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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
Recall from above that an n×n matrix exp(tA) amounts to a linear combination of the first n −1 powers of A by the Cayley–Hamilton theorem. For diagonalizable matrices, as illustrated above, e.g. in the 2×2 case, Sylvester's formula yields exp(tA) = B α exp(tα) + B β exp(tβ), where the B s are the Frobenius covariants of A.
Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy.It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
JAX is a machine learning framework for transforming numerical functions developed by Google with some contributions from Nvidia. [2] [3] [4] It is described as bringing together a modified version of autograd (automatic obtaining of the gradient function through differentiation of a function) and OpenXLA's XLA (Accelerated Linear Algebra).
SciPy (pronounced / ˈ s aɪ p aɪ / "sigh pie" [2]) is a free and open-source Python library used for scientific computing and technical computing. [3]SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering.
The LSE function is often encountered when the usual arithmetic computations are performed on a logarithmic scale, as in log probability. [5]Similar to multiplication operations in linear-scale becoming simple additions in log-scale, an addition operation in linear-scale becomes the LSE in log-scale:
This is a list of notable programming languages with features designed for object-oriented programming (OOP). The listed languages are designed with varying degrees of OOP support. Some are highly focused in OOP while others support multiple paradigms including OOP.
In the Go example, the Japanese ko rule is known to imply EXPTIME-completeness, but it is not known if the American or Chinese rules for the game are EXPTIME-complete (they could range from PSPACE to EXPSPACE). By contrast, generalized games that can last for a number of moves that is polynomial in the size of the board are often PSPACE ...