LSQR[1] is an algorithm for solving linear system Ax=b in least-square sense. LSQR is similar to, but is more robust on ill-conditioned problems (the condition number of A is large) than Conjugate Gradient method. Although I found several implementaions of LSQR, I want a LSQR library that can deal with matrix A and vector b defined with Eigen.
[1] Christopher C. Paige and Michael A. Saunders. 1982. LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Trans. Math. Softw. 8, 1 (March 1982), 43-71. DOI=http://dx.doi.org/10.1145/355984.355989
Source code of Eigen 3 ( See the webpage of Eigen. )
- Put the source code of Eigen 3 to the same directory as LSQR.cpp, LSQR.h, and example.cpp.
- In order to solve the linear system Ax =b, write the following code (See also example.cpp):
LSQR lsqr = LSQR(A, b, x, 1.0e-8);
where A, b and x must be SparseMatrix, VectorXd and VectorXd of Eigen. LSQR starts to solve the problem using given x as the initial solution. So please note that x must be initialized before solving. If you can guess x by the other ways, you can input the guess to x. Otherwise, x is initialized as a zero vector in general.
- We can get the solution by LSQR with:
x = lsqr.SolutionX();