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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]
Numba is an open-source JIT compiler that translates a subset of Python and NumPy into fast machine code using LLVM, via the llvmlite Python package.It offers a range of options for parallelising Python code for CPUs and GPUs, often with only minor code changes.
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.
SciPy (pronounced / ˈ s aɪ p aɪ / "sigh pie" [3]) is a free and open-source Python library used for scientific computing and technical computing. [4]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.
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff.
Theano: The reference deep-learning library for Python with an API largely compatible with the popular NumPy library. Allows user to write symbolic mathematical expressions, then automatically generates their derivatives, saving the user from having to code gradients or backpropagation.
"Don't repeat yourself" (DRY), also known as "duplication is evil", is a principle of software development aimed at reducing repetition of information which is likely to change, replacing it with abstractions that are less likely to change, or using data normalization which avoids redundancy in the first place.