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MATLAB (an abbreviation of "MATrix LABoratory" [18]) 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.
Functions involving two or more variables require multidimensional array indexing techniques. The latter case may thus employ a two-dimensional array of power[x][y] to replace a function to calculate x y for a limited range of x and y values. Functions that have more than one result may be implemented with lookup tables that are arrays of ...
If f is a function from X to A and g is a function from Y to B, then their Cartesian product f × g is a function from X × Y to A × B with (,) = ((), ()). This can be extended to tuples and infinite collections of functions. This is different from the standard Cartesian product of functions considered as sets.
If F and G are (covariant) functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism η X : F(X) → G(X) in D such that for every morphism f : X → Y in C, we have η Y ∘ F(f) = G(f) ∘ η X; this means that the following diagram is commutative:
A modern dialect of APL, enhanced with features for functional and object-oriented programming. Euler Math Toolbox: René Grothmann 1987 1988 2022-02-10 10 February 2022: Free GPL: Also a computer algebra system through interface with Maxima: Fityk: Marcin Wojdyr 2002 1.3.1 19 December 2016: $115 (1.x binaries), Free (source code and 0.x ...
Here some test functions are presented with the aim of giving an idea about the different situations that optimization algorithms have to face when coping with these kinds of problems. In the first part, some objective functions for single-objective optimization cases are presented.
One has always X ⊆ f −1 (f(X)) and f(f −1 (Y)) ⊆ Y, where f(X) is the image of X and f −1 (Y) is the preimage of Y under f. If f is injective, then X = f −1 (f(X)), and if f is surjective, then f(f −1 (Y)) = Y. For every function h : X → Y, one can define a surjection H : X → h(X) : x → h(x) and an injection I : h(X) → Y ...
Dynamically scoped variants do not support closures or need a special construct to create closures. [22] In Common Lisp, the identifier of a function in the function namespace cannot be used as a reference to a first-class value. The special operator function must be used to retrieve the function as a value: (function foo) evaluates to a ...