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SPICE (Spacecraft Planet Instrument C-matrix Events) is a NASA ancillary information system used to compute geometric information used in planning and analyzing science observations obtained from robotic spacecraft. It is also used in planning missions and conducting numerous engineering functions needed to carry out those missions.
EJML is free, written in 100% Java and has been released under an Apache v2.0 license. EJML has three distinct ways to interact with it: 1) Procedural, 2) SimpleMatrix, and 3) Equations. The procedural style provides all capabilities of EJML and almost complete control over matrix creation, speed, and specific algorithms.
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.
C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen: Benoît Jacob C++ 2008 3.4.0 / 08.2021 Free MPL2: Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5]
Matrix Toolkit Java (MTJ) is an open-source Java software library for performing numerical linear algebra. The library contains a full set of standard linear algebra operations for dense matrices based on BLAS and LAPACK code. Partial set of sparse operations is provided through the Templates project.
In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well. In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
The matrix left-division operator concisely expresses some semantic properties of matrices. As in the scalar equivalent, if the (determinant of the) coefficient (matrix) A is not null then it is possible to solve the (vectorial) equation A * x = b by left-multiplying both sides by the inverse of A: A −1 (in both MATLAB and GNU Octave ...