Initial tests for the gauss seidel algorithm

The implementation works in both float and double-precision
Signed-off-by: EdwinMindcraft <edwin.mindcraft@gmail.com>

.gitignore

+.idea/**
+cmake-build-debug/**
\ No newline at end of file

CMakeLists.txt

+cmake_minimum_required(VERSION 3.14)
+project(GaussSeidel Fortran)
+
+
+enable_language(Fortran)
+add_executable(GaussSeidel main.f gauss_seidel.f)
\ No newline at end of file

README.md

+Gauss-Seidel
+------------
+This is a Fortran implementation of the Gauss-Seidel algorithm to solve linear systems.
\ No newline at end of file

gauss_seidel.f

+      module gauss_seidel
+        implicit none
+        private
+        public :: solve_system
+
+        interface solve_system
+          procedure solve_system_double, solve_system_real
+        endinterface
+      contains
+
+        subroutine solve_system_double(A, b, x)
+          implicit none
+          integer :: An(2), n(1), i, j
+          double precision :: A(:,:), b(:), x(:), tmp
+          n = shape(b)
+
+          do i=1,n(1)
+            tmp = 0
+            do j=1,n(1)
+              if (j /= i) then
+                tmp = tmp + A(i,j) * x(j)
+              endif
+            enddo
+            x(i) = (b(i) - tmp) / A(i, i)
+          enddo
+
+        end subroutine solve_system_double
+
+        subroutine solve_system_real(A, b, x)
+          implicit none
+          integer :: n(1), i, j
+          real :: A(:,:), b(:), x(:), tmp
+          n = shape(b)
+
+          do i=1,n(1)
+            tmp = 0
+            do j=1,n(1)
+              if (j /= i) then
+                tmp = tmp + A(i,j) * x(j)
+              endif
+            enddo
+            x(i) = (b(i) - tmp) / A(i, i)
+          enddo
+
+        end subroutine solve_system_real
+      end module
\ No newline at end of file

main.f

+      program main
+      use gauss_seidel
+      implicit none
+      integer i
+      real :: A(2,2), b(2), x(2)
+
+      A = reshape((/1, 0, 1, 2/), shape(A))
+      b = (/13, 11/)
+      x = (/1, 2/)
+
+      do i=1,3000000
+        call solve_system(A, b, x)
+        if (norm2(matmul(A, x) - b) < 0.0001) then
+          exit
+        endif
+      enddo
+      write(*,*) x, matmul(A, x)
+      end