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Website. numpy.org. NumPy (pronounced / ˈnʌmpaɪ / 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] The predecessor of NumPy, Numeric, was originally created by Jim ...
The formula is valid for all index values, and for any n (when n = 0 or n = 1, this is the empty product). However, computing the formula above naively has a time complexity of O( n 2 ) , whereas the sign can be computed from the parity of the permutation from its disjoint cycles in only O( n log( n )) cost.
Kronecker product. In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a ...
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.
Tensor contraction. In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components, it is expressed as a sum of products of scalar components of the tensor (s) caused by applying the summation convention to a pair of dummy indices that are bound to ...
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances. Under zero-based numbering, the initial element is sometimes termed the zeroth element, [ 1 ] rather than the first element; zeroth is ...
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a ...
Zernike polynomials have the property of being limited to a range of −1 to +1, i.e. . The radial polynomials are defined as. for an even number of n − m, while it is 0 for an odd number of n − m. A special value is.