Infinite loop in Newton bisection - fortran

Question

program main
implicit none
double precision x0, a, b
x0 = -3
call findzero(x0)
contains
function f(x)
implicit none
double precision x,f
f = SIN(x) - exp(-x)
end function
function fprime(x)
implicit none
double precision fprime, x
fprime = COS(x) + exp(-x)
end function
subroutine findbracket(x0,a,b)
implicit none
double precision x0, a, b
double precision fa, fb
double precision dx
dx = 0.001d0
a = x0
b = x0
do
fa = f(a)
fb = f(b)
!print*,"bracket[", a, b, "]"
a = a - dx
if (fa*fb < 0) then
exit
end if
b = b + dx
if (fa*fb < 0) then
exit
end if
dx = dx*2
end do
end subroutine
subroutine findzero(x0)
implicit none
double precision x0, a, b
double precision p, tol
while (x0 <11) do
x0 = -3
print*, "what is x0", x0
call findbracket(x0,a,b)
call newtonbisection (p,a,b,tol)
print*, "this is x0, x", x0, p
x0 = x0 + 1
end do
end subroutine
Using this subroutine I am trying to solve for the zeros of
f(x) = sinx - e^-x
with x0 = -3, -2, ..., 10.
I have working subroutines findbracket and newtonbisection. Using findbracket I intend to get [a,b] and using those a and b, I want to find p for each x0.
When I compile, my code falls into an infinite loop, I tried it with commenting out
call newtonbisection (p,a,b,tol)
so I assume the problem is with findbracket. But if I just use the subroutine to find [a,b] with x0 = -3, it works but not when I combine them.
Why do I have an infinite loop?

Answer 1

Let's narrow this loop down:
do while (x0 < 11)
x0 = -3
call findbracket(x0, a, b)
x0 = x0 + 1
end do
This is a loop that gets executed as long as x0 is smaller than eleven. Inside the loop, you explicitly set x0 to minus 3, then call a subroutine that uses x0, finally increment x0
I didn't see any location inside the findbracket routine where the value of x0 would be changed, so it will still be -3 at the end of the call. Then it gets incremented by one, so it's now -2, which is still smaller than 11, so the loop starts again. The first thing it does is to reset x0 to -3, and the whole spiel starts at the same point again.
So the condition x0 < 11 will always be true, since in every iteration, x0 will get reset to -3. The loop will never exit. Your program hangs.
You need to move the x0 = -3 to before the loop, like this:
x0 = -3
do while (x0 < 11)
call findbracket(x0, a, b)
x0 = x0 + 1
end do
That way, x0 won't get reset to -3 in every iteration of the loop and will eventually become larger than 11 so that the loop ends.

Answer 2

An "infinite" for loop is achieved as follows:
do
** Some executable statements
if (conditional_statement) exit
end do
In brief, a set of statements are executed repetitively until the conditional statement is satisfied, that is,
conditional_statement .eqv. .true.
When this occurs, program control jumps to the next executable statement immediately following the do construct.