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In multilinear algebra, a reshaping of tensors is any bijection between the set of indices of an order-tensor and the set of indices of an order-tensor, where <.The use of indices presupposes tensors in coordinate representation with respect to a basis.
FreeMat is a free open-source numerical computing environment and programming language, [1] similar to MATLAB and GNU Octave. [2] In addition to supporting many MATLAB functions and some IDL functionality, it features a codeless interface to external C, C++, and Fortran code, further parallel distributed algorithm development (via MPI), and has plotting and 3D visualization capabilities. [3]
Programming languages that implement matrices may have easy means for vectorization. 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.
MATLAB (an abbreviation of "MATrix LABoratory" [18]) 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.
GNU Octave is a scientific programming language for scientific computing and numerical computation.Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.
ML.NET is a free-software machine-learning library for the C# programming language. [4] [5] NAG Library is an extensive software library of highly optimized numerical-analysis routines for various programming environments. O-Matrix is a proprietary licensed matrix programming language for mathematics, engineering, science, and financial analysis.
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 use of optimization software requires that the function f is defined in a suitable programming language and connected at compilation or run time to the optimization software. The optimization software will deliver input values in A , the software module realizing f will deliver the computed value f ( x ) and, in some cases, additional ...