# Hi,Below is a fortran program to calculate the roots of an

1. Aug 9, 2011

### Belgium 12

Hi,

Below is a fortran program to calculate the roots of an equation by newton's method.
I compile the program with the free compiler g95:
g95 -c newton.f95 then g95 newton.f95 -o newton.exe

When I run the program newton.exe I get the error can't assign value INTENT(IN)::x to

x=x-fx/g(x).It goes wrong at the do loop.When I change x1=x-fx/g(x) I get six times
the same result.
4 33.
What goes wrong with the program.I'm not a specialist.

Thank you for help

! Numerical Mathematics and Computing, Fifth Edition
! Ward Cheney & David Kincaid
! Brooks/Cole Publ. Co.
! For educational use with the Cheney-Kincaid textbook.
! Absolutely no warranty implied or expressed.
!
! Section 3.2
!
! File: newton.f90
!
! Sample Newton's method program using subroutine newton(f,fp,x,m)
!
program main
integer, parameter :: dp = kind (1d0)
real (kind = dp) :: x, true
integer :: m

interface
function f(x)
integer, parameter :: dp = kind(1d0)
real (kind=dp), intent(in) :: x
end function f
function g(x)
integer, parameter :: dp = kind (1d0)
real (kind=dp), intent(in) :: x
end function g
end interface

m = 6
x = 4.0_dp
call newton(f,g,x,m)
end program main

subroutine newton(f,g,x,m)
interface
function f(x)
integer, parameter :: dp = kind(1d0)
real (kind=dp), intent(in) :: x
end function f
function g(x)
integer, parameter :: dp = kind(1d0)
real (kind =dp), intent(in) :: x
end function g
end interface
integer, parameter :: dp = kind(1d0)
real (kind=dp), intent(in) :: x
integer, intent(in) :: m

print *, "n x f(x)"
fx = f(x)
print *, 0, x, fx
do n = 1,m
x = x - fx/g(x)
fx = f(x)
print "(i2, f20.16, f20.16)", n, x, fx
end do
end subroutine newton

function f(x)
integer, parameter :: dp = kind (1d0)
real (kind = dp) , intent(in) :: x
f = ((x - 2.0_dp)*x + 1.0_dp)*x - 3.0_dp
end function f

function g(x)
integer, parameter :: dp = kind (1d0)
real (kind = dp), intent(in) :: x
g = (3.0_dp*x - 4.0_dp)*x + 1.0_dp
end function g

2. Aug 9, 2011

### uart

Re: Fortran

Because Fortran passes all parameters by reference the "intent" modifier was added to the language to help prevent unwanted side effects to passed variables. Intent(in) simply informs the compiler that the variable should not be modified during the subroutine or function.

Since your newton subroutine declares "x" with intent(in) it is not allowed to modify it. Either remove the intent(in) statement and write the main program in such a way that it is immune to any side effects in x, or keep intent(in) and use a new local variable for x within the subroutine.

BTW. The return type of the functions f and g, as well as that of some other variables like fx, doesn't seem to have been declared. You should be really wary of using Fortrans implicit typing.

3. Aug 10, 2011

### Belgium 12

Fortran

Hi,

Thanks to Uart for his help.I changed the program with your suggestions and it works fine.
Here is the program:!

! Numerical Mathematics and Computing, Fifth Edition
! Ward Cheney & David Kincaid
! Brooks/Cole Publ. Co.
! For educational use with the Cheney-Kincaid textbook.
! Absolutely no warranty implied or expressed.
!
! Section 3.2
!
! File: newton.f90
!
! Sample Newton's method program using subroutine newton(f,fp,x,m)
!
program main
integer, parameter :: dp = kind (1d0)
real (kind = dp) :: x, true
integer :: m

interface
function f(x)
integer, parameter :: dp = kind(1d0)
real (kind=dp), intent(in) :: x
end function f
function g(x)
integer, parameter :: dp = kind (1d0)
real (kind=dp), intent(in) :: x
end function g
end interface

m = 6
x = 4.0_dp
call newton(f,g,x,m)
end program main

subroutine newton(f,g,x,m)
interface
function f(x)
integer, parameter :: dp = kind(1d0)
real (kind=dp) :: x
end function f
function g(x)
integer, parameter :: dp = kind(1d0)
real (kind =dp) :: x
end function g
end interface
integer, parameter :: dp = kind(1d0)
real (kind=dp) :: x
integer, intent(in) :: m

print *, "n x f(x)"
fx = f(x)
print *, 0, x, fx
do n = 1,m
x = x - fx/g(x)
fx = f(x)
print "(i2, f20.16, f20.16)", n, x, fx
end do
end subroutine newton

function f(x)
integer, parameter :: dp = kind (1d0)
real (kind = dp) , intent(in) :: x
f = ((x - 2.0_dp)*x + 1.0_dp)*x - 3.0_dp
end function f

function g(x)
integer, parameter :: dp = kind (1d0)
real (kind = dp), intent(in) :: x
g = (3.0_dp*x - 4.0_dp)*x + 1.0_dp
end function g

I removed the INTENT(IN) instructions in the subprogramma newton.

Thanks