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For example, in the Pascal programming language, the declaration type MyTable = array [1.. 4, 1.. 2] of integer, defines a new array data type called MyTable. The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices.
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.
While the terms allude to the rows and columns of a two-dimensional array, i.e. a matrix, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to lexicographic and colexicographic orders, respectively. It is also worth noting that matrices, being commonly represented as ...
In computer programming, the stride of an array (also referred to as increment, pitch or step size) is the number of locations in memory between beginnings of successive array elements, measured in bytes or in units of the size of the array's elements. The stride cannot be smaller than the element size but can be larger, indicating extra space ...
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 ...
Slicing of higher-dimensional arrays works similarly: A[-1, *] % The last row of A A[[1:5], [2:7]] % 2d array using rows 1-5 and columns 2-7 A[[5:1:-1], [2:7]] % Same as above except the rows are reversed Array indices can also be arrays of integers. For example, suppose that I = [0:9] is an
For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write 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)
Fortran and C use different schemes for their native arrays. Fortran uses "Column Major" , in which all the elements for a given column are stored contiguously in memory. C uses "Row Major" (SoA), which stores all the elements for a given row contiguously in memory. LAPACK defines various matrix representations in memory.