C++ Implementation of A Linear Algebra Library
This library contains a basic implementation of three different classes on the real numbers domain: Polynomial, Vector and Matrix. Here, a brief overview of the functionalities for each kind of object is provided.
To have a more precise idea of all the available methods just have a look to the header file linalg.hpp.
-
Polynomial
- basic algebraic operations (addition, subtraction, multiplication and division)
- evaluation in a specific point
- evaluation of the derivative in a specific point
- computation of the zeros (if all real)
-
Vector
- basic algebraic operations (addition, subtraction)
- multiplication by a scalar
- Hadamard product (element-wise)
- dot product
- outer product
- computation of the Lp norm (default: L2)
- projection onto another Vector
-
Matrix
- basic algebraic operations (addition, subtraction)
- multiplication by a scalar
- matrix multiplication
- computation of the norm (L2, nuclear, default: Frobenius)
- transposition
- gaussian elimination
- inversion
- determination of the rank
- computation of the trace
- computation of the determinant by different methods (Laplace, default: Gauss)
- eigendecomposition (only for symmetric matrices)
- singular values decomposition (SVD) for rectangular matrices
- QR decomposition
- Cholesky decomposition for positive definite matrices
- LU decomposition
- computation of the characteristic Polynomial
-
Others
- dot product between Matrix and Vector
- Gram-Schmidt orthonormalization
- 1D convolution between vectors
- 2D convolution between matrices
First of all, you have to clone the repository and change directory:
git clone https://github.com/ryandoren/Linalg.git
cd linalgThen, you can easily build the linalg library (on Linux system only) using CMake:
cmake .
makeFinally, you can run as an example the executable example.out simply typing:
./example.out