Calling function - fortran

I don't know is this right room to ask this question of not. If not I am sorry for that.
I am new user for the fortran and spending a lot of time for the following stuff.
I have constructed a function called "loglike" which returns a real number depending on two parameters. I want to use this function to construct a mcmc algorithm
which goes like this.
psi = min(0, loglike(propalpha,propbeta) - loglike(currentalpha,currentbeta))
where propalpha = currentalpha + noise, and propbeta = currentbeta + noise, noises are random samples from some distribution.
Now I want to use this algorithm by calling previously constructed function "loglike".
1) how can I call the function 'loglike' for new program called main program
2) how can I use this for the subroutine?
Any help is very great for me.
Thanks in advance
EDIT:
module mcmc
implicit none
contains
subroutine subru(A,B, alphaprop, betaprop)
real, intent(in)::A,B
real, intent(out)::alphaprop, betaprop
end subroutine subru
real function aloglike(A,B)
real:: A,B,U, aloglike
aloglike = U
end function aloglike
end module mcmc
program likelihood
use mcmc
implicit none
real :: alpha,beta,dist1,dist2,prob1,prob2
real:: psi,a(1000),b(1000), u1, u2,u, alphaprop, betaprop
real, dimension(1:1):: loglike
integer :: t,i,j,k,l
real, dimension(1:625):: x
real, dimension(1:625):: y
integer, dimension(1:625):: inftime
alpha = 0.5
beta = 2.0
open(10, file = 'epidemic.txt', form = 'formatted')
do l = 1,625
read(10,*,end = 200) x(l), y(l), inftime(l)
enddo
200 continue
loglike = 0.0
do t=1,10
do i=1,625
if(inftime(i)==0 .or. t < (inftime(i)-1)) then
dist1 = 0.0
do j = 1, 625
if(t >= inftime(j) .and. inftime(j)/=0)then
dist1 = dist1 + sqrt((x(i) - x(j))**2 + (y(i) - y(j))**2)**(-beta)
endif
enddo
prob1 = 1 - exp(-alpha * dist1)
loglike = loglike + log(1 - prob1)
endif
if(inftime(i) .eq. (t+1)) then
dist2 = 0.0
do k=1, 625
if(t >= inftime(k) .and. inftime(k)/=0) then
dist2 = dist2 + sqrt((x(i) - x(k))**2 + (y(i) - y(k))**2)**(-beta)
endif
enddo
prob2 = 1 - exp(-alpha * dist2)
loglike = loglike + log(prob2)
endif
enddo
enddo
do i = 2, 1000
a(1)= 0.0
b(1) = 0.0
call subru(a(i),b(i), alphaprop, betaprop)
call random_number(u1)
call random_number(u2)
alphaprop = a(i-1) + (u1*0.4)-0.2
betaprop= b(i-1) + (u2*0.4)-0.2
if(alphaprop> 0 .and. alphaprop < 0.2 .and. betaprop > 0 .and. betaprop < 0.2)then
psi = min(0.0,aloglike(alphaprop,betaprop)- aloglike(a(i-1),b(i-1)))
call random_number(u)
if(u < psi)then
a(i)= alphaprop
b(i) = betaprop
else
a(i) = a(i-1)
b(i) = b(i-1)
endif
endif
enddo
do j = 1, 1000
print *, A(j), A(j), LOGLIKE
enddo
end program

The easiest and most reliable technique is to place your functions and subroutines in a module and "use" that module from your main program. This can be done in one file. This method makes the interfaces of the procedures (functions and subroutines) known so that the compiler can check consistency between arguments in the call (actual arguments) and called (dummy arguments). Sketch:
module mysubs
implicit none
contains
subroutine sub1 (xyz)
declarations
code
end subroutine sub1
function func2 (u)
declarations
code
func2 = ...
end func2
end module mysubs
program myprog
use mysubs
implicit none
declarations...
call sub1 (xyz)
q = func2 (z)
end program myprog
ADDED: "implicit none" is used to disable implicit typing, which is dangerous in my opinion. So you will need to type all of your variables, including the function name in the function. You can call the subroutines and functions from other procedures of the module -- they will automatically be known. So you can use "func2" from "sub1", if you wish. For entities outside of the module, such as your main program, you must "use" the module.

This is the general way it would look. Note that functions return a value by assigning the result to its own name. A return statement is not necessary.
C "loglike" is renamed "aloglike" so implicit typing uses REAL
C A type declaration could be used instead
function aloglike (alpha, beta)
aloglike = ... (expression which computes value)
end
program whateveryouwanttocallit
...
propalpha = ...
propbeta = ...
currentalpha = ...
currentbeta = ...
...
psi = min(0, aloglike(propalpha,propbeta) - aloglike(currentalpha,currentbeta))
print *, 'psi = ', psi
end

Related

Fortran Subroutines/Functions: Returned Value Changes If Subroutines/Functions Is Called More Often?

I am currently implementing integrals in Fortran as subroutines. The subroutines on their own return the correct values. If i now call the e.g. same subroutine twice after each other, with the same input values, their returned value differs significantly?
The main program only calls the function like this:
program main
use types
use constants
use integrals
use basis
real(dp), dimension(2,3) :: molecule_coords
real(dp), dimension(2) :: z
type(primitive_gaussian), allocatable :: molecule(:,:)
molecule_coords(1,:) = (/0.,0.,0./)
molecule_coords(2,:) = (/0.,0.,1.6/)
molecule = def_molecule(molecule_coords)
z = (/1.0, 1.0/)
call overlap(molecule) ! Correct Value returned
call overlap(molecule) ! Wrong Value returned
end program main
My function for the overlap looks like this:
module integrals
use types
use constants
use basis
use stdlib_specialfunctions_gamma!, only: lig => lower_incomplete_gamma
contains
subroutine overlap(molecule)
implicit none
type(primitive_gaussian), intent(in) :: molecule(:,:)
integer :: nbasis, i, j, k, l
real(dp) :: norm, p, q, coeff, Kab
real(dp), dimension(3) :: Q_xyz
real(dp), dimension(INT(size(molecule,1)),INT(size(molecule,1))) :: S
nbasis = size(molecule,1)
do i = 1, nbasis
do j = 1, nbasis
! Iterate over l and m primitives in basis
do k = 1, size(molecule(i,:))
do l = 1, size(molecule(j,:))
norm = molecule(i, k)%norm() * molecule(j, l)%norm()
! Eq. 63
Q_xyz = (molecule(i, k)%coords - molecule(j, l)%coords)
! Eq. 64, 65
p = (molecule(i, k)%alpha + molecule(j, l)%alpha)
q = (molecule(i, k)%alpha * molecule(j, l)%alpha) / p
! Eq. 66
Kab = exp(-q * dot_product(Q_xyz,Q_xyz))
coeff = molecule(i, k)%coeff * molecule(j, l)%coeff
S(i,j) = S(i,j) + norm * coeff * Kab * (pi / p) ** (1.5)
end do
end do
end do
end do
print *, S
end subroutine overlap
end module integrals
I am a bit lost, why this would be the case, but I am also rather new to Fortran.
Any help is appreciated! Thanks!

Storing a Variable with a Multi-Dimensional Index in Fortran

Question
Consider the following code:
program example
implicit none
integer, parameter :: n_coeffs = 1000
integer, parameter :: n_indices = 5
integer :: i
real(8), dimension(n_coeffs) :: coeff
integer, dimension(n_coeffs,n_indices) :: index
do i = 1, n_coeffs
coeff(i) = real(i*3,8)
index(i,:) = [2,4,8,16,32]*i
end do
end
For any 5 dimensional index I need to obtain the associated coefficient, without knowing or calculating i. For instance, given [2,4,8,16,32] I need to obtain 3.0 without computing i.
Is there a reasonable solution, perhaps using sparse matrices, that would work for n_indices in the order of 100 (though n_coeffs still in the order of 1000)?
A Bad Solution
One solution would be to define a 5 dimensional array as in
real(8), dimension(2000,4000,8000,16000,32000) :: coeff2
do i = 1, ncoeffs
coeff2(index(i,1),index(i,2),index(i,3),index(i,4),index(i,5)) = coeff(i)
end do
then, to get the coefficient associated with [2,4,8,16,32], call
coeff2(2,4,8,16,32)
However, besides being very wasteful of memory, this solution would not allow n_indices to be set to a number higher than 7 given the limit of 7 dimensions to an array.
OBS: This question is a spin-off of this one. I have tried to ask the question more precisely having failed in the first attempt, an effort that greatly benefited from the answer of #Rodrigo_Rodrigues.
Actual Code
In case it helps here is the code for the actual problem I am trying to solve. It is an adaptive sparse grid method for approximating a function. The main goal is to make the interpolation at the and as fast as possible:
MODULE MOD_PARAMETERS
IMPLICIT NONE
SAVE
INTEGER, PARAMETER :: d = 2 ! number of dimensions
INTEGER, PARAMETER :: L_0 = 4 ! after this adaptive grid kicks in, for L <= L_0 usual sparse grid
INTEGER, PARAMETER :: L_max = 9 ! maximum level
INTEGER, PARAMETER :: bound = 0 ! 0 -> for f = 0 at boundary
! 1 -> adding grid points at boundary
! 2 -> extrapolating close to boundary
INTEGER, PARAMETER :: max_error = 1
INTEGER, PARAMETER :: L2_error = 1
INTEGER, PARAMETER :: testing_sample = 1000000
REAL(8), PARAMETER :: eps = 0.01D0 ! epsilon for adaptive grid
END MODULE MOD_PARAMETERS
PROGRAM MAIN
USE MOD_PARAMETERS
IMPLICIT NONE
INTEGER, DIMENSION(d,d) :: ident
REAL(8), DIMENSION(d) :: xd
INTEGER, DIMENSION(2*d) :: temp
INTEGER, DIMENSION(:,:), ALLOCATABLE :: grid_index, temp_grid_index, grid_index_new, J_index
REAL(8), DIMENSION(:), ALLOCATABLE :: coeff, temp_coeff, J_coeff
REAL(8) :: temp_min, temp_max, V, T, B, F, x1
INTEGER :: k, k_1, k_2, h, i, j, L, n, dd, L1, L2, dsize, count, first, repeated, add, ind
INTEGER :: time1, time2, clock_rate, clock_max
REAL(8), DIMENSION(L_max,L_max,2**(L_max),2**(L_max)) :: coeff_grid
INTEGER, DIMENSION(d) :: level, LL, ii
REAL(8), DIMENSION(testing_sample,d) :: x_rand
REAL(8), DIMENSION(testing_sample) :: interp1, interp2
! ============================================================================
! EXECUTABLE
! ============================================================================
ident = 0
DO i = 1,d
ident(i,i) = 1
ENDDO
! Initial grid point
dsize = 1
ALLOCATE(grid_index(dsize,2*d),grid_index_new(dsize,2*d))
grid_index(1,:) = 1
grid_index_new = grid_index
ALLOCATE(coeff(dsize))
xd = (/ 0.5D0, 0.5D0 /)
CALL FF(xd,coeff(1))
CALL FF(xd,coeff_grid(1,1,1,1))
L = 1
n = SIZE(grid_index_new,1)
ALLOCATE(J_index(n*2*d,2*d))
ALLOCATE(J_coeff(n*2*d))
CALL SYSTEM_CLOCK (time1,clock_rate,clock_max)
DO WHILE (L .LT. L_max)
L = L+1
n = SIZE(grid_index_new,1)
count = 0
first = 1
DEALLOCATE(J_index,J_coeff)
ALLOCATE(J_index(n*2*d,2*d))
ALLOCATE(J_coeff(n*2*d))
J_index = 0
J_coeff = 0.0D0
DO k = 1,n
DO i = 1,d
DO j = 1,2
IF ((bound .EQ. 0) .OR. (bound .EQ. 2)) THEN
temp = grid_index_new(k,:)+(/ident(i,:),ident(i,:)*(grid_index_new(k,d+i)-(-1)**j)/)
ELSEIF (bound .EQ. 1) THEN
IF (grid_index_new(k,i) .EQ. 1) THEN
temp = grid_index_new(k,:)+(/ident(i,:),ident(i,:)*(-(-1)**j)/)
ELSE
temp = grid_index_new(k,:)+(/ident(i,:),ident(i,:)*(grid_index_new(k,d+i)-(-1)**j)/)
ENDIF
ENDIF
CALL XX(d,temp(1:d),temp(d+1:2*d),xd)
temp_min = MINVAL(xd)
temp_max = MAXVAL(xd)
IF ((temp_min .GE. 0.0D0) .AND. (temp_max .LE. 1.0D0)) THEN
IF (first .EQ. 1) THEN
first = 0
count = count+1
J_index(count,:) = temp
V = 0.0D0
DO k_1 = 1,SIZE(grid_index,1)
T = 1.0D0
DO k_2 = 1,d
CALL XX(1,temp(k_2),temp(d+k_2),x1)
CALL BASE(x1,grid_index(k_1,k_2),grid_index(k_1,k_2+d),B)
T = T*B
ENDDO
V = V+coeff(k_1)*T
ENDDO
CALL FF(xd,F)
J_coeff(count) = F-V
ELSE
repeated = 0
DO h = 1,count
IF (SUM(ABS(J_index(h,:)-temp)) .EQ. 0) THEN
repeated = 1
ENDIF
ENDDO
IF (repeated .EQ. 0) THEN
count = count+1
J_index(count,:) = temp
V = 0.0D0
DO k_1 = 1,SIZE(grid_index,1)
T = 1.0D0
DO k_2 = 1,d
CALL XX(1,temp(k_2),temp(d+k_2),x1)
CALL BASE(x1,grid_index(k_1,k_2),grid_index(k_1,k_2+d),B)
T = T*B
ENDDO
V = V+coeff(k_1)*T
ENDDO
CALL FF(xd,F)
J_coeff(count) = F-V
ENDIF
ENDIF
ENDIF
ENDDO
ENDDO
ENDDO
ALLOCATE(temp_grid_index(dsize,2*d))
ALLOCATE(temp_coeff(dsize))
temp_grid_index = grid_index
temp_coeff = coeff
DEALLOCATE(grid_index,coeff)
ALLOCATE(grid_index(dsize+count,2*d))
ALLOCATE(coeff(dsize+count))
grid_index(1:dsize,:) = temp_grid_index
coeff(1:dsize) = temp_coeff
DEALLOCATE(temp_grid_index,temp_coeff)
grid_index(dsize+1:dsize+count,:) = J_index(1:count,:)
coeff(dsize+1:dsize+count) = J_coeff(1:count)
dsize = dsize + count
DO i = 1,count
coeff_grid(J_index(i,1),J_index(i,2),J_index(i,3),J_index(i,4)) = J_coeff(i)
ENDDO
IF (L .LE. L_0) THEN
DEALLOCATE(grid_index_new)
ALLOCATE(grid_index_new(count,2*d))
grid_index_new = J_index(1:count,:)
ELSE
add = 0
DO h = 1,count
IF (ABS(J_coeff(h)) .GT. eps) THEN
add = add + 1
J_index(add,:) = J_index(h,:)
ENDIF
ENDDO
DEALLOCATE(grid_index_new)
ALLOCATE(grid_index_new(add,2*d))
grid_index_new = J_index(1:add,:)
ENDIF
ENDDO
CALL SYSTEM_CLOCK (time2,clock_rate,clock_max)
PRINT *, 'Elapsed real time1 = ', DBLE(time2-time1)/DBLE(clock_rate)
PRINT *, 'Grid Points = ', SIZE(grid_index,1)
! ============================================================================
! Compute interpolated values:
! ============================================================================
CALL RANDOM_NUMBER(x_rand)
CALL SYSTEM_CLOCK (time1,clock_rate,clock_max)
DO i = 1,testing_sample
V = 0.0D0
DO L1=1,L_max
DO L2=1,L_max
IF (L1+L2 .LE. L_max+1) THEN
level = (/L1,L2/)
T = 1.0D0
DO dd = 1,d
T = T*(1.0D0-ABS(x_rand(i,dd)/2.0D0**(-DBLE(level(dd)))-DBLE(2*FLOOR(x_rand(i,dd)*2.0D0**DBLE(level(dd)-1))+1)))
ENDDO
V = V + coeff_grid(L1,L2,2*FLOOR(x_rand(i,1)*2.0D0**DBLE(L1-1))+1,2*FLOOR(x_rand(i,2)*2.0D0**DBLE(L2-1))+1)*T
ENDIF
ENDDO
ENDDO
interp2(i) = V
ENDDO
CALL SYSTEM_CLOCK (time2,clock_rate,clock_max)
PRINT *, 'Elapsed real time2 = ', DBLE(time2-time1)/DBLE(clock_rate)
END PROGRAM
For any 5 dimensional index I need to obtain the associated
coefficient, without knowing or calculating i. For instance, given
[2,4,8,16,32] I need to obtain 3.0 without computing i.
function findloc_vector(matrix, vector) result(out)
integer, intent(in) :: matrix(:, :)
integer, intent(in) :: vector(size(matrix, dim=2))
integer :: out, i
do i = 1, size(matrix, dim=1)
if (all(matrix(i, :) == vector)) then
out = i
return
end if
end do
stop "No match for this vector"
end
And that's how you use it:
print*, coeff(findloc_vector(index, [2,4,8,16,32])) ! outputs 3.0
I must confess I was reluctant to post this code because, even though this answers your question, I honestly think this is not what you really want/need, but you dind't provide enough information for me to know what you really do want/need.
Edit (After actual code from OP):
If I decrypted your code correctly (and considering what you said in your previous question), you are declaring:
REAL(8), DIMENSION(L_max,L_max,2**(L_max),2**(L_max)) :: coeff_grid
(where L_max = 9, so size(coeff_grid) = 21233664 =~160MB) and then populating it with:
DO i = 1,count
coeff_grid(J_index(i,1),J_index(i,2),J_index(i,3),J_index(i,4)) = J_coeff(i)
ENDDO
(where count is of the order of 1000, i.e. 0.005% of its elements), so this way you can fetch the values by its 4 indices with the array notation.
Please, don't do that. You don't need a sparse matrix in this case either. The new approach you proposed is much better: storing the indices in each row of an smaller array, and fetching on the array of coefficients by the corresponding location of those indices in its own array. This is way faster (avoiding the large allocation) and much more memory-efficient.
PS: Is it mandatory for you to stick to Fortran 90? Its a very old version of the standard and chances are that the compiler you're using implements a more recent version. You could improve the quality of your code a lot with the intrinsic move_alloc (for less array copies), the kind constants from the intrinsic module iso_fortran_env (for portability), the [], >, <, <=,... notation (for readability)...

Why is my Lagrange interpolation algorithm not working?

For some reason it never interpolates, but it gives 0 as an answer. The code is:
PROGRAM LAGRANGE
REAL X(0:100), Y(0:100), INTERP
REAL TEMP = 1.0
REAL POLINOM = 0.0
N=10
OPEN(1,FILE="datos.txt")
DO I=0,100 !We 'clean' the arrays: all positions are 0
X(I)=0.0
Y(I)=0.0
END DO
DO I=0,10 !We read the data file and we save the info
READ(1,*) X(I), Y(I)
END DO
CLOSE(1)
WRITE(*,*) "Data table:"
DO I=0,10
WRITE(*,*) X(I), Y(I)
END DO
WRITE(*,*) "Which value of X do you want to interpolate?"
READ(*,*) INTERP
DO I=0,N
DO J=0,N
IF(J.NE.I) THEN !Condition: J and I can't be equal
TEMP=TEMP*(INTERP-X(J))/(X(I)-X(J))
ELSE IF(J==I) THEN
TEMP=TEMP*1.0
ELSE
END IF
END DO
POLINOM=POLINOM+TEMP
END DO
WRITE(*,*) "Value: ",POLINOM
STOP
END PROGRAM
Where did I fail? I basically need to implement this:
Lagrange interpolation method
Thanks a lot in advance.
In addition to the "symbol-concatenation" problem (explained in the other answer), it seems that TEMP needs to be reset to 1.0 for every I (to calculate the Lagrange polynomial for each grid point), plus we need to multiply it by the functional value on that point (Y(I)). After fixing these
PROGRAM LAGRANGE
implicit none !<-- always recommended
REAL :: X(0:100), Y(0:100), INTERP, TEMP, POLINOM
integer :: I, J, K, N
N = 10
X = 0.0
Y = 0.0
!! Test data (sin(x) over [0,2*pi]).
DO I = 0, N
X(I) = real(I) / real(N) * 3.14159 * 2.0
Y(I) = sin( X(I) )
END DO
WRITE(*,*) "Data table:"
DO I = 0, N
WRITE(*,*) X(I), Y(I)
END DO
interp = 0.5 !! test value
POLINOM = 0.0
DO I = 0, N
TEMP = 1.0 !<-- TEMP should be reset to 1.0 for every I
DO J = 0, N
IF( J /= I ) THEN
TEMP = TEMP * (interp - X(J)) / (X(I) - X(J))
END IF
END DO
TEMP = TEMP * Y(I) !<-- also needs this
POLINOM = POLINOM + TEMP
END DO
print *, "approx : ", POLINOM
print *, "exact : ", sin( interp )
end
we get a pretty good agreement between the approximate (= interpolated) and exact results:
Data table:
0.00000000 0.00000000
0.628318012 0.587784827
1.25663602 0.951056182
1.88495409 0.951056957
2.51327205 0.587786913
3.14159012 2.53518169E-06
3.76990819 -0.587782800
4.39822626 -0.951055467
5.02654409 -0.951057792
5.65486193 -0.587789178
6.28318024 -5.07036339E-06
approx : 0.479412317
exact : 0.479425550
Consider the (complete) program
real x = 1.
end
What does this do?
If this is free-form source then it is an invalid program. If it is fixed-form source then it is a valid program.
In fixed-form source, spaces after column 6 largely have no effect. The program above is exactly like
realx=1.
end
and we can see that we're just setting an implicitly declared real variable called realx to have value 1..
implicit none
real x = 1.
end
will show a problem.
In free-form source, initialization in a declaration statement requires ::, like so:
real :: x = 1.
end
And: use implicit none.

What is wrong with my sub-function definition of sinc?

implicit none
character*20 fflname,oflname
integer length_sgnl
real*8 pi, dt, m, n, theta
parameter ( length_sgnl=11900, dt=0.01d0, m=1, n=1, pi=3.1416
& ,theta=0.2 )
integer i
complex*16 cj, coeff ,sgnl(1 : length_sgnl)
real*8 t(1 : length_sgnl)
parameter ( cj = dcmplx(0, 1) )
real*8 time, real_sgnl, imag_sgnl
oflname="filtered.data"
fflname="artificial"
open(11, file = oflname)
do i=1, length_sgnl
read(11, *) time, real_sgnl, imag_sgnl
sgnl(i) = dcmplx(real_sgnl, imag_sgnl)
t(i) = (i*dt - m) / (2**n)
enddo
coeff = 0
do i=1, length_sgnl
coeff = coeff
& + sgnl(i) * sinc (t(i)) * exp (-cj*2*pi*t(i))
enddo
do i=1, length_sgnl
sgnl(i) = sgnl(i)
& - coeff * sinc (t(i)) * exp (-cj*2*pi*t(i))
& + coeff * sinc (t(i)) * exp (-cj*2*pi*t(i))
& * exp (cj*theta)
enddo
open(12, file = fflname)
do i=1, length_sgnl
write(12, *) i*dt, sgnl(i)
enddo
close(12)
real*8 function sinc (a)
real*8 :: sinc, a
if (abs(a) < 1.0d-6) then
sinc = 1
else
sinc = sin(pi*a) / (pi*a)
end if
end function
stop
end
At the last part of a sub-defined function sinc, I assume the problem is there but I am not sure what it is exactly. The gfortran noticed that I did not define sinc and a, and the "end function" should be "end program"?
I have tried to update your program into standards-compliant modern Fortran:
program sinctest
use :: iso_fortran_env
implicit none
! Declare parameters
integer, parameter :: length_sgnl=11900
real(real64), parameter :: pi=3.1416, dt=0.01, m=1, n=1, theta=0.2
complex(real64), parameter :: cj = cmplx(0, 1)
! Declare variables
character(len=20) :: fflname, oflname
complex(real64) :: coeff, sgnl(length_sgnl)
real(real64) :: time, real_sgnl, imag_sgnl, t(length_sgnl)
integer :: i, ofl, ffl
! Define filenames
oflname="filtered.data"
fflname="artificial"
! Read the input file
open(newunit = ofl, file = oflname)
do i=1, length_sgnl
read(ofl, *) time, real_sgnl, imag_sgnl
sgnl(i) = cmplx(real_sgnl, imag_sgnl, kind=real64)
t(i) = (i*dt - m) / (2**n)
end do
close(ofl)
! Process the input signal
coeff = 0
do i=1, length_sgnl
coeff = coeff &
+ sgnl(i) * sinc(t(i)) * exp(-cj*2*pi*t(i))
end do
do i=1, length_sgnl
sgnl(i) = sgnl(i) &
- coeff * sinc(t(i)) * exp(-cj*2*pi*t(i)) &
+ coeff * sinc(t(i)) * exp(-cj*2*pi*t(i)) &
* exp(cj*theta)
end do
! Save the output file
open(newunit = ffl, file = fflname)
do i=1, length_sgnl
write(ffl, *) i*dt, sgnl(i)
enddo
close(ffl)
contains
pure function sinc(a) result(r)
! This function calculates sinc(a)=sin(pi*a)/(pi*a).
real(real64), intent(in) :: a
real(real64) :: r
if (abs(a) < 1.0e-6) then
r = 1
else
r = sin(pi*a) / (pi*a)
end if
end function
end program
To compile it using e.g. GFortran:
gfortran -std=f2008 -ffree-form sinctest.f
These are the syntax errors that I fixed:
Added a contains section before defining your sinc-function;
Moved your continuation characters (&) from the beginning of a continued line to the end of the previous line;
These are not required changes, just merely style suggestions:
Used the intrinsic module iso_fortran_env to get the real64 variable, which lets you define variables as real(real64) instead of real*8, as the former is portable while the latter is not;
Merged the specification of the variable type (e.g. real) and parameter into a single lines;
Used the Fortran2008 newunit argument to open instead of hard-coding in unit numbers, as this saves you some headache if you write large programs and have a modern compiler;
Made sure that you close the input file as well;
Declared your sinc-function to be pure, as it has no side-effects;
Used the result notation for your sinc-function, so that you don't have to specify the type real*8 in front of the function name;
Rewrote the program in the form program...end program instead of ...stop end.
EDIT:
I also wanted to note that using modern Fortran, the math itself can be written considerably more consise using 'array notation' and 'elemental functions'. For instance, if you define your sinc-function:
elemental function sinc(a) result(r)
! This function calculates sinc(a)=sin(pi*a)/(pi*a).
real(real64), intent(in) :: a
real(real64) :: r
if (abs(a) < 1.0e-6) then
r = 1
else
r = sin(pi*a) / (pi*a)
end if
end function
Then the elemental keyword says that if you apply the sinc-function to an array, it should return a new array where the sinc-function has been evaluated for each element. So this piece of code:
coeff = 0
do i=1, length_sgnl
coeff = coeff &
+ sgnl(i) * sinc(t(i)) * exp(-cj*2*pi*t(i))
end do
Can then actually be written as a one-liner:
coeff = sum(sgnl * sinc(t) * exp(-2*pi*cj*t))
So I would highly recommend that you look into the modern array notation too :).
EDIT 2:
Tried to emphasize what changes are relevant to fixing errors, and what changes are just style suggestions (thanks Vladimir F).

Shooting method in fortran (neutron star oscillation)

I have been writing a script in fortran 90 for solving the radial oscillation problem of a neutron star with the use of shooting method. But for unknown reason, my program never works out. Without the shooting method component, the program runs smoothly as it successfully constructed the star. But once the shooting comes in, everything dies.
PROGRAM ROSCILLATION2
USE eos_parameters
IMPLICIT NONE
INTEGER ::i, j, k, l
INTEGER, PARAMETER :: N_ode = 5
REAL, DIMENSION(N_ode) :: y
REAL(8) :: rho0_cgs, rho0, P0, r0, phi0, pi
REAL(8) :: r, rend, mass, P, phi, delta, xi, eta
REAL(8) :: step, omega, omegastep, tiny, rho_print, Radius, B, a2, s0, lamda, E0, E
EXTERNAL :: fcn
!!!! User input
rho0_cgs = 2.D+15 !central density in cgs unit
step = 1.D-4 ! step size dr
omegastep = 1.D-2 ! step size d(omega)
tiny = 1.D-8 ! small number P(R)/P(0) to define star surface
!!!!!!!!!
open(unit=15, file="data.dat", status="new")
pi = ACOS(-1.D0)
a2 =((((1.6022D-13)**4)*(6.674D-11)*((2.997D8)**-7)*((1.0546D-34)**-3)*(1.D6))**(0.5D0))*a2_MeV !convert to code unit (km^-1)
B = ((1.6022D-13)**4)*(6.674D-11)*((2.997D8)**-7)*((1.0546D-34)**-3)*(1.D6)*B_MeV !convert to code unit (km^-2)
s0 = (1.D0/3.D0) - (1/(6*pi**2))*a2*((1/(16*pi**2)*a2**2 + (pi**-2)*a4*(rho0 - B))**-0.5) !square of the spped of sound at r=0
lamda = -0.5D0*log(1-2*y(1)/r)
E0 = (r0**-2)*s0*exp(lamda + 3*phi0)
rho0 = rho0_cgs*6.67D-18 / 9.D0 !convert rho0 to code unit (km^-2)
!! Calculate central pressure P0
P0 = (1.D0/3.D0)*rho0 - (4.D0/3.D0)*B - (1.D0/(a4*(12.D0)*(pi**2)))*a2**2 - &
&(a2/((3.D0)*a4))*(((1.D0/(16.D0*pi**4))*a2**2+(1.D0/(pi**2))*a4*(rho0-B))**0.5D0)
!! initial value for metric function phi
phi0 = 0.1D0 ! arbitrary (needed to be adjusted later)
r0 = 1.D-30 ! integration starting point
!! Set initial conditions
!!!!!!!!!!!!!!!!!
!!Start integration loop
!!!!!!!!!!!!!!!!!
r = r0
y(1) = 0.D0
y(2) = P0
y(3) = phi0
y(4) = 1/(3*E0)
y(5) = 1
omega = 2*pi*1000/(2.997D5) !omega of 1kHz in code unit
DO l = 1, 1000
omega = omega + omegastep !shooting method part
DO i = 1, 1000000000
rend = r0 + REAL(i)*step
call oderk(r,rend,y,N_ode,fcn)
r = rend
mass = y(1)
P = y(2)
phi = y(3)
xi = y(4)
eta = y(5)
IF (P < tiny*P0) THEN
WRITE(*,*) "Central density (10^14 cgs) = ", rho0_cgs/1.D14
WRITE(*,*) " Mass (solar mass) = ", mass/1.477D0
WRITE(*,*) " Radius (km) = ", r
WRITE(*,*) " Compactness M/R ", mass/r
WRITE(15,*) (omega*2.997D5/(2*pi)), y(5)
GOTO 21
ENDIF
ENDDO
ENDDO
21 CONTINUE
END PROGRAM roscillation2
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE fcn(r,y,yprime)
USE eos_parameters
IMPLICIT NONE
REAL(8), DIMENSION(5) :: y, yprime
REAL(8) :: r, m, P, phi, rho, pi, B, a2, xi, eta, W, Q, E, s, lamda, omega
INTEGER :: j
pi = ACOS(-1.D0)
a2 =((((1.6022D-13)**4)*(6.674D-11)*((2.997D8)**-7)*((1.0546D-34)**-3)*(1.D6))**(0.5D0))*a2_MeV !convert to code unit (km^-1)
B = ((1.6022D-13)**4)*(6.674D-11)*((2.997D8)**-7)*((1.0546D-34)**-3)*(1.D6)*B_MeV !convert to code unit (km^-2)
m = y(1)
P = y(2)
phi = y(3)
xi = y(4)
eta = y(5)
rho = 3.D0*P + 4.D0*B +((3.D0)/(4.D0*a4*(pi**2)))*a2**2+(a2/a4)*&
&(((9.D0/((16.D0)*(pi**4)))*a2**2+((3.D0/(pi**2))*a4*(P+B)))**0.5D0)
s = (1.D0/3.D0) - (1/(6*pi**2))*a2*((1/(16*pi**2)*a2**2 + (pi**-2)*a4*(rho - B))**-0.5) !square of speed of sound
W = (r**-2)*(rho + P)*exp(3*lamda + phi)
E = (r**-2)*s*exp(lamda + 3*phi)
Q = (r**-2)*exp(lamda + 3*phi)*(rho + P)*((yprime(3)**2) + 4*(r**-1)*yprime(3)- 8*pi*P*exp(2*lamda))
yprime(1) = 4.D0*pi*rho*r**2
yprime(2) = - (rho + P)*(m + 4.D0*pi*P*r**3)/(r*(r-2.D0*m))
yprime(3) = (m + 4.D0*pi*P*r**3)/(r*(r-2.D0*m))
yprime(4) = y(5)/(3*E)
yprime(5) = -(W*omega**2 + Q)*y(4)
END SUBROUTINE fcn
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!! Runge-Kutta method (from Numerical Recipes)
!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine oderk(ri,re,y,n,derivs)
INTEGER, PARAMETER :: NMAX=16
REAL(8) :: ri, re, step
REAL(8), DIMENSION(NMAX) :: y, dydx, yout
EXTERNAL :: derivs,rk4
call derivs(ri,y,dydx)
step=re-ri
CALL rk4(y,dydx,n,ri,step,yout,derivs)
do i=1,n
y(i)=yout(i)
enddo
return
end subroutine oderk
SUBROUTINE RK4(Y,DYDX,N,X,H,YOUT,DERIVS)
INTEGER, PARAMETER :: NMAX=16
REAL(8) :: H,HH,XH,X,H6
REAL(8), DIMENSION(N) :: Y, DYDX, YOUT
REAL(8), DIMENSION(NMAX) :: YT, DYT, DYM
EXTERNAL :: derivs
HH=H*0.5D0
H6=H/6D0
XH=X+HH
DO I=1,N
YT(I)=Y(I)+HH*DYDX(I)
ENDDO
CALL DERIVS(XH,YT,DYT)
DO I=1,N
YT(I)=Y(I)+HH*DYT(I)
ENDDO
CALL DERIVS(XH,YT,DYM)
DO I=1,N
YT(I)=Y(I)+H*DYM(I)
DYM(I)=DYT(I)+DYM(I)
ENDDO
CALL DERIVS(X+H,YT,DYT)
DO I=1,N
YOUT(I)=Y(I)+H6*(DYDX(I)+DYT(I)+2*DYM(I))
ENDDO
END SUBROUTINE RK4
Any reply would be great i am just really depressed for the long debugging.
Your program is blowing up because of this line:
yprime(5) = -(W*omega**2 + Q)*y(4)
in subroutine fcn. In this subroutine, omega is completely independent of the one declared in your main program. This one is uninitialized and used in an expression, which will either contain random values or zero, if your compiler is nice enough (or told) to initialize variables.
If you want the variable omega from your main program to be the same variable you use in fcn then you need to pass that variable to fcn somehow. Due to the way you've architected this program, passing it would require modifying all of your procedures to pass omega so that it can be provided to all of your calls to DERIVS (which is the dummy argument you are associating with fcn).
An alternative would be to put omega into a module and use that module where you need access to omega, e.g. declare it in eos_parameters instead of declaring it in the scoping units of fcn and your main program.