx] + 0.5 * dt * v[idx] \n", + " v[idx+1] = v[idx] - 1.0 * dt * x[idx+1]\n", + " x[idx+1] = x[idx+1] + 0.5 * dt * v[idx+1]\n", + " energy = 0.5 * x**2 + 0.5 * v**2\n", + " return x, v, energy " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "69716065-2126-45bc-97e6-417a2561957e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.0, 10.0, 100.0, 1000.0, 10000.0]\n", + "[1.12041156 1.15050957 1.20061426 1.29994154 1.5797836 ]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dts = [0.00001,0.0001,0.001,0.01,0.1]\n", + "err = []\n", + "\n", + "\n", + "Nt = 100000\n", + "\n", + "def euler_b(xb,vb,dt,Nt):\n", + " for idx in range(Nt):\n", + " vb[idx+1] = vb[idx] - dt * xb[idx]\n", + " xb[idx+1] = xb[idx] + dt * vb[idx+1]\n", + " \n", + " energy = 0.5 * xb**2 + 0.5 * vb**2\n", + " return xb, vb, energy \n", + "\n", + "for dt in dts:\n", + " xb = np.zeros((Nt+1))\n", + " vb = np.zeros((Nt+1))\n", + " vb[0] = 1.0\n", + " \n", + " t = np.arange(Nt+1)*dt\n", + "\n", + " xth = np.sin(t)\n", + " vth = np.cos(t)\n", + " eth = 0.5*xth**2 + 0.5*vth**2\n", + " \n", + " _, _, energy = euler_b(xb,vb,dt,Nt)\n", + " err_in_energy = np.abs(energy - eth).max()\n", + " err.append(err_in_energy)\n", + " \n", + "err_th = [ (10**expn)**1.0 for expn in range(len(dts))]\n", + "print(err_th)\n", + "err_th = np.array(err_th) * err[0]\n", + "\n", + "print(np.log(err) / np.log(dts))\n", + "\n", + "plt.figure()\n", + "plt.loglog(dts, err, '-o', label='order of convergence of the Euler-B method')\n", + "plt.loglog(dts, err_th, '--', label='theoretical 1st. order convergence')\n", + "plt.loglog()\n", + "plt.ylabel(r\"log(error in the energy)\")\n", + "plt.xlabel(r\"log(time step-size $\\Delta t$)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c1a4f16a-f625-4359-a538-d32355fecd0d", + "metadata": {}, + "source": [ + "## Exercise 3: The Störmer-Verlet method\n", + "The explicit Euler and the semi-implicit Euler methods are [*first-order methods*](https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)#Local_truncation_error). We now turn our attention to the [Störmer-Verlet method](https://en.wikipedia.org/wiki/Verlet_integration), which is a second-order numerical integrator.\n", + "\n", + "The discretised equations are:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1/2} &= \\dot{x}^n - \\frac{\\Delta t}{2} \\, x^n, \\label{eq:sv1} \\tag{13a}\\\\\n", + " x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1/2}, \\label{eq:sv2} \\tag{13b}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^{n+1/2} - \\frac{\\Delta t}{2} \\, x^{n+1}. \\label{eq:sv3} \\tag{13c}\\\\\n", + "\\end{align}$$\n", + "\n", + "Notice that ([13a](#mjx-eqn-eq:sv1)) is akin to an explicit Euler update, ([13b](#mjx-eqn-eq:sv2)) is a [midpoint method](https://en.wikipedia.org/wiki/Midpoint_method), and ([13c](#mjx-eqn-eq:sv3)) is an implicit update.\n", + "\n", + "Now, for the tasks:\n", + "1. Implement equation ([13](#mjx-eqn-eq:sv3)).\n", + "2. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "3. Plot $v$ and $x$ and the energy. Are these results in line with your expectations?\n", + "4. Plot the intermediate time steps in ([13a](#mjx-eqn-eq:sv1)). What do you observe?" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "id": "50f9f65b-56fe-43f8-abb5-9292accefb27", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dt = 0.1\n", + "Nt = int(np.ceil(2.0 * np.pi / dt))\n", + "\n", + "t = np.arange(Nt+1)*dt\n", + "x = np.zeros((Nt+1))\n", + "v = np.zeros((Nt+1))\n", + "intermediate = np.zeros((Nt+1))\n", + "\n", + "xth = np.sin(t)\n", + "vth = np.cos(t)\n", + "\n", + "v[0] = 1.0\n", + "\n", + "def sVerlet(x,v,dt):\n", + " for idx in range(Nt):\n", + " intermediate[idx] = v[idx] - 0.25 * dt * x[idx]\n", + " x[idx+1] = x[idx] + 0.5 * dt * intermediate[idx]\n", + " v[idx+1] = intermediate[idx] - 0.25 * dt * x[idx+1]\n", + " \n", + " intermediate[idx] = x[idx+1] + 0.25 * dt * v[idx+1]\n", + " v[idx+1] = v[idx+1] - 0.5 * dt * intermediate[idx]\n", + " x[idx+1] = intermediate[idx] + 0.25 * dt * v[idx+1]\n", + " \n", + " energy = 0.5 * x**2 + 0.5 * v**2\n", + " return x, v, energy\n", + "\n", + "# x[1] = x[0] + dt * v[0] - 0.5 * dt * dt * (x[0] + 1.0 * dt * v[0])\n", + "# for idx in range(1,Nt):\n", + "# pass\n", + "# # intermediate[idx] = x[idx] + 0.5 * dt * v[idx]\n", + "# # v[idx+1] = v[idx] - dt * x[idx] + 0.5 * dt * v[idx]\n", + "# # x[idx+1] = x[idx] + 1.0 * dt * v[idx] - 0.5 * dt * dt * x[idx] + 0.5 * 0.5 * dt * dt * v[idx]\n", + "# x[idx+1] = x[idx] + dt * v[idx] - 0.5 * dt * dt * (x[idx] + 0.5 * dt * v[idx])\n", + "# v[idx] = (x[idx+1] + x[idx-1]) / (2.0 * dt)\n", + "# \n", + "# x[idx+1] = 2.0 * x[idx] - x[idx-1] - 1.0 * dt * dt * (x[idx] + 1.0 * dt * (np.random.random()-0.5)*2.0)\n", + "\n", + "x, v, energy = sVerlet(x,v,dt)\n", + "energy = 0.5 * x**2 + 0.5 * v**2\n", + "eth = 0.5 * xth**2 + 0.5 * vth**2\n", + "\n", + "xt_plot(t,x,xth, title=\"Störmer-Verlet\")\n", + "vx_plot(v,x,xth,vth, title=\"Stömer-Verlet\")\n", + "xt_plot(t[1:],energy[1:],eth[1:], title=\"Energy\")" + ] + }, + { + "cell_type": "code", + "execution_count": 157, + "id": "cb9936a2-1b42-4d6d-aafd-f23f67649f51", + "metadata": {}, + "outputs": [], + "source": [ + "def sVerlet(x,v,dt):\n", + " for idx in range(Nt): \n", + " \n", + " # v[idx] = (x[idx+1] + x[idx-1]) / (2.0 * dt) \n", + " x[idx+1] = 2.0 * x[idx] - x[idx-1] - 1.0 * dt * dt * ( x[idx] + 0.5 * v[idx] )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "77ef2918-eecb-4e04-9fa2-0cd57471a2ed", + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [] + }, + "outputs": [], + "source": [ + "intermediate[idx] = v[idx] - 0.25 * dt * x[idx]\n", + "x[idx+1] = x[idx] + 0.5 * dt * intermediate[idx]\n", + "v[idx+1] = intermediate[idx] - 0.25 * dt * x[idx+1]\n", + "\n", + "intermediate[idx] = x[idx+1] + 0.25 * dt * v[idx+1]\n", + "v[idx+1] = v[idx+1] - 0.5 * dt * intermediate[idx]\n", + "x[idx+1] = intermediate[idx] + 0.25 * dt * v[idx+1]" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "id": "0c6088b4-ecce-4aaf-aa79-20377bfec6fc", + "metadata": { + "collapsed": true, + "jupyter": { + "outputs_hidden": true, + "source_hidden": true + }, + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 5/5 [00:00<00:00, 3996.86it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "32\n", + "4.440892098500626e-16\n", + "[1, 100, 10000, 1000000, 100000000]\n", + "[3.07050596 3.7101616 3.63436717 3.45226183 3.05169206]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from tqdm import tqdm\n", + "\n", + "dts = [0.00001,0.0001,0.001,0.01,0.1]\n", + "err = []\n", + "Nt = int(np.ceil(1.0 * np.pi / dt))\n", + "print(Nt)\n", + "Nt = 10\n", + "\n", + "for dt in tqdm(dts):\n", + " t = np.arange(Nt+1)*dt\n", + " x = np.zeros((Nt+1))\n", + " v = np.zeros((Nt+1))\n", + " v[0] = 1.0\n", + " intermediate = np.zeros((Nt+1))\n", + "\n", + " xth = np.sin(t)\n", + " vth = np.cos(t)\n", + " \n", + " eth = 0.5*xth**2 + 0.5*vth**2\n", + "\n", + " _, _, energy = sVerlet(x,v,dt)\n", + " err_in_energy = np.abs(energy - eth).max()\n", + " err.append(err_in_energy)\n", + " \n", + "print(err[0])\n", + "err_th = [ (10**expn)**2 for expn in range(len(dts))]\n", + "print(err_th)\n", + "err_th = np.array(err_th) * err[0]\n", + "\n", + "print(np.log(err) / np.log(dts))\n", + "\n", + "plt.figure()\n", + "plt.loglog(dts, err, '-o')\n", + "plt.loglog(dts, err_th, '--')\n", + "plt.loglog()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4f5a9ed8-3b39-4e15-8d9b-3f0776d14c02", + "metadata": {}, + "source": [ + "## Further reading\n", + "\n", + "The implicit and explicit Euler methods are part of a family of numerical integrators called the [*Runge-Kutta*](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) methods. The generalised Runge-Kutta method allows us to build higher-order integrators, and Wikipedia has such [a list](https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods). You will come across the Runge-Kutta methods frequently, especially as time integrators. We will go more in detail when we move on to numerical solution of PDEs later in this tutorial." + ] + }, + { + "cell_type": "markdown", + "id": "7f7281e0-ac5a-408b-9ff1-e40bfc4f2201", + "metadata": {}, + "source": [ + "## References\n", + "[1] Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2005.\n", + "\n", + "[2] Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations; 2nd ed. Springer, Dordrecht, 2006." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a26ff85-eb87-4cb1-93a4-a754844859d5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.3 64-bit ('anaconda3': virtualenv)", + "language": "python", + "name": "python37364bitanaconda3virtualenv7a28dc8db0264e168ad4f93d8f9f620c" + }, + "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": 5 +} diff --git a/w2/for-loops_and_list_comprehensions.ipynb b/w2/for-loops_and_list_comprehensions.ipynb new file mode 100644 index 0000000..8a1abaa --- /dev/null +++ b/w2/for-loops_and_list_comprehensions.ipynb @@ -0,0 +1,377 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "8bcf6d2f-ce7a-48c2-93db-82cf216d5e31", + "metadata": {}, + "source": [ + "Before we start, let's import the library we need." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6ad9309e-b542-4726-845f-2af72b3c941e", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "id": "7ddd2e9b-52e5-4ae1-9abd-9c377f698ea6", + "metadata": {}, + "source": [ + "# Definition: for-loops\n", + "The for-loop is a simple concept. Over a range of numbers or items, a for-loop will go through each number or item sequentially and terminates when it reaches the end of the range. In python, the for-loop is initialised with a `for in :`. The code snippet below provides a few examples.\n", + "\n", + "**Note**: Unlike in many other programming languages, we want to avoid using for-loops in Python as they may be excruciatingly slow here. In future exercises, we will encounter more concrete scenarios where using a for-loop may be the easiest solution, and we will learn how to efficiently *vectorise* our code to avoid using unnecessary for-loops.\n", + "\n", + "In situations such as numerical intergration over time or over dimensions, a for-loop may be unavoidable. For unavoidable for-loops that are in critical parts of the code, you may want to use a *just-in-time compiler* such as [numba](https://numba.pydata.org/). " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7e2665a6-ad64-4d96-9d18-06670e06c399", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n", + "\n", + "============\n", + "\n", + "1\n", + "2\n", + "3\n", + "a\n", + "dog\n", + "item\n", + "10.0\n", + "55.5\n", + "1e-06\n", + "\n", + "[[ 0 1 2 3 4]\n", + " [ 5 6 7 8 9]\n", + " [10 11 12 13 14]\n", + " [15 16 17 18 19]\n", + " [20 21 22 23 24]]\n", + "\n", + "============\n", + "\n", + "index = 0, item = 1\n", + "index = 1, item = 2\n", + "index = 2, item = 3\n", + "index = 3, item = a\n", + "index = 4, item = dog\n", + "index = 5, item = item\n", + "index = 6, item = 10.0\n", + "index = 7, item = 55.5\n", + "index = 8, item = 1e-06\n", + "index = 9, item = \n", + "index = 10, item = [[ 0 1 2 3 4]\n", + " [ 5 6 7 8 9]\n", + " [10 11 12 13 14]\n", + " [15 16 17 18 19]\n", + " [20 21 22 23 24]]\n" + ] + } + ], + "source": [ + "# A basic for-loop loops over a given range:\n", + "r = 10 # we want to count 0,1,2,...,9\n", + "for number in range(r):\n", + " print(number)\n", + " \n", + "print(\"\\n============\\n\")\n", + "\n", + "# A for-loop works for a collection of items in a list too:\n", + "def sample_func(): return None # initialise an arbitrary function\n", + "array = np.arange(25).reshape(5,5) # and an array\n", + "lst = [1,2,3,'a','dog','item',10.0,55.5,1e-6,sample_func,array]\n", + "\n", + "for item in lst:\n", + " print(item)\n", + "\n", + "print(\"\\n============\\n\")\n", + "\n", + "# The enumerate function provides a pythonic way of looping over items and keeping count of the loop:\n", + "for index, item in enumerate(lst):\n", + " print(\"index = %i, item = %s\" %(index, str(item)))" + ] + }, + { + "cell_type": "markdown", + "id": "f9764cf7-1967-40d5-8a50-c32890308840", + "metadata": {}, + "source": [ + "-----" + ] + }, + { + "cell_type": "markdown", + "id": "5aea3e10-fd5d-4654-a60e-f272be1db149", + "metadata": {}, + "source": [ + "# List comprehensions\n", + "A powerful feature of Python is *list comprehension*. In the last tutorial, we were introduced to the basics of lists in Python. Now, we see how we can make use of list comprehensions to write compact code.\n", + "\n", + "A common operation in Python is zipping. Say you have two lists, A and B, and you want to create a third list, C that has the first element of A with the first element of B, second element of A with the second element of B and so on. To do this, you use the `zip` function. Let's see how we can do this in a for-loop:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "5a53b4cc-2373-473f-b883-8a8fd4d1e18e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "list A is: [410 686 33 580 381 550 406 233]\n", + "list B is: [100 101 102 103 104 105 106 107]\n", + "list C is: [(410, 100), (686, 101), (33, 102), (580, 103), (381, 104), (550, 105), (406, 106), (233, 107)]\n", + "list D is: [(410, 100), (686, 101), (33, 102), (580, 103), (381, 104), (550, 105), (406, 106), (233, 107)]\n" + ] + } + ], + "source": [ + "# Let's use the help of numpy to generate some random lists A and B:\n", + "\n", + "# What does numpy.random.seed() do?\n", + "# Try commenting out this line below and re-run this cell multiple times. Print out the list A.\n", + "# What happens to the entries of A if the seed is enabled versus not specifying the seed?\n", + "np.random.seed(555) \n", + "A = np.random.randint(0,1000,size=(8))\n", + "print(\"list A is: %s\" %A)\n", + "\n", + "# What is numpy.arange?\n", + "B = np.arange(100,108,1)\n", + "print(\"list B is: %s\" %B)\n", + "\n", + "# we create C as an empty list.\n", + "C = []\n", + "\n", + "# now we loop through lists A and B and zip the items in the list together:\n", + "for zipped_item in zip(A,B):\n", + " C.append(zipped_item) \n", + "print(\"list C is: %s\" %C)\n", + "\n", + "# If we were to use list comprehension...\n", + "D = [zipped_item for zipped_item in zip(A,B)]\n", + "print(\"list D is: %s\" %D)" + ] + }, + { + "cell_type": "markdown", + "id": "611089a0-87af-4dbc-9a26-0a7fad7f5b4d", + "metadata": {}, + "source": [ + "You may have noticed that inside each list, the elements are now grouped pair-wise between (parenthesis) brackets, i.e. `()`. We know that lists are defined by the square brackets `[]`. These parenthesis are *not* lists, but tuples. If you do not already know, find out the difference between a list and a tuple.\n", + "\n", + "Now let's play around a little more with the list D." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "7a38a7ee-557d-44d2-b285-1b860321648c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the entries of the list D are:\n", + "\n", + "entry index 0 is: (410, 100)\n", + "entry index 1 is: (686, 101)\n", + "entry index 2 is: (33, 102)\n", + "entry index 3 is: (580, 103)\n", + "entry index 4 is: (381, 104)\n", + "entry index 5 is: (550, 105)\n", + "entry index 6 is: (406, 106)\n", + "entry index 7 is: (233, 107)\n", + "\n", + "list E is: [410, 100, 686, 101, 33, 102, 580, 103, 381, 104, 550, 105, 406, 106, 233, 107]\n" + ] + } + ], + "source": [ + "# Let's loop the entries in D. We see that each entry is a tuple!\n", + "# In other words, the size of list D is actually 8 rows by 2 columns, or 8x2.\n", + "print(\"the entries of the list D are:\\n\")\n", + "for idx, entry in enumerate(D):\n", + " print(\"entry index %i is: %s\" %(idx, entry))\n", + " \n", + "print(\"\")\n", + "\n", + "# What if we want to \"flatten\" D? I.e. to make the list a flat list of 16 entries?\n", + "# Let's try it with list comprehension:\n", + "E = [item for item_pair in D for item in item_pair]\n", + "print(\"list E is: %s\" %E)" + ] + }, + { + "cell_type": "markdown", + "id": "a0547351-9be4-4ddc-8280-0c25d8a42b7e", + "metadata": {}, + "source": [ + "\n", + "Try to make sense of the list comprehension for `E` above. How would you write it in terms of for-loops?" + ] + }, + { + "cell_type": "markdown", + "id": "97500139-db1a-4d0c-af46-c4f79dab603b", + "metadata": {}, + "source": [ + "----" + ] + }, + { + "cell_type": "markdown", + "id": "32d9e14f-4d85-4506-bb94-1e3c4c968006", + "metadata": {}, + "source": [ + "# Warning!\n", + "\n", + "Python lists are different from numpy lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "4b0600ee-4c93-4f81-9fef-f957cf54004f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the list numpy_t is: [0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n", + "the list python_t is: [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + } + ], + "source": [ + "# We did the following the code above with a numpy list:\n", + "numpy_lst = np.arange(10)*0.1\n", + "# Let's see what the results are\n", + "print(\"the list numpy_t is: %s\" %numpy_lst)\n", + "\n", + "# On the other hand, if we were to muliply a Python list:\n", + "python_lst = [10]*10\n", + "print(\"the list python_t is: %s\" %python_lst)\n", + "\n", + "print(\"\")\n", + "# To check the type of list you have,\n", + "print(type(numpy_lst))\n", + "print(type(python_lst))\n", + "\n", + "print(\"\")\n", + "# To convert a python list to a numpy list:\n", + "new_numpy_lst = np.array(python_lst)\n", + "print(type(new_numpy_lst))\n", + "\n", + "# And to convert a numpy list to a python list:\n", + "new_python_lst = list(numpy_lst)\n", + "print(type(new_python_lst))" + ] + }, + { + "cell_type": "markdown", + "id": "83bf81f3-ff8e-4020-96ac-922f3c01711b", + "metadata": {}, + "source": [ + "There are a few other subtle differences between the two types of list. For example, Python lists can be just a collection of items, while numpy lists have stricter rules on what *types* its entries are." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "8d7e5c3d-07d2-4c03-b00d-a678f5d7b16b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ray/anaconda3/envs/playground/lib/python3.7/site-packages/ipykernel_launcher.py:7: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n", + " import sys\n" + ] + } + ], + "source": [ + "# Let's initialise the Python list we have above:\n", + "def sample_func(): return None # initialise an arbitrary function\n", + "array = np.arange(25).reshape(5,5) # and an array\n", + "lst = [1,2,3,'a','dog','item',10.0,55.5,1e-6,sample_func,array]\n", + "\n", + "# This is entirely valid as a Python list. However, if we were to convert it to a numpy list...\n", + "numpy_lst = np.array(lst)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "31ee3b8b-3b3b-491e-a583-1e0c1c7e4134", + "metadata": {}, + "outputs": [], + "source": [ + "# Numpy complains that the entries of the list are not of the same type.\n", + "# To tell numpy that the list is meant to contain entries of different types, we need to explicitly specify that:\n", + "numpy_lst_ok = np.array(lst, dtype='object')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1d87c267-1fed-405b-917f-b3e416e77a10", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w2/lotka-volterra.ipynb b/w2/lotka-volterra.ipynb new file mode 100644 index 0000000..13d0e8e --- /dev/null +++ b/w2/lotka-volterra.ipynb @@ -0,0 +1,109 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "88c85725-5dd0-4f61-ba54-289120190191", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "ed9418a9-1532-4e9e-b5d7-19a76f474683", + "metadata": {}, + "outputs": [], + "source": [ + "# Some helper functions for plots\n", + "def xt_plot(t, b, c, xth=None, title=\"\"):\n", + " plt.plot(t, b, label='baboons')\n", + " plt.plot(t, c, label='cheetahs')\n", + " plt.legend(loc='best')\n", + " plt.xlabel('time')\n", + " plt.ylabel(\"population\")\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.grid()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "821c008d-2259-4da5-b345-1248c8b65148", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dt = 0.01\n", + "Nt = 10000\n", + "\n", + "baboons_gain = 1.1\n", + "baboons_loss = 0.4\n", + "\n", + "cheetahs_gain = 0.1\n", + "cheetahs_loss = 0.4\n", + "\n", + "t = np.arange(Nt+1)*dt\n", + "baboons = np.zeros((Nt+1))\n", + "cheetahs = np.zeros((Nt+1))\n", + "\n", + "baboons[0] = 10.0\n", + "cheetahs[0] = 10.0\n", + "\n", + "for idx in range(Nt):\n", + " cheetahs[idx+1] = cheetahs[idx] + 0.5 * dt * (cheetahs_gain * baboons[idx] * cheetahs[idx] - cheetahs_loss * cheetahs[idx])\n", + " baboons[idx+1] = baboons[idx] + dt * (baboons_gain * baboons[idx] - baboons_loss * baboons[idx] * cheetahs[idx+1])\n", + " cheetahs[idx+1] = cheetahs[idx+1] + 0.5 * dt * (cheetahs_gain * baboons[idx+1] * cheetahs[idx+1] - cheetahs_loss * cheetahs[idx+1])\n", + "\n", + "xt_plot(t,baboons, cheetahs, title=\"Lotka-Volterra model\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "01e3973b-7b6c-445c-ba87-7a740b25b6ef", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.3 64-bit ('anaconda3': virtualenv)", + "language": "python", + "name": "python37364bitanaconda3virtualenv7a28dc8db0264e168ad4f93d8f9f620c" + }, + "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": 5 +} diff --git a/w2/soln/ex1a.png b/w2/soln/ex1a.png new file mode 100644 index 0000000..6437f88 Binary files /dev/null and b/w2/soln/ex1a.png differ diff --git a/w2/soln/ex1b.png b/w2/soln/ex1b.png new file mode 100644 index 0000000..309dbbc Binary files /dev/null and b/w2/soln/ex1b.png differ diff --git a/w2/soln/ex1c.png b/w2/soln/ex1c.png new file mode 100644 index 0000000..dd01a28 Binary files /dev/null and b/w2/soln/ex1c.png differ diff --git a/w2/w2_ex4.pdf b/w2/w2_ex4.pdf new file mode 100644 index 0000000..850f911 Binary files /dev/null and b/w2/w2_ex4.pdf differ diff --git a/w3/discrete_oscillator.ipynb b/w3/discrete_oscillator.ipynb new file mode 100644 index 0000000..c3901c0 --- /dev/null +++ b/w3/discrete_oscillator.ipynb @@ -0,0 +1,340 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ada769df-0827-4614-a16a-5cb7ff34b0db", + "metadata": {}, + "source": [ + "# Tutorial 3\n", + "Before we start, let's import our libraries." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "319505e0-e5f9-4ef9-8a76-3c683d64b89b", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "09c32f0c-1395-4678-b057-f7d13577b61a", + "metadata": {}, + "source": [ + "## Finite differencing and the explicit Euler method\n", + "\n", + "Today we want to solve the oscillator problem (again). But this time, we do not rely on a fancy ODE solver like the `odeint`. Instead, we want to solve the problem with a [finite difference](https://en.wikipedia.org/wiki/Finite_difference_method) method.\n", + "\n", + "The finite difference method is a numerical method to solve differential equations. The broad idea behind the method is to approximate the differential with a discrete difference. For example, in our oscillator problem, we have the time derivative of $x$. This can be *discretised* as \n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} \\approx \\frac{x(t+\\Delta t) - x(t)}{\\Delta t}\\tag{1}.\n", + "\\end{equation}\n", + "\n", + "The process of approximating a continuous quantity with its discrete form is called *discretisation*.\n", + "\n", + "Say now we have an ODE\n", + "\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} = F(t,x(t))\\tag{2},\n", + "\\label{eq:differential}\n", + "\\end{equation}\n", + "\n", + "discretising this yields\n", + "\\begin{equation}\n", + "x(t+\\Delta t) = x(t) + \\Delta t \\, F(t,x(t)) \\tag{3} \\label{eq:discretised}\n", + "\\end{equation}\n", + "\n", + "Generally, we write equation \\eqref{eq:discretised} as \n", + "\\begin{equation}\n", + "x^{n+1} = x^n + \\Delta t \\, F(t^n,x^n), \\tag{4}\\label{eq:euler_method}\n", + "\\end{equation}\n", + "\n", + "where $n$ indexes the time-step at time $t$ and $n+1$ indexes the time-step at $t+\\Delta t$. Note that the notion of a \"time-step\" now makes sense, as we are integrating the problem discretely in time.\n", + "\n", + "Given a time-step size of $\\Delta t$, if we have the solution $(t^n,x^n)$ at time $n$, then we can evaluate the right-hand side of \\eqref{eq:euler_method}, and this gives us the solution of $x$ at the new time $n+1$.\n", + "\n", + "The method of numerically integrating an ODE with \\eqref{eq:euler_method} is also known as the [explicit Euler method](https://en.wikipedia.org/wiki/Euler_method).\n", + "\n", + "Now that we have some idea on a finite difference method, let's apply it..." + ] + }, + { + "cell_type": "markdown", + "id": "5f600fad-cdd7-4075-914e-24991adf7f37", + "metadata": {}, + "source": [ + "## Setting up the harmonic oscillator problem\n", + "\n", + "We want to use the simple harmonic oscillator problem without damping and without forcing as an exercise to get an intuition of the finite difference numerical methods:\n", + "$$m \\ddot{x} = -c x, \\qquad m,c > 0. \\tag{5}$$\n", + "\n", + "The analytical solution to this free oscillation scenario is on page 20, equation (75) of the lecture notes,\n", + "\n", + "$$x(t) = a \\cos(\\omega t) + b \\sin(\\omega t), \\tag{6}$$\n", + "\n", + "where $\\omega=\\sqrt{c/m}$.\n", + "\n", + "We can make our lives much easier by choosing the constants $c,m=1$, the initial position $x(t=0)=0$, and the initial velocity $\\dot{x}(t=0)=1$. This gives us the following analytical solutions:\n", + "$$\\begin{align}\n", + "x &= \\sin(t), \\tag{7a}\\\\\n", + "\\dot{x} &= \\cos(t), \\tag{7b}\\\\\n", + "\\ddot{x} &= -x. \\tag{7c}\n", + "\\end{align}$$\n", + "This is equivalent to\n", + "$$\\begin{align}\n", + "\\frac{dx}{dt} &= \\dot{x}, \\tag{8a}\\\\\n", + "\\frac{d\\dot{x}}{dt} &= -x. \\tag{8b}\n", + "\\end{align}$$\n", + "\n", + "Discretising this with the explicit Euler method,\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{9a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^n. \\tag{9b}\n", + "\\label{eq:ee_discretised}\n", + "\\end{align}$$\n", + "\n", + "Please go through the working above on your own to verify that it makes sense!" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "24bdebe0-9f71-4659-973e-2097c12b791a", + "metadata": {}, + "outputs": [], + "source": [ + "# Some helper functions for plots\n", + "def xt_plot(t, x, xth=None, title=\"\", ylabel=\"x\"):\n", + " plt.plot(t, x, label='num. x')\n", + " if xth is not None:\n", + " plt.plot(t, xth, '--', label='theo. x')\n", + " plt.legend(loc='best')\n", + " plt.xlabel('t')\n", + " plt.ylabel(ylabel)\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.grid()\n", + " plt.show()\n", + "\n", + "def vx_plot(x, v, xth, vth, title=\"\"):\n", + " plt.plot(x,v, label=\"num. sol.\")\n", + " plt.plot(xth,vth, '--', label=\"theo. sol.\")\n", + " plt.legend()\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"v\")\n", + " if len(title) > 0:\n", + " plt.title(title)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ec7d32a-b82e-4c32-800d-406b72f8cf07", + "metadata": {}, + "source": [ + "## Exercise 1: The explicit Euler method \n", + "1. Implement equation ([9](#mjx-eqn-eq:ee_discretised)). How would you do it?\n", + "2. Compare the result for various step-sizes, e.g. `dt=0.1` and `dt=0.01`.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and the analytical solution. What do you see?\n", + "4. We know that the potential energy in a spring is given by $PE=\\frac{1}{2}kx^2$ while the kinetic energy of the spring is $KE=\\frac{1}{2}mv^2$. Compute and compare the energy of the numerical solution with the theoretical energy. What happens with the energy?" + ] + }, + { + "cell_type": "markdown", + "id": "40b00eb7-5e8c-41bb-b5e7-165eaa4a4365", + "metadata": {}, + "source": [ + "### Hints:" + ] + }, + { + "cell_type": "markdown", + "id": "95cad889-d746-4c5a-9590-af0763d51a75", + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [] + }, + "source": [ + "1. We will need a *for-loop*. A short introduction to the features of the for-loop in Python is provided in the supplementary materials.\n", + "2. What are we looping over?\n", + "3. What do we have to do in each step of the loop?" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "11b3fc8b-eeb5-4649-a55c-5ac7696d68a5", + "metadata": {}, + "outputs": [], + "source": [ + "# Here are some helper code to get you started.\n", + "\n", + "# Let's specify the number of time-steps\n", + "Nt = 10000\n", + "# and a time-step size\n", + "dt = 0.01\n", + "\n", + "# What are numpy.arange and numpy.zeros?\n", + "# Why do we need to initialise these arrays?\n", + "t = np.arange(Nt+1)*dt\n", + "x = np.zeros((Nt+1))\n", + "v = np.zeros((Nt+1))\n", + "\n", + "# Since we know the analytical solution,\n", + "# let's compare our numerical solution against them.\n", + "xth = np.sin(t)\n", + "vth = np.cos(t)\n", + "\n", + "# Fill in the rest of the code here:\n", + "# ...\n", + "\n", + "# xt_plot(t,x,xth, title=\"explicit Euler\")\n", + "# vx_plot(x,v,xth,vth, title=\"explicit Euler\")" + ] + }, + { + "cell_type": "markdown", + "id": "67d02d8f-e732-4e45-86c8-98e56d0bf80c", + "metadata": {}, + "source": [ + "## Exercise 2: Euler-A and Euler-B methods\n", + "Notice that our discretisation of equation ([2](#mjx-eqn-eq:differential)) is not unique, and there are actually many ways to discretise a differential. For example, we can write equation ([4](#mjx-eqn-eq:euler_method)) as\n", + "\n", + "$$x^{n+1} = x^n - \\Delta t \\, F(t^{n+1},x^{n+1}), \\tag{10} \\label{eq:implicit_euler} $$\n", + "\n", + "which would give us the [implicit Euler method](https://en.wikipedia.org/wiki/Backward_Euler_method).\n", + "\n", + "For the system of equations we are solving in ([9](#mjx-eqn-eq:ee_discretised)), we can apply the [semi-implicit Euler method](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method). This is given by the following updates:\n", + "\n", + "a. For the Euler-A method:\n", + "$$\\begin{align}\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^n, \\tag{11a}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n+1}. \\tag{11b}\n", + "\\label{eq:euler_a}\n", + "\\end{align}$$\n", + "b. For the Euler-B method:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1} &= \\dot{x}^n - \\Delta t \\, x^{n}, \\tag{12a}\\\\\n", + "x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1}. \\tag{12b}\n", + "\\label{eq:euler_b}\n", + "\\end{align}$$\n", + "\n", + "Now on to the tasks:\n", + "1. Implement equations ([11](#mjx-eqn-eq:euler_a)) and ([12](#mjx-eqn-eq:euler_b)).\n", + "2. Again, try around with different number of time-steps and time-step sizes.\n", + "3. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "4. Can you explain your observation?\n", + "5. Again, let's compare the energy of the numerical solution with the theoretical energy." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d65c9086-f241-48d0-9118-875b37727c90", + "metadata": {}, + "outputs": [], + "source": [ + "# Fill in the code here:\n", + "# ...\n", + "\n", + "# xt_plot(t, xb, xth, title=\"Euler B\")\n", + "# vx_plot(xb,vb,xth,vth, title=\"Euler B\")" + ] + }, + { + "cell_type": "markdown", + "id": "c1a4f16a-f625-4359-a538-d32355fecd0d", + "metadata": {}, + "source": [ + "## Exercise 3: The Störmer-Verlet method\n", + "The explicit Euler and the semi-implicit Euler methods are [*first-order methods*](https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)#Local_truncation_error). We now turn our attention to the [Störmer-Verlet method](https://en.wikipedia.org/wiki/Verlet_integration), which is a second-order numerical integrator.\n", + "\n", + "The discretised equations are:\n", + "$$\\begin{align}\n", + "\\dot{x}^{n+1/2} &= \\dot{x}^n - \\frac{\\Delta t}{2} \\, x^n, \\label{eq:sv1} \\tag{13a}\\\\\n", + " x^{n+1} &= x^n + \\Delta t \\, \\dot{x}^{n+1/2}, \\label{eq:sv2} \\tag{13b}\\\\\n", + "\\dot{x}^{n+1} &= \\dot{x}^{n+1/2} - \\frac{\\Delta t}{2} \\, x^{n+1}. \\label{eq:sv3} \\tag{13c}\\\\\n", + "\\end{align}$$\n", + "\n", + "Notice that ([13a](#mjx-eqn-eq:sv1)) is akin to an explicit Euler update, ([13b](#mjx-eqn-eq:sv2)) is a [midpoint method](https://en.wikipedia.org/wiki/Midpoint_method), and ([13c](#mjx-eqn-eq:sv3)) is an implicit update.\n", + "\n", + "Now, for the tasks:\n", + "1. Implement equation ([13](#mjx-eqn-eq:sv3)).\n", + "2. Plot $\\dot{x}$ against $x$ for the numerical and analytical solutions. What do you observe?\n", + "3. Plot $v$ and $x$ and the energy. Are these results in line with your expectations?\n", + "4. Plot the intermediate time steps in ([13a](#mjx-eqn-eq:sv1)). What do you observe?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "50f9f65b-56fe-43f8-abb5-9292accefb27", + "metadata": {}, + "outputs": [], + "source": [ + "# Fill in the code here:\n", + "# ...\n", + " \n", + "# xt_plot(t,x,xth, title=\"Störmer-Verlet\")\n", + "# vx_plot(v,x,xth,vth, title=\"Stömer-Verlet\")" + ] + }, + { + "cell_type": "markdown", + "id": "4f5a9ed8-3b39-4e15-8d9b-3f0776d14c02", + "metadata": {}, + "source": [ + "## Further reading\n", + "\n", + "The implicit and explicit Euler methods are part of a family of numerical integrators called the [*Runge-Kutta*](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) methods. The generalised Runge-Kutta method allows us to build higher-order integrators, and Wikipedia has such [a list](https://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods). You will come across the Runge-Kutta methods frequently, especially as time integrators. We will go more in detail when we move on to numerical solution of PDEs later in this tutorial." + ] + }, + { + "cell_type": "markdown", + "id": "7f7281e0-ac5a-408b-9ff1-e40bfc4f2201", + "metadata": {}, + "source": [ + "## References\n", + "[1] Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2005.\n", + "\n", + "[2] Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations; 2nd ed. Springer, Dordrecht, 2006." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a26ff85-eb87-4cb1-93a4-a754844859d5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.7.3 64-bit ('anaconda3': virtualenv)", + "language": "python", + "name": "python37364bitanaconda3virtualenv7a28dc8db0264e168ad4f93d8f9f620c" + }, + "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": 5 +} diff --git a/w3/img/euler_a_ps.png b/w3/img/euler_a_ps.png new file mode 100644 index 0000000..c27b83c Binary files /dev/null and b/w3/img/euler_a_ps.png differ diff --git a/w3/img/euler_a_ps_small_ts.png b/w3/img/euler_a_ps_small_ts.png new file mode 100644 index 0000000..3387b40 Binary files /dev/null and b/w3/img/euler_a_ps_small_ts.png differ diff --git a/w3/orders_and_errors.ipynb b/w3/orders_and_errors.ipynb new file mode 100644 index 0000000..9269d46 --- /dev/null +++ b/w3/orders_and_errors.ipynb @@ -0,0 +1,153 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ba171e57-bfe7-4e94-80dd-a7e289953484", + "metadata": {}, + "source": [ + "# Tutorial 4\n", + "\n", + "Let's import some libraries..." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "c28e888a-34e1-4be3-baf4-2ca5465dcc96", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "70fa3f3c-4575-4ac5-a515-812a94ba540d", + "metadata": {}, + "source": [ + "## The order of a numerical method\n", + "\n", + "Last week, we came across the explicit Euler, and the Euler-A and Euler-B methods. These are first-order methods, while the Störmer-Verlet is a second-order method. The \"order\" here refers to [order of accuracy](https://en.wikipedia.org/wiki/Order_of_accuracy) of the numerical method.\n", + "\n", + "We saw that for the Euler-A and Euler-B methods, a step size of $\\Delta t=0.1$ is unable to reproduce the theoretical phase space diagram. The example phase space plot for the Euler-A method is provided below:\n", + "\n", + "
\n", + "\n", + "On the other hand, if we were decrease the time step-size to $\\Delta t=0.01$, i.e. to run our problem at a higher resolution, our numerical solution is able to better reproduce the theoretical phase space diagram:\n", + "\n", + "
\n", + "\n", + "This observation is related to the order of the numerical method. Loosely speaking, the order of a numerical method tells us the answer to the question:\n", + "\n", + " How much improvement can I get from the numerical method if I were to increase the resolution of my problem? \n", + " \n", + "Mathematically, if we have a numerical solution $u_h$ and an exact solution $u$, then a $n$-th order numerical method gives us\n", + "\n", + "$$\\Vert u_h - u \\Vert = \\mathcal{O}(h^n), \\tag{1}$$\n", + "\n", + "where $h$ is our step size, e.g. $\\Delta t$ above." + ] + }, + { + "cell_type": "markdown", + "id": "9a849520-24e6-483e-9e92-5fbbc5e8d2f9", + "metadata": {}, + "source": [ + "## A simple example\n", + "\n", + "Now let us develop an intuition of the order of accuracy of a numerical method with our harmonic oscillator problem. We pick the Euler-A method, and the literature tells us that this is a first-order method. Can we verify this?\n", + "\n", + "First of all, taking the log on both sides of equation (1) above and rearraging gives us\n", + "\n", + "$$\\frac{\\log(\\Vert u_h - u \\Vert)}{\\log( h )} \\sim n.$$\n", + "\n", + "Let's try to code this up..." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b22e2831-6fbe-4a25-aaed-88efcd3e5ba1", + "metadata": {}, + "outputs": [], + "source": [ + "# ...\n", + "\n", + "# plt.figure()\n", + "# plt.loglog(dts, err, '-o', label='order of convergence of the Euler-B method')\n", + "# plt.loglog(dts, err_th, '--', label='theoretical 1st. order convergence')\n", + "# plt.loglog()\n", + "# plt.ylabel(r\"log(error in the energy)\")\n", + "# plt.xlabel(r\"log(time step-size $\\Delta t$)\")\n", + "# plt.legend()\n", + "# plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "95d9bcf4-bcd8-46c1-8652-1b030af8e6ee", + "metadata": {}, + "source": [ + "## Local vs global truncation error\n", + "\n", + "Quoting [Wikipedia](https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)) as usual, \n", + "\n", + "\"Truncation errors in numerical integration are of two kinds:\"\n", + " - local truncation errors – the error caused by one iteration, and\n", + " - global truncation errors – the cumulative error caused by many iterations.\n", + "\n", + "Above, we computed the global truncation error which is normally what gives us the order of a numerical method. However, let's repeat our experiment with fewer number of time-steps, say 10. What happens now? " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "372c62b0-abe9-4983-bbfd-94dcfa80d728", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "d7faf198-0c15-4c09-a599-abfce5f8063c", + "metadata": {}, + "source": [ + "## Exercise 1\n", + "1. Do a error convergence study for the Störmer-Verlet method. Try with say 100,000 time-steps. Do your results verify that the method is indeed second-order?\n", + "2. Re-run the study with 10 time-steps. Now what is the order of convergence? Can you explain why? (Hint: This [Wikipedia page](https://en.wikipedia.org/wiki/Verlet_integration#Error_terms) may be helpful.)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "541fdf00-5fd2-47e3-8c0e-3d87445cd58c", + "metadata": {}, + "outputs": [], + "source": [ + "# Try out the exercise here" + ] + } + ], + "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": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w3/orders_and_errors_soln.ipynb b/w3/orders_and_errors_soln.ipynb new file mode 100644 index 0000000..1b1e5ad --- /dev/null +++ b/w3/orders_and_errors_soln.ipynb @@ -0,0 +1,320 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ba171e57-bfe7-4e94-80dd-a7e289953484", + "metadata": {}, + "source": [ + "# Tutorial 4\n", + "\n", + "Let's import some libraries..." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "c28e888a-34e1-4be3-baf4-2ca5465dcc96", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "70fa3f3c-4575-4ac5-a515-812a94ba540d", + "metadata": {}, + "source": [ + "## The order of a numerical method\n", + "\n", + "Last week, we came across the explicit Euler, and the Euler-A and Euler-B methods. These are first-order methods, while the Störmer-Verlet is a second-order method. The \"order\" here refers to [order of accuracy](https://en.wikipedia.org/wiki/Order_of_accuracy) of the numerical method.\n", + "\n", + "We saw that for the Euler-A and Euler-B methods, a step size of $\\Delta t=0.1$ is unable to reproduce the theoretical phase space diagram. The example phase space plot for the Euler-A method is provided below:\n", + "\n", + "
\n", + "\n", + "On the other hand, if we were decrease the time step-size to $\\Delta t=0.01$, i.e. to run our problem at a higher resolution, our numerical solution is able to better reproduce the theoretical phase space diagram:\n", + "\n", + "
\n", + "\n", + "This observation is related to the order of the numerical method. Loosely speaking, the order of a numerical method tells us the answer to the question:\n", + "\n", + " How much improvement can I get from the numerical method if I were to increase the resolution of my problem? \n", + " \n", + "Mathematically, if we have a numerical solution $u_h$ and an exact solution $u$, then a $n$-th order numerical method gives us\n", + "\n", + "$$\\Vert u_h - u \\Vert = \\mathcal{O}(h^n), \\tag{1}$$\n", + "\n", + "where $h$ is our step size, e.g. $\\Delta t$ above." + ] + }, + { + "cell_type": "markdown", + "id": "9a849520-24e6-483e-9e92-5fbbc5e8d2f9", + "metadata": {}, + "source": [ + "## A simple example\n", + "\n", + "Now let us develop an intuition of the order of accuracy of a numerical method with our harmonic oscillator problem. We pick the Euler-A method, and the literature tells us that this is a first-order method. Can we verify this?\n", + "\n", + "First of all, taking the log on both sides of equation (1) above and rearraging gives us\n", + "\n", + "$$\\frac{\\log(\\Vert u_h - u \\Vert)}{\\log( h )} \\sim n.$$\n", + "\n", + "Let's try to code this up..." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b22e2831-6fbe-4a25-aaed-88efcd3e5ba1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1e-05, 0.0001, 0.001, 0.01, 0.1]\n", + "\n", + "\n", + "[1.21732153 1.12041156 1.15050957 1.20061426 1.29994154 1.5797836 ]\n", + "[1.0, 10.0, 100.0, 1000.0, 10000.0, 100000.0]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# First, we need a set of time-step sizes (dt) to test our problem.\n", + "# Now we note that the dts array is a Python list.\n", + "dts = [0.000001,0.00001,0.0001,0.001,0.01,0.1]\n", + "dts_new = [(10**(n-5)) for n in range(5)]\n", + "print(dts_new)\n", + "\n", + "# Then we want to code a function for the Euler-B method,\n", + "# so that we can reuse the code for each dt.\n", + "def euler_b(xb,vb,dt,Nt):\n", + " for idx in range(Nt):\n", + " vb[idx+1] = vb[idx] - dt * xb[idx]\n", + " xb[idx+1] = xb[idx] + dt * vb[idx+1]\n", + " \n", + " energy = 0.5 * xb**2 + 0.5 * vb**2\n", + " return xb, vb, energy\n", + "\n", + "# Now let's define the number of time steps and\n", + "# an array to store our results.\n", + "err = []\n", + "Nt = 100000\n", + "\n", + "# a for-loop to loop through the dt's\n", + "for dt in dts:\n", + " # and for each dt, we have to redefine the \n", + " # solution arrays and the initial condition.\n", + " xb = np.zeros((Nt+1))\n", + " vb = np.zeros((Nt+1))\n", + " vb[0] = 1.0\n", + " \n", + " # Because dt changes, recompute the time\n", + " t = np.arange(Nt+1)*dt\n", + "\n", + " # and we also recompute the exact solutions\n", + " xth = np.sin(t)\n", + " vth = np.cos(t)\n", + " eth = 0.5*xth**2 + 0.5*vth**2\n", + " \n", + " # we obtain the solution for the \n", + " _, _, energy = euler_b(xb,vb,dt,Nt)\n", + " \n", + " # to compute the error in the numerical solution,\n", + " # we use the max. norm.\n", + " err_in_energy = np.abs(energy - eth).max()\n", + " \n", + " # we store the error we computed\n", + " err.append(err_in_energy)\n", + " \n", + "# note that both dts and err are Python lists.\n", + "print(type(dts))\n", + "# but let's do something cool...\n", + "print(type(np.log(dts)))\n", + "\n", + "# now we can compute equation (2) above to obtain\n", + "# as estimate for n.\n", + "print(np.log(err) / np.log(dts))\n", + "\n", + "# what does first-order convergence actually means?\n", + "# let's implement our theoretical understanding.\n", + "err_th = [ (10**expn)**1.0 for expn in range(len(dts)) ]\n", + "print(err_th)\n", + "# we can do better...\n", + "err_th = np.array(err_th) * err[0]\n", + "\n", + "plt.figure()\n", + "plt.loglog(dts, err, '-o', label='order of convergence of the Euler-B method')\n", + "plt.loglog(dts, err_th, '--', label='theoretical 1st. order convergence')\n", + "plt.loglog()\n", + "plt.ylabel(r\"log(error in the energy)\")\n", + "plt.xlabel(r\"log(time step-size $\\Delta t$)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "881a8a2e-9b0a-44fe-9f15-01e562751c34", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "456 µs ± 2.87 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "a = []\n", + "for i in range(10000):\n", + " a.append(i)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "f8d6a25e-7fa2-4580-ac3a-0156ce4f3821", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.78 ms ± 158 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "b = np.array([])\n", + "for i in range(1000):\n", + " b = np.append(b, i)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "1f9c3920-7f77-4b35-a90e-610e08857dc4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "721 µs ± 9.95 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "b = np.zeros((10000))\n", + "for i in range(10000):\n", + " b[i] = i" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "0cda045f-1361-42a2-8b77-ce7820b31eea", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "307 µs ± 15.9 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "b = [0] * 10000\n", + "for i in range(10000):\n", + " b[i] = i" + ] + }, + { + "cell_type": "markdown", + "id": "95d9bcf4-bcd8-46c1-8652-1b030af8e6ee", + "metadata": {}, + "source": [ + "## Local vs global truncation error\n", + "\n", + "Quoting [Wikipedia](https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)) as usual, \n", + "\n", + "\"Truncation errors in numerical integration are of two kinds:\"\n", + " - local truncation errors – the error caused by one iteration, and\n", + " - global truncation errors – the cumulative error caused by many iterations.\n", + "\n", + "Above, we computed the global truncation error which is normally what gives us the order of a numerical method. However, let's repeat our experiment with fewer number of time-steps, say 10. What happens now? " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "372c62b0-abe9-4983-bbfd-94dcfa80d728", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "d7faf198-0c15-4c09-a599-abfce5f8063c", + "metadata": {}, + "source": [ + "## Exercise 1\n", + "1. Do a error convergence study for the Störmer-Verlet method. Try with say 100,000 time-steps. Do your results verify that the method is indeed second-order?\n", + "2. Re-run the study with 10 time-steps. Now what is the order of convergence? Can you explain why? (Hint: This [Wikipedia page](https://en.wikipedia.org/wiki/Verlet_integration#Error_terms) may be helpful.)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "541fdf00-5fd2-47e3-8c0e-3d87445cd58c", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w3/orders_and_erros_soln b/w3/orders_and_erros_soln new file mode 100644 index 0000000..86841da --- /dev/null +++ b/w3/orders_and_erros_soln @@ -0,0 +1,62 @@ +# First, we need a set of time-step sizes (dt) to test our problem. +# Now we note that the dts array is a Python list. +dts = [0.00001,0.0001,0.001,0.01,0.1] +dts_new = [(10**(n-5)) for n in range(5)] +print(dts_new) + +# Then we want to code a function for the Euler-B method, +# so that we can reuse the code for each dt. +def euler_b(xb,vb,dt,Nt): + for idx in range(Nt): + vb[idx+1] = vb[idx] - dt * xb[idx] + xb[idx+1] = xb[idx] + dt * vb[idx+1] + + energy = 0.5 * xb**2 + 0.5 * vb**2 + return xb, vb, energy + +# Now let's define the number of time steps and +# an array to store our results. +err = [] +Nt = 10000 + +# a for-loop to loop through the dt's +for dt in dts: + # and for each dt, we have to redefine the + # solution arrays and the initial condition. + xb = np.zeros((Nt+1)) + vb = np.zeros((Nt+1)) + vb[0] = 1.0 + + # Because dt changes, recompute the time + t = np.arange(Nt+1)*dt + + # and we also recompute the exact solutions + xth = np.sin(t) + vth = np.cos(t) + eth = 0.5*xth**2 + 0.5*vth**2 + + # we obtain the solution for the + _, _, energy = euler_b(xb,vb,dt,Nt) + + # to compute the error in the numerical solution, + # we use the max. norm. + err_in_energy = np.abs(energy - eth).max() + + # we store the error we computed + err.append(err_in_energy) + +# note that both dts and err are Python lists. +print(type(dts)) +# but let's do something cool... +print(type(np.log(dts))) + +# now we can compute equation (2) above to obtain +# as estimate for n. +print(np.log(err) / np.log(dts)) + +# what does first-order convergence actually means? +# let's implement our theoretical understanding. +err_th = [ (10**expn)**1.0 for expn in range(len(dts)) ] +print(err_th) +# we can do better... +err_th = np.array(err_th) * err[0] diff --git a/w4/good_practices.ipynb b/w4/good_practices.ipynb new file mode 100644 index 0000000..76eeb3a --- /dev/null +++ b/w4/good_practices.ipynb @@ -0,0 +1,700 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "50035589-4f81-4796-9184-5c66804b88cb", + "metadata": {}, + "source": [ + "# Tutorial 5\n", + "Let's first import some libraries..." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "539bb281-c836-4451-b5a0-3637aea6b65e", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "3b588e69-48f2-491c-9dab-e2d350abb27e", + "metadata": {}, + "source": [ + "## 1. Preallocate arrays\n", + "\n", + "For large arrays, it is more efficient to preallocate your arrays than to change its size on the fly. In other words, we want to avoid \"append\". Let's take a closer look..." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "04fdcd52-fa84-40c3-bfd9-18e53a485062", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "49.4 µs ± 1.93 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "# we initialise an empty Python list\n", + "A = [] \n", + "for i in range(1000):\n", + " # we append 1000 elements in the array\n", + " A.append(i)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "26fd4f5f-94d6-47b2-a3e3-223852fbcc51", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.71 ms ± 97.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "# now we append to a numpy array...\n", + "B = np.zeros((0))\n", + "for i in range(1000):\n", + " # note that the Python list.append() will not work for numpy arrays!\n", + " B = np.append(B,i)" + ] + }, + { + "cell_type": "markdown", + "id": "0710f27d-223c-456a-afe9-837e3185f6e1", + "metadata": {}, + "source": [ + "Now let's how much faster it is if we were to preallocate the array:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "6789ac17-ea7f-4087-bb5a-aa6a2327f86e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "28.2 µs ± 363 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "# this is how we preallocate an pure Python list\n", + "C = [0]*1000\n", + "for i in range(1000):\n", + " C[i] = i" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a3c4c7f4-096b-4e58-90bb-8fe0019b4fe8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "77.3 µs ± 2.96 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "D = np.zeros((1000))\n", + "for i in range(1000):\n", + " D[i] = i" + ] + }, + { + "cell_type": "markdown", + "id": "9f04e1ba-15ae-46cc-88a7-13d732423ebe", + "metadata": {}, + "source": [ + "We get a speed-up of **2 times** for the normal Python list, and a speed-up of **48 times** for the numpy array!" + ] + }, + { + "cell_type": "markdown", + "id": "7c24af46-9ee0-4173-85fe-91415b8eedc4", + "metadata": {}, + "source": [ + "-----" + ] + }, + { + "cell_type": "markdown", + "id": "a05355e1-edec-4d47-aea8-e2dcea907658", + "metadata": {}, + "source": [ + "## 2. Careful iteration through a for-loop" + ] + }, + { + "cell_type": "markdown", + "id": "70fa1365-6b7d-41e7-b1dc-7496d97e8ad7", + "metadata": {}, + "source": [ + "We should try to \n", + "\n", + " 1. loop through the most relevant axis of the array,\n", + " 2. use enumerate when needed, and\n", + " 3. use numpy functions, e.g. sum() as much as possible:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "c10d08ca-323f-48d6-b798-1ee636ee8237", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.02 ms ± 28.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "np.random.seed(555)\n", + "A = np.random.random((1000,5,5))\n", + "B = np.zeros((1000))\n", + "for idx, a in enumerate(A):\n", + " B[idx] = a.sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "1fc23ae0-af3b-4335-b3cc-2ed4af0d97ea", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.51 ms ± 19.3 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "np.random.seed(555)\n", + "A = np.random.random((1000,5,5))\n", + "B = np.zeros((1000))\n", + "for idx in range(1000):\n", + " b = 0\n", + " for i in range(5):\n", + " for j in range(5):\n", + " # this is equivalent to b = b + A[idx,i,j]\n", + " b += A[idx,i,j] \n", + " B[idx] = b" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b5180fe1-8026-406a-8b75-cd1f724d52e4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "152 µs ± 5.59 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit\n", + "np.random.seed(555)\n", + "A = np.random.random((1000,5,5))\n", + "B = np.zeros((1000))\n", + "B[...] = A.sum(axis=(1,2))" + ] + }, + { + "cell_type": "markdown", + "id": "9fbd1233-c9ab-448b-ae41-3de16a495d24", + "metadata": {}, + "source": [ + "-----" + ] + }, + { + "cell_type": "markdown", + "id": "fc1bfe30-e3e6-40eb-aa02-69f3c8750344", + "metadata": {}, + "source": [ + "## 3. Computer precision\n", + "Numbers in a computer are stored as, for example, `int` (integers) or `float` (decimal point numbers). The implication of this is that there is a finite precision of how a computer can store, compute, and process numbers. \n", + "\n", + "See [floating-point arithmetic](https://en.wikipedia.org/wiki/Floating-point_arithmetic) for more details." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "08c9d3a5-c1de-4b98-bf7c-d8b9932edd17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Type of a random number = \n", + "Random number is 0.206334907384653\n", + "Precision of a 'float' is 15\n", + "\n", + "We obtained a string 9146690504665504194393334 of length 25\n", + "Converting the string to float: 9.146690504665504e+24\n" + ] + } + ], + "source": [ + "# Let's draw a random number and check what is its type:\n", + "A = np.random.random()\n", + "print(\"Type of a random number =\", type(A))\n", + "print(\"Random number is\", A)\n", + "\n", + "# Now let's check the precision of a float\n", + "print(\"Precision of a 'float' is\", np.finfo(float).precision)\n", + "# This means that a float is only able to store up to 15 decimal places accurately.\n", + "\n", + "print(\"\")\n", + "\n", + "# Let's artifically create a very long number by\n", + "# first creating a string of text...\n", + "string = ''\n", + "np.random.seed(555)\n", + "for _ in range(25):\n", + " string = string + str(np.random.randint(0,10))\n", + " \n", + "# Now we print the string and its length:\n", + "print(\"We obtained a string %s of length %i\" %(string,len(string)))\n", + "\n", + "# Now we convert the string to a float:\n", + "print(\"Converting the string to float:\", float(string))" + ] + }, + { + "cell_type": "markdown", + "id": "e10be6e9-8f15-472a-95d7-fd36739ea3a5", + "metadata": {}, + "source": [ + "You can see that everything after the 15th decimal place have been truncated, i.e. lost, because the precision of a float on a computer is only up to 15 decimal places!\n", + "\n", + "There are \"more precise\" floating-point number types but we should generally avoid them, e.g. numpy's `long double`. See [Numpy's data types page](https://numpy.org/doc/stable/user/basics.types.html) for more details." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "97c8cd75-0494-4aec-84d9-ebd6e5484fb4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Precision of a 'long double' is 18\n", + "9.1466905046655041945e+24\n" + ] + } + ], + "source": [ + "print(\"Precision of a 'long double' is\", np.finfo(np.longdouble).precision)\n", + "\n", + "# With a long double, we have gained 4 decimal places of precision!\n", + "print(np.longdouble(string))" + ] + }, + { + "cell_type": "markdown", + "id": "b501d32f-e6fb-4e14-9aea-6b3c3cfe1ffb", + "metadata": {}, + "source": [ + "-----" + ] + }, + { + "cell_type": "markdown", + "id": "7dfd39a8-2d86-4190-a60e-649c727b9190", + "metadata": {}, + "source": [ + "## 4. Numpy broadcasting, slicing, and vectorisation\n", + "\n", + "These are three big topics, and I encourage you to read up on it on your own.\n", + "\n", + "Here, we look at them briefly, and we will be using more examples through the tutorial." + ] + }, + { + "cell_type": "markdown", + "id": "e69eb0e2-f99b-4c52-b860-b6a4d00d0a7e", + "metadata": {}, + "source": [ + "### 4.1: Broadcasting\n", + "\n", + "We have already seen this in the computation of the kinetic and potential energy of the simple harmonic oscillator. Basically, numpy allows us to do element-wise operations on arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "da1c3848-0e27-42f5-8a11-d68992b0d28d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.23976742 0.03450459 0.14859311 0.81086617 0.65310538 0.54446869\n", + " 0.04119477 0.46816625 0.88874673 0.47625856]\n", + "[0.47953484 0.06900918 0.29718623 1.62173235 1.30621075 1.08893737\n", + " 0.08238953 0.9363325 1.77749347 0.95251711]\n" + ] + } + ], + "source": [ + "np.random.seed(555)\n", + "A = np.random.random((10,10))\n", + "print(A[1])\n", + "\n", + "# this is equivalent to A = A * 2.0\n", + "A *= 2.0\n", + "print(A[1])" + ] + }, + { + "cell_type": "markdown", + "id": "50788210-85dc-4466-8165-ffac5e5bbc05", + "metadata": {}, + "source": [ + "### 4.2: Slicing\n", + "Slicing are fancy ways of indexing an array in Python. Normally, how you would index is `a = A[5,5]`.\n", + "\n", + "Let's take a look at a few examples of slices:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "cc6086e2-a5ba-466e-8e54-c55fb11edd0c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A.shape = (12, 12)\n", + "B.shape = (10, 10)\n", + "C.shape = (10, 12)\n", + "D.shape = (4, 5, 6, 7, 8)\n", + "E.shape = (4, 3, 6, 7, 8)\n", + "F.shape = (5, 5)\n", + "F = 0.0\n", + "G = \n", + " [[0 0 0 0 0]\n", + " [0 0 0 0 0]\n", + " [0 0 0 0 0]\n", + " [0 0 0 0 0]\n", + " [0 0 0 0 0]]\n" + ] + } + ], + "source": [ + "# A is a 12x12 array\n", + "A = np.arange(144).reshape(12,12)\n", + "print(\"A.shape = \", A.shape)\n", + "\n", + "# Now let's say we want to access only access the middle 10 elements:\n", + "B = A[1:-1,1:-1]\n", + "# The comand in the square brackets says: \n", + "# let's take all elements not including the first element \n", + "# and not including last element in both the x and y directions.\n", + "print(\"B.shape = \", B.shape)\n", + "\n", + "# This says: let's only take all elements not including \n", + "# the first element and not including last element in\n", + "# the x-direction; leave the y-axis alone.\n", + "C = A[1:-1,:]\n", + "print(\"C.shape = \", C.shape)\n", + "\n", + "# Let's define a high-dimensional array\n", + "D = np.arange(6720).reshape(4,5,6,7,8)\n", + "print(\"D.shape = \", D.shape)\n", + "\n", + "# But let's pretend that we do not know the shape of \n", + "# the array, except that the the first two axes are\n", + "# the grid that we want to remove the last two indices\n", + "# off the second axis:\n", + "E = D[:,:-2,...]\n", + "print(\"E.shape = \", E.shape)\n", + "\n", + "# The three dots are Python ellipsis and they can be used\n", + "# in a few tricks...\n", + "F = np.arange(25).reshape(5,5)\n", + "print(\"F.shape = \", F.shape)\n", + "\n", + "F = 0.0\n", + "# We have set F from a 5x5 array to a float that is zero!\n", + "print(\"F = \", F)\n", + "\n", + "G = np.arange(25).reshape(5,5)\n", + "# print(\"G = \\n\", G)\n", + "# But with the ellipses, we can set *all* elements to zero instead.\n", + "G[...] = 0.0\n", + "print(\"G = \\n\", G)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4f4f37a8-484a-49c5-9635-4e364535d315", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "original shape of J = \n", + " (5, 5, 5)\n", + "shape after improper assignment of J = \n", + " (6, 5, 5)\n", + "original shape of K = \n", + " (5, 5, 5)\n" + ] + }, + { + "ename": "ValueError", + "evalue": "could not broadcast input array from shape (6,5,5) into shape (5,5,5)", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0mK\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"original shape of K = \\n\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m \u001b[0mK\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m...\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mI\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mValueError\u001b[0m: could not broadcast input array from shape (6,5,5) into shape (5,5,5)" + ] + } + ], + "source": [ + "# Ellipsis can also be used as an implicit assert statement\n", + "# to make sure that we do not change the size of our\n", + "# arrays unwittingly\n", + "H = np.arange(125).reshape(5,5,5)\n", + "I = np.arange(150).reshape(6,5,5)\n", + "\n", + "# We want to preserve the (5,5,5) structure, but make H\n", + "# an array that is 5 times of I:\n", + "J = np.copy(H)\n", + "print(\"original shape of J = \\n\", J.shape)\n", + "J = I\n", + "print(\"shape after improper assignment of J = \\n\", J.shape)\n", + "\n", + "# But with the ellipsis, we implicitly assert that the shape\n", + "# of the array cannot be changed!\n", + "K = np.copy(H)\n", + "print(\"original shape of K = \\n\", K.shape)\n", + "K[...] = I" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "dc1a4789-8772-4eb2-8126-26d7da787d6b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A.shape = (12, 12)\n", + "B.shape = (10, 10)\n", + "C.shape = (10, 10)\n", + "Our dimension-free slicer is (slice(1, -1, None), slice(1, -1, None), slice(1, -1, None), slice(1, -1, None), slice(1, -1, None))\n", + "E.shape = (2, 3, 4, 5, 6)\n" + ] + } + ], + "source": [ + "# Let us take a short look into slice functions...\n", + "# We have seen this before.\n", + "A = np.arange(144).reshape(12,12)\n", + "print(\"A.shape = \", A.shape)\n", + "B = A[1:-1,1:-1]\n", + "print(\"B.shape = \", B.shape)\n", + "\n", + "# this is equivalent to the indexing we saw before...\n", + "slc = (slice(1,-1),slice(1,-1))\n", + "C = A[slc]\n", + "print(\"C.shape = \", C.shape)\n", + "\n", + "# A nice thing about the slice function is dimension-free slicing:\n", + "D = np.arange(6720).reshape(4,5,6,7,8)\n", + "\n", + "# slc_dfree = []\n", + "# for _ in range(D.ndim):\n", + "# slc_dfree.append(slice(1,-1))\n", + "# slc_dfree = tuple(slc_dfree)\n", + "\n", + "slc_dfree = tuple([slice(1,-1)]*D.ndim)\n", + "\n", + "print(\"Our dimension-free slicer is\", slc_dfree)\n", + "# How does it work then?\n", + "E = D[slc_dfree]\n", + "print(\"E.shape = \", E.shape)" + ] + }, + { + "cell_type": "markdown", + "id": "08ccb48b-195b-41ff-85bc-7980dc68a7e1", + "metadata": {}, + "source": [ + "### 4.3: Vectorisation\n", + "We have since broadcasting in action... Can we broadcast arrays with different shapes to do some computations?" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "762d071e-9386-45c5-a247-ad5a18e98624", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Set x-extent\n", + "xmin = -4\n", + "xmax = +4\n", + "# Set spatial step-size\n", + "dx = 0.1\n", + "# Set x-grid\n", + "xh = np.arange(xmin,xmax+dx,dx)\n", + "\n", + "# Now, we define a 1D Gaussian function...\n", + "x = np.exp(-xh**2)\n", + "\n", + "plt.figure()\n", + "plt.plot(xh, x)\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "ddf81406-7bfd-4b8f-be09-dd768c3d00a6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x.shape = (81,)\n", + "X.shape = (81, 1)\n", + "Y.shape = (1, 81)\n", + "Z.shape = (81, 81)\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Now we want to define a 2D Gaussian...\n", + "# We want a 2D array with all the elements to be on the first axis\n", + "print(\"x.shape = \", x.shape)\n", + "\n", + "X = x.reshape(-1,1)\n", + "print(\"X.shape = \", X.shape)\n", + "\n", + "# Then we define a second vector with all the elements on the second\n", + "# axis\n", + "Y = x.reshape(1,-1)\n", + "print(\"Y.shape = \", Y.shape)\n", + "\n", + "# Then we broadcast the arrays together:\n", + "Z = X * Y\n", + "print(\"Z.shape =\", Z.shape)\n", + "\n", + "plt.figure()\n", + "plt.imshow(Z, origin='lower')\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9fe288af-2ee2-4b47-b42d-906fec8bfc28", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w4/heat_eqn.ipynb b/w4/heat_eqn.ipynb new file mode 100644 index 0000000..7a61de6 --- /dev/null +++ b/w4/heat_eqn.ipynb @@ -0,0 +1,179 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "41fb1c47-8b94-4d49-9b50-613498b24e46", + "metadata": {}, + "source": [ + "# Tutorial 5\n", + "\n", + "## Exercise 2: The 2D heat equation" + ] + }, + { + "cell_type": "markdown", + "id": "81db7972-06b7-4332-89d3-687596dd9bee", + "metadata": {}, + "source": [ + "Let's import some libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "5c60ef8a-3412-40ff-8e18-46092323a0dd", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "id": "cd7acfb6-e9cc-4d8c-a463-28b391ddc906", + "metadata": {}, + "source": [ + "We want to solve the 2D heat equation:\n", + " $$ \\frac{\\partial}{\\partial t} u(t,x,y) = \\Delta u(t,x,y). \\tag{1}$$\n", + " \n", + "This is a [partial differential equation](https://en.wikipedia.org/wiki/Partial_differential_equation), since $u$ is dependent on both time $t$ and the spatial variables $(x,y)$ and $u$ has a first-order derivative w.r.t $t$ on the left-hand side, and a second-order derivative w.r.t $(x,y)$ on the right.\n", + "\n", + "When we worked on our oscillator problem, we only had one first-order derivative w.r.t $t$ and in this case, we needed only an *initial condition*. Now as we are dealing with spatial derivatives, we also need a set of *boundary conditions* and a *spatial grid*.\n", + "\n", + "For the initial condition, we take\n", + "$$ u^0 = \\exp(-r^2), $$\n", + "where $r = \\sqrt{x^2 + y^2}$.\n", + "\n", + "To define the spatial grid, we take $x \\in [-4,4]$ and $y \\in [-4,4]$. Finally, we say that $u$ is periodic both $x$ and $y$.\n", + "\n", + "### The 1D problem\n", + "In 1D, the problem is somewhat easier:\n", + " $$ \\frac{\\partial}{\\partial t} u(t,x,y) = \\frac{\\partial^2 }{\\partial x^2} u(t,x,y), \\tag{2} $$\n", + " $$ u^0 = \\exp(-x^2), $$\n", + "with $x \\in [-4,4]$, so we first try to deal with this 1D problem. \n", + "\n", + "We learnt how to discretise a problem in time. Now let's apply what we learnt:\n", + "1. Can you discretise the left-hand side of equation (2) with the [explicit midpoint method](https://en.wikipedia.org/wiki/Midpoint_method)?\n", + "2. We want second-order schemes in both time and space. The explicit midpoint method is a second-order time-integrator. We want to use the second-order [central difference method](https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences) for spatial discretisation. Can you discretise the right-hand side of (2) with this method?\n", + "3. Now what are the components that you need to implement this problem? (List them out)\n", + "4. Implement the components... see what works and what doesn't.\n", + "\n", + "**Try to use slicing, broadcasting, and vectorisation as you code!**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d2deeb5e-f74a-4185-9c6c-42e964139ec6", + "metadata": {}, + "outputs": [], + "source": [ + "# spatial step-size\n", + "dx = 0.1\n", + "# temporal step-size\n", + "dt = 0.001\n", + "# simulation end time\n", + "T = 1.0\n", + "# the time axis\n", + "t = np.arange(0.0,T+dt,dt)\n", + "\n", + "# your code here:\n", + "# ...\n", + "\n", + "# Here is a code to check if you initialised the initial condition correctly.\n", + "plt.figure()\n", + "plt.imshow(z, origin='lower')\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "92fdb634-5854-4b75-a716-84e575199d8d", + "metadata": {}, + "source": [ + "### The 2D problem\n", + "Now that we have the 1D solution of the heat equation, \n", + "1. Can you discretise the right-hand of (1) in 2D? Hint: You will obtain the famous [5-point stencil](https://en.wikipedia.org/wiki/Five-point_stencil) for the [Laplace operator](https://en.wikipedia.org/wiki/Laplace_operator).\n", + "2. Now, the challenge is to solve the 2D heat equation by changing your 1D code *as little as possible*. Can you do that?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "71c2dabe-9b36-4c84-9b30-bae2edfc97cb", + "metadata": {}, + "outputs": [], + "source": [ + "# your code here\n", + "# ..." + ] + }, + { + "cell_type": "markdown", + "id": "0ce75ca5-068b-4220-98cb-835e6d6d9ae8", + "metadata": {}, + "source": [ + "Below is a code snippet that saves your solution as an animation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dbc0ceea-178a-4d95-b9f5-8f81cfbe05c9", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.animation as animation\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "X,Y = np.meshgrid(xh,xh)\n", + "plot = [ax.plot_surface(X, Y, sol[0,:,:], color='1.0', rstride=1, cstride=1, cmap=\"magma\")]\n", + "\n", + "def update_plot(i, sol, plot):\n", + " plot[0].remove()\n", + " plot[0] = ax.plot_surface(X, Y, sol[i,:,:], cmap=\"magma\")\n", + "\n", + "ax.set_zlim(0,1.1)\n", + "ani = animation.FuncAnimation(fig, update_plot, 2001, fargs=(sol, plot), interval=1)\n", + "ani.save('heat_eqn_soln.mp4', fps=30, extra_args=['-vcodec', 'libx264'])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1b42d56a-3920-4325-8e81-21a86e126829", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w4/heat_eqn_soln.ipynb b/w4/heat_eqn_soln.ipynb new file mode 100644 index 0000000..7d72e41 --- /dev/null +++ b/w4/heat_eqn_soln.ipynb @@ -0,0 +1,16562 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "41fb1c47-8b94-4d49-9b50-613498b24e46", + "metadata": {}, + "source": [ + "# Tutorial 5\n", + "\n", + "## Exercise 2: The 2D heat equation" + ] + }, + { + "cell_type": "markdown", + "id": "81db7972-06b7-4332-89d3-687596dd9bee", + "metadata": {}, + "source": [ + "Let's import some libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "5c60ef8a-3412-40ff-8e18-46092323a0dd", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "id": "cd7acfb6-e9cc-4d8c-a463-28b391ddc906", + "metadata": {}, + "source": [ + "We want to solve the 2D heat equation:\n", + " $$ \\frac{\\partial}{\\partial t} u(t,x,y) = \\Delta u(t,x,y). \\tag{1}$$\n", + " \n", + "This is a [partial differential equation](https://en.wikipedia.org/wiki/Partial_differential_equation), since $u$ is dependent on both time $t$ and the spatial variables $(x,y)$ and $u$ has a first-order derivative w.r.t $t$ on the left-hand side, and a second-order derivative w.r.t $(x,y)$ on the right.\n", + "\n", + "When we worked on our oscillator problem, we only had one first-order derivative w.r.t $t$ and in this case, we needed only an *initial condition*. Now as we are dealing with spatial derivatives, we also need a set of *boundary conditions* and a *spatial grid*.\n", + "\n", + "For the initial condition, we take\n", + "$$ u^0 = \\exp(-r^2), $$\n", + "where $r = \\sqrt{x^2 + y^2}$.\n", + "\n", + "To define the spatial grid, we take $x \\in [-4,4]$ and $y \\in [-4,4]$. Finally, we say that $u$ is periodic both $x$ and $y$.\n", + "\n", + "### The 1D problem\n", + "In 1D, the problem is somewhat easier:\n", + " $$ \\frac{\\partial}{\\partial t} u(t,x) = \\frac{\\partial^2 }{\\partial x^2} u(t,x), \\tag{2} $$\n", + " $$ u^0 = \\exp(-x^2), $$\n", + "with $x \\in [-4,4]$, so we first try to deal with this 1D problem. \n", + "\n", + "We learnt how to discretise a problem in time. Now let's apply what we learnt:\n", + "1. Can you discretise the left-hand side of equation (2) with the [explicit midpoint method](https://en.wikipedia.org/wiki/Midpoint_method)?\n", + "2. We want second-order schemes in both time and space. The explicit midpoint method is a second-order time-integrator. We want to use the second-order [central difference method](https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences) for spatial discretisation. Can you discretise the right-hand side of (2) with this method?\n", + "3. Now what are the components that you need to implement this problem? (List them out)\n", + "4. Implement the components... see what works and what doesn't.\n", + "\n", + "**Try to use slicing, broadcasting, and vectorisation as you code!**" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "id": "d2deeb5e-f74a-4185-9c6c-42e964139ec6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1.26641655e-14 2.79041771e-14 6.02665001e-14 ... 6.02665001e-14\n", + " 2.79041771e-14 1.26641655e-14]\n", + " [2.79041771e-14 6.14839641e-14 1.32790991e-13 ... 1.32790991e-13\n", + " 6.14839641e-14 2.79041771e-14]\n", + " [6.02665001e-14 1.32790991e-13 2.86797501e-13 ... 2.86797501e-13\n", + " 1.32790991e-13 6.02665001e-14]\n", + " ...\n", + " [6.02665001e-14 1.32790991e-13 2.86797501e-13 ... 2.86797501e-13\n", + " 1.32790991e-13 6.02665001e-14]\n", + " [2.79041771e-14 6.14839641e-14 1.32790991e-13 ... 1.32790991e-13\n", + " 6.14839641e-14 2.79041771e-14]\n", + " [1.26641655e-14 2.79041771e-14 6.02665001e-14 ... 6.02665001e-14\n", + " 2.79041771e-14 1.26641655e-14]]\n" + ] + }, + { + "data": { + "image/png": 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WVZEgSHJe4qOwBa/tujq6LKlcbFVUcC5E0fGpZVEVap9TZ4j4pqRCoBG2aLsGEvadxL3Qb2k013U0zkSrooh8EXie+NdTq+qdInIz8EvAq4AvAj+sql89mdPcIYbqtfrdfEoHlZfL7fq1WL0kfCNipctyWbyy25LGXcXnKFRhkoTL9YUrHroc2C+Hi2XRqYSUn9eYZJfkwsQRhUmI7kukGSTCKYBDgqKVIDiUEN2XJwp0WahaJu1zvZdKm7AnJfKbe+XafFd5z+eEytzYGOJXcQaEK/E9qvpcsXw/8IiqvktE7k/L52sm60X1Tvntfm6rP54WtDmr9H6n9TCLVjWQhC/yWVqlfJcTwjQ6rjB1UbAEwrQNDbVqxUpzH+nswgrH1f27ldZ1aSFWTY6rFTF1RCcWFGZpR05xs4BqEjNRxJNaHBWtQSqNglelnFdutnQp2Z9bG11xcjqQ78ohY/EdLO0SZK5rkLNcDnEP8Ib0+gHg45wn4TpCiDhfypAEqiwuzXVaVdWK1KRqttfpJLqnqmpCxDBxUAmhcoRp3E+YCDppXVZ0WMTXTahI4b6Keq6eeJWilVsTo3ClvJenES5X07ynVez6o3VqKFBFneB8QL3gnDQhI0mXhHQeqmmkiSSO0NZ5pYJVEbWQ8YTY9tsxVrgU+HURUeB/T7NT36KqTwOkSWFfMfRBEbkPuA/gAhc3cMo7SD+vlZ7n3FdZp1WGh+VyykflELHTgihtol2rwkk5CDmn5QqhqlIEllsck2i1NV3xqew/HcUrip+ItqImQIjHFNFojJIYOo2J+zykTa7liueeEv4hOrNuWCgdh9XUealvb1luTfW+GzJafdeRUYRwRloVv1tVn0ri9DER+b2xB0gidxngJXLzufhLmnNbcxsUoWF+7ue1UliolYsOo3Koc9FpOdCJa53WxEUnVUkTFoYJjdOK72XHlQSsSqFi4bjKcLEfKbS1WzStix3H5WPoGB2XEHwsP4uJdJJYKTnX5VwSN9V2VuJAW7DqJVXl5w7cVTffVYaM2bUN2QTLax2Jbf+hjp1X8an0/KyI/ArwWuAZEbk1ua1bgWdP8Dy3nyRSS2u2+iFi/txQgWkWLec6rYdleKjTWJ/l9xwkgfJ7Ufz8tBCuaduKGKbEvFdFDCWzULnuMwyHihJ6zwpSg/PxAzojtTLSOqu8z7QfV4N30oSdgWQkU3chrdP9yqUSEN1YaoVs+jam/o2dDtlDifrie1ErmVjNhpPzInI38G5is/D7VPVdA9u8AfhZYAo8p6p/cdk+V/pBEbkkIjfl18BfAj4NPATcmza7F/jIyOvYfQZCvPltBnJbJWVlfLnfgRbEJhyUXniYSxhyC2EKGZuwMLmq+GiXwySJVpP3isvRpWnz0PQInUe7bRNy5uWBYzWCWXXPkU5ebfjaOq2o5T1Zdg+bWynt+hEtvasaWs4dOvKxAhGpgPcAbwReA7xVRF7T2+alwD8BflBV/3Pgzav2O8Zx3QL8SvrxTYD/Q1V/TUQeBR4UkbcBT4452JlgnT/wZTVbRUK+U69VtiBOUoI+uSytcp1WdFzZafk9lwQpOq7ssvw0CkSYtsISJkTHNSEKU3ZZOcfldK6eC2jDxFA853KIWnB13MZN4npXR/EiQFUpOkt9FNPxmu5AaV0TNgYFH/Nn8YSlLVBN6wRirixXvAa3OlE/9rvd9qz0dWKDjuu1wBOq+gUAEfkgsWHvM8U2PwJ8WFWfjMfWldHbSuFKB/z2gfVfBu4adernhEVh4sLZo7OAlWFk4zBcx4m0+a6cwxLa2qzockLVOqHSVYVpTs6nsNFp4YZAK+0IFwuES/vClcsgRJsyiCaMTKGhpFFsmryYB1IllzpBUMJEUgkFaOWiPhGgLobu6TRSpGR8MyGHNve2kZ28zcB3tHLE1HOOAiGMFq6Xi8hjxfLllNfO3AZ8qVi+Aryut4//DJiKyMeBm4B3q+ovLDuoVc4flxVhyOA8iK4IY1z5g0xhU+5j6KJQlcWloYp1WjHPlcKrRrSkEC5JIpVDwGRg9rQth5gmd1XF+qkoWIuFq2lR1ChamgYulZlE/U2DCYqnI1y5lVBCdlppuyRkLtD0oaxcW6RKFWL3oErRELv7NMn5fL98sS5oR7A6/RgtrzWe9D2P5DlVvXPJ+0M76v/PMQH+DNEI3QD8exH5TVX9D4t2asK1DmPCxCVTgXX6IvZrtsqEvMh8nVYqLm1aDfcEn177PWnEye+nUHGPRrj8vrbua1+j45ooJKfFJCDJabkqx4TtX1zzV6ZCSF171LvY8heAPUFqiWLmksuqoSqS8+1wNlGYNIWWUuWdx9ZGCa4pUnUpBMyFqCpFbVdVtYn67L5yX8bie1raj9FquhaywVtwBXhlsXw78NTANs+p6gvACyLyG8Qob6FwbXexxnlhqEsPFAnq5EhcsZyT2mVdVlmf1X+4lNOqNLbtOCCJl1SKmyhuEnCVp6pCfEx8fKRlV/m4zUSRSYjCN0niV7X7X3oOvUfjMIXOtbbjhPUS9TCYjDc2zIaS88CjwB0i8moR2QPeQmzYK/kI8F+KyERELhJDyc8u26k5ruMwYuiasuC0+UxyXW2FfBEiNkPVtPms2KUn9T9MNVlhAn5KU+KQ67bCXgoJp8lpJZcVJsSQcC92HpRpwE3jqA2Tqce5EGurJD4kPSAmalXjXHtBhRAE7x2+rmI+ZOLQmYMgBHHgwc3S5QbI3i3WekkTjkaHpimklPS+w2kskFCXRoUKEkeHUEWDK8a5r+L4XuUIEvg2Ob9g8EGbXGMVsrHkvKrWIvIO4KPE/zLfr6qPi8jb0/vvVdXPisivAZ8iJi3fp6qfXrZfE64NsLR7D8zntoYcVjPWlmtLA9LQNLnDdGgKTHM+K4qYn8buPWHa1mz5fU0ipjE8nChMAm7fIw6qiWeaBGtaeaZVQESZutAIl0vCFQrhmgWHqjDzjpmvCMExqyr8pEIDBJmATx27SUKVc1ouJ+5T5b3XNsEfwInGUHQiMW3lHdQhirhPYaLLIhWKe5dyXDHGjAWp/VxXL1y0JP0KNnhrVPVh4OHeuvf2lv8B8A/G7tOE6yRZ1JqYl8uRTzufo5usb17TPDrh1lC46FLrYW41rIqwUJSqioIlouxNfCNY08rjWCBcCM5XBI3delQFFSUEQYMQROJxiDmSOFChNl2N0PbcJJ+75pAxh4gaGyZCcQ98uidlI2ETNrpmgMLy3jZJ+UVDPhuLUdDxrYqnggnXWMYUncJ8/kXKJH0ueeiVPuS6raodV6sJESftEDVh2naYbloNK/B7NEWgfj+WOoT95LQqhf2Am3pcpexfmFG5wP605uJ0hohyw2TGnvNMnGfP+RQuBqokXF6FoI6gwmGoqEPFYah4cTJFVbg6mXIwmeCD4wAIXgizKpZo+fZ+tKEiKVRMtyJ1EZIAMo3JfwfoTIiFaIr4OIa9BIdqMfVZ/m5yaUQ57E0/0b6opsvCxQFMuM4nridsTZjoeoWpZdJdmlCxGVerKY+gcS5hoCK+qeHq1HFFl+X2YpJ9MgnsT2dMq8CFSc3F6SETF7g4OWTP1VSi3FDNcEThKh1XUEdAeNFP8SochgkTF6hTZ1wnysw7QhDqOq4LPoaEYdqWSIQJTWLXZUeWzt+RXJdLbi6Hm+k+lDVd6iSG6L4QombomwUCNRZrWdxoqHgSmHCdJMvKJ/oFp+X2jq5YSSta6srXeYwtus+T1NqXWv6cUyaTwGTim7DwwmTGxUkUrkvVIftVzUQ8+66OoSRd4fJEx5WGAORFr1HQXByfPIePs5RX0uAIKWyMdWIAqSuQL8JclRTSxvAuX1fMR6V7IZIGKuzdq05+MFW65tCy/A4WFKMaSzDhOgMsEaChkSDmEvNl7ZYrnEPptHLLYRkqNsLUFpuWHadzqBhyYn6vDQ91mhLxKTzcn87Ym3j+2P419irPjZMDbppeYyqBS5MDLrpDKglcdIcxTEyuCyCowxNd19Wwh0/PL1T7zNQxcYH9eo9DH4uyDqsK52LeSb0QdEJQh9RFK6PEWi9xMWR0NQSJXYfCJOXfK0lTLKZ7kqvpK9cM75wT820CPn0XLhWQpfzW0KQaSxP059l1rVeAeiqYcJ0mfaeVXse+gvNJec0Pl+u4eol4ic+xrkpTVKpULjCtAlMX2Ks8e65mv6rZdzVT8Vx0h1xws/T6oHFcVRIurw6PY5aGTM3PtXM4rbihmjUh49QFtBJqHx1bSKEfqZEghr5KrkGTXDWfyiKafpJCk6QXstmSNkm/6D8Tya2Yy+675bRWse2abcK1SRaNBFEw3Peum6inCRNpR3koi0vTcxgq8kwFoTIJTfHo/rTmwqTmwmTGjZMD9quamybXeNn0KlPx3Fhdi46LwCV30DiuqdQEXBKu6LhekH080XFBK2IAL/rAwWQSBUuFWV3hvcYSjtrRTNIRkqtKo9NIHo1V+9eZRK/Kzori3ulcA8cIyTp+/uu8YK2KZ5C5IVEGWhhTbqU7EkSxXVl02mldbBPysZaLNmwsc1l5PK2U08p9D3M1u5sGplPPtPJcnM64OD3k4uSQm6bX2Hc1L5te5WWTF5iK5yb3IpfcIVOpueQOmjAxtguS8ltRvC6GfWY64YLsMRXPQZg2l7TnaurgqOokanXFzFWpWDWGeTpVNOR8lsAEtKYZ/z7mwKRxkVQSh34WiaOllqG1F0Sl29hRFKN2RoygFy6a61qKbLm2m3BtCU3XFphriW5CxKa7D23o6LrPpJooJ4pzsai0coFJekwlMBXfecQwsWYvLVdkxxUT2jOt8BJwOPbSuj2p4vuOZj9BHE6USTqu5HPI19Q71zIsLPPuzXuZvJ3meyCdmYc2gglZy/juPKeGCdf1pl942oSHNC1o2Yl1EvSdRxwNopPjyv0GJwGplGoSC0z3Jp79qubi5JBL1WGTiL+xusZN7kX2xPMSd42L7oA9PBfdjCmxhqtqZjQUvAozHHt4DqkaATvUilma6/FqCFzyezhR6uC4Np0gdcXhxOMnDsU1LYzqo4MUba8pu7CmcDaFh+1gg8m0li2MRSGqFZpuiv7/HNuHCddJ0K/hatZ3k/Cd5/y6/JtpHEmRoM8/3PJ1Uz2viFNclSvjY0L+QjVrEvI5EX/RHXLJHXLBHcZQUWZMJXBBPGn8QXL2yqMEUWZp4L4LWoOLojXVCdf0kAMXQ8YbqhlehT3nm0R97KCtBA1xvC1XCLVrr0OLKvp4zTroyObotOIKDOmXCdt6mOM6uyzsWN1nwXaa1qvM/yrL//CaaQQlh5TMtzSWrXEpTKtSNx4nSiXKpAgP96RmKjUVmnJaikOZShz0uxJphg6pAK9RRKYamIljT33juipi+DmTCkc6VqrAj+FiGiqnEGYtxag5/9iFaNH1x5veTc63w+UM3PMRpVvWZ3EBW67xJlwnTTlQILSFp4vo1Hi1DqR1Iu1yk8DOD4luy6V8VpX6Hu45zw3VjH1XJ7d1wAWZcckdpBKIGZekZipwUYSpOCoEl6QrEPCN4wqN8zrkgKlWXHUHXNPsuA4JCAd+wrTysWg15bqoBC/5fIsQUeavLY/j1QwemF1nQlMrYue+ZVd1nmuwNsEO1HEtiGnmEZFKRD4pIr+alm8WkY+JyOfT88tO7jTPIEPiNbiufTk47+Gg26J1XIWbyn0QnWhKwit7eKaExmll0ZpK1TwceZ1L2xDzYLSFqlPxzb7nj6nJWemCcy6WF1z70nu0CBu368iIjnucFqOFC/gpuoN73Q88oqp3AI+kZWNdhkJEl19Lu67HYKvboBZmsWqFJheX5sr4Kk3gWol0nJZDcEgKG6N45RAyJ+9zzVe573y83LIo5V/4wLkuDAuLe7CUdcTMGMfmBhI8EUYJl4jcDvwV4H3F6nuAB9LrB4Af2uiZbSuLRoXoMzRT9cJtWZrjisuFiBU5r75YxVRROyxNzm85aR1XJQGXHFN2XnlQVIdjKhUTKipxVOKY0DqvnLTP5RJZBLMQDh2zEbD+dffcY5vLk3mxduW2MnjPhhj9HRg7xdgc188Cf5c4A0fmFlV9GiBNCvuKoQ+KyH3AfQAXuHj0MzW2FrftmVxjbba9AHWlfRCRHwCeVdXfOsoBVPWyqt6pqndO2T/KLraLsUWKA7MpL96WuWRy/w8nF1xKYdFlwK4rzA217MthlzV24Qm0/Q89gk+nEZp/iteA10CNL9bHxjqPpM86ZjqJ+0xjdvWPmc9n7m6UeZLitajO/3BCua0O3rMhRn8HRouShsse8Tglxjiu7wZ+UETeBFwAXiIi/xx4RkRuTW7rVmDlJI7GAAOClbUxjuwpaZ5B5rZr98HCnIM2gwBGoYoi5RqhQXwUGVG8amz101jLlf9f86qxZRFNr+Pggrn/YrNPpOkeFNS1gtVJYs2fqyx4ne/BSkycNs+W39KVjktVf1pVb1fVVxFn6PhXqvqjxJk67k2b3UucqcMYy9CPbXBd+zI7rNKl0H+d5j1UTeNkkZwPreMKKo3TOqRihsMrzICZRoGaqW8eWbRmGtI2xM/Qdr4u9z1/zHhOsXiruIbiMeQeB38864iU1WcdmW1vVTxOHde7gAdF5G3Ak8CbN3NKZ4ygMZudf3B59plFaLJXQUFTcaXSPDc/9JAfcXRRraCZ91AcdXCxm45Pwyz7KRPxXEudoi+4GS+EffbEs4encopTBReYqk+th7GCMzosZQa8kMTwaphyNexzqBUvhH2uhn2uhj0OwoQX/ZTDUDHzFbM0yGAILs3J2IYZefbqORHrX3PQdF/aX8qcE1NtK+PNgR2fLb+FawmXqn4c+Hh6/WXizLPnFg06rno+j8zZQ0Kaul517rfWD5+U/L+czjmX/NCO64qOq0pDzHgVaq2YaUWlgUOdMNMJlYSUr3JMJcSRkCUKVdvlJ4pXdlpBo1M71Crmt3KuTB21VvFYoWon2Qiy8Jy769rc1sLwsRQwVWSRqxrptqxqfgFbfluscv4kCCHOlzi3XtvgvPjxNSS3NRcK9sSK0n2F9iF5th0P3jtmPg7tcs1P2as8Bz4042hdDXtckD08wpQ4ykOlinczprq4k/XVMMUjXA37XNMp18KUq2GveT7wEw7DJDqu4NI49NFtaYizXXfPOTmr0HeVujqULO9beY8XfSfGKE47DByDCdf1pglpqtY9qKbwqXVfcTp6BaENqQI4DwHFeYm7kfTj92la+zrOguPrOO+hqnAwnXA1jZF1Q71P7RxVqna/pmnsLCoqlEPiKBFAZ1gbgEMqroZ9PMLz/ga+Fm5gphVf9xf4Wn2BgzDlBb/H1XqPF+spB7MJdXDUsyoOJOgFvLRzKXqKsFfT9WkRBsd7IOkeSW5NzC2KpfsKwULETWIDCRpjyD9OhUFnUYaJnSR9yhHlXFEOF3NeSUXxIea86uCYaRxueZYeANfCtBnxdKoVAYeTgE+tgeVAgjk8PCz2cS1M0+v2OE1JRnDtNfXOtQwX+2Uec//jN+/p5sfigvFlLucEc1xnEc3z9y1YhsZZqXOIhjg9fOwxHN8P8dcpQdtaI43zB1Ilt+EVRHBeCULjVCC6FamBCUgdZ9iRGqhj4jtM4gzTIcR5D+Mh43Azh1XdnOZUPLOq4poesic1V8N+rIhP1fVAM3zzTCuu6ZRDnXA17PF1f4GZVnytvsDz9QUO/ISvz/a5Vk+5OouOy3tHmDmYuShcM0nnnlxXna4lz6voC6cViLNdJ9clXjtOS3LSvgwPNc32o6mObpETM6FajgnXOSIn25d0M1FNXV/KHFfOfTVhI23OJ6Rp6l37w4b47DxJ0KJuSi1ILTEKrR2+rtAgnXHg9yrPYWjzb1PxeHUcuOnKyTKCxtxWdllfq6NwPV9f4PnZPodhwtVZnO3nYDahnlXRcc1czG35VqRc3V5DV7T6AkacOzF0RWtuWYv/AJbceyuRGIHluIylaHRUUcSkWScqTU5Hi4R12XrYhI1lWYRqTNCLgo8z5ASJrYs5UZ+nEDvwnj03IYjjakpc++Qal01PlsPCWPowZaauTcj7NiGf51rUQJu/C5JCRemVPWgnfGwbHtqwUHLCvrx3i+6pcXy2/DaacI0hC8zQW7kkoggXG1cF7fhQLqQaprYEIoeLqIIPiHNp0og41TxBEREkKK4GddGpoILO4nLQvA7IE65WEJwjuAoq5VCUEKSZrHXqAofTWN81cYEX/XT0hLAHYUKtFQd+wgt+jzo4vj7b5+psj1lwvHCwR11XzA4n+IMqJuMPHe4wukF3KLjD6LTcrO++Yjjo6vScw0QfQz5J7+PDnPPquKkcLhYtiR03lsLEpaUQ51wABwdn3CJMuE6SJYLXGfCucF7RZUWx0kDMXQVSPiw5rOZ1al308eM5DEMFaqCK4yF77xrvf1hVaCU4mTYTWwDMNNZ81dUsjaPVFa6gLs1gPcWrxLCwjsJ1rZ5Gt+UddV1R16nYtGxJrKUbDjZhofae0+vGdWWRZ66GqxWv0IpWX4y0K2DG2cCE66ToV8hndyUpUe/a9RI0hnfpRybORSeXcl/xfUk/7jgeVmjyXTEH5tIQN6EGqjQzdBW72oRZM8AXB25K7QMhtRhWLlAHx4VqhhPlwE+K4W+iCPiiO89hKiy95qcc+Ak+uDYRHxyzwwkhCGFWxVmnvTSOKrsr17gsbdcXQkYWr+S4mpCxn5ifE6nQ3uvjcM7dFmCh4pmh756GWhJhvko+hTEiKZxUAdK4xJ3WxBDFKU01L8HFkAiHVHGgP2bE2aBdDLNUYg6pqpKpUKjSXIzN4Z3EXH/tCJPQDKU8qytmdYWIsj+tmbr9ODJq5XG043nFS0qlDcQuREGFWXAczCaxTiwn4lVieFg7qAV3zUVROhSqg9ia6GbpUZehYgoPA7hZChHrHCYGxIcmVCQv94Qs3lttw8BeF6Hmuxn8bs2RdbDk/DmncF0x79UKmqoiucK+L4rlkC2dJH3RbSa3OiYdLFvjoC1KzY6smYzCC8EJ3iszV8V5D+sYPlYuCluVwsdSuAB86v+Yk/11iFXxPlXHa6BbZOrpFM+WD/rLKUnfScqXeau+thSFp/3WxM6yhYlHw4Tr7DOXoO+XRWQBy+Gio5uYb/I0Ep2FCPhU/+AEqdJgyk7RmbYzWjtQFaqZpt93moMxxNegzUxCIQlKCAKVEiaC93EC19kkUFVxqOU8mSvQPOdhaVSlKS6Ns1OnDtQz11TGyyy5rTo6LQlQHUjrrg6zw0qOK2jruFKCvnFcdYiuqw5R5Jv71HNcZT1XaAWt+X76iXtWJOYNE64zTdmSuKjDdXZVjbtqi1FVBfE+ilrOZfmUtK/js0AMjXDNVF8aYgiIQAjaTJyKxlyYNmVabdgoNegEQsqvaeXwdcAL1JM47yGSZ79On5kTrvT5NAqF1i4eN9dpBZrWQ/FRsGL4FwUrhopJtOokYDnvNcuhYoii5aNo4fMjNCF1I1Lep5CwLTpt7nn5PPe1zbcwGi3C9rcqrjNZhnFS9AsqE21Cuq0mbzti5yT1fBjWVKL3W/BSCNcM95BcmHoh1BLzYL6KbsrHAlZft8vBV3GbOn4mql7qNO3T/svWw/5jKGRsKuDpXGteliJkbsPDgfyVsTlyO9KIxxhE5G4R+ZyIPCEiCyfVEZE/KyJeRP7bVfs0x7UOy8obmm169VzFHH+ahKap6fIeraroupIrEx+nohcnaSgbwaUZoePUgZL+aqLb0QpoSiFyeBg/18xN6IUwiduKT0n9iaKT1FYwcXF+RiGOgDowCUc5UGEUlyhaorTdeDQ5Ll8k30MKD5Ojqg5ap1XNUr3WTKkOA2hyXD7VbNUBvMb7E5IDy2Fidlvet0n53H2qELWhMLHzXQ19x8bGQkURqYD3AN8PXAEeFZGHVPUzA9v9r8BHx+zXhOu4DPZTzCUPMl+MWlVtfquSbnefoODiD1yDIhJQ4iSnkkNFH+LszV7JabVQxanEQNHcqihKEyrGt1BPWhdrxdSnPJknCqWQJpZlsXCl6neygyvdVYjFpXkUi0a4Uk6reZ1bEmdtgWnjKIuCU3xqwMhhY9+ZlrVbi3Jb5XdijGdz+v1a4AlV/QKAiHyQOEPYZ3rb/STwy8CfHbNTE64NsjTP5XouLC7QlEb0Z2AOKTGvMcejhOiWfMx7uVrxTpA8xA2KIw5t08x+LcmYuahHWhFLKpyk6gGNBspLM/1Xkx8bEC7pC1dI5q+WJhR0RWjo6rhdzmm172vTF5EkZjmfVZY+9Gu3Og0Z8YbPu6vyni/4jozVrFEO8XIReaxYvqyql4vl24AvFctXgNd1jiVyG/BfA9+LCdcJMSZczJQ1XU3LYm/ECEdMyLtULCESX/s0K46Lx5OUIHcpv9SMR5h275wQpkRn5VIZgk9howetJDqzSXJZVSxQzVPeN8KVHRrFs7bP0heuMq8WWpcVQ8B2Xa7Tqmat03IHIYaXdUAOQ+xrOUstiF6hTiFiErMmIZ9fNw6sNxJEKVrrCJWFiS3jb8VzqnrnkveHfiz9vf8s8E5V9WPnwVwpXCJyAfgNYD9t/yFV/RkRuRn4JeBVwBeBH1bVr4466q4zphh1UWlEJmjMdZVV9I2jIFkkbRLU6lMrn9M4+oNXxCVhDCAkF1PF/Ja6nF/Lp6Y4lTiaRCgi1BRGkg1faq2EVhSlI1y9ZwVJ1fAojZPqJuQ1vV9Ww2fHlpxWfq9YHix56LiqNrc1/xUtyW0NrTPRasnf72a4AryyWL4deKq3zZ3AB9Nv5OXAm0SkVtX/c9FOxziuA+B7VfXrIjIF/q2I/AvgvwEeUdV3pZaC+4F3jr2aM0cSqkXhYlNwWroucjV9AE+bqHcuhmSk/5pqj1QujnCa3Ff8kgNSpTqtieBiWqsRoyY5H1Ln65w/E0Eq0v5oasIa90UrWplmLPhCuJrXvhWsHBLmivhujiu5rdSR2vnorFwdmkQ8uWarCRmz2wptsWmZkIc5tzU0vI2VQKzJ5nT8UeAOEXk18AfEmcJ+pHMo1Vfn1yLy88CvLhMtGCFcGv8Kvp4Wp+mhxATbG9L6B4iTaJxf4SoYGjGiu0GRVIb4I3XSJu29bxydpNosVJEq2aTUX1HVNWGjBEn1XLFDda5YRyD4mMCPSX1AtAkXNbusPMW9FKLVCxXnRl5NnaGHxtHKCXi0TcSjUB3motJUWKqKzHwULk0tiFm06iRQPsR7ku9Zv9i0vKfzX8ba35+xVo5rKapai8g7iK2FFfB+VX1cRN6e3n/vUfY7KseVmip/C/iTwHtU9RMicouqPp0O/rSIvGLBZ+8D7gO4wMWjnOPu0++/CK3r6oWcmt1U/nFW0hW6HEb62J+wCRuh6YiNSDO4YB6TPgpdfK90UyIQiKISh5hoo+ChUDHXkHW76tCWQ3TGjC/CxlSz1dZpFaOa5vcC3RqtMkTM598TosZtpXvauefG0dng7VPVh4GHe+sGBUtV/8aYfY4SLlX1wHeIyEuBXxGRbxvzufTZy8BlgJfIzWfnr2koST9USd/PdeUfVz9R74mlEt6j4tqMZi6nEEGr9DrlteIPW3BB0crhKkWCi84qz6gjINPoxvJ4XjkJHx2XxAZPIY5QUTquHv3x4XOOqnFcmloMc14ruayy07SbhVTyEGIiXlN46H2TfG+q45tnHxswtF2Ot2Y+Ib+ye4/Vbq0mfb/bzLrzKv4nEfk4cDfwjIjcmtzWrcCzJ3GCW82KFsa5fNdQoj6XQQBNP0aS88o5saLVMYaN0ZVpTdPaGLs9plmsXZr2PsQWSpTYz9HFQtQmr+XjaKllS2JnZIkiXM00SVstxCqNpZXDwqbMIQ25nAcGbEd70FRQ2q3Varr0dFoNQ+u0lvRHjF+HzjmtleUPJlpzCJsLFU+KlV1+ROQbk9NCRG4Avg/4PeAh4N602b3AR07oHHeLES1Y/Ukc2skycn2Sdn64c61qyY00LXDFCKGNm6nbzsquGfcquqDYX7BIkufkea54b14XnZ876yk+p00Oy82Ss/L0jp0FqXeuTStiaK9z2bUX96icYGQwIT+mJdFYyCa7/JwEYxzXrcADKc/lgAdV9VdF5N8DD4rI24AngTef4HluL0cIGRfWdgWInf4c4Bu3HsND14aNgE7icDgxHxYH7aMKuOBiWOkC6tNrL7GbTwoXcfG1c0k4czci6NZxzV1r33HFz7QDABajmWoULrQd5SG/bgQrJ9/7ifgsRnVOyPtO6cPKmi0LEY/Plt+aMa2KnwK+c2D9l4G7TuKkzixDtV3F6BGNeLlAzLqn7fMPtAwbfUjDzMeQUERi7bzEaniB9ENWII0+oRrDyZzgr3J8SCNWWZi0J8ZtZ2ea50a4cl5LyxqtwmXlqvjsEEvRyeHhkNPK92xItGBpXss4JrsuXMYIxrquuY91O2HPOa+qAk3OK3f/gSZ73iTtAZyLwpTX5xFWJZZZSHJZuNRqmXJccVNpd9ucp863KkLcV1puHZc2jQWdPofZZaX6LKBNwucarSxEZSK+yWX59l72nVZxDwe/EnNbR+eUw8AxmHBtinVCRqDTCXuopbEXNqLSa22somvKgiap83WTuHbtOF/OpWGh4zGyQGkqf+iUSORr6Gc/mxAxiZWm10ozY1Gs7wq0E1yk16UwhbLDdGhErGkpLFsPV4SHjWjl7ZrbbqJ1bLb8FplwnSZD9V2wIGxUmtbGHGJKKovII5YGUEnrNYdmxA7azqEhVdunrkBUgEan1Whujh57f7htLVcbMjZzHhYzTItv3WPzumhUaMcU64WG0G09hOHwcOgeGhtn2wcSNOHaJOuEjL18F9CWP8Cw83I0dV6t00rJ+dw5OxeZFvuSNOKqiKA5ryUpL5adWHnei0o8SjVLBaOdPoV0RSxO9sGwy8r1WFrMibjKaeX7UjqtfC+b221uaxNYqHjeGCFewGBL48qwUaXJe6GCpok22lZHafYlQWIoSXIyuSYrZJWU9pHDwv55ywL71QjHvHA1YpWT7jBc0hFCFFdo+x7m16E472XhYb639ASrWD943sZyFAsVzyUrxGtw/aqwsZl4I/1F5UEIIf73mEWgqmL46GjCSUmDDyIShaUQqyg8RXK+xLUCVdIZTjk/9+rMpLfccVnlZ/qvm1s4Ijxc1IJoonV8tvx2mXBdT9YNG6F1XgDqmgksms84QYvXjahUVSueIvFY2WGldbk1Ma/v6Nac8A64rhwe9vsXlkKV13W66QyHhe37ZSHucqeV72XnHhvHYhcq5024Tooh19XfZIF4NWFjTsI7lxLxPfdVDEYIoRkaB1LZQRykPm7rtcmDtcn7QrigFbIVSOmU+s9znaRDm8eCecdVCtBxRWsR5rbWRsbc11PEhOskWRQywkrnNShe0IhXHB1C2sEISaFmdjb9BD60eTBoRSwj0rYkjU3OZ4bEKr3WvkB1QsQiAZ+urUzCx82P6bRMtNbHclzGQue1LGEPSYwYDh2Tm2oFLP+opc2juZi70rjjNKJEaN1aeU6uyL2tnMWoFKwwt36wtmpArLrbHkOweu8tPFdjLSxUNI5H331lylAqh49BU90XdIaEJswLYecYxQ+/FLHB85kXq/hyQGiGRGxRLqvY99y+jOvPlt96E67rQf4hrhs25vfyj70czwu64WNabgsHfREWuraFMLcgFseN+yo6fo9hUZi2RKzi24sFq31/cQho4eH1wRyX0bJu2Nh7r2x1hF74CKk4tchn5TxYX8QyrvjrXJXfKq+hz5CYDIWD/c/3HdaifWHh4XVny2+jCde20KvzGkzaQ6feazB5n0nr2m3SX6IrfvCh9xkn4374y0Sk767yuczt4wREy9gMal1+jD6LwkYYFC/oJe2L0BHanBXed3NgOYkP3SFqCssm/XjAM1wEWzKQd1o4EeuC9QvFClaXOpjTOnGsjstYzLKwEcYJGAw7MGiFIg1AGD8jXQEZSsT79i8272vR0DENfUe1SMj6+xrrsHrvz7+35b+yXWTL76kJ12myrEh1oIvQquR9bn3MSClUpYBlViTitUj+r7yOPkdwWHHRRGsbMMdlLGdV6AiL3Ve5DczlrMpEfg4bF05xPui+/MLTXiRmg+7sKGI1sF3vQIvfM47HDhSgjpks45Ui8q9F5LMi8riI/FRaf7OIfExEPp+eX3byp3uGWfZDHPgBj3ImQedEQ8vuN51tw3qPudMf2O/A8Ucn1k20TpXu3JiLH6fFSuECauDvqOqfAl4P/ISIvAa4H3hEVe8AHknLxnFYJV4DTiU/5rbrt/T1HlloNvUYOsaycxo89wXXOfoeGRtj24VrzGQZTwN5xurnReSzwG3APcAb0mYPAB8H3nkiZ3meWBY6QvdHPRBCtm/JsACUSf2TYIHoLO0MPcaFmWBdP5Stv99r5bhE5FXEGX8+AdySRI00KewrFnzmPuA+gAtcPNbJnitGjC6xcIwveon8/mcyCz67NiuEx0Rr9zgzyXkRuRH4ZeBvqerXFiZ5e6jqZeAywEvk5i2/HVvGKvcFS4VoSDA6YnYChZzjhpkZm+eyP5dTY8tv/SjhEpEpUbR+UVU/nFY/IyK3Jrd1K/DsSZ3kuWeMgMEoN7VMWAYd2pr7WPKhNbbd8l/NGWcXClDHtCoK8E+Bz6rqPyreegi4N72+F/jI5k/P6LDOD3ooSb/yIzrqcZLnYKK1BWg7P+aqx2kxxnF9N/DXgd8Vkd9J6/4e8C7gQRF5G/Ak8OYTOUOjS/+HPSZkXyQc1ynHtfyzJlRbyZZ/LWNaFf8tveGbCu7a7OkYazMmib/wsysEJwvbSXVqNtHaWrY9VLTK+bNAKQBHFbHB/Z6AYJlYbT/K1g/iaMJ11hgShk2K2TqYSO0uW/7VbSjJYWw1qu3jLB3LODFExz1G7UvkbhH5nIg8ISJzPWxE5K+JyKfS49+JyLev2qc5rvOGCYoxgk21GIpIBbwH+H7gCvCoiDykqp8pNvt94C+q6ldF5I3Eus/XLduvOS7DMLroGo/VvBZ4QlW/oKqHwAeJ3QXbw6n+O1X9alr8TeD2VTs1x2UYRodYgDracb1cRB4rli+n3jKZ24AvFctXWO6m3gb8i1UHNeEyDGOe8Q3Kz6nqnUveH2oZGlRFEfkeonD9+VUHNeEyDGOONRzXKq4AryyWbweemjueyJ8G3ge8UVW/vGqnluMyDKPLZnNcjwJ3iMirRWQPeAuxu2CDiHwT8GHgr6vqfxizU3NchmH02Fw/RFWtReQdwEeBCni/qj4uIm9P778X+PvANwD/JI06U68IP024DMMYYINlM6r6MPBwb917i9c/Dvz4Ovs04TIMo4vahLCGYewiW16obMJlGMY8261bJlyGYcwjqyYBPmVMuAzD6KKsU4B6KphwGYbRQdBNFqCeCGPGnH+/iDwrIp8u1tks1oZxlimHJ1r2OCXGVM7/PHB3b53NYm0YZ5ldFy5V/Q3gK73V9xBnryY9/9BmT8swjFMj57jGPE6Jo+a4Rs1ibRjGbnLuWxVF5D7gPoALXDzpwxmGcWy2f+jto44O8UyavZpVs1ir6mVVvVNV75yyf8TDGYZx3VB2P8e1AJvF2jDOMrue4xKRDwBvIA7RegX4GWwWa8M402x7HdeYmazfuuAtm8XaMM4quy5chmGcM1TBn/NWRcMwdhBzXIZh7BwmXIZh7BQKbGjM+ZPChMswjB4KajkuwzB2CcWS84Zh7CCW4zIMY+cw4TIMY7fY/k7WJlyGYXRR4LwPa2MYxg5ijsswjN3CuvwYhrFrKKjVcRmGsXNY5bxhGDuH5bgMw9gpVK1V0TCMHcQcl2EYu4Wi3p/2SSzlqJNlACAid4vI50TkCRGx2awN4yyQh7UZ8zgljixcIlIB7wHeCLwGeKuIvGZTJ2YYximiYdzjlDiO43ot8ISqfkFVD4EPAvds5rQMwzgtFNCgox5jWBWZSeQfp/c/JSLftWqfxxGu24AvFctX0rr+Sd0nIo+JyGMzDo5xOMMwrguqG3NcIyOzNwJ3pMd9wM+t2u9xhEsG1s1JsM1kbRi7h3o/6jGCMZHZPcAvaOQ3gZeKyK3LdnqcVsUrwCuL5duBp5Z94Hm++ty/1A+9ADx3jONuKy/HrmtXOIvXBPG6Lh13J8/z1Y/+S/3Qy0dufkFEHiuWL6vq5WJ5KDJ7XW8fi6K3pxcd9DjC9Shwh4i8GvgD4C3Ajyz7gKp+o4g8pqp3HuO4W4ld1+5wFq8Jmut61XH3o6p3b+B0MmMis1HRW8mRhUtVaxF5B/BRoALer6qPH3V/hmGcScZEZmtHb8cqQFXVh4GHj7MPwzDONGMis4eAd4jIB4lh5B+p6sIwEU6ncv7y6k12Eruu3eEsXhNs4XUtisxE5O3p/fcSzc+bgCeAq8CPrdqv6Jb3STIMw+hzrC4/hmEYp4EJl2EYO8d1Fa6z0ClbRF4pIv9aRD4rIo+LyE+l9TeLyMdE5PPp+WWnfa5HQUQqEfmkiPxqWt756xKRl4rIh0Tk99L39l/s+nWJyN9Of3+fFpEPiMiFXb+mdbhuwnWGOmXXwN9R1T8FvB74iXQd9wOPqOodwCNpeRf5KeCzxfJZuK53A7+mqt8KfDvx+nb2ukTkNuBvAneq6rcRk95vYYevaV2up+M6E52yVfVpVf3t9Pp54o/gNuK1PJA2ewD4oVM5wWMgIrcDfwV4X7F6p69LRF4C/AXgnwKo6qGq/id2/LqIFQE3iMgEuEise9r1axrN9RSuUZ2ydwkReRXwncAngFty7Ul6fsUpntpR+Vng7wJl79ldv65vBv4Q+GcpBH6fiFxih69LVf8A+IfAk8RuMX+kqr/ODl/TulxP4Vq7rH+bEZEbgV8G/paqfu20z+e4iMgPAM+q6m+d9rlsmAnwXcDPqep3Ai+w4yFUyl3dA7wa+OPAJRH50dM9q+vL9RSutcv6txURmRJF6xdV9cNp9TO5R3t6fva0zu+IfDfwgyLyRWIY/70i8s/Z/eu6AlxR1U+k5Q8RhWyXr+v7gN9X1T9U1RnwYeDPsdvXtBbXU7ia0n8R2SMmEx+6jsffCCIixHzJZ1X1HxVvPQTcm17fC3zkep/bcVDVn1bV21Mn3bcA/0pVf5Tdv67/CHxJRL4lrboL+Ay7fV1PAq8XkYvp7/EuYq51l69pLa5r5byIvImYR8ml///LdTv4hhCRPw/8G+B3aXNBf4+Y53oQ+CbiH9abVfUrp3KSx0RE3gD8j6r6AyLyDez4dYnIdxAbHPaALxC7lDh2+LpE5H8C/iqxlfuTwI8DN7LD17QO1uXHMIydwyrnDcPYOUy4DMPYOUy4DMPYOUy4DMPYOUy4DMPYOUy4DMPYOUy4DMPYOf5/w3bxXQ+IhSUAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "xmin = -4\n", + "xmax = +4\n", + "dx = 0.1\n", + "xh = np.arange(xmin,xmax+dx,dx)\n", + "yh = np.copy(xh).reshape(1,-1)\n", + "\n", + "xh = xh.reshape(-1,1)\n", + "z = np.exp(-(xh**2+yh**2))\n", + "z = (np.random.random((81,81))-0.5)*2.0\n", + "# z = np.zeros_like(z)\n", + "x = np.exp(-xh**2)\n", + "y = np.copy(x)\n", + "\n", + "x = x.reshape(-1,1)\n", + "y = y.reshape(1,-1)\n", + "\n", + "# print(x.shape)\n", + "# print(y.shape)\n", + "\n", + "z = x * y\n", + "# print(z.shape)\n", + "\n", + "plt.figure()\n", + "plt.imshow(z, origin='lower')\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "5ec92435-d68c-4221-bdec-a036d89ba184", + "metadata": {}, + "outputs": [], + "source": [ + "def boundary_handling(z):\n", + " # periodic boundary conditions\n", + " z = np.pad(z, ((1,1),(0,0)), mode='wrap')\n", + " return z" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "464c314f-7e1f-4227-a4d6-66570a5eb646", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(79, 81)\n", + "(79, 81)\n", + "(79, 81)\n" + ] + } + ], + "source": [ + "print(z[:-2,:].shape)\n", + "print(z[2:,:].shape)\n", + "print(z[1:-1,:].shape)\n", + "\n", + "def c_diff(z,dx):\n", + " dzdx = z[:-2,:] - 2.0*z[1:-1,:] + z[2:,:]\n", + " return dzdx / dx**2" + ] + }, + { + "cell_type": "markdown", + "id": "92fdb634-5854-4b75-a716-84e575199d8d", + "metadata": {}, + "source": [ + "### The 2D problem\n", + "Now that we have the 1D solution of the heat equation, \n", + "1. Can you discretise the right-hand of (1) in 2D? Hint: You will obtain the famous [5-point stencil](https://en.wikipedia.org/wiki/Five-point_stencil) for the [Laplace operator](https://en.wikipedia.org/wiki/Laplace_operator).\n", + "2. Now, the challenge is to solve the 2D heat equation by changing your 1D code *as little as possible*. Can you do that?" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "71c2dabe-9b36-4c84-9b30-bae2edfc97cb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0.001 0.002 ... 0.998 0.999 1. ]\n" + ] + } + ], + "source": [ + "dt = 0.001\n", + "T = 1.0\n", + "t = np.arange(0.0,T+dt,dt)\n", + "print(t)\n", + "\n", + "zn = np.copy(z)\n", + "sol = np.zeros((len(t),len(xh),len(xh)))\n", + "\n", + "def space_update(z,dx):\n", + " z_xbc = boundary_handling(z)\n", + " d2zdx2 = c_diff(z_xbc, dx)\n", + " z_y = np.moveaxis(z,0,-1)\n", + " z_ybc = boundary_handling(z_y)\n", + " d2zdy2 = c_diff(z_ybc, dx)\n", + " d2zdy2 = np.moveaxis(d2zdy2, 0, -1)\n", + " return d2zdx2 + d2zdy2\n", + "\n", + "for idx, _ in enumerate(t):\n", + " fz = space_update(zn,dx)\n", + " midpt = zn + 0.5 * dt * fz\n", + " fz = space_update(midpt,dx)\n", + " zn = zn + dt * fz\n", + " sol[idx] = zn" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "262d814a-19e5-46a9-9463-eef0d981e53f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(sol[0,40], label='t=0')\n", + "plt.plot(sol[int(len(t)/2),40], label='t=1')\n", + "plt.plot(sol[-1,40], label='t=2')\n", + "plt.ylim([0,1])\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "0ce75ca5-068b-4220-98cb-835e6d6d9ae8", + "metadata": {}, + "source": [ + "Below is a code snippet that saves your solution as an animation." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "dbc0ceea-178a-4d95-b9f5-8f81cfbe05c9", + "metadata": {}, + "outputs": [ + { + "ename": "IndexError", + "evalue": "index 1001 is out of bounds for axis 0 with size 1001", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_zlim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0mani\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manimation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFuncAnimation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mupdate_plot\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2001\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfargs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterval\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mani\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'test.mp4'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'-vcodec'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'libx264'\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 17\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\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[0;32m~/anaconda3/envs/playground/lib/python3.7/site-packages/matplotlib/animation.py\u001b[0m in \u001b[0;36msave\u001b[0;34m(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs, progress_callback)\u001b[0m\n\u001b[1;32m 1155\u001b[0m \u001b[0;32mfor\u001b[0m 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.animation as animation\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "X,Y = np.meshgrid(xh,xh)\n", + "plot = [ax.plot_surface(X, Y, sol[0,:,:], color='1.0', rstride=1, cstride=1, cmap=\"magma\")]\n", + "\n", + "def update_plot(i, sol, plot):\n", + " plot[0].remove()\n", + " plot[0] = ax.plot_surface(X, Y, sol[i,:,:], cmap=\"magma\")\n", + "\n", + "ax.set_zlim(0,1.1)\n", + "ani = animation.FuncAnimation(fig, update_plot, 2001, fargs=(sol, plot), interval=1)\n", + "ani.save('test.mp4', fps=30, extra_args=['-vcodec', 'libx264'])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "id": "1b42d56a-3920-4325-8e81-21a86e126829", + "metadata": { + "collapsed": true, + "jupyter": { + "outputs_hidden": true + }, + "tags": [] + }, + 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# spatial step-size\n", + "dx = 0.1\n", + "# temporal step-size\n", + "dt = 0.001\n", + "# simulation end time\n", + "T = 1.0\n", + "# the time axis\n", + "t = np.arange(0.0,T+dt,dt)\n", + "\n", + "# your code here:\n", + "x = np.arange(-4,4+dx,dx)\n", + "print(x.shape)\n", + "# u = np.exp(-x**2).reshape(1,-1) * np.exp(-x**2).reshape(-1,1)\n", + "# sol = np.zeros((len(t),len(x),len(x)))\n", + "\n", + "u = np.exp(-x**2)\n", + "sol = np.zeros((len(t),len(x)))\n", + "\n", + "def bc(u):\n", + " ghost_cells = [(0,0)]*u.ndim\n", + " ghost_cells[0] = (1,1)\n", + " u = np.pad(u, (ghost_cells), mode='wrap')\n", + " return u\n", + "\n", + "def rhs(u, dx):\n", + " u = bc(u)\n", + " lu = u[:-2,...]\n", + " ru = u[2:,...]\n", + " cu = u[1:-1,...]\n", + " \n", + " return (lu - 2.0*cu + ru) / dx**2\n", + "\n", + "def fu(u, dx):\n", + " fu = np.zeros_like(u)\n", + " for _ in range(u.ndim):\n", + " fu += rhs(u, dx)\n", + " u = np.moveaxis(u, 0,-1)\n", + " fu = np.moveaxis(fu, 0,-1)\n", + " return fu\n", + "\n", + "print(u)\n", + "print(u.shape)\n", + "for tidx, time in enumerate(t):\n", + " unphalf = u + 0.5 * dt * fu(u, dx)\n", + " print(unphalf)\n", + " u[...] = u + dt * fu(unphalf, dx)\n", + " sol[tidx] = u\n", + "\n", + "# plt.figure()\n", + "# plt.plot(sol[0,40], label='t=0')\n", + "# plt.plot(sol[int(len(t)/2),40], label='t=1')\n", + "# plt.plot(sol[-1,40], '--', label='t=2')\n", + "# # plt.ylim([0,1])\n", + "# plt.legend()\n", + "# plt.grid()\n", + "# plt.show()\n", + "\n", + "plt.figure()\n", + "plt.plot(sol[0], label='t=0')\n", + "plt.plot(sol[int(len(t)/2)], label='t=1')\n", + "plt.plot(sol[-1], label='t=2')\n", + "plt.ylim([0,1])\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "# Here is a code to check if you initialised the initial condition correctly.\n", + "# plt.figure()\n", + "# plt.imshow(u, origin='lower')\n", + "# plt.colorbar()\n", + "# plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "72692ffb-729d-4c7a-8366-761c0feae287", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(1, 1), (0, 0), (0, 0)]\n" + ] + } + ], + "source": [ + "# this only works for python lists, NOT numpy list\n", + "ndim = 3\n", + "A = [(0,0)] * ndim\n", + "A[0] = (1,1)\n", + "print(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "id": "507b7d60-a085-466e-b8da-df3f45defca8", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "id": "91ad3622-e4b3-4f0d-9cf2-2c13186481ee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 2 3 4 5 6 7 8 9]]\n" + ] + } + ], + "source": [ + "\n", + "\n", + "A = np.arange(10)\n", + "print(A.reshape((1,-1)))" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "id": "26e1452e-6348-4008-8a65-d9f86ebe8381", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]), array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])]\n" + ] + } + ], + "source": [ + "B = np.meshgrid(A,0)\n", + "print(B)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17a28763-0c1c-4a53-82e3-6bef18256eb0", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w4/soln/ex2_heat_eqn.mp4 b/w4/soln/ex2_heat_eqn.mp4 new file mode 100644 index 0000000..0759a2b Binary files /dev/null and b/w4/soln/ex2_heat_eqn.mp4 differ diff --git a/w4/soln/some_other_ics/bar.mp4 b/w4/soln/some_other_ics/bar.mp4 new file mode 100644 index 0000000..4d6402c Binary files /dev/null and b/w4/soln/some_other_ics/bar.mp4 differ diff --git a/w4/soln/some_other_ics/block.mp4 b/w4/soln/some_other_ics/block.mp4 new file mode 100644 index 0000000..2fb6e28 Binary files /dev/null and b/w4/soln/some_other_ics/block.mp4 differ diff --git a/w4/soln/some_other_ics/random.mp4 b/w4/soln/some_other_ics/random.mp4 new file mode 100644 index 0000000..458217a Binary files /dev/null and b/w4/soln/some_other_ics/random.mp4 differ diff --git a/w6/conservation_laws.pdf b/w6/conservation_laws.pdf new file mode 100644 index 0000000..0ac043c Binary files /dev/null and b/w6/conservation_laws.pdf differ diff --git a/w7/burgers_eqn.ipynb b/w7/burgers_eqn.ipynb new file mode 100644 index 0000000..1d50079 --- /dev/null +++ b/w7/burgers_eqn.ipynb @@ -0,0 +1,45779 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tutorial 7\n", + "\n", + "## Exercise 1: The 1D Burgers' equation\n", + "\n", + "References:\n", + "1. Animation in Jupyter notebook: http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/\n", + "2. Time stamp animation: https://stackoverflow.com/questions/16512308/show-elapsed-timeframe-number-in-matplotlib\n", + "3. Wikipedia Burgers' Equation: https://en.wikipedia.org/wiki/Burgers%27_equation" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A 1D problem. $u:[0,T] \\times \\mathbb{R} \\rightarrow \\mathbb{R}$,\n", + "$$ u_t + (f(u))_x = 0 \\quad \\text{in } [0,T] \\times \\mathbb{R}, $$\n", + "$$ u(0,x) = v(x) \\quad \\text{for } x \\in \\mathbb{R}. $$\n", + "\n", + "For the inviscid 1D Burgers' equation, $f,v \\in C^1(\\mathbb{R})$,\n", + "$$ f(u) = \\frac{1}{2} u^2,$$\n", + "$$ v(x) = \\exp(-x^2).$$\n", + "\n", + "The Lax-Friedrichs scheme for the above problem is\n", + "$$ U^{l+1}_j = \\frac{1}{2} \\left( U_{j+1}^l + U_{j-1}^l \\right) - \\frac{k}{2h}\\left( f(U_{j+1}^l) - f(U_{j-1}^l) \\right), \\quad l,j \\in \\mathbb{Z}, l \\geq 0, $$\n", + "$$ U_j^0 = v(x_j), \\quad j \\in \\mathbb{Z}, $$\n", + "where $x_j = jh$, $h, k > 0$ denote the spatial and temporal step sizes respectively.\n", + "\n", + "Finally, the exact solution to the Burger's equation is given implicitly as\n", + "$$ u(x,t) = v(x - ut). $$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# define function for the initial condition.\n", + "def v(xh):\n", + " return np.exp(-xh**2)\n", + " \n", + "# non-linear function of f(u).\n", + "def f(uh):\n", + " return 0.5 * uh**2\n", + " \n", + "def lfscheme():\n", + " # lax-friedrich method\n", + " pass\n", + " # return U" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# extent of space domain\n", + "xmin = -3.\n", + "xmax = 4.\n", + "\n", + "# extent of temporal domain\n", + "tmin = 0.\n", + "tmax = 3.\n", + "\n", + "# N = number of grid points\n", + "p = 8\n", + "N = 2.**p\n", + "# spatial grid-size\n", + "h = 1./N\n", + "# temporal grid-size\n", + "k = 0.5 * h\n", + "\n", + "# temporal and spatial grids\n", + "xh = np.arange(xmin,xmax+h,h)\n", + "tk = np.arange(tmin,tmax+k,k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plots\n", + "Plot the animation of the numerical and exact solutions of the 1D Burgers' equation." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
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Recall how you implemented your solution to the 2D heat equation.\n", + "2. You can reuse the animation code snippet from the heat equation.\n", + "3. The Wikipedia article on the heat equation has an animation of 2D solution." + ] + }, + { + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/w7/burgers_eqn_soln.ipynb b/w7/burgers_eqn_soln.ipynb new file mode 100644 index 0000000..286f745 --- /dev/null +++ b/w7/burgers_eqn_soln.ipynb @@ -0,0 +1,50382 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Lax-Friedrichs Scheme (1D)\n", + "\n", + "References:\n", + "1. Animation in Jupyter notebook: http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/\n", + "2. Time stamp animation: https://stackoverflow.com/questions/16512308/show-elapsed-timeframe-number-in-matplotlib\n", + "3. Wikiepdia Burgers' Equation: https://en.wikipedia.org/wiki/Burgers%27_equation" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import fsolve\n", + "from scipy import sparse\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A 1D problem. $u:[0,T] \\times \\mathbb{R} \\rightarrow \\mathbb{R}$,\n", + "$$ u_t + (f(u))_x = 0 \\quad \\text{in } [0,T] \\times \\mathbb{R}, $$\n", + "$$ u(0,x) = v(x) \\quad \\text{for } x \\in \\mathbb{R}. $$\n", + "\n", + "For the inviscid 1D Burgers' equation, $f,v \\in C^1(\\mathbb{R})$,\n", + "$$ f(u) = \\frac{1}{2} u^2,$$\n", + "$$ v(x) = \\exp(-x^2).$$\n", + "\n", + "The Lax-Friedrichs scheme for the above problem is\n", + "$$ U^{l+1}_j = \\frac{1}{2} \\left( U_{j+1}^l + U_{j-1}^l \\right) - \\frac{k}{2h}\\left( f(U_{j+1}^l) - f(U_{j-1}^l) \\right), \\quad l,j \\in \\mathbb{Z}, l \\geq 0, $$\n", + "$$ U_j^0 = v(x_j), \\quad j \\in \\mathbb{Z}, $$\n", + "where $x_j = jh$, $h, k > 0$ denote the spatial and temporal step sizes respectively.\n", + "\n", + "Finally, the exact solution to the Burger's equation is given implicitly as\n", + "$$ u(x,t) = v(x - ut). $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define function for the initial condition.\n", + "def v(xh):\n", + " return np.exp(-xh**2)\n", + " \n", + "# non-linear function of u.\n", + "def f(uh):\n", + " return 0.5 * uh**2\n", + "\n", + "# solver for the implicit exact solution\n", + "def u_ex(u,x,t):\n", + " return u - np.exp(-(x - u*t)**2)\n", + " \n", + "def lfscheme(t,xmin,xmax,h,k):\n", + " # set number of time steps.\n", + " l = np.floor(t/k)\n", + " # set min step for grid.\n", + " jmin = np.ceil(xmin/h)\n", + " # set max step for grid.\n", + " jmax = np.floor(xmax/h)\n", + " \n", + " # define extended grid.\n", + " xh = h * np.arange(jmin-l,jmax+l+1)\n", + " \n", + " # get initial values.\n", + " U = v(xh)\n", + "\n", + " # recursion for the Lax-Friedrichs scheme.\n", + " while l > 0:\n", + " U = 0.5 * (U[2:] + U[:-2]) - k / (2. * h) * (f(U[2:]) - f(U[:-2]))\n", + " l -= 1\n", + "\n", + " return U" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# space domain\n", + "xmin = -3.\n", + "xmax = 4.\n", + "\n", + "# time\n", + "tmin = 0.\n", + "tmax = 3.\n", + "\n", + "p = 8\n", + "N = 2.**p\n", + "h = 1./N\n", + "k = 0.5 * h\n", + "\n", + "# temporal and spatial grids\n", + "xh = np.arange(xmin,xmax+h,h)\n", + "tk = np.linspace(tmin,tmax,240)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plots\n", + "Plot the animation of the numerical and exact solutions of the 1D Burgers' equation." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
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Objects have `attributes` and `methods`, and we will look into these shortly.\n", + "\n", + "[`Classes`](https://docs.python.org/3/tutorial/classes.html) allow us to create new types of objects in Python. Let's take a look at a specific example.\n", + "\n", + "Let us pretend that we work at an animal shelter, and our shelter takes in dogs, cats, and iguanas. We want to create a new object type that stores the information of all our residents." + ] + }, + { + "cell_type": "code", + "execution_count": 395, + "id": "253b213b-763f-43bf-bf51-0fde37821e75", + "metadata": {}, + "outputs": [], + "source": [ + "# we define a class. This class provides us with a template \n", + "# to generate objects of type 'resident'\n", + "class resident(object):\n", + " # We use classes to define and generate specific types of objects.\n", + " # Each time we initialise an object from a class, we call it an \"instance\".\n", + " \n", + " # A function within a class is a method. It allows us to modify the properties\n", + " # of the object generated by the class.\n", + " \n", + " # \"self\" is a special keyword that allows us to access the state of the instance.\n", + " def __init__(self,name,species):\n", + " # variables defined within the class are attributes.\n", + " # Attributes describe the properties of the object\n", + " # generated by the class instance.\n", + " \n", + " # name and species are attributes associated with the instance\n", + " self.name = name\n", + " self.species = species\n", + " \n", + " # __repr__ is a special method we define here that tells the Python interpreter\n", + " # what to do when we print an instance of this class.\n", + " def __repr__(self):\n", + " return \"%s the %s\" %(self.name, self.species)\n", + " \n", + " # we can define more complex methods.\n", + " def get_age(self):\n", + " # attributes of a class can be accessed by special functions, e.g.\n", + " # getattr, setattr, and hasattr.\n", + " # hasattr checks if the instance of class has an attirbute defined.\n", + " # if yes, return True else return False.\n", + " if hasattr(self,'birthday'):\n", + " age_in_years = (datetime.date.today() - self.birthday).days / 365.25\n", + " return print(\"%s is %.2f years old\" %(self.name, age_in_years))\n", + " else:\n", + " return print(\"no records of resident's birthday\")\n", + " \n", + " # classes accept special methods too, and these special methods are\n", + " # defined by decorators defined by the \"@\" symbol.\n", + " \n", + " # Unlike the attribute 'birthday', we now want to define an attribute that\n", + " # should not be accessed directly from code outside of our class definition.\n", + " # In Python, we prefix such attributes with an underscore, e.g. _relations.\n", + " # In other languages, e.g. C++, such attributes are called \"private attributes\".\n", + " @property\n", + " def relations(self):\n", + " return self._relations\n", + " \n", + " # By defining a property decorator above, we can expose our attribute through a \n", + " # \"setter\" method. Every time we set this attribute to our class instance, the\n", + " # code in the following function is executed.\n", + " @relations.setter\n", + " def relations(self, relationship):\n", + " if not hasattr(self,'relations'):\n", + " self._relations = relationship\n", + " else:\n", + " for item in relationship.items():\n", + " if not item[0] in self._relations:\n", + " self._relations[item[0]] = item[1]\n", + " else:\n", + " # if resident already has a mother, raise a warning and do not\n", + " # make any changes by using the continue keyword.\n", + " if item[0] == 'mother':\n", + " warnings.warn(\"resident already has a mother. no changes made.\")\n", + " continue\n", + " \n", + " [self._relations[item[0]].append(member) for member in item[1]]\n", + " \n", + " # Unlike a list, a \"set\" does not allow duplicated entries\n", + " # By converting our list to a set and then back to a list,\n", + " # we are removing duplicated entries. E.g. following our\n", + " # example below, Molly cannot be listed twice as a friend\n", + " # of Jack.\n", + " self._relations[item[0]] = list(set(self._relations[item[0]]))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 402, + "id": "a7ca0dc1-2524-4b98-bcc8-6355036eedc6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'friends': [luisa the cat, artur the cat]}\n", + "{'friends': [luisa the cat, artur the cat], 'father': [harry the cat], 'mother': [luisa the cat]}\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ray/anaconda3/envs/playground/lib/python3.7/site-packages/ipykernel_launcher.py:63: UserWarning: resident already has a mother. no changes made.\n" + ] + } + ], + "source": [ + "lui = resident('lui', 'cat')\n", + "lui.birthday = datetime.date(2004,6,1)\n", + "setattr(lui, 'birthday', datetime.date(2004,6,1))\n", + "# print(lui.birthday)\n", + "# lui.get_age()\n", + "# print(id(lui))\n", + "\n", + "luisa = resident('luisa', 'cat')\n", + "# luisa.get_age()\n", + "# print(id(luisa))\n", + "\n", + "artur = resident('artur', 'cat')\n", + "\n", + "friends = {'friends' : [luisa, artur]}\n", + "# setattr(lui, 'relations', friends)\n", + "lui.relations = friends\n", + "print(lui.relations)\n", + "\n", + "harry = resident('harry', 'cat')\n", + "lui.relations = {'father' : [harry]}\n", + "lui.relations = {'mother' : [luisa]}\n", + "lui.relations = {'mother' : [artur]}\n", + "print(lui.relations)" + ] + }, + { + "cell_type": "code", + "execution_count": 327, + "id": "cee2c913-c906-4998-b4e4-fe2eb0c1ccee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "molly the dog\n", + "jack the cat\n", + "peter the iguana\n", + "joe the iguana\n" + ] + } + ], + "source": [ + "# let us initialise a few instances of the 'resident' class.\n", + "# recall that we need to supply two arguments for each\n", + "# instance of the class: name and species.\n", + "molly = resident('molly', 'dog')\n", + "jack = resident('jack', 'cat')\n", + "peter = resident('peter', 'iguana')\n", + "joe = resident('joe', 'iguana')\n", + "\n", + "print(molly)\n", + "print(jack)\n", + "print(peter)\n", + "print(joe)\n", + "# What happens if we did not define the __repr method?" + ] + }, + { + "cell_type": "code", + "execution_count": 328, + "id": "3c29e81d-03ee-4b17-862b-cbc4ec086eee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "no records of resident's birthday\n", + "{'name': 'jack', 'species': 'cat'}\n" + ] + } + ], + "source": [ + "# now, we want to get the age of Jack, but that doesn't make\n", + "# sense yet because we do not know when Jack was born.\n", + "jack.get_age()\n", + "\n", + "# let's check the attributes that the Jack instance has\n", + "print(vars(jack))" + ] + }, + { + "cell_type": "code", + "execution_count": 329, + "id": "bcdab8cd-696f-46ad-8a20-797a6cc6fcde", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "jack is 5.33 years old\n", + "{'name': 'jack', 'species': 'cat', 'birthday': datetime.date(2016, 8, 6)}\n" + ] + } + ], + "source": [ + "# But say after some investigation, we know Jack's birthday and\n", + "# now we can add a new attribute to Jack's instance of the resident\n", + "# class.\n", + "jack.birthday = datetime.date(2016,8,6)\n", + "# now, the notion of an \"age\" for Jack makes sense.\n", + "jack.get_age()\n", + "\n", + "# Now let's check the attributes again\n", + "print(vars(jack))" + ] + }, + { + "cell_type": "code", + "execution_count": 330, + "id": "f537d32e-8d0f-45db-9230-85509b6b4744", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'friends': [molly the dog]}\n", + "{'name': 'jack', 'species': 'cat', 'birthday': datetime.date(2016, 8, 6), '_relations': {'friends': [molly the dog]}}\n" + ] + } + ], + "source": [ + "# Jack has made a new friend, Molly the dog.\n", + "friends = {'friends': [molly]}\n", + "# We can now add Molly as a friend. 'setattr' is another way to add\n", + "# an attribute to Jack's instance of the resident class.\n", + "setattr(jack, 'relations', friends)\n", + "print(jack.relations)\n", + "\n", + "print(vars(jack))" + ] + }, + { + "cell_type": "code", + "execution_count": 331, + "id": "97bf9d08-a83c-4791-8f0b-595d95a18cad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'friends': [peter the iguana, joe the iguana, molly the dog]}\n" + ] + } + ], + "source": [ + "# Jack, being a friendly cat, makes friends with Peter and Joe\n", + "# the Iguanas. So we update these relationships to our database.\n", + "friends = {'friends': [peter,joe]}\n", + "# Because we have programmed the machinary to append friends,\n", + "# the following line of code works.\n", + "setattr(jack, 'relations', friends)\n", + "print(jack.relations)" + ] + }, + { + "cell_type": "code", + "execution_count": 332, + "id": "184f4ead-93b4-4afb-b46f-2e11891ca7ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'friends': [peter the iguana, joe the iguana, molly the dog], 'mother': [kelly the cat]}\n" + ] + } + ], + "source": [ + "# A new cat has arrived at the shelter, and she is Jack's mother.\n", + "# So we now update the relation of Jack:\n", + "kelly = resident('kelly', 'cat')\n", + "jack.relations = {'mother' : [kelly]}\n", + "print(jack.relations)" + ] + }, + { + "cell_type": "code", + "execution_count": 333, + "id": "37f8bd28-79a9-485b-b19e-b78449b658ae", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'friends': [peter the iguana, joe the iguana, molly the dog], 'mother': [kelly the cat], 'father': [john the cat]}\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ray/anaconda3/envs/playground/lib/python3.7/site-packages/ipykernel_launcher.py:64: UserWarning: resident already has a mother. no changes made.\n" + ] + } + ], + "source": [ + "# Another new cat has arrived, and he is Jack's father. We want to\n", + "# update this relationship into the database. Furthermore, a new\n", + "# colleague of yours thinks that Molly is actually Jack's mother due\n", + "# to their close friendship. So she tries to update Molly as Jack's\n", + "# mom. This will not work as we say that each resident can have only\n", + "# one mother...\n", + "jack.relations = {'mother' : [molly], 'father': [john]}\n", + "print(jack.relations)" + ] + }, + { + "cell_type": "markdown", + "id": "46665316-6c3a-483c-ae2f-22589bd83120", + "metadata": {}, + "source": [ + "One commonly used concept that we did not cover above is *class inheritance*. You can read more about it [here](https://docs.python.org/3/tutorial/classes.html#inheritance). When working with classes, I prefer *composition* over *inheritance*, and you can read more about the differences [here](https://realpython.com/inheritance-composition-python/).\n", + "\n", + "*Composition*: In our example above, we could replace the `relations` attribute with an instance of a `relationship` class, and this would be more flexible and extendable than what we have implemented above. Below is a rudimentary example, try extending it!" + ] + }, + { + "cell_type": "code", + "execution_count": 404, + "id": "8e84cbba-0b20-4114-8f03-c450ee2a1f3b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "jack the cat\n", + "-----\n", + "jack's relationships are: \n", + "mother: molly the dog\n", + "friends: [peter the iguana, joe the iguana]\n", + "\n" + ] + } + ], + "source": [ + "class resident(object):\n", + " def __init__(self,name,species):\n", + " self.name = name\n", + " self.species = species\n", + " \n", + " def __repr__(self):\n", + " base = \"%s the %s\" %(self.name, self.species)\n", + " if hasattr(self, 'relations'):\n", + " base += '\\n-----\\n'\n", + " base += '%s\\'s relationships are: \\n' %self.name\n", + " base += str(relations)\n", + " return base\n", + " \n", + " def get_age(self):\n", + " if hasattr(self,'birthday'):\n", + " age_in_years = (datetime.date.today() - self.birthday).days / 365.25\n", + " return print(\"%s is %.2f years old\" %(self.name, age_in_years))\n", + " else:\n", + " return print(\"no records of resident's birthday\")\n", + "\n", + "\n", + "class relationship(object):\n", + " def __init__(self):\n", + " # write method to make sure that we can define only one father and one mother\n", + " self.father = None \n", + " self.mother = None\n", + " # write method to extend siblings and friends list\n", + " # what happens if two residents are no longer friends,\n", + " # can we erase the corresponding friend entry?\n", + " self.siblings = None\n", + " self.friends = None\n", + " \n", + " def __repr__(self):\n", + " base = ''\n", + " for key, value in vars(self).items():\n", + " if value is not None:\n", + " base += key + ': ' + str(value) + '\\n'\n", + " return base\n", + " \n", + "molly = resident('molly', 'dog')\n", + "jack = resident('jack', 'cat')\n", + "peter = resident('peter', 'iguana')\n", + "joe = resident('joe', 'iguana')\n", + "\n", + "# define an instance of the relationship class\n", + "relations = relationship()\n", + "# fill up the attributes that we have\n", + "relations.mother = molly\n", + "relations.friends = [peter,joe]\n", + "# set the relations attribute of Jack's instance \n", + "# of the resident class to the instance of the\n", + "# relationship class we initialised above.\n", + "jack.relations = relations\n", + "\n", + "print(jack)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8d241d65-3d67-42c4-8974-9069f4389624", + "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", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/w9/heat_eqn/data/__input__.py b/w9/heat_eqn/data/__input__.py new file mode 100644 index 0000000..e69de29 diff --git a/w9/heat_eqn/data/grid.py b/w9/heat_eqn/data/grid.py new file mode 100644 index 0000000..c5fda5d --- /dev/null +++ b/w9/heat_eqn/data/grid.py @@ -0,0 +1,35 @@ +import numpy as np + +class sGrid(object): + def __init__(self, ud): + self.Nx = ud.Nx + self.xmin = ud.xmin + self.xmax = ud.xmax + + self.x = np.linspace(self.xmin, self.xmax, self.Nx).reshape(-1,1) + self.dx = np.diff(self.x.flatten())[0] + + if ud.Ny > 1: + self.Ny = ud.Ny + self.ymin = ud.ymin + self.ymax = ud.ymax + + self.y = np.linspace(self.ymin, self.ymax, self.Ny).reshape(1,-1) + self.dy = np.diff(self.y.flatten())[0] + else: + self.y = 0.0 + self.dy = np.nan + + self.dxy = (self.dx, self.dy) + self.xg, self.yg = np.meshgrid(self.x, self.y) + + +class tGrid(object): + def __init__(self, ud): + self.T = ud.T + self.dt = ud.dt + self.t = np.arange(0.0, self.T+self.dt, self.dt) + + + + diff --git a/w9/heat_eqn/data/io.py b/w9/heat_eqn/data/io.py new file mode 100644 index 0000000..64219a4 --- /dev/null +++ b/w9/heat_eqn/data/io.py @@ -0,0 +1,69 @@ +import argparse +import os +import h5py +import numpy as np + +class writer(object): + def __init__(self, folder='./output/', filename='heat_eqn.h5'): + self.OUTPUT_FOLDER = folder + self.OUTPUT_FILENAME = filename + self.FILE_PATH = self.OUTPUT_FOLDER + '/' + self.OUTPUT_FILENAME + + # If directory does not exist, create it. + if not os.path.exists(self.OUTPUT_FOLDER): + os.mkdir(self.OUTPUT_FOLDER) + + # If file exists, rename it with old. + if os.path.exists(self.FILE_PATH): + os.rename(self.FILE_PATH, self.FILE_PATH+'_old') + + file = h5py.File(self.FILE_PATH, 'a') + file.close() + + def f(self): + file = h5py.File(self.FILE_PATH, 'r+') + return file + + def write(self, time, name, data): + time = np.around(time, 4) + file = self.f() + file.create_dataset(str(time) + '/' + str(name), data=data, chunks=True, compression='gzip', compression_opts=4) + file.close() + + def write_attr(self,obj): + file = self.f() + for key, value in vars(obj).items(): + try: + file.attrs.create(key,value) + except: + file.attrs.create(key,repr(value),dtype='" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.imshow(u0)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "388f2ba9-f31a-4759-880d-90ace2328b7d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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