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# scipy-optimize NPM Module ## <a name='contents' href='#'/> Contents [What is scipy's optimize package?](https://github.com/acjones617/scipy-node/tree/master/optimize#about) [Setup Process](https://github.com/acjones617/scipy-node/tree/master/optimize#setup) [API](https://github.com/acjones617/scipy-node/tree/master/optimize#use) ------------------------------------------------------------------------------------------------------------ [The appropriate format for the "func" argument](https://github.com/acjones617/scipy-node/tree/master/optimize#func) [Find Minimum Value of a Mathematical Expression](https://github.com/acjones617/scipy-node/tree/master/optimize#min) [Find the Root of a Function](https://github.com/acjones617/scipy-node/tree/master/optimize#root) [Find the best-fit curve given data](https://github.com/acjones617/scipy-node/tree/master/optimize#fit) [Least Squares](https://github.com/acjones617/scipy-node/tree/master/optimize#nnls) [Calculate Partial Derivative Values at a Point](https://github.com/acjones617/scipy-node/tree/master/optimize#derive) ------------------------------------------------------------------------------------------------------------ [Testing](https://github.com/acjones617/scipy-node/tree/master/optimize#testing) ## <a name='about' href='#about'/> What is scipy's optimize package? Scipy is an extensively used, well-documented Python library for all your scientific needs. Optimize is a module of the library concerned with optimization of functions. This npm module is a node wrapper for which you can use JavaScript to access the power of the optimize module. It exists on the npm registry under the name "scipy-optimize". The code can be seen at my <a href='https://github.com/acjones617/scipy-node/tree/master/optimize'>scipy/optimize</a> github repo. A demo application is forthcoming. npm install scipy-optimize Using the node.js command line interface, the underlying python engine is launched as a child process, with the results streamed to node. These results are divided into various variables based on the type of data they hold, and a user can gain access to all this raw analysis. ## <a name='setup' href='#setup'/> Setup Process To utilize the Product-Recommender NPM module, the first step would be to make sure one has successfully installed node.js, npm, and a python version of >= 2.7. To install these items, I would recommend you check out http://nodejs.org/download/ and https://www.python.org/download/. In addition to these prerequisites, you will need to install scipy and sympy. For installation instructions on scipy, please go to http://www.scipy.org/install.html. For installation instructions on sympy, please go to http://docs.sympy.org/dev/install.html. Some other python modules used in this project are argparse, ast, and json, though these should be included in the Python Standard Library so there is likely no need to download these. ## <a name='use' href='#use'/> API To use my scipy-optimize algorithm, first install scipy-optimize: npm install --save scipy-optimize Then, require scipy-optimize in your js file. I'm going to use the variable 'opt' to represent the module var opt = require('scipy-optimize'); opt is an object with many of the SciPy Optimization methods (and the rest to hopefully soon follow). Currently, the methods on opt are: <b> [opt.localMinimize(func, options, callback) and opt.globalMinimize(func, options, callback)](https://github.com/acjones617/scipy-node/tree/master/optimize#min) [opt.findRoot(func, lower, upper, options, callback)](https://github.com/acjones617/scipy-node/tree/master/optimize#root) [opt.fitCurve.linear(xData, yData, callback), opt.fitCurve.quadratic(xData, yData, callback), and opt.fitCurve(func, xData, yData, options, callback)](https://github.com/acjones617/scipy-node/tree/master/optimize#fit) [opt.minimizeEuclideanNorm(A, b, callback)](https://github.com/acjones617/scipy-node/tree/master/optimize#nnls) [opt.calcDerivatives(func, point, options, callback)](https://github.com/acjones617/scipy-node/tree/master/optimize#derive) </b> Many of these require the user to pass in a "func" argument to optimize. Func requires a very specific format: ## <a name='func' href='#func'/> Appropriate format for "func" Func represents the mathematical expression you want to optimize. It can be one of two things: For all but fitCurve, func can be a function that takes a single argument. Make sure that the entire mathematical expression follows the "return" statement. For example, the following <b>IS</b> a valid function to pass to func: func = function (x){ return Math.pow(x - 10, 4) + Math.log(Math.abs(x + 1)) - 10 * x; }; // this is equivalent to f(x) = (x - 10)^4 + log(|x+1|) - 10 * x // minimizes to around -107.66 when x is around 11.35 However, the following is <b>NOT</b> a valid function to pass to func, both because it takes multiple arguments, and because it conducts relevant operations outside of the specific "return" statement: func = function (x, y){ var res = x * y; res = Math.pow(res - 10, 4); return res; }; For fitCurve, func can take multiple arguments. The first argument must be the independent variable, and the following arguments will be the parameters we are trying to fit. For example: func = function(ind, param1, param2, param3) { return param1 * pow(ind, 2) + param2 * ind + param3; } Func can also be a string representing the expression. You must use "x" as the independent variable, unless otherwise specified in the options object. Func could be: func = 'Math.pow(x - 10, 4) + Math.log(Math.abs(x + 1)) - 10 * x'; If we were to use a different independent variable, we would need to pass that information through the options argument, on the "variable" property. For example, if were to use "ind" as the independent variable, our options argument would at least need to be: options = { variable: 'ind' } If we were to use a string to represent the expression for fitCurve, we need to pass an array with the variable names to the "variables" property on the options object. The first variable would be the independent variable, and the remaining would be the parameters. For example: options = { variables: ['ind', 'param1', 'param2', 'param3'] } Your true range of possible operations is much greater than merely what is found in the JavaScript Math object. For example, while the JavaScript Math.log(x) by default is the natural logarithm, base e, you can compute the logarithm of any base with "log(x, base)." For example, log(x, 10) would be the logarithm of x, base 10. Please check the SymPy lambdify documentation for what it will take as an "expression" for more information. For example, you could write func without the Math. object entirely, like below: func = 'pow((x-10),4) - 5 * x + 3' // this is equivalent to f(x) = (x-10)^4 - 5x + 3 // minimizes to around -51.04 when x is around 11.07 ## <a name='min' href='#min'/> Find Minimum Value of a Univariate Mathematical Expression Two functions are available: opt.localMinimize(func[, options[, callback]]) and opt.globalMinimize(func[, options[, callback]]), in case your expression may have many local minima and you want to ensure that you're finding the global minimum. Example: opt.localMinimize(function(x) { return Math.pow(x-4, 4) - Math.pow(x, 3) + 10 * x - 1; }, { bounds: [-10, 10] }, function(results) { console.log(results); }); results = { status : 0, nfev : 15, success : true, fun : -198.63648235818988, x : 7.3684735542053241, message : "Solution found." } Both opt.localMinimize and opt.globalMinimize take up to three arguments: #### func (required) See above for details on how to [format func](https://github.com/acjones617/scip