ForSolver

ForSolver is a Fortran library that provides numerical solvers for linear and non-linear systems.

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Table of Contents

• ForSolver
  • Table of Contents
  • Installation
    • fpm
  • Linear system solver
  • Nonlinear system solver
  • Tests
  • Examples
    • Example 1: Linear System Solver
    • Example 2: Newton's Method for Root Finding
  • Documentation
  • Contributing

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Installation

fpm

ForSolver can be cloned and then built using fpm, following the instructions provided in the documentation available on Fortran Package Manager.

git clone https://github.com/gha3mi/forsolver.git
cd forsolver
fpm install --perfix .

Or you can easily include this package as a dependency in your fpm.toml file.

[dependencies]
forsolver = {git="https://github.com/gha3mi/forsolver.git"}

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Linear system solver

use forsolver, only : solve
x = solve(A,b,method)

available methods (optional):

• gesv
• gels

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Nonlinear system solver

use forsolver, only : nlsolver

call nls%set_options(&
      lin_method,&
      nl_method,&
      fdm_method,&
      fdm_tol,&
      cs_tol,&
      TolFun,&
      maxit,&
      nmp,&
      verbosity )

call nls%solve(F, dFdx, x0, x_sol)

available nl_methods:

• newton
• newton-modified
• newton-quasi-fd
• newton-quasi-fd-modified
• newton-quasi-cs
• newton-quasi-cs-modified

fd: finite difference method

cs: complex step method

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Tests

The tests directory contains test programs to verify the functionality of the forsolver module. To run the tests using fpm, you can use response files for specific compilers:

• For Intel Fortran Compiler (ifort):

fpm @ifort

• For Intel Fortran Compiler (ifx):

fpm @ifx

• For NVIDIA Compiler (nvfortran):

fpm @nvidia

• For GNU Fortran Compiler (gfortran):

fpm @gfortran

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Examples

Example 1: Linear System Solver

program test1

   use kinds
   use forsolver, only : solve

   implicit none

   real(rk), dimension(:,:), allocatable :: A
   real(rk), dimension(:)  , allocatable :: x, b
   integer                               :: m,n, i, j

   m = 4
   n = 3

   allocate(A(m,n),b(m),x(n))

   call random_number(A)
   call random_number(b)
   A = A*10.0_rk
   b = b*10.0_rk

   X = solve(A, b)

   ! Print A
   print *, "A:"
   print "(4F10.6)", (A(:,j), j = 1, m)

   ! Print b
   print *, "b:"
   print "(4F10.6)", b


   ! Print x
   print *, "x:"
   print "(4F10.6)", x

   deallocate(A,b,x)

end program test1

Example 2: Newton's Method for Root Finding

program test3

   use kinds
   use functions_module
   use forsolver, only : nlsolver

   implicit none

   type(nlsolver) :: nls
   real(rk)       :: x_sol

   call nls%set_options(&
      nl_method   = 'newton',&
      maxit       = 100,&
      TolFun      = 1e-15_rk,&
      verbosity   = 1)

   call nls%solve(F=F1, dFdx=dF1dx, x0=10.0_rk, x_sol=x_sol)

end program test3

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Documentation

To generate the documentation for the ForSolver module using ford run the following command:

ford ford.yml

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Contributing

Contributions to ForSolver are welcome! If you find any issues or would like to suggest improvements, please open an issue or submit a pull request.