{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Matplotlib" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_format = 'svg'\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first line above which begins with a `%` is called a [magic command](https://ipython.readthedocs.io/en/stable/interactive/magics.html), which here sets the figure format to svg, which is a vector graphics format but looks prettier than default format.\n", "\n", "There are two main approaches to use Matplotlib. The simplest one, which is somewhat similar to Matlab is described first. An object oriented approach is described in the end." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single graph\n", "$$\n", "f(x) = x \\sin(x) \\sin(50 x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: x * np.sin(x) * np.sin(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "\n", "plt.plot(x, f(x))\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.title('Plot of f(x)')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple graphs" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: x * np.sin(x) * np.sin(50*x)\n", "g = lambda x: x * np.cos(x) * np.cos(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "\n", "plt.plot(x,f(x),x,g(x))\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.title('Plot of f(x) and g(x)')\n", "plt.legend(('f(x)','g(x)'))\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The line colors are set to different values automatically, which is useful to distinguish the graphs.\n", "\n", "## Control line style\n", "\n", "We can however control the [line style](https://matplotlib.org/stable/gallery/lines_bars_and_markers/linestyles.html) ourselves." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: x * np.sin(x) * np.sin(50*x)\n", "g = lambda x: x * np.cos(x) * np.cos(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "\n", "plt.plot(x,f(x),'r-',linewidth=2,label='f(x)')\n", "plt.plot(x,g(x),'b--',label='g(x)')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.title('Plot of f(x) and g(x)')\n", "plt.legend()\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also specify parameters like this" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,f(x),c='red',ls='dashed',lw=2)\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Show symbols" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: x * np.sin(x) * np.sin(50*x)\n", "g = lambda x: np.cos(x) * np.cos(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "\n", "plt.plot(x,f(x),'k-o',markevery=10)\n", "plt.plot(x,g(x),'r--s',markevery=10)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.title('Plot of f(x) and g(x)')\n", "plt.legend(('f(x)','g(x)'),loc='upper right')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matrix of plots" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "y1 = np.sin(50*x)\n", "y2 = np.log(x+1) + np.tanh(x)\n", "y3 = x**2 + x * np.cos(10*x)\n", "y4 = np.cos(10*x) + np.sin(5*x)\n", "\n", "plt.figure(figsize=(10,8))\n", "lw = 1.5\n", "\n", "plt.subplot(221)\n", "plt.plot(x,y1,'k-',linewidth=lw)\n", "plt.xlabel('$x$'); plt.ylabel('$y_1$')\n", "plt.title('y1')\n", "\n", "plt.subplot(222)\n", "plt.plot(x,y2,'r--',linewidth=lw)\n", "plt.xlabel('$x$'); plt.ylabel('$y_2$')\n", "plt.title('y2')\n", "\n", "plt.subplot(223)\n", "plt.plot(x,y3,'g-.',linewidth=lw)\n", "plt.xlabel('$x$'); plt.ylabel('$y_3$')\n", "plt.title('y3')\n", "\n", "plt.subplot(224)\n", "plt.plot(x,y4,'b:',linewidth=lw)\n", "plt.xlabel('$x$'); plt.ylabel('$y_4$');\n", "plt.title('y4');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot in log scale: semilogy\n", "\n", "$$\n", "y = \\exp(x), \\qquad x \\in [-100,0]\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(-100,0,n)\n", "y = np.exp(x)\n", "plt.plot(x,y)\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The y axis has very small to very large values and the usual linear scale plot does not show this variation properly. We next plot the y axis in log scale." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(x,y)\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The linear curve clearly shows the exponential character of the function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot in log scale: loglog\n", "\n", "$$\n", "y = x^{-2}, \\qquad x \\in [10^{-3}, 10^{-2}]\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 10\n", "x = np.linspace(1e-3,1e-2,n)\n", "y = 1.0/x**2\n", "plt.plot(x,y,'o-')\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variations in both axes are too large, so we plot both axes in log scale." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(x,y,'o-')\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Scientific notation for tick values" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(0.1,1,n)\n", "y = 1e-4 * np.exp(x)\n", "plt.plot(x,y)\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,y)\n", "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(0,0));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Control tick values\n", "\n", "Which tick values are labelled is automatically chosen by matplotlib, but we can control this ourselves." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(0.0,1.0,n)\n", "y = np.sin(2.0*np.pi*x)\n", "plt.plot(x,y)\n", "plt.xticks([0.0, 0.25, 0.5, 0.75, 1.0])\n", "plt.yticks([-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0])\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2-D contour plots\n", "$$\n", "\\psi = \\sin(2\\pi x) \\cos(2\\pi y), \\qquad (x,y) \\in [0,1] \\times [0,1]\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(0.0, 1.0, n)\n", "y = np.linspace(0.0, 1.0, n)\n", "X, Y = np.meshgrid(x,y)\n", "\n", "psi = np.sin(2*np.pi*X) * np.cos(2*np.pi*Y)\n", "\n", "plt.figure(figsize=(5,5))\n", "plt.contour(X,Y,psi,levels=20)\n", "plt.xticks([0, 0.25, 0.5, 0.75, 1.0])\n", "plt.yticks([0, 0.25, 0.5, 0.75, 1.0])\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2-D filled plots" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(0.0, 1.0, n)\n", "y = np.linspace(0.0, 1.0, n)\n", "X, Y = np.meshgrid(x,y)\n", "\n", "psi = np.sin(2*np.pi*X) * np.cos(2*np.pi*Y)\n", "\n", "cf = plt.contourf(X,Y,psi,levels=20,cmap='jet')\n", "plt.colorbar(cf)\n", "plt.xticks([0, 0.25, 0.5, 0.75, 1.0])\n", "plt.yticks([0, 0.25, 0.5, 0.75, 1.0])\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$')\n", "plt.axis('equal')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2-D surface plot\n", "\n", "We have use OO interface, which is explained below." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(0.0, 1.0, n)\n", "y = np.linspace(0.0, 1.0, n)\n", "X, Y = np.meshgrid(x,y)\n", "\n", "psi = np.sin(2*np.pi*X) * np.cos(2*np.pi*Y)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "surf = ax.plot_surface(X, Y, psi, cmap='viridis',\n", " linewidth=0, antialiased=False,\n", " vmin=-1, vmax=1)\n", "fig.colorbar(surf, shrink=0.5, aspect=5)\n", "ax.set_zlim(-1.01, 1.01)\n", "ax.set_xlabel('X Label')\n", "ax.set_ylabel('Y Label');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Object oriented approach*\n", "\n", "A single plot." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: 0.5*x*np.sin(x)*np.sin(50*x)\n", "g = lambda x: 0.5*x*np.cos(x)*np.cos(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,2.0,n)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x,f(x),'r-',linewidth=2,label='f(x)')\n", "ax.plot(x,g(x),'b--',label='g(x)')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_title('Plot of f(x) and g(x)')\n", "ax.set_xlim(-0.1,2.1)\n", "ax.set_ylim(-1,1)\n", "ax.set_xticks([0,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.0])\n", "ax.legend()\n", "ax.grid(True)\n", "ax.set_aspect('equal')\n", "ax.text(0, -0.4, '$\\mu=115,\\ \\sigma=15$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A $1 \\times 2$ matrix of plots." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: x*np.sin(x)*np.sin(50*x)\n", "g = lambda x: x*np.cos(x)*np.cos(50*x)\n", "\n", "n = 200\n", "x = np.linspace(0.0,1.0,n)\n", "\n", "fig, ax = plt.subplots(2,2,figsize=(8,5))\n", "\n", "ax[0,0].plot(x,f(x),'r-',linewidth=2,label='f')\n", "ax[0,0].set_xlabel('x')\n", "ax[0,0].set_ylabel('f(x)')\n", "ax[0,0].set_title('Plot of f(x)')\n", "ax[0,0].set_xlim(-0.1,1.1)\n", "ax[0,0].set_ylim(-1,1)\n", "ax[0,0].grid(True)\n", "ax[0,0].legend()\n", "\n", "ax[0,1].plot(x,g(x),'b--',label='g')\n", "ax[0,1].set_xlabel('x')\n", "ax[0,1].set_ylabel('g(x)')\n", "ax[0,1].set_title('Plot of g(x)')\n", "ax[0,1].set_xlim(-0.1,1.1)\n", "ax[0,1].set_ylim(-1,1)\n", "ax[0,1].grid(True)\n", "ax[0,1].legend()\n", "\n", "ax[1,0].plot(x,f(x)-g(x),'r-',linewidth=2,label='f-g')\n", "ax[1,0].set_xlabel('x')\n", "ax[1,0].set_ylabel('f(x)-g(x)')\n", "ax[1,0].set_title('Plot of f(x)-g(x)')\n", "ax[1,0].set_xlim(-0.1,1.1)\n", "ax[1,0].set_ylim(-1,1)\n", "ax[1,0].grid(True)\n", "ax[1,0].legend()\n", "\n", "ax[1,1].plot(x,f(x)+g(x),'b--',label='f+g')\n", "ax[1,1].set_xlabel('x')\n", "ax[1,1].set_ylabel('f(x)+g(x)')\n", "ax[1,1].set_title('Plot of f(x)+g(x)')\n", "ax[1,1].set_xlim(-0.1,1.1)\n", "ax[1,1].set_ylim(-1,1)\n", "ax[1,1].grid(True)\n", "ax[1,1].legend()\n", "\n", "fig.suptitle('2x2 matrix of plots');" ] } ], "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": "3.10.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }