如何实现阶乘函数代码？ [英] How to implement factorial function into code?

问题描述

因此，我使用泰勒级数来计算fortran90中的sin（0.75），直到某个点，所以我需要在do while循环中运行它（直到满足条件）。这意味着我需要使用factorial，这是我的代码：

 程序taylor 
隐式无
 real :: x = 0.75 
 real :: y 
 integer :: i = 3 
 do while（abs（y  -  sin（0.75））> 10.00 **（ -  7）） 
i = i + 2 
y = x  - （（x ** i）/ fact（i））
 print *，y 
 end do 
 end program taylor 
  

在哪里我写了fact（i）是我需要factorial的地方。不幸的是，Fortran没有内在的！功能。我将如何在此程序中实现此功能？

谢谢。

解决方案

<下面的简单功能回答你的问题。注意它是如何返回一个 real ，而不是一个整数。如果演出不是问题，那么对泰勒系列来说这是很好的。

 实际功能fact（n）
整数，意图（in）:: n 
 
整数:: i 
 
 if（n <0）错误停止'factorial对于负整数是单数'
 fact = 1.0 
 do i = 2，n 
 fact = fact * i 
 enddo 
 end function fact 
  

但真正的答案是Fortran 2008 does 具有阶乘的内在函数： Gamma函数。对于一个正整数 n ，它定义为 Gamma（n + 1）== fact（n）。

（我可以想象 Gamma函数

a>是不熟悉的，它是阶乘函数的泛化： Gamma（x）是为所有复杂 x 定义的，除非是非正整数，定义中的偏移是出于历史原因，不必要的混淆你问我。）

So I am using the taylor series to calculate sin(0.75) in fortran 90 up until a certain point, so I need to run it in a do while loop (until my condition is met). This means I will need to use a factorial, here's my code:

program taylor
implicit none
real :: x = 0.75  
real :: y
integer :: i = 3
do while (abs(y - sin(0.75)) > 10.00**(-7)) 
 i = i + 2
 y = x - ((x**i)/fact(i))
 print *, y
end do
end program taylor

Where i've written fact(i) is where i'll need the factorial. Unfortunately, Fortran doesn't have an intrinsic ! function. How would I implement the function in this program?

Thanks.

解决方案

The following simple function answers your question. Note how it returns a real, not an integer. If performance is not an issue, then this is fine for the Taylor series.

real function fact(n)
  integer, intent(in) :: n

  integer :: i

  if (n < 0) error stop 'factorial is singular for negative integers'
  fact = 1.0
  do i = 2, n
    fact = fact * i
  enddo
end function fact

But the real answer is that Fortran 2008 does have an intrinsic function for the factorial: the Gamma function. For a positive integer n, it is defined such that Gamma(n+1) == fact(n).

(I can imagine the Gamma function is unfamiliar. It's a generalization of the factorial function: Gamma(x) is defined for all complex x, except non-positive integers. The offset in the definition is for historical reasons and unnecessarily confusing it you ask me.)

这篇关于如何实现阶乘函数代码？的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！