🚀 go-pugleaf

In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
	[Integration of step function]

>Does anyone know if there is a good way to get thru this?
>Thanks a million for your attention.

You will find that integrands which are easy for the simple approaches to
numerical quadrature are _smooth_. When you have a discontinuity in a 
derivative, or in the function itself, other methods are appropriate.

Usually the best thing to do is to break the integral up into pieces over
which the integrand is 'nice'. Failing this, you should consider using
adaptive quadrature with extrapolation. A reasonable approach is afforded
by the quadpack routine QAGS, which can deal automatically with some kinds
of singularities. You should take a look in the QUADPACK user's guide, or
in the excellent book by Davis and Rabinowitz on numerical quadrature for
more information.

Later,
Andrew Mullhaupt

In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>I am having trouble doing the integral using either qtrap
>or qsimp from Numerical Recipes:
>
>    b
>    /
>    | f(x)dx,      	with a < 1, b > 2
>    /
>    a
>   			and f(x) = 1 (1 <= x <= 2)
>				 = 0  otherwise
>
>For example a=0, b=4 or the like the results were nonsense.
>
>Does anyone know if there is a good way to get thru this?
>Thanks a million for your attention.

Since f(x) will be one from x=1 to x=2, and this range is included by
the a<1 and b>2 guarantee, and the function is zero everywhere else,
then the integral just becomes:

  2
 /
 | 1 dx, otherwise known as 1.  Is there a reason you were trying to
 /
 1

solve this numerically?
-- 
+-----------
| Jeffrey Oliver Breen   Harvard-Smithsonian Center for Astrophysics,
| (617) 495-7252         60 Garden St., Room B-340, MS 6, Cambridge, MA  02138
|

In article <1992Aug28.011918.22579@harlow.harvard.edu> job@head-cfa.harvard.edu (Jeffrey Oliver Breen) writes:
>In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>>I am having trouble doing the integral using either qtrap
>>or qsimp from Numerical Recipes:

>>    b
>>    /
>>    | f(x)dx,      	with a < 1, b > 2
>>    /
>>    a
>>   			and f(x) = 1 (1 <= x <= 2)
>>				 = 0  otherwise

>>For example a=0, b=4 or the like the results were nonsense.

>>Does anyone know if there is a good way to get thru this?
>>Thanks a million for your attention.

>Since f(x) will be one from x=1 to x=2, and this range is included by
>the a<1 and b>2 guarantee, and the function is zero everywhere else,
>then the integral just becomes:

>  2
> /
> | 1 dx, otherwise known as 1.  Is there a reason you were trying to
> /
> 1

>solve this numerically?

THIS function can be done that way, but what if things are more complicated?
It is not too difficult to handle discontinuous functions, or functions with
discontinuous derivatives, if one knows where the discontinuities are, and
the programmer breaks up the range.  For infinities, the problem is worse,
and for unknown discontinuities, still worse.  

Some integrators will attempt to handle this, but most assume that the 
function is sufficiently smooth that this problem does not arise.

-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)