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Since these situations normally coincide with the case of very large matrices (which exceed the cache size), performing the transposition in-place with minimal additional storage becomes desirable. Also, as a purely mathematical problem, in-place transposition involves a number of interesting number theory puzzles that have been worked out over ...
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of objects in a set into a configuration of points mapped into an abstract Cartesian space.
Using the XOR swap algorithm to exchange nibbles between variables without the use of temporary storage. In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required.
To avoid installing the large SciPy package just to get an array object, this new package was separated and called NumPy. Support for Python 3 was added in 2011 with NumPy version 1.5.0. [15] In 2011, PyPy started development on an implementation of the NumPy API for PyPy. [16] As of 2023, it is not yet fully compatible with NumPy. [17]
The Standard Template Library overloads its built-in swap function to exchange the contents of containers efficiently this way. [1] As pointer variables are usually of a fixed size (e.g., most desktop computers have pointers 64 bits long), and they are numeric, they can be swapped quickly using XOR swap.
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...
In computer programming, indentation style is a convention, a.k.a. style, governing the indentation of blocks of source code.An indentation style generally involves consistent width of whitespace (indentation size) before each line of a block, so that the lines of code appear to be related, and dictates whether to use space or tab characters for the indentation whitespace.
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.