计算cosx时出现Fortran错误 [英] Fortran error when calculating cosx

问题描述

我被分配了以下问题：

创建一个Fortran程序，该程序可以读取检查有效范围（不是类型）的程度[0-360]和它将能够从下面的等式中计算和打印 cos（x），其中 x 以弧度为单位：

  cos（x）= 1-x ^ 2/2！ + x ^ 4/4！-x ^ 6/6！+ x ^ 8/8！-... 
  

作为一个收敛条件，假定 10 ^（ - 5）使用两次连续重复之间的绝对误差（我想它意味着do的）。

为了计算！，应该使用最大可能类型的整数。最后，应该在屏幕上打印重复的总数。

所以我的代码是这样的：

 程序ex6_pr2 
隐式无
！变量和常量
 integer :: i 
 real * 8 :: fact，fact2！fact = factorial 
 real，parameter :: pi = 3.14159265 
 double precision :: degree，radiants，cosradiants，s，oldcosradiants，difference！degree，radiants = angle 
 print *，'该程序读取并计算角度' （角度<0度或> 360度），请输入角度'
 read *，degree 
'的度数！数字范围
 read *，degree 
 print *，'Error input degree'
 cycle 
 end do 
 radiants =（degree * pi / 180）
 fact = 1 
 fact2 = 1 
s = 0 
 cosradiants = 0 
！重复结构
 do i = 2,200,1 
 fact = fact * i 
 fact2 = fact2 *（i + 2）
 oldcosradiants = cosradiants 
 cosradiants =（ - （radiant）** i / fact）+（（radiant）**（i + 2））/ fact2） 
差额= cosradiants-oldcosra （abs（差异）<1e-5）退出
 end do 
！打印结果
 print *，s + 1。 
 
结束程序
  

我得到正确的结果，例如45度或 pi / 4 ），对于其他例如90度或180度的错误。我检查了我的分解因子我相信这个错误是隐藏的（至少对我来说）。

那么我创建了另一个代码，由于以下错误似乎无法运行：FUNCTION name，（RESULT of PROJECT2_EX6〜FACT），用于没有预料到的地方，可能缺少'（）'bb
$ b

  program project2_ex6 
 implicit none 
 integer（kind = 3）:: degrees，i，sign 
 integer :: n 
 double precision :: x，err_limit，s_old，s 
 real，parameter :: pi = 3.14159265359 
 print *，'这个程序计算出cos（x）'
 print *，输入角度度数
 read *，degrees 
 do 
 if（degrees < ; 0.or.degrees> 360）然后
 print *，'Degrees必须介于0-360'之间
其他
x = pi *度/ 180 
出口
结束如果
结束
标志= 1 
 sign = sign *（ -  1）
 err_limit = 1e-5 
n = 0 
s = 0 
 s_old = 0 
 do 
 do i = 1， n 
 end do 
s =（（（ -  1。）** n /（fact（2. * n）））* x **（2. * n））* sign 
s = s + s_old 
 
n = n + 1 
 if（abs（s-s_old）< 1e-5）then 
 exit 
 else 
 s_old = s 
 cycle 
 end if 
 end do 
 print *，s，i，n 
包含
实函数fact（i）
 double precision：fact 
 integer :: i $ b $ if if（i> = 1）then 
 fact = i * fact（i-1）
 else 
 fact = 1 
 end if 
 return 
 end function 
 end program 
  

解决方案

虽然这是你的功课，我会帮​​你在这里。第一个错误的是你需要替换的因式分解

  fact = 1 
 do j = 1 ，我
 fact = fact * j 
 enddo 
  

你让你的循环做这项工作，以便运行它作为

  do i = 4,200,2 
  
 
 
并且在do loob之外预定义cosradians与$ / $> 
 
 
  cosradiants = 1-radiants ** 2/2 
  
另外您需要考虑改变你可以在循环中使用的符号
  sign = sign *（ -  1）
  
，并在循环之前以 sign = 1 开头
 
 
 
在循环中它然后 
 
 
  cosradiants = cosradiants +符号* radiants ** i /事实上
  
如果你已经包含了这些东西，它应该可以工作（至少我的代码是这样的） p> 
I was assigned the following problem:


Make a Fortran program which will be able to read a degree[0-360] checking validity range(not type) and it will be able to calculate and print the cos(x) from the following equation, where x is in radians:
cos(x)=1-x^2/2! + x^4/4!-x^6/6!+x^8/8!-...
As a convergence criteria assume 10^(-5) using the absolute error between two successive repeats (I suppose it means do's). 

For the calculation of the ! the greatest possible kind of integer should be used. Finally the total number of repeats should be printed on screen.

So my code is this:
    program ex6_pr2
implicit none
!Variables and Constants
integer::i
real*8::fact,fact2 !fact=factorial
real,parameter::pi=3.14159265
double precision::degree,radiants,cosradiants,s,oldcosradiants,difference                         !degree,radiants=angle
print*,'This program reads and calculates an angle`s co-sinus'
print*,'Please input the degrees of the angle'
read*,degree
do while(degree<0 .or. degree>360) !number range
read*,degree
print*,'Error input degree' 
cycle
end do
radiants=(degree*pi/180)
fact=1
fact2=1
s=0
cosradiants=0
!repeat structure
do i=2,200,1
fact=fact*i
fact2=fact2*(i+2)
oldcosradiants=cosradiants
cosradiants=(-(radiants)**i/fact)+(((radiants)**(i+2))/fact2)
difference=cosradiants-oldcosradiants
s=s+cosradiants
if(abs(difference)<1e-5) exit
end do
!Printing results
print*,s+1.

end program
I get right results for angles such as 45 degrees (or pi/4) and wrong for other for example 90 degrees or 180.

I have checked my factorials where I believe the error is hidden (at least for me).

Well I created another code which seems unable to run due to the following error:FUNCTION name,(RESULT of PROJECT2_EX6~FACT),used where not expected,perhaps missing '()'
    program project2_ex6
implicit none
integer(kind=3)::degrees,i,sign
integer::n
double precision::x,err_limit,s_old,s
real,parameter::pi=3.14159265359
print*,'This program calculates the cos(x)'
print*,"Enter the angle's degrees"
read*,degrees
do
if(degrees<0.or.degrees>360) then
  print*,'Degrees must be between 0-360'
  else
   x=pi*degrees/180
    exit
    end if
    end do
    sign=1
    sign=sign*(-1)
    err_limit=1e-5
 n=0
    s=0
    s_old=0
do
  do i=1,n
    end do
  s=(((-1.)**n/(fact(2.*n)))*x**(2.*n))*sign
 s=s+s_old

n=n+1
if(abs(s-s_old)<1e-5) then
  exit
  else
    s_old=s
    cycle
    end if
  end do
  print*,s,i,n
contains
real function fact(i)
double precision::fact
integer::i
if(i>=1) then
  fact=i*fact(i-1)
  else
fact=1
    end if
return
end function
  end program

解决方案
Although it is your homework, I will help you here. The first thing which is wrong is ýour factorial which you need to replace with
 fact  = 1
 do j = 1,i
    fact = fact*j
 enddo
second it is easier if you let your do loop do the job so run it as
do i=4,200,2
and predefine cosradians outside the do loob with 
cosradiants = 1-radiants**2/2
additionally you need to take into account the changing sign which you can do in the loop using
   sign = sign*(-1)
and starting it off with sign = 1 before the loop

in the loop its then
   cosradiants= cosradiants+sign*radiants**i/fact
If you have included these things it should work (at least with my code it does)

                        
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