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https://github.com/jacobwilliams/lsqr
Modern Fortran sparse linear systems solver
https://github.com/jacobwilliams/lsqr
conjugate-gradient fortran fortran-package-manager least-squares linear-algebra linear-equations lsqr
Last synced: about 6 hours ago
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Modern Fortran sparse linear systems solver
- Host: GitHub
- URL: https://github.com/jacobwilliams/lsqr
- Owner: jacobwilliams
- License: other
- Created: 2019-11-06T21:31:42.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2024-01-27T15:24:35.000Z (10 months ago)
- Last Synced: 2024-01-29T08:48:56.933Z (9 months ago)
- Topics: conjugate-gradient, fortran, fortran-package-manager, least-squares, linear-algebra, linear-equations, lsqr
- Language: Fortran
- Homepage:
- Size: 982 KB
- Stars: 22
- Watchers: 3
- Forks: 4
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
============
### Status
[](https://github.com/topics/fortran)
[](https://github.com/jacobwilliams/LSQR/releases/latest)
[](https://github.com/jacobwilliams/LSQR/actions)
[](https://codecov.io/gh/jacobwilliams/LSQR)
[](https://github.com/jacobwilliams/LSQR/commits/master)
### Brief Description
A Fortran 2008 edition of LSQR, a conjugate-gradient type method for solving sparse linear equations and sparse least-squares problems.
LSQR can solve linear systems of the form: `A * x = b` or `[A; damp*I]*x = [b; 0]`. Where `A` is a matrix with `m` rows and `n` columns, `b` is an `m`-vector, and `damp` is a scalar. The matrix `A` is intended to be large and sparse, and may be square or rectangular (over-determined or under-determined).
### Usage
There are two classes in the library that can be used, `lsqr_solver` (which is more low-level) and `lsqr_solver_ez` (which has a simpler interface).
To use the `lsqr_solver_ez` class, you have to provide the matrix `A` in sparse form, using three arrays: the row indices, column indices, and the nonzero elements. Here is an example:
```fortran
program main
use lsqr_kinds
use lsqr_module, only: lsqr_solver_ez
implicit none
! define a 3x3 dense system to solve:
integer,parameter :: m = 3 !! number of rows in `A` matrix
integer,parameter :: n = 3 !! number of columns in `A` matrix
real(wp),dimension(m),parameter :: b = real([1,2,3],wp) !! RHS vector
integer,dimension(m*n),parameter :: icol = [1,1,1,2,2,2,3,3,3] !! col indices of nonzero elements of `A`
integer,dimension(m*n),parameter :: irow = [1,2,3,1,2,3,1,2,3] !! row indices of nonzero elements of `A`
real(wp),dimension(m*n),parameter :: a = real([1,4,7,2,5,88,3,66,9],wp) !! nonzero elements of `A`
type(lsqr_solver_ez) :: solver !! main solver class
real(wp),dimension(n) :: x !! solution to `A*x = b`
integer :: istop !! solver exit code
call solver%initialize(m,n,a,irow,icol) ! use defaults for other optional inputs
call solver%solve(b,zero,x,istop) ! solve the linear system
write(*,*) 'istop = ', istop
write(*,'(1P,A,*(E16.6))') 'x = ', x
end program main
```
The result from this example is:
```
istop = 1
x = 1.242424E+00 -6.060606E-02 -4.040404E-02
```
### Compiling
A [Fortran Package Manager](https://github.com/fortran-lang/fpm) manifest file is included, so that the library and test cases can be compiled with FPM. For example:
```
fpm build --profile release
fpm test --profile release
```
To use `lsqr` within your fpm project, add the following to your `fpm.toml` file:
```toml
[dependencies]
lsqr = { git="https://github.com/jacobwilliams/lsqr.git" }
```
### Documentation
The latest API documentation can be found [here](https://jacobwilliams.github.io/LSQR/). This was generated from the source code using [FORD](https://github.com/Fortran-FOSS-Programmers/ford).
### License
The lsqr source code and related files and documentation are distributed under a permissive free software [license](https://github.com/jacobwilliams/LSQR/blob/master/LICENSE.txt) (BSD-style).
### See also
* [LSMR](https://github.com/jacobwilliams/LSMR)
* [LUSOL](https://github.com/jacobwilliams/lusol)
* [nlesolver-fortran](https://github.com/jacobwilliams/nlesolver-fortran)
### References
* The original Fortran 77 version of this algorithm can be found here: [https://web.stanford.edu/group/SOL/software/lsqr/](https://web.stanford.edu/group/SOL/software/lsqr/) The updated version has been significantly refactored.
* C.C. Paige and M.A. Saunders, [LSQR: An algorithm for sparse linear equations and sparse least squares](https://stanford.edu/group/SOL/software/lsqr/lsqr-toms82a.pdf), ACM Transactions on Mathematical Software 8, 1 (March 1982), pp. 43-71.
* C.C. Paige and M.A. Saunders, [Algorithm 583, LSQR: Sparse linear equations and least-squares problems](https://web.stanford.edu/group/SOL/software/lsqr/lsqr-toms82b.pdf), ACM Transactions on Mathematical Software 8, 2 (June 1982), pp. 195-209.
* C.L. Lawson, R.J. Hanson, D.R. Kincaid and F.T. Krogh, [Basic linear algebra subprograms for Fortran usage](https://dl.acm.org/citation.cfm?id=355847), ACM Transactions on Mathematical Software 5, 3 (Sept 1979), pp. 308-323 and 324-325.