如何在do循环中区分结果和前一个结果

Question

此子程序用于确定复合梯形，因此

我想抽象出最终结果(积分(和上一个结果(积分-1(之间的(差(，并将该差用作重复我的间隔数的限制。

Subroutine Trapezoid(a,b,n,integration)
real,external :: f
real :: h,a,b,summ,p
real,intent(out) :: integration
integer :: n
integer :: i,j
!Here as we have the whole equation is (h/2)*[f(a)+f(b)+2*sum(Xi)
!So we calculate the first part (h/2)*[f(a)+f(b) and then calculate the anoter part
do i=1,n
n=2**i !Double the number of interval
h=(b-a)/n  !Calculate the delta X
p=(h/2.)*(f(a)+f(b))
summ=0
do j=1,n-1
summ=summ+h*f(a+j*h)   !h/2 *2* sum[f(Xi)
enddo  
if(n == 256) then      !put a limit for the number of interval 
Stop
end if
integration = p + summ   !Here the sum the both parts
print*,n,'              ',integration 
enddo
end Subroutine

因此，我想确定差值，当差值小于10*-8时，停止我试了很多，但没有得到我想要的。

Answer 1

我会做下面这样的事情(很快就被破解了(。请注意，对于默认类型reals 1e-8，期望的精度是不切实际的，因此公差较低。如果你想要更高的精度，你需要使用更高精度的实物。

还请注意，我已经把它变成了一个完整的程序。有问题请自己回答。用纯粹自私的话来说，你会更有可能得到一个有用的答案。

不管怎样，这是代码

Program integ

Implicit None

Real, Parameter :: pi = 3.1415927

Real :: value, delta

Integer :: n_used

Intrinsic :: sin

Call Trapezoid( sin, 0.0, pi / 2.0, 20, n_used, value, delta )

Write( *, * ) 'final result', value, ' with ', 2 ** n_used, ' intervals'

Contains

Subroutine Trapezoid(f,a,b,n_max,n_used,integration,delta)
Implicit None
Real, Parameter :: tol = 1e-4
Interface
Function f( x ) Result( r )
Real :: r
Real, Intent( In )  :: x
End Function f
End Interface
Real   , Intent( In    ) :: a
Real   , Intent( In    ) :: b
Integer, Intent( In    ) :: n_max
Integer, Intent(   Out ) :: n_used
Real   , Intent(   Out ) :: integration
Real   , Intent(   Out ) :: delta
Real :: h,summ,p
Real :: integration_old
Integer :: n
Integer :: i,j
!Here as we have the whole equation is (h/2)*[f(a)+f(b)+2*sum(Xi)
!So we calculate the first part (h/2)*[f(a)+f(b) and then calculate the anoter part
delta = - Huge( delta )
integration_old = Huge( integration_old )
Do i=1,n_max
n=2**i !Double the number of interval
h=(b-a)/n  !Calculate the delta X
p=(h/2.)*(f(a)+f(b))
summ=0
Do j=1,n-1
summ=summ+h*f(a+j*h)   !h/2 *2* sum[f(Xi)
Enddo
integration = p + summ   !Here the sum the both parts
If( i /= 1 ) Then
delta = integration - integration_old
Write( *, * ) n,'              ',integration , delta
If( Abs( delta ) < tol ) Exit
End If
integration_old = integration
Enddo
n_used = i
End Subroutine Trapezoid

End Program

ian@eris:~/work/stack$ gfortran --version
GNU Fortran (Ubuntu 7.4.0-1ubuntu1~18.04.1) 7.4.0
Copyright (C) 2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

ian@eris:~/work/stack$ gfortran -Wall -Wextra -fcheck=all -O -std=f2008 integ.f90 
ian@eris:~/work/stack$ ./a.out
4                 0.987115800       3.90563607E-02
8                 0.996785223       9.66942310E-03
16                 0.999196708       2.41148472E-03
32                 0.999799252       6.02543354E-04
64                 0.999949872       1.50620937E-04
128                 0.999987483       3.76105309E-05
final result  0.999987483      with          128  intervals