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项目作者： jacobwilliams

项目描述 ：
Modern Fortran sparse linear systems solver
高级语言： Fortran
项目地址: git://github.com/jacobwilliams/LSQR.git
创建时间： 2019-11-06T21:31:42Z
项目社区：https://github.com/jacobwilliams/LSQR
开源协议：Other
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" class="reference-link">LSQR

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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:

  1. program main
  3.  use lsqr_kinds
  4.  use lsqr_module, only: lsqr_solver_ez
  6.  implicit none
  8.  ! define a 3x3 dense system to solve:
  9.  integer,parameter :: m = 3 !! number of rows in `A` matrix
  10.  integer,parameter :: n = 3 !! number of columns in `A` matrix
  11.  real(wp),dimension(m),parameter :: b = real([1,2,3],wp)  !! RHS vector
  12.  integer,dimension(m*n),parameter :: icol = [1,1,1,2,2,2,3,3,3] !! col indices of nonzero elements of `A`
  13.  integer,dimension(m*n),parameter :: irow = [1,2,3,1,2,3,1,2,3] !! row indices of nonzero elements of `A`
  14.  real(wp),dimension(m*n),parameter :: a = real([1,4,7,2,5,88,3,66,9],wp)  !! nonzero elements of `A`
  16.  type(lsqr_solver_ez) :: solver  !! main solver class
  17.  real(wp),dimension(n) :: x   !! solution to `A*x = b`
  18.  integer :: istop  !! solver exit code
  20.  call solver%initialize(m,n,a,irow,icol) ! use defaults for other optional inputs
  21.  call solver%solve(b,zero,x,istop)       ! solve the linear system
  23.  write(*,*) 'istop = ', istop
  24.  write(*,'(1P,A,*(E16.6))') 'x = ', x
  26. end program main

The result from this example is:

  1.  istop = 1
  2.  x = 1.242424E+00   -6.060606E-02   -4.040404E-02

Compiling

A Fortran Package Manager manifest file is included, so that the library and test cases can be compiled with FPM. For example:

  1. fpm build --profile release
  2. fpm test --profile release

To use lsqr within your fpm project, add the following to your fpm.toml file:

  1. [dependencies]
  2. lsqr = { git="https://github.com/jacobwilliams/lsqr.git" }

Documentation

The latest API documentation can be found here. This was generated from the source code using FORD.

License

The lsqr source code and related files and documentation are distributed under a permissive free software license (BSD-style).

See also

References