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! fortran_library
! Mean-Squared Displacement for a time lag `t`
function msd(a, t) result(b)
implicit none
real(kind=8), intent(in) :: a(:,:)
integer(kind=8), intent(in) :: t
integer(kind=8) :: i, j
real(kind=8) :: s(size(a,1)-t, size(a,2))
real(kind=8) :: b(size(a,1)-t)
s(:, :) = a((t + 1):(size(a,1)), :) - a(1:(size(a,1)-t),:)
do i = 1, size(a, 1)-t
b(i) = 0.0
do j = 1, size(a, 2)
b(i) = b(i) + s(i, j) ** 2
end do
b(i) = sqrt(b(i))
end do
end function msd
! Mean-Squared Displacement for a time lag `t`
function mmsd(a, t) result(z)
implicit none
real(kind=8), intent(in) :: a(:,:)
integer(kind=8), intent(in) :: t
integer(kind=8) :: i, j
real(kind=8) :: s(size(a,1)-t, size(a,2))
real(kind=8) :: b(size(a,1)-t)
real(kind=8) :: z
s(:, :) = a((t + 1):(size(a,1)), :) - a(1:(size(a,1)-t),:)
do i = 1, size(a, 1)-t
b(i) = 0.0
do j = 1, size(a, 2)
b(i) = b(i) + s(i, j) ** 2
end do
b(i) = sqrt(b(i))
end do
z = sum(b(:)) / (size(b, 1))
end function mmsd
! Mean-Squared Displacement for time lags up to `T`
function msds(a, Ts) result(b)
implicit none
real(kind=8), intent(in) :: a(:,:)
integer(kind=8), intent(in) :: Ts
integer(kind=8) :: i, j
integer(kind=8) :: t
real(kind=8) :: s(size(a,1), size(a,2))
real(kind=8) :: b(size(a,1),Ts+1)
do t = 0, Ts
s(:, :) = a((t + 1):(size(a,1)), :) - a(1:(size(a,1)-t),:)
do i = 1, size(a, 1)
b(i,t+1) = 0.0
if (i <= size(a, 1) - t) then
do j = 1, size(a, 2)
b(i,t+1) = b(i,t+1) + s(i, j) ** 2
end do
b(i,t+1) = sqrt(b(i,t+1))
end if
end do
end do
end function msds
! Mean-Squared Displacement for time lags up to `T`
! Return the mean for each time lag
function mmsds(a, Ts) result(z)
implicit none
real(kind=8), intent(in) :: a(:,:)
integer(kind=8), intent(in) :: Ts
integer(kind=8) :: i, j
integer(kind=8) :: t
real(kind=8) :: s(size(a,1), size(a,2))
real(kind=8) :: b(size(a,1),Ts+1)
real(kind=8) :: z(Ts+1)
do t = 0, Ts
s(:, :) = a((t + 1):(size(a,1)), :) - a(1:(size(a,1)-t),:)
do i = 1, size(a, 1)
b(i,t+1) = 0.0
if (i <= size(a, 1) - t) then
do j = 1, size(a, 2)
b(i,t+1) = b(i,t+1) + s(i, j) ** 2
end do
b(i,t+1) = sqrt(b(i,t+1))
end if
end do
z(t+1) = sum(b(1:(size(a, 1) - t),t+1)) / (size(a, 1) - t)
end do
end function mmsds
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