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General

TLIB(TTM) is header-only library with C++ functions that compute the mode-q tensor-matrix product. It provides free C++ functions for parallel computing the mode-q tensor-times-matrix product of the general form

$$\underset{―}{\mathbf{C}}=\underset{―}{\mathbf{A}}{\bullet }_q\mathbf{B}:\iff \underset{―}{\mathbf{C}}(i_1,\dots ,i_{q-1},j,i_{q+1},\dots ,i_p)=\sum _{i_q=1}^{n_q}\underset{―}{\mathbf{A}}(i_1,\dots ,i_q,\dots ,i_p)\cdot \mathbf{B}(j,i_q).$$

where $q$ is the contraction mode, $\underset{―}{\mathbf{A}}$ and $\underset{―}{\mathbf{C}}$ are tensors of order $p$ with shapes ${\mathbf{n}}_a=(n_1,\dots n_{q-1},n_q,n_{q+1},\dots ,n_p)$ and ${\mathbf{n}}_c=(n_1,\dots ,n_{q-1},m,n_{q+1},\dots ,n_p)$, respectively. The order $2$ tensor $\mathbf{B}$ is a matrix with shape ${\mathbf{n}}_b=(m,n_q)$.

Flexibility

The number of dimensions (order) $p$ and the dimensions $n_r$ as well as the linear tensor layout of the tensors $\underset{―}{\mathbf{A}}$, $\mathbf{B}$ and $\underset{―}{\mathbf{C}}$ can be chosen at runtime, while $\underset{―}{\mathbf{A}}$ and $\underset{―}{\mathbf{C}}$ must have the same tensor layout. The tensor layout is defined with thelp of a permutation tuple $\pi$ of length $p$. We have free C++ function which will help you to generate any $k$ order tensor layout, including the first-order (column-major) or the last-order (row-major) storage formats.

Implementation

All C++ functions are based on the Loops-Over-GEMM (LoG) approach and utilize high-performance gemv, gemm or gemm_batch routines of BLAS such as OpenBLAS or Intel MKL without transposing tensors. Depending on the combination of $q$ , $p$ and $\pi$ , the matrix $\mathbf{B}$ might be transposed.

Interfaces

TLIB provides three C++ interfaces to compute the tensor-matrix product, see cpp-interfaces.

Using the the two low-level interfaces, you can specify different versions using tags. TLIB provides 8 different C++ function templates that compute the tensor-matrix product, see cpp-functions.

Usage & Installation

You don't need to install TLIB. However, it needs to be linked with either OpenBLAS or Intel MKL or BLIS/ AOCL when it is used. Support for "standalone" will follow, see installation for more info on usage and test installation.

Issues & Contribution

Users should feel free to report any bugs or problems in issues. For discussions, feel free to comment and discuss any related topics in discussions.