R help - Mar 2005 - strange result of acos

Hi all,

I have to calculate an expression using acos -function.  A strange 
result of acos appears

*1. case with error*

ss <- sin(10.74*pi/180)**2 
+(cos(10.74*pi/180)*cos(10.74*pi/180)*cos(0*pi/180))
 ss
 acos(ss)


[1] NaN
Warning message:
NaNs produced in: acos(ss)

*2. case without  error*

 ss <- sin(10.7*pi/180)**2 
+(cos(10.7*pi/180)*cos(10.7*pi/180)*cos(0*pi/180))
 ss
 acos(ss)



In both cases the variable ss equals 1.   I  think there is a problem 
with precision. If I multiply ss  by 0.999999999  (ss*0.99999999) no 
error occurs.  How  the results can be explained ?

Regards

Klaus-P.



-- 

Dr. Klaus-Peter Pleissner
Max Planck Institute for Infection Biology
Core Facility Bioinformatics
Campus Charit? Mitte
Schumannstr. 21/22
D-10117 Berlin
Germany

*Phone:* +49-30-28460-119
*Fax:*   +49-30-28460-507
*URL:*   http://web.mpiib-berlin.mpg.de/bioinformatik
<http://web.mpiib-berlin.mpg.de/bioinformatik/>
*Email:* pleissner at mpiib-berlin.mpg.de  <mailto:pleissner at
mpiib-berlin.mpg.de>

On 29-Mar-05 Klaus-Peter Pleissner wrote:
> Hi all,
> I have to calculate an expression using acos -function.
> A strange result of acos appears
> 
> *1. case with error*
> 
> ss <- sin(10.74*pi/180)**2 
> +(cos(10.74*pi/180)*cos(10.74*pi/180)*cos(0*pi/180))
>  ss
>  acos(ss)
> 
> [1] NaN
> Warning message:
> NaNs produced in: acos(ss)
> 
> *2. case without  error*
> 
>  ss <- sin(10.7*pi/180)**2 
> +(cos(10.7*pi/180)*cos(10.7*pi/180)*cos(0*pi/180))
>  ss
>  acos(ss)
> 
> In both cases the variable ss equals 1. I  think there
> is a problem with precision. If I multiply ss  by
> 0.999999999 (ss*0.99999999) no error occurs. How the
> results can be explained ?
The explanation is:

sin(10.74*pi/180)**2
+(cos(10.74*pi/180)*cos(10.74*pi/180)
*cos(0*pi/180))
-1

[1] 2.220446e-16

I.e. the expression, as internally evaluated, is very
slightly greater than 1. When you multiply ss by
0.999999999, you bring it back down a bit.

Theoretically, of course, it is sin(t)^2 + cos(t)^2,
which should be exactly 1, but you can't count on it
in digital computation. As you suspected, it is indeed
a question of precision.

Best wishes,
Ted.


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Date: 29-Mar-05                                       Time: 11:59:28
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