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Multidimensional arrays in languages such as Java, Python (multidimensional lists), Ruby, Visual Basic .NET, Perl, PHP, JavaScript, Objective-C (when using NSArray, not a row-major C-style array), Swift, and Atlas Autocode are implemented as Iliffe vectors. Iliffe vectors were used to implement sparse multidimensional arrays in the OLAP product ...
A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows). An Iliffe vector is an alternative to a multidimensional array structure. It uses a one-dimensional array of references to arrays of one dimension less. For two dimensions, in particular, this alternative structure would be a vector of pointers to ...
A two-dimensional array, in particular, would be implemented as a vector of pointers to its rows. Thus an element in row i and column j of an array A would be accessed by double indexing (A[i][j] in typical notation). This way of emulating multi-dimensional arrays allows the creation of jagged arrays, where each row may have a different size ...
Zarr is an open standard for storing large multidimensional array data. It specifies a protocol and data format, and is designed to be "cloud ready" including random access, by dividing data into subsets referred to as chunks. [1] [2] Zarr can be used within many programming languages, including Python, Java, JavaScript, C++, Rust and Julia. [3]
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.
In contrast, two-dimensional arrays are always rectangular [4] so jagged arrays should not be confused with multidimensional arrays, but the former is often used to emulate the latter. Arrays of arrays in languages such as Java, PHP, Python (multidimensional lists), Ruby, C#.NET, Visual Basic.NET , Perl, JavaScript, Objective-C, Swift, and ...
A 1-dimensional thing is a line, and 2-dimensional thing is a plane. For these low numbers, mathematicians have proven the maximum possible kissing number for spheres of that many dimensions.
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.