Description
Solving Ax = b Nimbly in C++.
Description
Routines for solving large systems of linear equations and eigenproblems in R. Direct and iterative solvers from the Eigen C++ library are made available. Solvers include Cholesky, LU, QR, and Krylov subspace methods (Conjugate Gradient, BiCGSTAB). Dense and sparse problems are supported.
README.md
sanic: Solving Ax = b Nimbly in C++
Routines for solving large systems of linear equations in R. Direct and iterative solvers from the EigenC++ library are made available. Solvers include Cholesky, LU, QR, and Krylov subspace methods (Conjugate Gradient, BiCGSTAB). Both dense and sparse problems are supported.
Installation
sanic is available on CRAN. The development version can be installed from GitHub.
install.packages("sanic")
devtools::install_github("nk027/sanic")
Usage
To solve a linear system of equations, use the solve2() function for automatic dispatch to a specific solver or access the LU, QR, Cholesky or Conjugate Gradient solvers directly.
To solve an eigenproblem, use the eigen2() or svd2() functions, or the arnoldi() function.
Solvers
| Solver | Function | Notes | Sparse | Reference |
|---|---|---|---|---|
| LU decomposition | solve_lu() | Partial pivoting, full pivoting | Yes | 1, 2, 3 |
| Householder QR decomposition | solve_qr() | Column pivoting, full pivoting, no pivoting | Yes | 1, 2, 3, 4 |
| Cholesky decomposition | solve_chol() | LDLT for semidefinite problems, LLT for positive definite problems | Yes | 1, 23, 4 |
| Conjugate Gradient (CG) | solve_cg() | Biconjugate gradient stabilised (BiCGTAB) for square problems, least squares (LSCG) for rectangular problems, classic CG for symmetric positive definite problems, preconditioners | Always | 1, 2, 3 |
Eigenproblems
| Solver | Function | Notes | Sparse | Reference |
|---|---|---|---|---|
| Spectral decomposition | eigen2() | Square and symmetric problems | No | 1, 2 |
| Singular value decomposition | svd2() | Bidiagonal Divide and Conquer SVD for large and Jacobi SVD for small problems | No | 1, 2 |
| Arnoldi iteration | arnoldi() | Square problems using an iteratively constructed Hessenberg matrix | Always | 1 |
| Lanczos algorithm | lanczos() | Symmetric problems using an iteratively constructed tridiagonal matrix | Always | 1 |