Unexpected assignment statement in modules

Question

I want to define inside a module some constants that are shared by several subroutines, but I get many error messages when I try to compile it (with the -c command):

Error: Unexpected assignment statement in MODULE

If I use the same code in a subroutine it works. Here's the code of the module:

module rkSetup
!High order embedded Runge-Kutta formulae, by P.J.Prince and J.R.Dormand,
!Journal of Computational and Applied Mathematics, vol. 7, 1981, pages 67-75

    implicit none
    INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(15)
    integer, parameter :: s = 13 ! number of stages
    integer, parameter :: p = 8 !< Order of the method
    real(dp), dimension(s) :: a !< Runge-Kutta vector of nodes
    real(dp), dimension(s) :: c !< Runge-Kutta vector of weigths
    real(dp), dimension(s) :: d !< Runge-Kutta vector of weigths for high order 
    real(dp), dimension(s,s-1) :: b !< Runge-Kutta matrix

    a = (/0.0_dp, 1.0_dp/18.0_dp, 1.0_dp/12.0_dp, 1.0_dp/8.0_dp, &
        5.0_dp/16.0_dp,3.0_dp/8.0_dp,59.0_dp/400.0_dp,93.0_dp/200.0_dp, &
        5490023248.0_dp/9719169821.0_dp, 13.0_dp/20.0_dp, &
        1201146811.0_dp/1299019798.0_dp, 1.0_dp, 1.0_dp/)

    c = 0.0_dp
    d = 0.0_dp

    d(1) = 14005451.0_dp/335480064.0_dp
    d(6:) = (/-59238493.0_dp/1068277825.0_dp, &
        181606767.0_dp/758867731.0_dp, &
        561292985.0_dp/797845732.0_dp, &
        -1041891430.0_dp/1371343529.0_dp, &
        760417239.0_dp/1151165299.0_dp, &
        118820643.0_dp/751138087.0_dp, &
        -528747749.0_dp/2220607170.0_dp, 1.0_dp/4.0_dp/)

    c(1) = 13451932.0_dp/455176623.0_dp
    c(6:12) = (/-808719846.0_dp/976000145.0_dp, &
        1757004468.0_dp/5645159321.0_dp, &
        656045339.0_dp/265891186.0_dp, &
        -3867574721.0_dp/1518517206.0_dp, &
        465885868.0_dp/322736535.0_dp, &
        53011238.0_dp/667516719.0_dp, 2.0_dp/45.0_dp/)

    b = 0.0_dp

    b(:,1) = (/0.0_dp, 1.0_dp/18.0_dp, 1.0_dp/48.0_dp, &
        1.0_dp/32.0_dp, 5.0_dp/16.0_dp, 3.0_dp/80.0_dp, &
        29443841.0_dp/614563906.0_dp, 16016141.0_dp/946692911.0_dp, &
        39632708.0_dp/573591083.0_dp, 246121993.0_dp/1340847787.0_dp, &
        -1028468189.0_dp/846180014.0_dp, 185892177.0_dp/718116043.0_dp, &
        403863854.0_dp/491063109.0_dp/)
    b(3,2) = 1.0_dp/16.0_dp
    b(4:5,3) = (/3.0_dp/32.0_dp, -75.0_dp/64.0_dp /)
    b(5:,4) = (/75.0_dp/64.0_dp,3.0_dp/16.0_dp, &
        77736538.0_dp/692538347.0_dp, 61564180.0_dp/158732637.0_dp, &
        -433636366.0_dp/683701615.0_dp, -37695042795.0_dp/15268766246.0_dp, &
        8478235783.0_dp/508512852.0_dp, -3185094517.0_dp/667107341.0_dp, &
        -5068492393.0_dp/434740067.0_dp/)
    b(6:,5) = (/3.0_dp/20.0_dp, -28693883.0_dp/1125000000.0_dp, &
        22789713.0_dp/633445777.0_dp, -421739975.0_dp/2616292301.0_dp, &
        -309121744.0_dp/1061227803.0_dp, 1311729495.0_dp/1432422823.0_dp, &
        -477755414.0_dp/1098053517.0_dp, -411421997.0_dp/543043805.0_dp/)
    b(7:,6) = (/23124283.0_dp/1800000000.0_dp, &
        545815736.0_dp/2771057229.0_dp,100302831.0_dp/723423059.0_dp, &
        -12992083.0_dp/490766935.0_dp,-10304129995.0_dp/1701304382.0_dp, &
        -703635378.0_dp/230739211.0_dp,652783627.0_dp/914296604.0_dp/)
    b(8:,7) = (/-180193667.0_dp/1043307555.0_dp, &
        790204164.0_dp/839813087.0_dp, 6005943493.0_dp/2108947869.0_dp, &
        -48777925059.0_dp/3047939560.0_dp, 5731566787.0_dp/1027545527.0_dp, &
        11173962825.0_dp/925320556.0_dp/)
    b(9:,8) = (/800635310.0_dp/3783071287.0_dp, &
        393006217.0_dp/1396673457.0_dp, 15336726248.0_dp/1032824649.0_dp, &
        5232866602.0_dp/850066563.0_dp, -13158990841.0_dp/6184727034.0_dp /)
    b(10:,9) = (/123872331.0_dp/1001029789.0_dp, &
        -45442868181.0_dp/3398467696.0_dp,-4093664535.0_dp/808688257.0_dp, &
        3936647629.0_dp/1978049680.0_dp/)
    b(11:,10) = (/3065993473.0_dp/597172653.0_dp, &
        3962137247.0_dp/1805957418.0_dp, -160528059.0_dp/685178525.0_dp/)
    b(12:,11) = (/65686358.0_dp/487910083.0_dp, &
        248638103.0_dp/1413531060.0_dp/)

end module rkSetup

How can I solve this?

Answer 1

As per Table 2.2 in the Fortran 2008 Standard, you may not place executable statements into a module directly.

If you want to initialize this data, either (a) do it during declaration, or (b) add a dedicated subroutine that you can call to do the initialization.

(a)

real(dp), dimension(s),parameter :: a = &
    (/0.0_dp, 1.0_dp/18.0_dp, 1.0_dp/12.0_dp, 1.0_dp/8.0_dp, &
    5.0_dp/16.0_dp,3.0_dp/8.0_dp,59.0_dp/400.0_dp,93.0_dp/200.0_dp, &
    5490023248.0_dp/9719169821.0_dp, 13.0_dp/20.0_dp, &
    1201146811.0_dp/1299019798.0_dp, 1.0_dp, 1.0_dp/)

(b)

module rkSetup
!High order embedded Runge-Kutta formulae, by P.J.Prince and J.R.Dormand,
!Journal of Computational and Applied Mathematics, vol. 7, 1981, pages 67-75

    implicit none
    INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(15)
    !...
    contains
    subroutine init()
        a = (/0.0_dp, 1.0_dp/18.0_dp, 1.0_dp/12.0_dp, 1.0_dp/8.0_dp, &
            5.0_dp/16.0_dp,3.0_dp/8.0_dp,59.0_dp/400.0_dp,93.0_dp/200.0_dp, &
            5490023248.0_dp/9719169821.0_dp, 13.0_dp/20.0_dp, &
            1201146811.0_dp/1299019798.0_dp, 1.0_dp, 1.0_dp/)
        !....
    end subroutine
end module

Answer 2

Alexander Vogt is correct that you can define them in an initialization routine. However, if a,b,c,d are constants, the most efficient thing to do is define them as parameters. Here is an example of two ways to do this:

module params
   implicit none

   integer, parameter :: s = 5

   ! -- Initialization method 1
   real, parameter :: a(s) = (/ 1.2, 3.4, &
      5.6, 7.8, 9.0 /)

   ! -- Initialization method 2
   real :: b(s)
   parameter( b = (/ 1.2, 3.4, &
      5.6, 7.8, 9.0 /) )

end module params

program main
   use params
   write(*,'(a,5f6.2)') 'a is: ', a
   write(*,'(a,5f6.2)') 'b is: ', b
end program main

If you wish to set a large parameter array with more than one dimension, consider using reshape.