1. simpson.ex: The Simpson Rule
- Posted by Alan Tu <ATU5713 at COMPUSERVE.COM>
Dec 17, 1998
-
Last edited Dec 18, 1998
For all you calculists or whatever, the Simpson Rule for finding integrals
in Euphoria! SIMPSON.EX will ask for A, B, and N (N must be even). There
is one catch: the function f(atom x). This must be a global function in
function.e. And it must be, well, euphoric. For example, BASIC recognizes
the standard way of doing exponents on computer x^2 is x squared. But
Euphoria does not. To write x squared, you must do power(x,2). x cubed
would be power(x,3). Order of operations are consistent with standard
algebraic practice. sin, cos, and tan are self-explanatory; Euphoria has
these functions. All those who are interested in RAM programs (LRAM, MRAM,
and RRAM), I've written those too. So, without further waiting, this is
simpson.ex
Last thing, speed does matter, so suggestions to improve speed and all
other suggestions are welcome!
Alan
include get.e
include function.e
type even(integer x)
return integer(0.5*x)
end type
atom delta, coeff, solution, real, answer
object a, b, n
even subd
real = 0
clear_screen()
puts(1,"Enter A: ")
a = get(0)
a = a[2]
puts(1,"\nEnter B: ")
b = get(0)
b = b[2]
puts(1,"\nEnter N: ")
n = get(0)
subd = n[2]
delta = (b-a)/subd
coeff = (1/3)*delta
puts(1,"\n")
for i = 0 to subd do
solution = f(a+i*delta)
if i = 0 or i = subd then
real = real+solution
elsif 0.5*i != floor(0.5*i) then
real = real+4*solution
elsif 0.5*i = floor(0.5*i) then
real = real+2*solution
end if
end for
answer = coeff*real
puts(1,"The estimated integral is: ")
print(1,answer)
puts(1,"\nNote: Simpson's Rule often provides exact answers.")
--begin sample function.e
global function f(atom x)
return 1/x
end function
2. Re: simpson.ex: The Simpson Rule
Alan Tu wrote:
> Last thing, speed does matter, so suggestions to improve speed and all
> other suggestions are welcome!
> include get.e
> include function.e
> type even(integer x)
> return integer(0.5*x)
at this point, i'm not sure, but, since you are calling it so often,
return remainder(x,2) = 0
may be considerably faster...
> end type
> atom delta, coeff, solution, real, answer, current, temp, test
> object a, b, n
> even subd
> real = 0
> clear_screen()
> puts(1,"Enter A: ")
> a = get(0)
> a = a[2]
> puts(1,"\nEnter B: ")
> b = get(0)
> b = b[2]
> puts(1,"\nEnter N: ")
> n = get(0)
> subd = n[2]
> delta = (b-a)/subd
> coeff = (1/3)*delta
coeff = delta/3 would be faster, one less operation and one less
set
of () to parse...
--add this:
current = 0
> puts(1,"\n")
> for i = 0 to subd do
> solution = f(a+i*delta)
change this to
solution = f(a+current)
> if i = 0 or i = subd then
> real = real+solution
> elsif 0.5*i != floor(0.5*i) then
> real = real+4*solution
> elsif 0.5*i = floor(0.5*i) then
> real = real+2*solution
> end if
--change the compound if..then to:
if i = 0 or i = subd then
real = real + solution
else test = 0.5*i
temp = solution + solution
real = real + temp
if test != floor(test) then
real = real + temp
end if
end if
--add this:
current = current + delta
> end for
> answer = coeff*real
> puts(1,"The estimated integral is: ")
> print(1,answer)
> puts(1,"\nNote: Simpson's Rule often provides exact answers.")
>
a straight up typing of the newly modified function/program is thusly:
include get.e
include function.e
type even(integer x)
return remainder(x,2) = 0
end type
atom delta, coeff, solution, real, answer, current, temp, test
object a, b, n
even subd
real = 0
clear_screen()
puts(1,"Enter A: ")
a = get(0) a = a[2]
puts(1,"\nEnter B: ")
b = get(0) b = b[2]
puts(1,"\nEnter N: ")
n = get(0) subd = n[2]
delta = (b-a)/subd
coeff = delta/3
current = 0
puts(1,"\n")
for i = 0 to subd do
solution = f(a+current)
if i = 0 or i = subd then
real = real + solution
else test = 0.5*i
temp = solution + solution
real = real + temp
if test != floor(test) then
real = real + temp
end if
end if
current = current + delta
end for
answer = coeff*real
puts(1,"The estimated integral is: ")
print(1,answer)
puts(1,"\nNote: Simpson's Rule often provides exact answers.")
and the sample function is the 'same' of course....
hope this shows some speed improvements...
everyone knows i'm a sucker for tweaking :)
the benchmark program i posted for testing reverse() seemed
to provide everyone with a (seemingly?) stable platform for
testing functions across different processors and you are
welcome of course to use that to time the two versions :)
take care and care of,
_/ _/ _/_/_/ _/ _/ _/ _/ _/_/_/ _/
_/ _/ _/ _/ _/ _/ _/ _/ _/
_/_/_/ _/_/_/ _/ _/ _/_/ _/_/
_/ _/ _/ _/ _/_/_/ _/ _/ _/
_/ _/ _/ _/ _/_/_/ _/ _/ _/_/_/
({<=----------------------------------------=>})
({<=- http://members.xoom.com/Hawkes_Hovel> -=})
({<=----------------------------------------=>})
3. Re: simpson.ex: The Simpson Rule
- Posted by Alan Tu <ATU5713 at COMPUSERVE.COM>
Dec 17, 1998
-
Last edited Dec 18, 1998
Thanks, Hawke, for all the input!
See my other message "Using Euphoria to Solve Real World Problems". It'll
inspire you, hopefully.
Alan
4. Re: simpson.ex: The Simpson Rule
- Posted by Lucius Hilley III <lhilley at CDC.NET>
Dec 18, 1998
-
Last edited Dec 19, 1998
On Thu, 17 Dec 1998 17:56:35 -0800, Hawke' <mdeland at GEOCITIES.COM> wrote:
Alan Tu wrote:
> Last thing, speed does matter, so suggestions to improve speed and all
> other suggestions are welcome!
>
> type even(integer x)
> return integer(0.5*x)
> end type
Hawke' wrote:
>type even(integer x)
> return remainder(x,2) = 0
>end type
I, Lucius, write:
> I believe that the following use of and_bits() will be even faster
> than remainder.
>
>type even(integer x)
> return and_bits(x, 1) = 0
>end type
_________________________
Lucius L. Hilley III lhilley at cdc.net
http://www.cdc.net/~lhilley
http://www.americanantiques.com
http://www.dragonvet.com
_________________________
