Slope-Field-Grapher.ipynb

{"cells":[{"cell_type":"markdown","metadata":{},"source":["# Procedure\n","1. Import libraries\n","2. Define differential equation\n","3. Find matrix of slopes for each point in provided window\n","4. Graph line segment for each of these slopes"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import matplotlib.pyplot as plt\n","import numpy as np"]},{"cell_type":"code","execution_count":2,"metadata":{},"outputs":[],"source":["%matplotlib inline\n","def plot_slope_field(differential, xmin, xmax, ymin, ymax):\n","    \"\"\"\n","    differential = function taking in x and y, returning slope as float\n","    xmin = x min value for window\n","    xmax = x max value for window\n","    ymin = y min value for window\n","    ymax = y max value for window\n","    \"\"\"\n","    fig = plt.figure()\n","    axes = fig.add_axes([0,0,1,1])\n","    axes.set_xlim(xmin-0.3, xmax+0.3)\n","    axes.set_ylim(ymin-0.3, ymax+0.3)\n","\n","    for x in range(xmin, xmax+1):\n","        for y in range(ymin, ymax+1):\n","            slope = differential(x, y)\n","            segment = lambda inp: y + slope*(inp-x)\n","            if slope==0:\n","                b = 0.2\n","            else:\n","                b = 0.1 / (abs(slope) ** 0.5)\n","            out_section = segment(np.array([x-b, x+b]))\n","            axes.plot(np.array([x-b, x+b]), out_section)\n","\n","    axes.set_aspect('equal')\n","    axes.grid(True, which='both')\n","\n","    # set the x-spine (see below for more info on `set_position`)\n","    axes.spines['left'].set_position('zero')\n","\n","    # turn off the right spine/ticks\n","    axes.spines['right'].set_color('none')\n","    axes.yaxis.tick_left()\n","\n","    # set the y-spine\n","    axes.spines['bottom'].set_position('zero')\n","\n","    # turn off the top spine/ticks\n","    axes.spines['top'].set_color('none')\n","    axes.xaxis.tick_bottom()"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["diff = lambda x,y: (x*y) / (x**2 + 4)\n","plot_slope_field(diff, -4, 4, -4, 4)"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":[]}],"metadata":{"kernelspec":{"display_name":"Python 3.10.4 64-bit","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":"3.10.4"},"orig_nbformat":4,"vscode":{"interpreter":{"hash":"3ad933181bd8a04b432d3370b9dc3b0662ad032c4dfaa4e4f1596c548f763858"}}},"nbformat":4,"nbformat_minor":2}