module gms_math_derivative use datatype use mem_manager implicit none interface d_x module procedure d_x_x module procedure d_x_xy module procedure d_x_xz module procedure d_x_xyz end interface interface d_y module procedure d_y_y module procedure d_y_xy module procedure d_y_yz module procedure d_y_xyz end interface interface d_z module procedure d_z_z module procedure d_z_xz module procedure d_z_yz module procedure d_z_xyz end interface interface d_2x module procedure d_2x_x module procedure d_2x_xy module procedure d_2x_xz module procedure d_2x_xyz end interface interface d_2y module procedure d_2y_y module procedure d_2y_xy module procedure d_2y_yz module procedure d_2y_xyz end interface interface d_2z module procedure d_2z_z module procedure d_2z_xz module procedure d_2z_yz module procedure d_2z_xyz end interface interface d_4x module procedure d_4x_x module procedure d_4x_xy module procedure d_4x_xz module procedure d_4x_xyz end interface interface d_4y module procedure d_4y_y module procedure d_4y_xy module procedure d_4y_yz module procedure d_4y_xyz end interface interface d_4z module procedure d_4z_z module procedure d_4z_xz module procedure d_4z_yz module procedure d_4z_xyz end interface contains function d_x_x(input) result(output) type(var_x), intent(in) :: input type(var_x) :: output integer :: new_id call get_new_id_x(new_id) output%id = new_id output%grid(1) = mod( input%grid(1) + 1, 2 ) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_x(lb_axis1+output%grid(1) : ub_axis1-1+output%grid(1),:,:,new_id) & = ( work_x(lb_axis1+1:ub_axis1,:,:,input%id) & - work_x(lb_axis1:ub_axis1-1,:,:,input%id) ) / dx end function d_x_x function d_2x_x(input) result(output) type(var_x), intent(in) :: input type(var_x) :: output integer :: new_id call get_new_id_x(new_id) output%id = new_id output%grid = input%grid work_x(lb_axis1+1 : ub_axis1-1,:,:,new_id) & = ( work_x(lb_axis1+2:ub_axis1,:,:,input%id) & - work_x(lb_axis1:ub_axis1-2,:,:,input%id) ) / ( 2.0D0 * dx ) end function d_2x_x function d_4x_x(input) result(output) type(var_x), intent(in) :: input type(var_x) :: output integer :: new_id call get_new_id_x(new_id) output%id = new_id output%grid = input%grid work_x(lb_axis1+2 : ub_axis1-2,:,:,new_id) & = ( work_x(lb_axis1+4:ub_axis1,:,:,input%id) & - work_x(lb_axis1:ub_axis1-4,:,:,input%id) ) / ( 4.0D0 * dx ) end function d_4x_x function d_x_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid(1) = mod( input%grid(1) + 1, 2 ) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xy(lb_axis1+output%grid(1) : ub_axis1-1+output%grid(1),:,:,new_id) & = ( work_xy(lb_axis1+1:ub_axis1,:,:,input%id) & - work_xy(lb_axis1:ub_axis1-1,:,:,input%id) ) / dx end function d_x_xy function d_2x_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid = input%grid work_xy(lb_axis1+1 : ub_axis1-1,:,:,new_id) & = ( work_xy(lb_axis1+2:ub_axis1,:,:,input%id) & - work_xy(lb_axis1:ub_axis1-2,:,:,input%id) ) / ( 2.0D0 * dx ) end function d_2x_xy function d_4x_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid = input%grid work_xy(lb_axis1+2 : ub_axis1-2,:,:,new_id) & = ( work_xy(lb_axis1+4:ub_axis1,:,:,input%id) & - work_xy(lb_axis1:ub_axis1-4,:,:,input%id) ) / ( 4.0D0 * dx ) end function d_4x_xy function d_x_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid(1) = mod( input%grid(1) + 1, 2 ) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xz(lb_axis1+output%grid(1) : ub_axis1-1+output%grid(1),:,:,new_id) & = ( work_xz(lb_axis1+1:ub_axis1,:,:,input%id) & - work_xz(lb_axis1:ub_axis1-1,:,:,input%id) ) / dx end function d_x_xz function d_2x_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid = input%grid work_xz(lb_axis1+1 : ub_axis1-1,:,:,new_id) & = ( work_xz(lb_axis1+2:ub_axis1,:,:,input%id) & - work_xz(lb_axis1:ub_axis1-2,:,:,input%id) ) / ( 2.0D0 * dx ) end function d_2x_xz function d_4x_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid = input%grid work_xz(lb_axis1+2 : ub_axis1-2,:,:,new_id) & = ( work_xz(lb_axis1+4:ub_axis1,:,:,input%id) & - work_xz(lb_axis1:ub_axis1-4,:,:,input%id) ) / ( 4.0D0 * dx ) end function d_4x_xz function d_x_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = mod( input%grid(1) + 1, 2 ) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xyz(lb_axis1+output%grid(1) : ub_axis1-1+output%grid(1),:,:,new_id) & = ( work_xyz(lb_axis1+1:ub_axis1,:,:,input%id) & - work_xyz(lb_axis1:ub_axis1-1,:,:,input%id) ) / dx end function d_x_xyz function d_2x_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid = input%grid work_xyz(lb_axis1+1 : ub_axis1-1,:,:,new_id) & = ( work_xyz(lb_axis1+2:ub_axis1,:,:,input%id) & - work_xyz(lb_axis1:ub_axis1-2,:,:,input%id) ) / ( 2.0D0 * dx ) end function d_2x_xyz function d_4x_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid = input%grid work_xyz(lb_axis1+2 : ub_axis1-2,:,:,new_id) & = ( work_xyz(lb_axis1+4:ub_axis1,:,:,input%id) & - work_xyz(lb_axis1:ub_axis1-4,:,:,input%id) ) / ( 4.0D0 * dx ) end function d_4x_xyz function d_y_y(input) result(output) type(var_y), intent(in) :: input type(var_y) :: output integer :: new_id call get_new_id_y(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = mod( input%grid(2) + 1, 2 ) output%grid(3) = input%grid(3) work_y(:,lb_axis2+output%grid(2) : ub_axis2-1+output%grid(2),:,new_id) & = ( work_y(:,lb_axis2+1:ub_axis2,:,input%id) & - work_y(:,lb_axis2:ub_axis2-1,:,input%id) ) / dy end function d_y_y function d_2y_y(input) result(output) type(var_y), intent(in) :: input type(var_y) :: output integer :: new_id call get_new_id_y(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_y(:,lb_axis2+1 : ub_axis2-1,:,new_id) & = ( work_y(:,lb_axis2+2:ub_axis2,:,input%id) & - work_y(:,lb_axis2:ub_axis2-2,:,input%id) ) / (2.0D0 * dy ) end function d_2y_y function d_4y_y(input) result(output) type(var_y), intent(in) :: input type(var_y) :: output integer :: new_id call get_new_id_y(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_y(:,lb_axis2+2 : ub_axis2-2,:,new_id) & = ( work_y(:,lb_axis2+4:ub_axis2,:,input%id) & - work_y(:,lb_axis2:ub_axis2-4,:,input%id) ) / (4.0D0 * dy ) end function d_4y_y function d_y_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = mod( input%grid(2) + 1, 2 ) output%grid(3) = input%grid(3) work_xy(:,lb_axis2+output%grid(2) : ub_axis2-1+output%grid(2),:,new_id) & = ( work_xy(:,lb_axis2+1:ub_axis2,:,input%id) & - work_xy(:,lb_axis2:ub_axis2-1,:,input%id) ) / dy end function d_y_xy function d_2y_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xy(:,lb_axis2+1 : ub_axis2-1,:,new_id) & = ( work_xy(:,lb_axis2+2:ub_axis2,:,input%id) & - work_xy(:,lb_axis2:ub_axis2-2,:,input%id) ) / (2.0D0 * dy ) end function d_2y_xy function d_4y_xy(input) result(output) type(var_xy), intent(in) :: input type(var_xy) :: output integer :: new_id call get_new_id_xy(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xy(:,lb_axis2+2 : ub_axis2-2,:,new_id) & = ( work_xy(:,lb_axis2+4:ub_axis2,:,input%id) & - work_xy(:,lb_axis2:ub_axis2-4,:,input%id) ) / (4.0D0 * dy ) end function d_4y_xy function d_y_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = mod( input%grid(2) + 1, 2 ) output%grid(3) = input%grid(3) work_yz(:,lb_axis2+output%grid(2) : ub_axis2-1+output%grid(2),:,new_id) & = ( work_yz(:,lb_axis2+1:ub_axis2,:,input%id) & - work_yz(:,lb_axis2:ub_axis2-1,:,input%id) ) / dy end function d_y_yz function d_2y_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_yz(:,lb_axis2+1 : ub_axis2-1,:,new_id) & = ( work_yz(:,lb_axis2+2:ub_axis2,:,input%id) & - work_yz(:,lb_axis2:ub_axis2-2,:,input%id) ) / (2.0D0 * dy ) end function d_2y_yz function d_4y_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_yz(:,lb_axis2+2 : ub_axis2-2,:,new_id) & = ( work_yz(:,lb_axis2+4:ub_axis2,:,input%id) & - work_yz(:,lb_axis2:ub_axis2-4,:,input%id) ) / (4.0D0 * dy ) end function d_4y_yz function d_y_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = mod( input%grid(2) + 1, 2 ) output%grid(3) = input%grid(3) work_xyz(:,lb_axis2+output%grid(2) : ub_axis2-1+output%grid(2),:,new_id) & = ( work_xyz(:,lb_axis2+1:ub_axis2,:,input%id) & - work_xyz(:,lb_axis2:ub_axis2-1,:,input%id) ) / dy end function d_y_xyz function d_2y_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xyz(:,lb_axis2+1 : ub_axis2-1,:,new_id) & = ( work_xyz(:,lb_axis2+2:ub_axis2,:,input%id) & - work_xyz(:,lb_axis2:ub_axis2-2,:,input%id) ) / (2.0D0 * dy ) end function d_2y_xyz function d_4y_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xyz(:,lb_axis2+2 : ub_axis2-2,:,new_id) & = ( work_xyz(:,lb_axis2+4:ub_axis2,:,input%id) & - work_xyz(:,lb_axis2:ub_axis2-4,:,input%id) ) / (4.0D0 * dy ) end function d_4y_xyz function d_z_z(input) result(output) type(var_z), intent(in) :: input type(var_z) :: output integer :: new_id call get_new_id_z(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = mod( input%grid(3) + 1, 2 ) work_z(:,:,lb_axis3+output%grid(3) : ub_axis3-1+output%grid(3),new_id) & = ( work_z(:,:,lb_axis3+1:ub_axis3,input%id) & - work_z(:,:,lb_axis3:ub_axis3-1,input%id) ) / dz end function d_z_z function d_2z_z(input) result(output) type(var_z), intent(in) :: input type(var_z) :: output integer :: new_id call get_new_id_z(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_z(:,:,lb_axis3+1 : ub_axis3-1,new_id) & = ( work_z(:,:,lb_axis3+2:ub_axis3,input%id) & - work_z(:,:,lb_axis3:ub_axis3-2,input%id) ) / ( 2.0D0 * dz) end function d_2z_z function d_4z_z(input) result(output) type(var_z), intent(in) :: input type(var_z) :: output integer :: new_id call get_new_id_z(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_z(:,:,lb_axis3+2 : ub_axis3-2,new_id) & = ( work_z(:,:,lb_axis3+4:ub_axis3,input%id) & - work_z(:,:,lb_axis3:ub_axis3-4,input%id) ) / ( 4.0D0 * dz) end function d_4z_z function d_z_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = mod( input%grid(3) + 1, 2 ) work_xz(:,:,lb_axis3+output%grid(3) : ub_axis3-1+output%grid(3),new_id) & = ( work_xz(:,:,lb_axis3+1:ub_axis3,input%id) & - work_xz(:,:,lb_axis3:ub_axis3-1,input%id) ) / dz end function d_z_xz function d_2z_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xz(:,:,lb_axis3+1 : ub_axis3-1,new_id) & = ( work_xz(:,:,lb_axis3+2:ub_axis3,input%id) & - work_xz(:,:,lb_axis3:ub_axis3-2,input%id) ) / ( 2.0D0 * dz) end function d_2z_xz function d_4z_xz(input) result(output) type(var_xz), intent(in) :: input type(var_xz) :: output integer :: new_id call get_new_id_xz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xz(:,:,lb_axis3+2 : ub_axis3-2,new_id) & = ( work_xz(:,:,lb_axis3+4:ub_axis3,input%id) & - work_xz(:,:,lb_axis3:ub_axis3-4,input%id) ) / ( 4.0D0 * dz) end function d_4z_xz function d_z_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = mod( input%grid(3) + 1, 2 ) work_yz(:,:,lb_axis3+output%grid(3) : ub_axis3-1+output%grid(3),new_id) & = ( work_yz(:,:,lb_axis3+1:ub_axis3,input%id) & - work_yz(:,:,lb_axis3:ub_axis3-1,input%id) ) / dz end function d_z_yz function d_2z_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_yz(:,:,lb_axis3+1 : ub_axis3-1,new_id) & = ( work_yz(:,:,lb_axis3+2:ub_axis3,input%id) & - work_yz(:,:,lb_axis3:ub_axis3-2,input%id) ) / ( 2.0D0 * dz) end function d_2z_yz function d_4z_yz(input) result(output) type(var_yz), intent(in) :: input type(var_yz) :: output integer :: new_id call get_new_id_yz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_yz(:,:,lb_axis3+2 : ub_axis3-2,new_id) & = ( work_yz(:,:,lb_axis3+4:ub_axis3,input%id) & - work_yz(:,:,lb_axis3:ub_axis3-4,input%id) ) / ( 4.0D0 * dz) end function d_4z_yz function d_z_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = mod( input%grid(3) + 1, 2 ) work_xyz(:,:,lb_axis3+output%grid(3) : ub_axis3-1+output%grid(3),new_id) & = ( work_xyz(:,:,lb_axis3+1:ub_axis3,input%id) & - work_xyz(:,:,lb_axis3:ub_axis3-1,input%id) ) / dz end function d_z_xyz function d_2z_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xyz(:,:,lb_axis3+1 : ub_axis3-1,new_id) & = ( work_xyz(:,:,lb_axis3+2:ub_axis3,input%id) & - work_xyz(:,:,lb_axis3:ub_axis3-2,input%id) ) / ( 2.0D0 * dz) end function d_2z_xyz function d_4z_xyz(input) result(output) type(var_xyz), intent(in) :: input type(var_xyz) :: output integer :: new_id call get_new_id_xyz(new_id) output%id = new_id output%grid(1) = input%grid(1) output%grid(2) = input%grid(2) output%grid(3) = input%grid(3) work_xyz(:,:,lb_axis3+2 : ub_axis3-2,new_id) & = ( work_xyz(:,:,lb_axis3+4:ub_axis3,input%id) & - work_xyz(:,:,lb_axis3:ub_axis3-4,input%id) ) / ( 4.0D0 * dz) end function d_4z_xyz end module gms_math_derivative