LinearAlgebra

Library that provides implementations or wrappers for linear algebra operations in C#.

Features

• Basic matrix and vector operations: What you would expect from a BLAS library.

  • Vector-vector operations: Addition, subtraction, linear combinations, scaling, dot (inner) product
  • Matrix-vector operations: matrix-vector multiplication, back and forward substitution
  • Matrix-matrix operations: Addition, subtraction, linear combinations, scaling, matrix-matrix multiplication

• Sparse matrix and vector formats: Sparse formats avoid storing and processing zero entries, which reduces memory consumption and computational time.

  • Compressed Sparse Rows, Compressed Sparse Columns: Optimal for matrix-vector and matrix-matrix multiplications
  • Dictionary Of Keys: Optimal for creating a sparse matrix and then copying it to another format.
  • Skyline: Optimal for Cholesky/LDL factorization

• Direct linear system solvers: Solving linear systems using factorization.

  • LU factorization with pivoting for general matrices
  • Cholesky/LDL factorization for symmetric positive definite matrices
  • Reordering algorithms to reduce the fill-in of the factorization process, thereby reducing memory consumption and computational time

• Iterative linear system solvers: Solving large sparse linear systems using algorithms based on matrix-vector multiplication and vector-vector operations.

  • Generalized Minimum Residual method for general matrices
  • Minimum Residual method for symmetric matrices
  • Conjugate Gradient method for symmetric positive definite matrices
  • General purpose preconditioners

• Least squares problems: Solving least squares and minimum norm problems

  • QR and LQ factorizations of rectangular matrices
  • Only for dense matrices at the moment

• Matrix and vector I/O: Reading matrices and vectors from or writing them to files

  • File formats for dense or sparse matrices
  • Compatible with matrix market file formats
  • Compatible with matlab file formats

• Optimized native libraries: Assigning operations to high performance linear algebra libraries

  • Intel Math Kernel Library. Mainly for dense linear algebra operations.
  • SuiteSparse. For sparse direct solvers.
  • Only for win64 operating systems at the moment.
  • These are optional. If the user does not want to install these libraries or does not use a win64 OS, there are is an alternative, less efficient C# implementation of each feature.

Installation instructions

You can choose either to clone the solution or downloads it as a zip file.

Clone solution

1. Under the repository name, click Clone or Download option.

2. In the popup appearing choose the Use HTTPS option.

3. Use the to copy the link provided.

4. Open Visual Studio. In Team Explorer window appearing in your screen under Local Git Repositories click the Clone option. If Team Explorer window is not visible you can enable in View -> Team Explorer

5. In the text box appearing paste the link.

6. Click clone and Visual Studio will automatically download and import MGroup.LinearAlgebra

Download as ZIP

1. Under the repository name, click Clone or Download option

2. Click Download ZIP option. MGroup.LinearAlgebra will be downloaded as a ZIP file.

3. Extract the ZIP file to the folder of choice.

4. Double click on MGroup.LinearAlgebra.sln file to open the code with Visual Studio

Reference manual

For more information on the code functionality please refer to the reference manual that presents an in depth documentation: https://github.com/mgroupntua/LinearAlgebra/wiki