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gha3mi · Feb 2, 2024 · 4eaca69 · 4eaca69
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diff --git a/README.md b/README.md
@@ -1,55 +1,29 @@
-![ForSolver](media/logo.png)
-============
+[![GitHub](https://img.shields.io/badge/GitHub-ForSolver-blue.svg?style=social&logo=github)](https://github.com/gha3mi/forsolver)
+[![Version](https://img.shields.io/github/release/gha3mi/forsolver.svg)](https://github.com/gha3mi/forsolver/releases/latest)
+[![Documentation](https://img.shields.io/badge/ford-Documentation%20-blueviolet.svg)](https://gha3mi.github.io/forsolver/)
+[![License](https://img.shields.io/github/license/gha3mi/forsolver?color=green)](https://github.com/gha3mi/forsolver/blob/main/LICENSE)
+[![Build](https://github.com/gha3mi/forsolver/actions/workflows/CI_test.yml/badge.svg)](https://github.com/gha3mi/forsolver/actions/workflows/CI_test.yml)
 
-**ForSolver**: A Fortran library of linear and nonlinear solvers.
 
------
-
-## Table of Contents
-- [](#)
- - [Table of Contents](#table-of-contents)
- - [Installation](#installation)
- - [fpm](#fpm)
- - [Linear system solver](#linear-system-solver)
- - [Nonlinear system solver](#nonlinear-system-solver)
- - [Tests](#tests)
- - [Examples](#examples)
- - [Example 1: Linear System Solver](#example-1-linear-system-solver)
- - [Example 2: Newton's Method for Root Finding](#example-2-newtons-method-for-root-finding)
- - [Documentation](#documentation)
- - [Contributing](#contributing)
------
-
-## Installation
-
-### fpm
-ForSolver can be cloned and then built using [fpm](https://github.com/fortran-lang/fpm), following the instructions provided in the documentation available on Fortran Package Manager.
-
-```bash
-git clone https://github.com/gha3mi/forsolver.git
-cd forsolver
-fpm install --prefix .
-```
+**ForSolver**: A Fortran library of linear and nonlinear solvers.
 
-Or you can easily include this package as a dependency in your `fpm.toml` file.
+## Usage
 
-```toml
-[dependencies]
-forsolver = {git="https://github.com/gha3mi/forsolver.git"}
-```
------
+### Linear system solver
 
-## Linear system solver
 ```fortran
 use forsolver, only: solve
+
 x = solve(A,b,method)
 ```
+
 available methods (optional):
+
 - ```gesv```
 - ```gels```
------
 
-## Nonlinear system solver
+### Nonlinear system solver
+
 ```fortran
 use forsolver, only: nlsolver
 
@@ -66,7 +40,9 @@ call nls%set_options(&
 
 call nls%solve(F, dFdx, x0, x_sol)
 ```
+
 available nl_methods:
+
 - ```newton```
 - ```newton-modified```
 - ```newton-quasi-fd```
@@ -78,111 +54,117 @@ fd: finite difference method
 
 cs: complex step method
 
------
+## Requirements
 
-## Tests
+- A Fortran Compiler
+- BLAS Library
+- Fortran Package Manager (fpm)
 
-The `tests` directory contains test programs to verify the functionality of the `forsolver` module. To run the tests using `fpm`:
+## fpm Dependency
 
-- For Intel Fortran Compiler (ifort):
-```bash
-fpm @ifort
-```
+If you want to use `ForSolver` as a dependency in your own fpm project,
+you can easily include it by adding the following line to your `fpm.toml` file:
 
-- For Intel Fortran Compiler (ifx):
-```bash
-fpm @ifx
+```toml
+[dependencies]
+forsolver = {git="https://github.com/gha3mi/forsolver.git"}
 ```
 
-- For NVIDIA Compiler (nvfortran):
-```bash
-fpm @nvidia
-```
+## Runing Tests
+
+Execute the following commands to run tests with specific compilers:
 
-- For GNU Fortran Compiler (gfortran):
-```bash
-fpm @gfortran
+```shell
+fpm @<compiler>-test
 ```
------
+`compiler: ifx, ifort, gfortran, nvfortran`
+
 
 ## Examples
 
 ### Example 1: Linear System Solver
 
 ```fortran
-program test1
+program example1
 
  use kinds
- use forsolver, only: solve
+ use forsolver
 
  implicit none
 
  real(rk), dimension(:,:), allocatable :: A
  real(rk), dimension(:) , allocatable :: x, b
  integer :: m,n, i, j
 
- m = 4
- n = 3
+ m = 3
+ n = 2
 
  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)
+ A(1,:) = [ 1.0_rk, 5.0_rk]
+ A(2,:) = [ 3.0_rk, 1.0_rk]
+ A(3,:) = [-2.0_rk, 4.0_rk]
 
- ! Print b
- print *, "b:"
- print "(4F10.6)", b
+ b = [4.0_rk, -2.0_rk, 3.0_rk]
 
+ x = solve(A, b)
 
- ! Print x
- print *, "x:"
- print "(4F10.6)", x
-
- deallocate(A,b,x)
-
-end program test1
+end program example1
 ```
 
 ### Example 2: Newton's Method for Root Finding
 
 ```fortran
-program test3
-
+module my_function3
  use kinds
- use functions_module
- use forsolver, only: nlsolver
+ implicit none
+contains
+ function F1(x) result(F_val)
+ real(rk), intent(in) :: x
+ real(rk) :: F_val
+ F_val = 5.0_rk * x**3 + 8.0_rk * x - 5.0_rk
+ end function F1
+ function dF1dx(x) result(dFdx_val)
+ real(rk), intent(in) :: x
+ real(rk) :: dFdx_val
+ dFdx_val = 15.0_rk * x**2 + 8.0_rk
+ end function dF1dx
+end module my_function3
+
+program example2
+
+ use forsolver
+ use my_function3
 
  implicit none
 
  type(nlsolver) :: nls
- real(rk) :: x_sol
+ real(rk) :: x, expected_x
 
  call nls%set_options(&
  nl_method = 'newton',&
  maxit = 100,&
- TolFun = 1e-15_rk,&
+ TolFun = 1e-4_rk,&
  verbosity = 1)
 
- call nls%solve(F=F1, dFdx=dF1dx, x0=10.0_rk, x_sol=x_sol)
+ call nls%solve(F=F1, dFdx=dF1dx, x0=10.0_rk, x_sol=x)
 
-end program test3
+end program example2
 ```
------
 
-## Documentation
-To generate the documentation for the `ForSolver` module using [ford](https://github.com/Fortran-FOSS-Programmers/ford) run the following command:
-```bash
+## API Documentation
+
+The most up-to-date API documentation for the master branch is available
+[here](https://gha3mi.github.io/ForSolver/).
+To generate the API documentation for `ForSolver` using
+[ford](https://github.com/Fortran-FOSS-Programmers/ford) run the following
+command:
+
+```shell
 ford ford.yml
 ```
------
 
 ## 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.
+
+Contributions to `ForSolver` are welcome!
+If you find any issues or would like to suggest improvements, please open an issue.