# Gauss Elimination in Fortran

Gauss Elimination is a well known method for solving system of linear equations. It has time complexity of order $O(n^3)$ and hence, it fares better than cramer’s rule or Gauss-Jordan method.

The following is my implementation of Gauss elimination method in fortran. I’ve made use of scaled pivoting in order to reduce round-off errors.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76   ! Solves linear eqns: Ax = b for x. program gauss_elimination use, intrinsic :: iso_fortran_env, only : dp=>real64, error_unit, input_unit implicit none integer :: i, j, k, n, pos, istat ! n - Number of unknowns real(dp), allocatable :: ag(:,:), x(:) ! Augumented matrix and solution vector real(dp) :: factor character(len=1024) :: msg ! string for holding error messages write(*, '(a)', advance='no') "Number of unknowns: " read (input_unit, *, iostat=istat) n if (istat /= 0) stop 1 allocate(ag(n, n+1)) allocate(x(n)) call get_aug_matrix(ag) ! Forward elimination do k = 1, n-1 ! Partial scaled pivoting pos = maxloc( abs(ag(k:n, k)/maxval(ag(k:n, :), dim=2)), dim=1 ) j = k + pos - 1 if (.not. j == k) call swap(ag(j,:), ag(k,:)) ! Elimination do i = k+1, n factor = ag(i,k) / ag(k,k) ag(i, k:) = ag(i, k:) - factor*ag(k, k:) end do end do ! Back substitution x(n) = ag(n, n+1) / ag(n,n) do i = n-1, 1, -1 x(i) = ( ag(i,n+1) - dot_product(ag(i, i+1:n), x(i+1:n)) ) / ag(i,i) end do print *, 'The solution vector x is: ' print *, x deallocate(ag) deallocate(x) contains ! Subroutine to get the values of the Augumented Matrix subroutine get_aug_matrix(a) ! Note that read statements below make use of istat and msg from parent program real(dp), intent(inout) :: a(:,:) integer :: n n = size(a,1) print *, 'Enter the Coefficient Matrix A (Row-wise) ' do i = 1, n write(*, '("A(",i0,", :) ")', advance='no') i read (input_unit, *, iostat=istat, iomsg=msg) a(i,1:n) if (istat /= 0) stop trim(msg) end do print *, 'Enter the RHS constants vector (b): ' do i = 1, n write(*, '("b(",i0,") ")', advance='no') i read (input_unit, *, iostat=istat, iomsg=msg) a(i,n+1) if (istat /= 0) stop trim(msg) end do end subroutine get_aug_matrix ! Subroutine to swap rows of the matrix elemental subroutine swap(a, b) real(dp), intent(inout) :: a, b real(dp) :: temp temp = a a = b b = temp end subroutine swap end program gauss_elimination 

I’ll try to update with more information in the future. In the mean time, please let me if you have any specific doubt.