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Sample code for BiCGSTAB - Fortran 90

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	!-----------------------------------MIT LICENCE-----------------------------------------!
	!											!
	!	Copyright (c) 2015, Biswajit Ghosh					        !
	!	All rights reserved.								!
	!											!
	!	Permission is hereby granted, free of charge, to any person obtaining a copy	!
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	!	copies of the Software, and to permit persons to whom the Software is		!
	!	furnished to do so, subject to the following conditions:                        !
	!											!
	!	The above copyright notice and this permission notice shall be included in	!
	!	all copies or substantial portions of the Software.				!
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	!	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR	!
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	!---------------------------------------------------------------------------------------!


        !---------------------------------------------------------------------------------------!
        !       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!                   !
        !---------------------------------------------------------------------------------------!


program main
        implicit none

        interface BicgStab
                function BicgStab(A,b) result(x)
                        real    (kind=8), intent(in )   :: A(:,:)
                        real    (kind=8), intent(in )   :: b( : )
                        real    (kind=8)                :: x(1:size(b, dim=1))
                end function BicgStab
        end interface ! BicgStab

        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( : ) = (/5.0d0, 9.0d0,12.0d0,13.0d0/)
!-----------------------------END A,b DEFINATION--------------------------------!

        x = BicgStab(A,b)

        print*, "X is:",x

end program main





function BicgStab(A,b) result(x)
        implicit none

        interface mat_vec_mul
                function mat_vec_mul(a_mvm,b_mvm) result(c_mvm)
                       real    (kind=8), intent(in) :: a_mvm(:,:),b_mvm(:)
                       real    (kind=8)             :: c_mvm(1:size(b_mvm, dim=1))
                end function mat_vec_mul
        end interface ! mat_vec_mul

        interface dot_prod
                function dot_prod(a_dp,b_dp) result(c_dp)
                       real    (kind=8), intent(in) :: a_dp(:),b_dp(:)
                       real    (kind=8)             :: c_dp
                end function dot_prod
        end interface ! dot_prod

!--------------------------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-20
        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                                         :: m,n
        integer                                         :: i,j
        integer                                         :: it=0,err
!------------------------END PARAMETER AND VARIABLE-----------------------------!  

        m = size(A, dim=1)
        n = size(A, dim=2)

!---------------------------------------!
        x = 0.0d0                       !-------> GUESS X
!---------------------------------------!
        r  = b - mat_vec_mul(A,x)       !-------> STEP 1
        rs = r                          !
!---------------------------------------!
        rho   = 1.0d0                   !
        alpha = 1.0d0                   !-------> STEP 2
        omega = 1.0d0                   !
!---------------------------------------!
        v = 0.0d0                       !-------> STEP 3
        p = 0.0d0                       !
!                                       !
        norm_r = dsqrt(dot_prod(r,r))   !
        norm_b = dsqrt(dot_prod(b,b))   !
!---------------------------------------!

!-------------------START OF LOOP-----------------------!       
        do while(norm_r .GT. e*norm_b)                  !-------> STEP 4
!-------------------------------------------------------!

!-------------------------------------------------------!
        rho_prev = rho                                  !-------> STEP 5
        rho      = dot_prod(rs,r)                       !
!-------------------------------------------------------!
        beta    = (rho/rho_prev) * (alpha/omega)        !-------> STEP 6
!-------------------------------------------------------!
        p       = r + beta * (p - omega*v)              !-------> STEP 7
!-------------------------------------------------------!
        v       = mat_vec_mul(A,p)                      !-------> STEP 8
!-------------------------------------------------------!
        alpha   = rho/dot_prod(rs,v)                    !-------> STEP 9
!-------------------------------------------------------!
        s       = r - alpha*v                           !-------> STEP 10
!-------------------------------------------------------!
        t       = mat_vec_mul(A,s)                      !-------> STEP 11
!-------------------------------------------------------!
        omega   = dot_prod(t,s)/dot_prod(t,t)           !-------> STEP 12
!-------------------------------------------------------!
        x       = x + alpha*p + omega*s                 !-------> STEP 13
!-------------------------------------------------------!
        r       = s - omega*t                           !-------> STEP 17
!-------------------------------------------------------!

        norm_r = dsqrt(dot_prod(r,r))
        norm_b = dsqrt(dot_prod(b,b))   

        it = it + 1

        end do !END LOOP


        print*, "Iter :",it

return
end function BicgStab





function mat_vec_mul(a_mvm,b_mvm) result(c_mvm)
        implicit none
        
        real    (kind=8), intent(in) :: a_mvm(:,:),b_mvm(:)
        real    (kind=8)             :: c_mvm(1:size(b_mvm, dim=1))

        if (size(a_mvm, dim=2) /= size(b_mvm, dim=1)) stop &
        "Error: Improper dimension of matrix/vector in mat_vec_mul."

        c_mvm = matmul(a_mvm,b_mvm)

        return
end function mat_vec_mul





function dot_prod(a_dp,b_dp) result(c_dp)
        implicit none

        real    (kind=8), intent(in) :: a_dp(:),b_dp(:)
        real    (kind=8)             :: c_dp

        if (size(a_dp, dim=1) /= size(b_dp, dim=1)) stop &
        "Error: Improper dimension of matrices in dot_prod."

        c_dp = dot_product(a_dp,b_dp)

        return
end function dot_prod

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