Sample code for BiCGSTAB - Fortran 90
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! This is the classic version of BICGStab. Stopping criteria of these code ! | ! This is the classic version of BICGStab. Stopping criteria of these code ! | ||
! needs additional treatment to avoid/detect failure condition! ! | ! needs additional treatment to avoid/detect failure condition! ! | ||
+ | ! This code is tested with gFortran 5.01 ! | ||
!---------------------------------------------------------------------------------------! | !---------------------------------------------------------------------------------------! | ||
Revision as of 13:28, 25 August 2017
!---------------------------------------------------------------------------------------! ! REFERENCE : ! ! The Improved BiCGStab Method for Large and Sparse Unsymmetric Linear ! ! Systems on Parallel Distributed Memory Architectures; Yang et. al. ! ! ! ! NOTE: ! ! This is the classic version of BICGStab. Stopping criteria of these code ! ! needs additional treatment to avoid/detect failure condition! ! ! This code is tested with gFortran 5.01 ! !---------------------------------------------------------------------------------------! module BiCGStab_mod implicit none contains function BiCGStab(A,b) result(x) implicit none !--------------------------PARAMETER AND VARIABLE-------------------------------! real (kind=8), intent(in ) :: A (:,:) real (kind=8), intent(in ) :: b ( : ) real (kind=8), dimension(1:size(b, dim=1)) :: x real (kind=8), dimension(1:size(b, dim=1)) :: r, rs, v, p, s, t real (kind=8), parameter :: e = 1d-10 real (kind=8) :: rho , rho_prev real (kind=8) :: alpha , omega , beta real (kind=8) :: norm_r , norm_b real (kind=8) :: summesion, temp integer :: it=0,err !------------------------END PARAMETER AND VARIABLE-----------------------------! if(size(A, dim=1) /= size(A, dim=2)) stop & "Error: Improper dimension of matrix A in BiCGStab." !-------------------------------------------------------! x = 0.0d0 !-------> INITIAL GUESS !-------------------------------------------------------! r = b - matmul(A,x) !-------> LINE 1 rs = r ! !-------------------------------------------------------! rho = 1.0d0; alpha = 1.0d0; omega = 1.0d0 !-------> LINE 2 !-------------------------------------------------------! v = 0.0d0; p = 0.0d0 !-------> LINE 3 ! ! norm_r = dsqrt(dot_product(r,r)) ! norm_b = dsqrt(dot_product(b,b)) ! !-------------------------------------------------------! do while(norm_r .GT. e*norm_b) !-------> START OF LOOP !-------------------------------------------------------! rho_prev = rho !-------> LINE 5 rho = dot_product(rs,r) ! !-------------------------------------------------------! beta = (rho/rho_prev) * (alpha/omega) !-------> LINE 6 !-------------------------------------------------------! p = r + beta * (p - omega*v) !-------> LINE 7 !-------------------------------------------------------! v = matmul(A,p) !-------> LINE 8 !-------------------------------------------------------! alpha = rho/dot_product(rs,v) !-------> LINE 9 !-------------------------------------------------------! s = r - alpha*v !-------> LINE 10 !-------------------------------------------------------! t = matmul(A,s) !-------> LINE 11 !-------------------------------------------------------! omega = dot_product(t,s)/dot_product(t,t) !-------> LINE 12 !-------------------------------------------------------! x = x + alpha*p + omega*s !-------> LINE 13 !-------------------------------------------------------! r = s - omega*t !-------> LINE 17 !-------------------------------------------------------! norm_r = dsqrt(dot_product(r,r)) norm_b = dsqrt(dot_product(b,b)) it = it + 1 end do !-------> END OF LOOP print*, "Iteration Required :", it return end function BiCGStab end module BiCGStab_mod program main use BiCGStab_mod implicit none integer (kind=4), parameter :: m=4, n=4 real (kind=8), dimension(1:m,1:n) :: A real (kind=8), dimension(1:m ) :: x,b !-----------------------------A,b DEFINATION--------------------------------! A(1,:) = (/ 1.0d0, 1.0d0, 1.0d0, 1.0d0/) ![x(1)] = b(1) | A(2,:) = (/ 2.0d0, 3.0d0, 1.0d0, 1.0d0/) ![x(2)] = b(2) |---> [A]{x}={b} A(3,:) = (/ 3.0d0, 4.0d0, 1.0d0, 1.0d0/) ![x(3)] = b(3) | A(4,:) = (/ 3.0d0, 4.0d0, 1.0d0, 2.0d0/) ![x(4)] = b(4) | b( : ) = (/ 4.0d0, 7.0d0, 9.0d0,10.0d0/) !---------------------------END A,b DEFINATION------------------------------! !----CALL BiCGStab func-----! ! ! x = BiCGStab(A,b) ! ! ! !---------------------------! print*, x end program main