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CuPy is a part of the NumPy ecosystem array libraries [7] and is widely adopted to utilize GPU with Python, [8] especially in high-performance computing environments such as Summit, [9] Perlmutter, [10] EULER, [11] and ABCI.
PyTorch supports various sub-types of Tensors. [29] Note that the term "tensor" here does not carry the same meaning as tensor in mathematics or physics. The meaning of the word in machine learning is only superficially related to its original meaning as a certain kind of object in linear algebra. Tensors in PyTorch are simply multi-dimensional ...
import theano from theano import tensor # Declare two symbolic floating-point scalars a = tensor. dscalar b = tensor. dscalar # Create a simple expression c = a + b # Convert the expression into a callable object that takes (a, b) # values as input and computes a value for c f = theano. function ([a, b], c) # Bind 1.5 to 'a', 2.5 to 'b', and evaluate 'c' assert 4.0 == f (1.5, 2.5)
In the Python library NumPy, the outer product can be computed with function np.outer(). [8] In contrast, np.kron results in a flat array. The outer product of multidimensional arrays can be computed using np.multiply.outer.
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.
The use of indices presupposes tensors in coordinate representation with respect to a basis. The coordinate representation of a tensor can be regarded as a multi-dimensional array, and a bijection from one set of indices to another therefore amounts to a rearrangement of the array elements into an array of a different shape.
PyTorch: Tensors and Dynamic neural networks in Python with GPU acceleration. TensorFlow: Apache 2.0-licensed Theano-like library with support for CPU, GPU and Google's proprietary TPU, [116] mobile; Theano: A deep-learning library for Python with an API largely compatible with the NumPy library.
In Python, the function cholesky from the numpy.linalg module performs Cholesky decomposition. In Matlab, the chol function gives the Cholesky decomposition. Note that chol uses the upper triangular factor of the input matrix by default, i.e. it computes = where is upper triangular. A flag can be passed to use the lower triangular factor instead.