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GPU Posterior Simulation - Bayesian Simulated Annealing - Quantum Annealing

SABL-Projects: Common matrix operations in tensor form

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General expression

Symbol	Meaning
Dn	dimensions, indexed by n
|Dn|	size (cardinality) of dimension n

Explanation: The expression above allows any dimension of the two arrays to be a singleton (ie range 1:1). In such cases, the array(s) with the singleton dimension has its value broadcast to all elements along that dimension. Then the array T can be constructed with consistent dimensions from the result of an element-wise operation. T may subsequently be summed along a given dimension (a reduction).

For brevity, 5 dimensions are explicitly described, even though the number of dimensions can be arbitrarily large (higher dimensions that have not been explicitly described are assumed to be 1:1 ie singletons).

Form	Common	High dimensional
Scalar time Matrix
Expression
Example Matlab code	beta = 0.6; X = rand(8,10); T = beta*X;	beta = 0.6; X = rand(1,1,8,1,10); T = beta*X;
Vector times Vector Outer Product
Expression
Example Matlab code	beta = rand(18,1); X = rand(1,14); T = beta*X;	beta = rand(1,1,1,18,1); X = rand(1,14,1,1,1); T = bsxfun(@times,beta,X);
Matrix times Vector
Expression
Example Matlab code	beta = rand(14,16); X = rand(16,1); T = beta*X;	beta = rand(1,1,1,16,1); X = rand(1,1,1,16,14); T = bsxfun(@times,beta,X); T = sum(T,4);
Matrix times Matrix
Expression
Example Matlab code	beta = rand(12,16); X = rand(16,14); T = beta*X;	beta = rand(1,1,12,16,1); X = rand(1,1,1,16,14); T = bsxfun(@times,beta,X); T = sum(T,4);
Tensor times Vector
Expression	NA
Example Matlab code		beta = rand(18,14,12,10,1); X = rand(1,14,1,10,1); T = bsxfun(@times,beta,X); T = sum(sum(T,4),2);
Tensor Product
Expression	NA
Example Matlab code		beta = rand(12,1,14,1,1); X = rand(1,18,1,1,20); T = bsxfun(@times,beta,X);

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