{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#### New to Plotly?\n", "Plotly's Python library is free and open source! [Get started](https://plotly.com/python/getting-started/) by dowloading the client and [reading the primer](https://plotly.com/python/getting-started/).\n", "
You can set up Plotly to work in [online](https://plotly.com/python/getting-started/#initialization-for-online-plotting) or [offline](https://plotly.com/python/getting-started/#initialization-for-offline-plotting) mode, or in [jupyter notebooks](https://plotly.com/python/getting-started/#start-plotting-online).\n", "
We also have a quick-reference [cheatsheet](https://images.plot.ly/plotly-documentation/images/python_cheat_sheet.pdf) (new!) to help you get started!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Imports\n", "The tutorial below imports [NumPy](http://www.numpy.org/), [Pandas](https://plotly.com/pandas/intro-to-pandas-tutorial/), and [SciPy](https://www.scipy.org/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import plotly.plotly as py\n", "import plotly.graph_objs as go\n", "from plotly.tools import FigureFactory as FF\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import scipy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Add Two Matrices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Matrix is a 2D array that stores real or complex numbers. A _Real Matrix_ is one such that all its elements $r$ belong to $\\mathbb{R}$. Likewise, a _Complex Matrix_ has entries $c$ in $\\mathbb{C}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix1 = np.matrix(\n", " [[0, 4],\n", " [2, 0]]\n", ")\n", "\n", "matrix2 = np.matrix(\n", " [[-1, 2],\n", " [1, -2]]\n", ")\n", "\n", "matrix_sum = matrix1 + matrix2\n", "\n", "colorscale = [[0, '#EAEFC4'], [1, '#9BDF46']]\n", "font=['#000000', '#000000']\n", "\n", "table = FF.create_annotated_heatmap(matrix_sum.tolist(), colorscale=colorscale, font_colors=font)\n", "py.iplot(table, filename='matrix-sum')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiply Two Matrices\n", "How to find the product of two matrices" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix1 = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "matrix2 = np.matrix(\n", " [[-1, 2],\n", " [1, -2]]\n", ")\n", "\n", "matrix_prod = matrix1 * matrix2\n", "\n", "colorscale = [[0, '#F1FFD9'], [1, '#8BDBF5']]\n", "font=['#000000', '#000000']\n", "\n", "table = FF.create_annotated_heatmap(matrix_prod.tolist(), colorscale=colorscale, font_colors=font)\n", "py.iplot(table, filename='matrix-prod')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Solve Matrix Equation\n", "How to find the solution of $AX=B$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "B = np.matrix(\n", " [[-1, 2],\n", " [1, -2]]\n", ")\n", "\n", "X = np.linalg.solve(A, B)\n", "\n", "colorscale = [[0, '#497285'], [1, '#DFEBED']]\n", "font=['#000000', '#000000']\n", "\n", "table = FF.create_annotated_heatmap(X.tolist(), colorscale=colorscale, font_colors=font)\n", "py.iplot(table, filename='matrix-eq')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Find the Determinant" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-7.9999999999999982" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "det = np.linalg.det(matrix)\n", "det" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Find the Inverse" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "inverse = np.linalg.inv(matrix)\n", "\n", "colorscale = [[0, '#F1FAFB'], [1, '#A0E4F1']]\n", "font=['#000000', '#000000']\n", "\n", "table = FF.create_annotated_heatmap(inverse.tolist(), colorscale=colorscale, font_colors=font)\n", "py.iplot(table, filename='inverse')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Find Eigenvalues" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The eignevalues are 3.372281 and -2.372281\n" ] } ], "source": [ "matrix = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "eigvals = np.linalg.eigvals(matrix)\n", "print(\"The eignevalues are %f and %f\") %(eigvals[0], eigvals[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Find SVD\n", "How to find the Singular Value Decomposition of a matrix, i.e. break up a matrix into the product of three matrices: $U$, $\\Sigma$, $V^*$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix = np.matrix(\n", " [[1, 4],\n", " [2, 0]]\n", ")\n", "\n", "svd = np.linalg.svd(matrix)\n", "\n", "u = svd[0]\n", "sigma = svd[1]\n", "v = svd[2]\n", "\n", "u = u.tolist()\n", "sigma = sigma.tolist()\n", "v = v.tolist()\n", "\n", "colorscale = [[0, '#111111'],[1, '#222222']]\n", "font=['#ffffff', '#ffffff']\n", "\n", "matrix_prod = [\n", " ['$U$', '', '$\\Sigma$', '$V^*$', ''],\n", " [u[0][0], u[0][1], sigma[0], v[0][0], v[0][1]],\n", " [u[1][0], u[1][1], sigma[1], v[1][0], v[1][1]]\n", "]\n", "\n", "table = FF.create_table(matrix_prod)\n", "py.iplot(table, filename='svd')" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Collecting git+https://github.com/plotly/publisher.git\n", " Cloning https://github.com/plotly/publisher.git to /var/folders/ld/6cl3s_l50wd40tdjq2b03jxh0000gp/T/pip-JSnMuv-build\n", "Installing collected packages: publisher\n", " Found existing installation: publisher 0.10\n", " Uninstalling publisher-0.10:\n", " Successfully uninstalled publisher-0.10\n", " Running setup.py install for publisher ... \u001b[?25l-\b \b\\\b \b|\b \bdone\n", "\u001b[?25hSuccessfully installed publisher-0.10\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/brandendunbar/Desktop/test/venv/lib/python2.7/site-packages/IPython/nbconvert.py:13: ShimWarning: The `IPython.nbconvert` package has been deprecated. You should import from nbconvert instead.\n", " \"You should import from nbconvert instead.\", ShimWarning)\n", "/Users/brandendunbar/Desktop/test/venv/lib/python2.7/site-packages/publisher/publisher.py:53: UserWarning: Did you \"Save\" this notebook before running this command? Remember to save, always save.\n", " warnings.warn('Did you \"Save\" this notebook before running this command? '\n" ] } ], "source": [ "from IPython.display import display, HTML\n", "\n", "display(HTML(''))\n", "display(HTML(''))\n", "\n", "! pip install git+https://github.com/plotly/publisher.git --upgrade\n", "import publisher\n", "publisher.publish(\n", " 'python_Linear_Algebra.ipynb', 'python/linear-algebra/', 'Linear Algebra | plotly',\n", " 'Learn how to perform several operations on matrices including inverse, eigenvalues, and determinents',\n", " title='Linear Algebra in Python. | plotly',\n", " name='Linear Algebra',\n", " language='python',\n", " page_type='example_index', has_thumbnail='false', display_as='mathematics', order=10,\n", " ipynb= '~notebook_demo/104')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }