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That is, they loop over the cycles, moving the data from one location to the next in the cycle. In pseudocode form: for each length>1 cycle C of the permutation pick a starting address s in C let D = data at s let x = predecessor of s in the cycle while x ≠ s move data from x to successor of x let x = predecessor of x move data from D to ...
The core functionality of NumPy is its "ndarray", for n-dimensional array, data structure. These arrays are strided views on memory. [9] In contrast to Python's built-in list data structure, these arrays are homogeneously typed: all elements of a single array must be of the same type.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [6] or they can be used to build a pointer based quadtree.
As exchanging the indices of an array is the essence of array transposition, an array stored as row-major but read as column-major (or vice versa) will appear transposed. As actually performing this rearrangement in memory is typically an expensive operation, some systems provide options to specify individual matrices as being stored transposed.
The transpose of a matrix A, denoted by A T, [3] ⊤ A, A ⊤, , [4] [5] A′, [6] A tr, t A or A t, may be constructed by any one of the following methods: Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain A T; Write the rows of A as the columns of A T; Write the columns of A as the rows of A T
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:
Unlike object orientation which implicitly breaks down data to its constituent parts (or scalar quantities), array orientation looks to group data and apply a uniform handling. 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 ...
Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc.