Using matrices as arguments in functions and as output in subroutines in Fortran - function

Question

I was trying to create a program that requires me to use matrices as input for functions and subroutines and also requires me to take matrix as subroutine output in Fortran. But, I've encountered multiple errors while doing so. I am not able to understand the source of these errors and hence how to fix them.
I'm confident of the logic but I seem to be making errors in dealing with the matrices.
Program to solve system of linear equations(Gauss elimination with partial pivoting)
Code:
program solving_equations
implicit none
real, allocatable :: a(:,:),interchanged(:,:)
real, allocatable :: x(:)
real addition,multiplying_term,alpha,maximum
integer i,j,row,rth_ele,f_maxfinder,k,n,s,inte
read(*,*)n
allocate( a( n,(n+1) ) )
allocate( x(n) )
allocate( interchanged( n,(n+1) ) )
do i=1,n
read(*,*)( a(i,j),j=1,(n+1) )
end do
do rth_ele= 1,(n-1)
row=f_maxfinder( a , n , rth_ele )
if (row==rth_ele) then
continue
else
call interchanger(a,rth_ele,row,n,interchanged)
a = interchanged
end if
do i= (rth_ele+1) , n
! once i is fixed, multiplying term is fixed too
multiplying_term=( a(i,rth_ele)/a(rth_ele,rth_ele) )
do j=1,(n+1)
a(i,j)=a(i,j)-a(rth_ele,j)*multiplying_term
end do
end do
end do
x(n)=a(n,n+1)/a(n,n)
do i=(n-1),1,-1
addition=0.0
do s=n , (i+1) , -1
addition=addition+a(i,s)*x(s)
end do
x(i)= ( ( a(i,n+1)- addition )/a(i,i) )
end do
do i=1,n
print*,x(i)
end do
endprogram solving_equations
!=================
function f_maxfinder(a,n,rth_ele)
integer inte,f_maxfinder
real maximum
maximum=a(rth_ele,rth_ele)
do inte=n,nint(rth_ele+1),-1
if( a(inte,rth_ele) > maximum ) then
maximum = a(inte,rth_ele)
f_maxfinder=inte
else
continue
end if
end do
end
subroutine interchanger( a,rth_ele,row,n,interchanged )
integer i
real alpha
real, allocatable :: interchanged(:,:)
allocate( interchanged( n,(n+1) ) )
do i=1,n+1
alpha=a(row,i)
a(row,i)=a(rth_ele,i)
a(rth_ele,i)=alpha
end do
do i=1,n
do j=1,(n+1)
interchanged(i,j)=a(i,j)
end do
end do
end
Errors:
row=f_maxfinder( a , n , rth_ele )
1
Warning: Rank mismatch in argument 'a' at (1) (scalar and rank-2)
a(row,i)=a(rth_ele,i)
Error: The function result on the lhs of the assignment at (1) must have the pointer attribute.
a(rth_ele,i)=alpha
Error: The function result on the lhs of the assignment at (1) must have the pointer attribute.
call interchanger(a,rth_ele,row,n,interchanged)
1
Error: Explicit interface required for 'interchanger' at (1): allocatable argument
Thanks!

Answer 1

You're missing a declaration of a as an array in f_maxfinder. implicit none is your friend - be sure to use it all the time.
interchanger has a dummy argument interchanged that is an allocatable, assumed-shape array. This requires that an explicit interface to interchanger be visible in the caller. (See my post https://stevelionel.com/drfortran/2012/01/05/doctor-fortran-gets-explicit-again/ for more on this.
The interface issue could be solved by putting the subroutines in a module and adding a use of the module in the main program.
By the way, there's no need to make a allocatable in f_maxfinder, as you are not allocating or deallocating it. It is still an assumed-shape array so the explicit interface is still required.

Answer 2

Here is a working example taking into account #SteveLionel's advice and the following comments:
Always use implicit none, at least once in the main program and don't forget to pass the -warn flag to the compiler.
Either use a module for functions and subroutines, then add use <module> to the main program, or simply use contains and include them inside the main program as I did below.
The interchanged array is already alcated in the main program, you don't need to re-allocate it in the interchanger subroutine, just pass it as an assumed-shape array.
Remove unused variables; alpha, maximum, k, inte.
Define a in f_maxfinder function.
Function type is better written in front of the function name for readability; see your definition of f_maxfinder and don't declare the function again in main program, unless you're using an explicit interface.
The nint procedure accepts real input, you don't need it here.
Finally add any missing variable declarations in your function/subroutine.
program solving_equations
implicit none
real, allocatable :: a(:,:), interchanged(:,:), x(:)
real :: addition, multiplying_term
integer :: i, j, row, rth_ele, n, s
read (*,*) n
allocate ( a( n,(n+1) ) )
allocate ( x( n ) )
allocate ( interchanged( n,(n+1) ) )
do i = 1,n
do j = 1,(n+1)
read (*,*) a(i,j)
end do
end do
do rth_ele = 1,(n-1)
row = f_maxfinder( a , n , rth_ele )
if (row == rth_ele) then
continue
else
call interchanger(a, rth_ele, row, n, interchanged)
a = interchanged
end if
do i = (rth_ele+1) , n
! once i is fixed, multiplying term is fixed too
multiplying_term = a(i,rth_ele) / a(rth_ele,rth_ele)
do j = 1,(n+1)
a(i,j) = a(i,j) - a(rth_ele,j) * multiplying_term
end do
end do
end do
x(n) = a(n,n+1) / a(n,n)
do i = (n-1),1,-1
addition = 0.0
do s = n,(i+1),-1
addition = addition + a(i,s) * x(s)
end do
x(i)= (a(i,n+1) - addition) / a(i,i)
end do
do i = 1,n
print *, x(i)
end do
contains
integer function f_maxfinder(a, n, rth_ele)
integer :: n, rth_ele, inte
real :: maximum, a(:,:)
maximum = a(rth_ele,rth_ele)
do inte = n,rth_ele+1,-1
if (a(inte,rth_ele) > maximum) then
maximum = a(inte,rth_ele)
f_maxfinder = inte
else
continue
end if
end do
end
subroutine interchanger( a, rth_ele, row, n, interchanged )
integer :: i, rth_ele, row, n
real :: alpha, a(:,:), interchanged(:,:)
do i = 1,n+1
alpha = a(row,i)
a(row,i) = a(rth_ele,i)
a(rth_ele,i) = alpha
end do
do i = 1,n
do j = 1,(n+1)
interchanged(i,j) = a(i,j)
end do
end do
end
end program solving_equations
Entering a sample 3-by-4 array, you get the following output (check the results, you know your algorithm):
3
4
3
6
3
7
4
6
7
4
4
2
0
2.05263186
-2.15789509
0.210526198
Process returned 0 (0x0) execution time : 1.051 s
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