Search results
Results from the WOW.Com Content Network
The number of possible parenthesizations is given by the (n–1) th Catalan number, which is O(4 n / n 3/2), so checking each possible parenthesization (brute force) would require a run-time that is exponential in the number of matrices, which is very slow and impractical for large n. A quicker solution to this problem can be achieved by ...
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).
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
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 supported.
The programmer must then decide whether or not to rearrange the elements in memory, based on the actual usage (including the number of times that the array is reused in a computation). For example, the Basic Linear Algebra Subprograms functions are passed flags indicating which arrays are transposed. [24]
Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.
Programmable, direct support of 2D+3D plotting. Interfaces to many other software packages. Interfacing to external modules written in C, Java, Python or other languages. Language syntax similar to MATLAB. Used for numerical computing in engineering and physics. Smath Studio: SMath LLC (Andrey Ivashov) 2006 1.0.8348 11 September 2022: Free