https://github.com/harusametime/lsqrwitheigen

C++ Implementation of LSQR with Eigen
https://github.com/harusametime/lsqrwitheigen

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C++ Implementation of LSQR with Eigen

• Host: GitHub
• URL: https://github.com/harusametime/lsqrwitheigen
• Owner: harusametime
• License: apache-2.0
• Created: 2016-06-27T00:14:41.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2020-04-10T14:13:06.000Z (over 4 years ago)
• Last Synced: 2024-08-12T09:49:47.397Z (4 months ago)
• Language: C++
• Homepage:
• Size: 13.7 KB
• Stars: 15
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# LSQRwithEigen

## Motivation

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](http://eigen.tuxfamily.org/index.php). 

[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

## Requirement

Source code of Eigen 3 

( See the webpage of [Eigen](http://eigen.tuxfamily.org/index.php). )

## How to use it

1. Put the source code of Eigen 3 to the same directory as *LSQR.cpp*, *LSQR.h*, and *example.cpp*.

2. 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.

  

3. We can get the solution by LSQR with:

  ```

    x =	lsqr.SolutionX();

  ```