{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimizing functions using SciPy\n", "\n", "It is possible to use existing Python libraries in SciPy in order to find numerically minimizers of functions. The main algorithms are implemented. For a complete list check the online documentation. \n", "\n", "Below is a simple example that you can take as a starting point for the practical session. Keep in mind that each of the methods available in scipy.optimize.minimize may require different corresponding inputs. In any case, you hould provide:\n", "\n", "- the algorithm to be used in the optimization, using the parameter `method=`\n", "\n", "- an objective function of your choice\n", "\n", "- if a Gradient based algorithm is used the function computing the gradient may be given to the argument `jac=...`\n", "\n", "- if the Hessian matrix is needed, give it as an argument with `hess=...`\n", "\n", "- by default, the algorithm does not show you the optimization history. A callback function should be used if you want to recover information about the optimization history. An example of callback function is given below and it is provided to the minimization algorithm via the argument `calback=...`\n", "\n", "- you may also provide a tolerance for termination using `tol=...`. This parameter should be tune by looking at the documentation regarding each method." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 -1.029715 1.241966 7.419510\n", " 2 -1.057392 1.227979 5.440693\n", " 3 -1.098699 1.206567 4.404571\n", " 4 -1.094831 1.206799 4.394950\n", " 5 -1.088631 1.199017 4.381698\n", " 6 -1.069917 1.167096 4.334611\n", " 7 -0.671555 0.423311 2.870689\n", " 8 -0.656555 0.396630 2.862748\n", " 9 -0.542234 0.257183 2.514161\n", " 10 -0.402924 0.132259 2.058734\n", " 11 -0.292088 0.084680 1.669532\n", " 12 -0.199339 0.013767 1.505852\n", " 13 -0.077081 -0.039051 1.362541\n", " 14 -0.028445 -0.016065 1.086174\n", " 15 0.136811 -0.020803 0.901281\n", " 16 0.167562 0.021618 0.697125\n", " 17 0.335166 0.077922 0.560435\n", " 18 0.326465 0.100029 0.457940\n", " 19 0.429924 0.174557 0.335551\n", " 20 0.508023 0.238345 0.281020\n", " 21 0.581622 0.323552 0.196744\n", " 22 0.637653 0.408261 0.131571\n", " 23 0.697956 0.479843 0.096559\n", " 24 0.738412 0.533901 0.081314\n", " 25 0.792856 0.617496 0.055286\n", " 26 0.837698 0.699548 0.026821\n", " 27 0.876676 0.763255 0.018025\n", " 28 0.930921 0.860591 0.008400\n", " 29 0.949203 0.901621 0.002621\n", " 30 0.984586 0.967443 0.000625\n", " 31 0.988678 0.976804 0.000174\n", " 32 0.999317 0.998402 0.000006\n", " 33 0.999524 0.999096 0.000000\n", " 34 0.999991 0.999982 0.000000\n", " 35 1.000000 1.000000 0.000000\n", " 36 1.000000 1.000000 0.000000\n", " 37 1.000000 1.000000 0.000000\n" ] }, { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\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('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", "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 = $('
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