sanic: Solving Ax = b Nimbly in C++

CRAN month total

Routines for solving large systems of linear equations 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). Both dense and sparse problems are supported.


sanic is available on CRAN. The development version can be installed from GitHub.



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.


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, 2 3, 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


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