https://github.com/bassoy/ttm
C++ Header-Only Library for High-Performance Tensor-Matrix Multiplication
https://github.com/bassoy/ttm
linear-algebra multilinear-algebra tensor tensor-computation tensor-times-matrix
Last synced: 3 months ago
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C++ Header-Only Library for High-Performance Tensor-Matrix Multiplication
- Host: GitHub
- URL: https://github.com/bassoy/ttm
- Owner: bassoy
- License: lgpl-3.0
- Created: 2024-01-09T09:15:12.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-09-14T18:06:15.000Z (8 months ago)
- Last Synced: 2024-09-15T17:56:58.117Z (8 months ago)
- Topics: linear-algebra, multilinear-algebra, tensor, tensor-computation, tensor-times-matrix
- Language: C++
- Homepage:
- Size: 155 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
High-Performance Tensor-Matrix Multiplication Library - TLIB(TTM)
=====
[](https://en.wikipedia.org/wiki/C%2B%2B#Standardization)
[](https://github.com/bassoy/ttm/blob/master/LICENSE)
[](https://github.com/bassoy/ttm/wiki)
[](https://github.com/bassoy/ttm/discussions)
[](https://github.com/bassoy/ttm/actions)
## Summary
**TLIB(TTM)** is C++ high-performance tensor-matrix multiplication **header-only library**.
It provides free C++ functions for parallel computing the **mode-`q` tensor-times-matrix product** of the general form
$$
\underline{\mathbf{C}} = \underline{\mathbf{A}} \times_q \mathbf{B} \quad :\Leftrightarrow \quad
\underline{\mathbf{C}} (i_1, \dots, i_{q-1}, j, i_{q+1}, \dots, i_p) = \sum_{i_q=1}^{n_q} \underline{\mathbf{A}}({i_1, \dots, i_q, \dots, i_p}) \cdot \mathbf{B}({j,i_q}).
$$
where $q$ is the contraction mode, $\underline{\mathbf{A}}$ and $\underline{\mathbf{C}}$ 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 $\mathbf{n}\_b = (m,n\_{q})$.
## Usage & Installation
Please have a look at the [wiki](https://github.com/bassoy/ttm/wiki) page for more informations about library **usage**, function **interfaces** and the **parameters** settings.
## Key Features
### Flexibility
* Contraction mode $q$, tensor order $p$, tensor extents $n$ and tensor layout $\mathbf{\pi}$ can be chosen at runtime
* Supports any linear tensor layout inlcuding the first-order and last-order storage layouts
* Offers two high-level and one C-like low-level interfaces for calling the tensor-times-matrix multiplication
* Implemented independent of a tensor data structure (can be used with `std::vector` and `std::array`)
* Currently supports float and double
### Performance
* Multi-threading support with OpenMP v4.5 or higher
* Currently must be used with a BLAS implementation
* Performs in-place operations without transposing the tensor - no extra memory needed
* For large tensors reaches peak matrix-times-matrix performance
### Requirements
* Requires the tensor elements to be contiguously stored in memory
* Element types must be either `float` or `double`
## Python Example
```python
import numpy as np
import ttmpy as tp
A = np.arange(4*3*2, dtype=np.float64).reshape(4,3,2)
B = np.arange(5*4, dtype=np.float64).reshape(5,4)
C = tp.ttm(1,A,B)
D = np.einsum("ijk,xi->xjk", A, B)
np.all(np.equal(C,D))
```
## C++ Example
```cpp
/*main.cpp*/
#include
#include
#include
#include
int main()
{
using value_t = float;
using tensor_t = tlib::tensor;
auto A = tensor_t( {4,3,2} );
auto B = tensor_t( {5,4} );
std::iota(A.begin(),A.end(),1);
std::fill(B.begin(),B.end(),1);
std::cout << "A = " << A << std::endl;
std::cout << "B = " << B << std::endl;
/*
A =
{ 1 5 9 | 13 17 21
2 6 10 | 14 18 22
3 7 11 | 15 19 23
4 8 12 | 16 20 24 };
B =
{ 1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1};
*/
auto C = A (1)* B;
std::cout << "C = " << C << std::endl;
/* for q=1
C =
{ 1+..+4 5+..+8 9+..+12 | 13+..+16 17+..+20 21+..+24
.. .. .. | .. .. ..
1+..+4 5+..+8 9+..+12 | 13+..+16 17+..+20 21+..+24 };
*/
}
```