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The top row is a series of plots using the escape time algorithm for 10000, 1000 and 100 maximum iterations per pixel respectively. The bottom row uses the same maximum iteration values but utilizes the histogram coloring method. Notice how little the coloring changes per different maximum iteration counts for the histogram coloring method plots.
GNU Octave is an open source high level programming language and library, including a command line interface and GUI, analogous to commercial alternatives such as Maple, MATLAB, Mathematica, etc. APIs, functions and libraries can be called from many platforms, including high level engineering programs, where functions are, in many cases ...
Examples of symbolic computations are given below. Maple incorporates a dynamically typed imperative-style programming language (resembling Pascal), which permits variables of lexical scope. [3] There are also interfaces to other languages (C, C#, Fortran, Java, MATLAB, and Visual Basic), as well as to Microsoft Excel.
It can produce 2D/3D plots. FEATool Multiphysics is a Matlab GUI toolbox for finite element FEM and PDE multiphysics simulations. FEniCS Project is a collection of project for automated solutions to PDEs. Hermes is a C++ library of advanced adaptive finite element algorithms to solve PDEs and multiphysics coupled problems.
The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology. [2] [3] [4] FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT).
Figure 4: Example of how source code transformation could work. The source code for a function is replaced by an automatically generated source code that includes statements for calculating the derivatives interleaved with the original instructions. Source code transformation can be implemented for all programming languages, and it is also ...
The direct calculation of the constant-Q transform (either using naive discrete Fourier transform or slightly faster Goertzel algorithm) is slow when compared against the fast Fourier transform. However, the fast Fourier transform can itself be employed, in conjunction with the use of a kernel , to perform the equivalent calculation but much ...
Compute the Fourier transform (b j,k) of g.Compute the Fourier transform (a j,k) of f via the formula ().Compute f by taking an inverse Fourier transform of (a j,k).; Since we're only interested in a finite window of frequencies (of size n, say) this can be done using a fast Fourier transform algorithm.