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CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. [3]
The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication.It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
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]
Matrices are subject to standard operations such as addition and multiplication. [2] Most commonly, a matrix over a field F is a rectangular array of elements of F. [3] [4] A real matrix and a complex matrix are matrices whose entries are respectively real numbers or complex numbers. More general types of entries are discussed below. For ...
The lower bound of multiplications needed is 2mn+2n−m−2 (multiplication of n×m-matrices with m×n-matrices using the substitution method, m⩾n⩾3), which means n=3 case requires at least 19 multiplications and n=4 at least 34. [40] For n=2 optimal 7 multiplications 15 additions are minimal, compared to only 4 additions for 8 multiplications.