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Tensors in GeometricMachineLearning

We typically store training data as tensors with three axes in GeometricMachineLearning. This allows for a parallel computation of matrix products, also for the special arrays such as LowerTriangular, UpperTriangular, SymmetricMatrix and SkewSymMatrix and objects of Manifold type such as the StiefelManifold.

Library Functions

GeometricMachineLearning.tensor_mat_mul — Method
tensor_mat_mul(A::AbstractArray{<:Number, 3}, B::AbstractMatrix)

Multipliy the matrix B onto the tensor A from the right.

Internally this calls the inplace version tensor_mat_mul!.

Examples

using GeometricMachineLearning: tensor_mat_mul

A = [1 1 1; 1 1 1; 1 1 1;;; 2 2 2; 2 2 2; 2 2 2]
B = [3 0 0; 0 2 0; 0 0 1]

tensor_mat_mul(A, B)

# output

3×3×2 Array{Int64, 3}:
[:, :, 1] =
 3  2  1
 3  2  1
 3  2  1

[:, :, 2] =
 6  4  2
 6  4  2
 6  4  2
source
GeometricMachineLearning.tensor_mat_mul! — Method
mat_tensor_mul!(C::AbstractArray{<:Number, 3}, B::AbstractArray{<:Number, 3}, A::SymmetricMatrix)

Multiply the symmetric matrix A onto the tensor B from the right and store the result in C.

This performs an efficient multiplication based on the special structure of the symmetric matrix A.

source
GeometricMachineLearning.mat_tensor_mul — Method
mat_tensor_mul(A, B)

Multipliy the matrix A onto the tensor B from the left.

Internally this calls the inplace version mat_tensor_mul!.

Examples

using GeometricMachineLearning: mat_tensor_mul

B = [1 1 1; 1 1 1; 1 1 1;;; 2 2 2; 2 2 2; 2 2 2]
A = [3 0 0; 0 2 0; 0 0 1]

mat_tensor_mul(A, B)

# output

3×3×2 Array{Int64, 3}:
[:, :, 1] =
 3  3  3
 2  2  2
 1  1  1

[:, :, 2] =
 6  6  6
 4  4  4
 2  2  2
source
GeometricMachineLearning.mat_tensor_mul! — Method
mat_tensor_mul!(C, A::LowerTriangular, B)

Multiply the lower-triangular matrix A onto the tensor B from the left and store the result in C.

This performs an efficient multiplication based on the special structure of the lower-triangular matrix A.

source
GeometricMachineLearning.mat_tensor_mul! — Method
mat_tensor_mul!(C, A::UpperTriangular, B)

Multiply the upper-triangular matrix A onto the tensor B from the left and store the result in C.

This performs an efficient multiplication based on the special structure of the upper-triangular matrix A.

source
GeometricMachineLearning.mat_tensor_mul! — Method
mat_tensor_mul!(C, A::SkewSymMatrix, B)

Multiply skew-symmetric the matrix A onto the tensor B from the left and store the result in C.

This performs an efficient multiplication based on the special structure of the skew-symmetric matrix A.

source
GeometricMachineLearning.mat_tensor_mul! — Method
mat_tensor_mul!(C, A::SymmetricMatrix, B)

Multiply the symmetric matrix A onto the tensor B from the left and store the result in C.

This performs an efficient multiplication based on the special structure of the symmetric matrix A.

source