Math with Python
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x : array_like q : array_like lower or upper tail probability loc : array_like, optional location parameter (default=0)
: array_like : array_like lower or upper tail probability : array_like : array_like, optional
This page summarizes how to work with univariate probability distributions using Python's SciPy library. See also notes on working with distributions in Mathematica , Excel , and R/S-PLUS . Probability distribution classes are located in scipy.stats . The methods on continuous distribution classes are as follows. Functions such as pdf and cdf are defined over the entire real line.
Finite Difference Method using MATLAB This section considers transient heat transfer and converts the partial differential equation to a set of ordinary differential equations, which are solved in MATLAB. This method is sometimes called the method of lines. We apply the method to the same problem solved with separation of variables . It represents heat transfer in a slab, which is insulated at x = 0 and whose temperature is kept at zero at x = a.
In mathematics , finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. [ edit ] Derivation from Taylor's polynomial Assuming the function whose derivatives are to be approximated is properly-behaved, by Taylor's theorem , where n ! denotes the factorial of n , and R n ( x ) is a remainder term, denoting the difference between the Taylor polynomial of degree n and the original function.
Scipy , and Numpy , provide a host of functions for performing statistical calculations. This article will describe ways of performing a few simple statistical calculations, as an introduction to using Scipy. Scipy package is organized into several sub-packages. Before using any of these sub-packages, it must be explicitly imported.
Travis E. Oliphant October 21, 2004 1 Introduction SciPy is a collection of mathematical algorithms and convenience functions built on the Numeric extension for Python. It adds significant power to the interactive Python session by exposing the user to high-level commands and classes for the manipulation and visualization of data.
func : callable f(x,*args) Objective function to be minimized. ranges : tuple Each element is a tuple of parameters or a slice object to be handed to numpy.mgrid . args : tuple
Find alpha that satisfies strong Wolfe conditions. f : objective function myfprime : objective function gradient (can be None) xk : ndarray -- start point pk : ndarray -- search direction gfk : ndarray -- gradient value for x=xk args : additional arguments for user functions c1 : number -- parameter for Armijo condition rule c2 : number - parameter for curvature condition rule alpha0 : number -- required alpha (x_new = x0 + alpha * pk) fc : number of function evaluations gc : number of gradient evaluations Notes <p style="text-align:right;color:#A8A8A8"></p>
The scipy.optimize package provides several commonly used optimization algorithms. A detailed listing is available: scipy.optimize (can also be found by help(scipy.optimize) ). Below, several examples demonstrate their basic usage. Unconstrained minimization of multivariate scalar functions ( minimize ) The minimize function provides a common interface to unconstrained and constrained minimization algorithms for multivariate scalar functions in scipy.optimize . To demonstrate the minimization function consider the problem of minimizing the Rosenbrock function of
The support for TeX and LaTeX in MathJax consists of two parts: the tex2jax preprocessor, and the TeX input processor. The first of these looks for mathematics within your web page (indicated by math delimiters like $$...$$ ) and marks the mathematics for later processing by MathJax. The TeX input processor is what converts the TeX notation into MathJax’s internal format, where one of MathJax’s output processors then displays it in the web page. The tex2jax preprocessor can be configured to look for whatever markers you want to use for your math delimiters. See the tex2jax configuration options section for details on how to customize the action of tex2jax .
I am easily excited when I find yet another place where I can use LaTeX syntax to typeset mathematics ( Google Docs , OpenOffice , again , presentations using Beamer , Inkscape ). Finally, it seems, it is not incredibly clunky to write math in Blogger. In fact, it is as convenient as writing it in a native LaTeX document.
Lots of people have blogs where they talk about maths. Lots of these people just use plain text for mathematical notation which, while it gets the point across, isn’t as easy to read or as visually appealing as it could be. MathJax lets you write LaTeX and get beautifully typeset mathematical notation. And it’s really really easy to set up: you just need to paste some code into the header of your blog’s theme. To make it really really really easy, I’ve written some very detailed instructions of what to do for each big blogging service.
Imagine some red flowers growing in a meadow at the base of a mountain range. Suppose one of the plants has a mutation that makes its flowers blue. If the new color makes it easier for insects to find and pollinate it, then as the years go by, the mutation will likely spread and replace the original red color in nearby plants. But will the mutation be able to spread to the far side of the mountain range?
There are two ways to deal with matrices in numpy. The standard numpy array in it 2D form can do all kinds of matrixy stuff, like dot products, transposes, inverses, or factorisations, though the syntax can be a little clumsy. For those who just can’t let go of matlab, there’s a matrix object which prettifies the syntax somewhat.