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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]
c = a + b In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also ...
Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
Yorick is an interpreted programming language designed for numerics, graph plotting, and steering large scientific simulation codes. It is quite fast due to array syntax, and extensible via C or Fortran routines. It was created in 1996 by David H. Munro of Lawrence Livermore National Laboratory.
Blitz++ is a C++ template class library that provides high-performance multidimensional array containers for scientific computing. Boost uBLAS J. Walter, M. Koch C++ 2000 1.84.0 / 12.2023 Free Boost Software License uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Dlib
Some programming languages provide operations that return the size (number of elements) of a vector, or, more generally, range of each index of an array. In C and C++ arrays do not support the size function, so programmers often have to declare separate variable to hold the size, and pass it to procedures as a separate parameter.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: