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Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once.
The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. 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 ...
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
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.
For example, word2vec has been used to map a vector space of words in one language to a vector space constructed from another language. Relationships between translated words in both spaces can be used to assist with machine translation of new words.
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.
The flow field around an airplane is a vector field in R 3, here visualized by bubbles that follow the streamlines showing a wingtip vortex. Vector fields are commonly used to create patterns in computer graphics. Here: abstract composition of curves following a vector field generated with OpenSimplex noise.
Vector field reconstruction [1] is a method of creating a vector field from experimental or computer-generated data, usually with the goal of finding a differential equation model of the system. Definition