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MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
In size theory, the size function (,): + = {(,): <} associated with the size pair (,:) is defined in the following way. For every (,) +, (,) (,) is equal to the number of connected components of the set {: ()} that contain at least one point at which the measuring function (a continuous function from a topological space to [1] [2]) takes a value smaller than or equal to . [3]
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies ...
In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well. In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions.
A Method for Selecting the Bin Size of a Histogram; Histograms: Theory and Practice, some great illustrations of some of the Bin Width concepts derived above. Matlab function to plot nice histograms; Dynamic Histogram in MS Excel; Histogram construction and manipulation using Java applets, and charts on SOCR
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics , the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations , namely those whose matrix is positive-semidefinite .
In mathematics, size theory studies the properties of topological spaces endowed with -valued functions, with respect to the change of these functions. More formally, the subject of size theory is the study of the natural pseudodistance between size pairs. A survey of size theory can be found in . [1]