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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.
Domain coloring plot of the function f(x) = ( x2 − 1) ( x − 2 − i) 2 x2 + 2 + 2 i, using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
Definition. The Bode plot for a linear, time-invariant system with transfer function ( being the complex frequency in the Laplace domain) consists of a magnitude plot and a phase plot. The Bode magnitude plot is the graph of the function of frequency (with being the imaginary unit ). The -axis of the magnitude plot is logarithmic and the ...
Convergence rate. Precision. Robustness. General performance. 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.
In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A. [1] The function is named after its graph's resemblance to a boxcar, a type of railroad car. The boxcar function can be expressed in terms of the uniform distribution as where f(a,b;x) is the ...
Plot of the Bessel function of the first kind J n (z) with n = 0.5 in the complex plane from −2 − 2i to 2 + 2i Plot of Bessel function of the first kind, J α (x), for integer orders α = 0, 1, 2. Bessel functions of the first kind, denoted as J α (x), are solutions of Bessel's differential equation.
Plot of normalized function (i.e. ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] = = (), using ordinary frequency f, where is the normalized form [10] of the sinc function and = (/) / = (/), using angular frequency , where is the unnormalized form of the sinc function.
Comparison of Linear, Concave, and Convex Functions In original (left) and log10 (right) scales. In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight ...