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In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions. In R, function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization. [2] [3] [4]
TensorFlow: Apache 2.0-licensed Theano-like library with support for CPU, GPU, Google's proprietary tensor processing unit (TPU), [160] and mobile devices. Theano: The reference deep-learning library for Python with an API largely compatible with the popular NumPy library. Allows user to write symbolic mathematical expressions, then ...
More generally, a multidimensional array type can be called a tensor type, by analogy with the mathematical concept, tensor. [ 2 ] Language support for array types may include certain built-in array data types, some syntactic constructions ( array type constructors ) that the programmer may use to define such types and declare array variables ...
The softmax function takes as input a vector z of K real numbers, and normalizes it into a probability distribution consisting of K probabilities proportional to the exponentials of the input numbers.
Theano: A deep-learning library for Python with an API largely compatible with the NumPy library. Torch : A scientific computing framework with support for machine learning algorithms, written in C and Lua .
The first idea behind the Proper Orthogonal Decomposition (POD), as it was originally formulated in the domain of fluid dynamics to analyze turbulences, is to decompose a random vector field u(x, t) into a set of deterministic spatial functions Φ k (x) modulated by random time coefficients a k (t) so that:
This object is used by most other packages and thus forms the core object of the library. The Tensor also supports mathematical operations like max, min, sum, statistical distributions like uniform, normal and multinomial, and BLAS operations like dot product, matrix–vector multiplication, matrix–matrix multiplication and matrix product.