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#### Differences in Digits in Matlab

```I posted a thread over at...... http://www.mathworks.com/matlabcentral/newsreader/view_thread/257642#670417...... regarding differences in digits between Maple and Matlab which still has not been fully addressed....

However, the problem I observe is also seen in just Matlab on it's own.... The behavior has to do with the sym object class. (I am using the Maple toolbox for matlab and Matlab R 2009 A 64 bit)

As an example

>> digits(30)
>> vpa(sym('pi'))*.1

ans =

0.314159265358979342695820259867
>> vpa(sym('pi'))*(.9-.8)

ans =

0.314159265358979254731225959353

Both of the above are being multiplied by the same number .1 however the case where (.9-.8) is instead being multiplied yields a different result.....

Could anyone please shed some light on this for me.... Thanks.
``` 0 8/5/2009 3:16:01 AM comp.soft-sys.matlab  211264 articles. 26 followers. 10 Replies 691 Views Similar Articles

[PageSpeed] 32

```omegayen  <omegayen@ameritech.net> wrote:
>>> vpa(sym('pi'))*.1
>
> ans =
>
>                       0.314159265358979342695820259867
>>> vpa(sym('pi'))*(.9-.8)
>
> ans =
>
>                       0.314159265358979254731225959353
>
> Both of the above are being multiplied by the same number .1 however
> the case where (.9-.8) is instead being multiplied yields a different
> result.....

Seems like this is showing up almost daily lately.

The above are NOT being multiplied by the same number.
Binary computers have limited resolution so ( for instance)
1+1+1 is not necessarily the same as 2+1. Thats just the way
it is in any language ( Matlab included) on any digital computer.

Check any of the other similar threads on this topic or
look up IEE 64-bit floating point math.

Short story: with 64-bit math one gets about 15 significant
figures and that's it. Anything approaching this limit will
see the noise that digital qunatization creates.

Fortunately almost nothing in the real world need 15
significant figures, so std double precision is good enough
for most purposes.

Stan
``` 0 8/5/2009 3:34:40 AM
```>>isequal(.9-.8,.1)
ans =
0

Hmmm......
``` 0 8/5/2009 3:55:03 AM
```On Aug 5, 3:16=A0pm, "omegayen " <omega...@ameritech.net> wrote:
> I posted a thread over at......http://www.mathworks.com/matlabcentral/new=
n Maple and Matlab which still has not been fully addressed....
>
> However, the problem I observe is also seen in just Matlab on it's own...=
.. The behavior has to do with the sym object class. (I am using the Maple t=
oolbox for matlab and Matlab R 2009 A 64 bit)
>
> As an example
>
> >> digits(30)
> >> vpa(sym('pi'))*.1
>
> ans =3D
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A00.314159265358979342695820=
259867
>
> >> vpa(sym('pi'))*(.9-.8)
>
> ans =3D
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A00.314159265358979254731225=
959353
>
> Both of the above are being multiplied by the same number .1 however the =
case where (.9-.8) is instead being multiplied yields a different result...=
...
>
> Could anyone please shed some light on this for me.... Thanks.

By Golly, you're right!!
There is a definite discrepancy between these two answers at the
thirteenth place.
I think you deserve a Nobel Prize for this earth-shattering discovery!
Honestly, how can one do any decent calculations when you have to use
crappy software that gives such inaccurate answers.
Meanwhile, the rest of us will struggle on regardless, desperately
When you solve the problem, please get back to us on this forum ASAP.
However, I fear that you have embarked upon an avenue that will take a

Best Wishes
``` 0 8/5/2009 4:09:14 AM
```Stan Bischof <stan@newserve.worldbadminton.com> wrote in message <4a78fdd0\$0\$1612\$742ec2ed@news.sonic.net>...
>
> Binary computers have limited resolution so ( for instance)
> 1+1+1 is not necessarily the same as 2+1.

Good point, bad example. 1 *can* be represented exactly in every floating point scheme I am aware of, and so can the 2, 1+1+1, and 2+1. So you will always get exactly the same result for these particular cases.

James Tursa
``` 0 8/5/2009 4:17:03 AM
```"omegayen " <omegayen@ameritech.net> wrote in message <h5athh\$2qa\$1@fred.mathworks.com>...
> I posted a thread over at...... http://www.mathworks.com/matlabcentral/newsreader/view_thread/257642#670417...... regarding differences in digits between Maple and Matlab which still has not been fully addressed....
>
> However, the problem I observe is also seen in just Matlab on it's own.... The behavior has to do with the sym object class. (I am using the Maple toolbox for matlab and Matlab R 2009 A 64 bit)
>
> As an example
>
> >> digits(30)
> >> vpa(sym('pi'))*.1
>
> ans =
>
>                        0.314159265358979342695820259867
> >> vpa(sym('pi'))*(.9-.8)
>
> ans =
>
>                        0.314159265358979254731225959353
>
> Both of the above are being multiplied by the same number .1 however the case where (.9-.8) is instead being multiplied yields a different result.....
>
> Could anyone please shed some light on this for me.... Thanks.

I thought I answered this last night.

Try this in MATLAB:

(.9-.8) == 0.1
ans =
0

They are not the same. 0.1 is only accurate to roughly
16 decimal digits. Even multiplying it by a symbolic
pi, 0.1 is still crap past the 15th digit. And (0.9 - 0.8)
is different crap.

John
``` 0 8/5/2009 8:21:02 AM
```"omegayen "
> >> digits(30)
> >> vpa(sym('pi'))*.1
> ans =0.314159265358979342695820259867
> >> vpa(sym('pi'))*(.9-.8)
> ans =0.314159265358979254731225959353
> Both of the above are being multiplied by the same number .1 however the case where (.9-.8) is instead being multiplied yields a different result.....
> Could anyone please shed some light on this for me.... Thanks.

firstly, others have shed all the light on this...

HOWEVER, just a word of caution...
things are different if you use the mupad kernel: r2009a/symbolic math tbx 5.2...

od=digits;
digits(30);
spi=sym('pi');
r=[
vpa(spi)*.1
.1*vpa(spi)
vpa(spi)*(.9-.8)
(.9-.8)*vpa(spi)
];
disp(vpa(spi));
%    3.14159265358979323846264338328
disp(r);
%{
0.314159265358979323846264338328
0.314159265358979323846264338328
0.314159265358979323846264338328
0.314159265358979323846264338328
%}
disp(diff(double(r)));
%{
0
0
0
%}
digits(od);

it seems that the new approach by default converts every var into a SYM BEFORE calculation once it encounters a SYM in the command...

us
``` 0 8/5/2009 8:52:01 AM
```"us " <us@neurol.unizh.ch> wrote in message <h5bh7h\$loo\$1@fred.mathworks.com>...
> "omegayen "
> > >> digits(30)
> > >> vpa(sym('pi'))*.1
> > ans =0.314159265358979342695820259867
> > >> vpa(sym('pi'))*(.9-.8)
> > ans =0.314159265358979254731225959353
> > Both of the above are being multiplied by the same number .1 however the case where (.9-.8) is instead being multiplied yields a different result.....
> > Could anyone please shed some light on this for me.... Thanks.
>
> firstly, others have shed all the light on this...
>
> HOWEVER, just a word of caution...
> things are different if you use the mupad kernel: r2009a/symbolic math tbx 5.2...
>
>      od=digits;
>      digits(30);
>      spi=sym('pi');
>      r=[
>           vpa(spi)*.1
>           .1*vpa(spi)
>           vpa(spi)*(.9-.8)
>           (.9-.8)*vpa(spi)
>      ];
>      disp(vpa(spi));
> %    3.14159265358979323846264338328
>      disp(r);
> %{
>      0.314159265358979323846264338328
>      0.314159265358979323846264338328
>      0.314159265358979323846264338328
>      0.314159265358979323846264338328
> %}
>      disp(diff(double(r)));
> %{
>      0
>      0
>      0
> %}
>      digits(od);
>
> it seems that the new approach by default converts every var into a SYM BEFORE calculation once it encounters a SYM in the command...
>
>us

This seems to have been the default behavior also in R2008a and b:

>> digits(30)
>> isequal(vpa(sym('pi'))*(.9-.8),vpa(sym('pi'))*.1)

ans =

1

Furthermore,
>> isequal(vpa(pi)*(.9-.8),vpa(pi)*.1)

ans =

1

>> isequal(vpa(.9-.8),vpa(.1))

ans =

1

So it seems "vpa" has (had) the same effect as "sym"

The original problem on R2008b gives

>> vpa(sym('pi'))*.1

ans =

0.314159265358979323846264338328

>> vpa(sym('pi'))*(.9-.8)

ans =

0.314159265358979323846264338328

Finally, according to Matlab's documentation on sym (and also vpa):

"Statements like pi = sym('pi') and delta = sym('1/10') create symbolic
numbers which avoid the floating point approximations inherent in the
values of pi and 1/10."

So it seems that using   vpa(sym('pi'))*vpa(sym('1/10') or  vpa('pi')*vpa('1/10') should be preferable in general.

K.H.
``` 0 8/5/2009 10:38:02 AM
```"Khaled Hamed"
> "us "
> > HOWEVER, just a word of caution...
> > things are different if you use the mupad kernel: r2009a/symbolic math tbx 5.2...
> > it seems that the new approach by default converts every var into a SYM BEFORE calculation once it encounters a SYM in the command...

> This seems to have been the default behavior also in R2008a and b:

yes, because the mupad engine was introduced in r2007b

http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/rn/brqy13y-1.html

us
``` 0 8/5/2009 10:47:01 AM
```"us " <us@neurol.unizh.ch> wrote in message <h5bnv5\$ji7\$1@fred.mathworks.com>...
> "Khaled Hamed"
> > "us "
> > > HOWEVER, just a word of caution...
> > > things are different if you use the mupad kernel: r2009a/symbolic math tbx 5.2...
> > > it seems that the new approach by default converts every var into a SYM BEFORE calculation once it encounters a SYM in the command...
>
> > This seems to have been the default behavior also in R2008a and b:
>
> yes, because the mupad engine was introduced in r2007b
>
> http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/rn/brqy13y-1.html
>
> us

I appreciate all the help guys. It is quite clear now... Final results are illustrated below using matlab 2009 R A.

using maple toolbox for matlab (maple 13)

digits(30)
>> vpa(sym('pi'))*.1

ans =

0.314159265358979336412634952687

>> vpa(sym('pi'))*(.9-.8)

ans =

0.314159265358979248448040652173

>>vpa(sym('pi'))*vpa(sym('1/10'))

ans =

0.314159265358979323846264338328

using symbolic math toolbox 5.2  (switch by means of environmental variables)
digits(30)
>> vpa(sym('pi'))*.1

ans =

0.314159265358979323846264338328

>> vpa(sym('pi'))*(.9-.8)

ans =

0.314159265358979323846264338328
``` 0 8/5/2009 5:49:01 PM
```"omegayen " <omegayen@ameritech.net> wrote in message <h5cgmd\$hqi\$1@fred.mathworks.com>...
> "us " <us@neurol.unizh.ch> wrote in message <h5bnv5\$ji7\$1@fred.mathworks.com>...
> > "Khaled Hamed"
> > > "us "
> > > > HOWEVER, just a word of caution...
> > > > things are different if you use the mupad kernel: r2009a/symbolic math tbx 5.2...
> > > > it seems that the new approach by default converts every var into a SYM BEFORE calculation once it encounters a SYM in the command...
> >
> > > This seems to have been the default behavior also in R2008a and b:
> >
> > yes, because the mupad engine was introduced in r2007b
> >
> > http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/rn/brqy13y-1.html
> >
> > us
>
> I appreciate all the help guys. It is quite clear now... Final results are illustrated below using matlab 2009 R A.
>
> using maple toolbox for matlab (maple 13)
>
> digits(30)
> >> vpa(sym('pi'))*.1
>
> ans =
>
> 0.314159265358979336412634952687
>
> >> vpa(sym('pi'))*(.9-.8)
>
> ans =
>
> 0.314159265358979248448040652173
>
> >>vpa(sym('pi'))*vpa(sym('1/10'))
>
> ans =
>
> 0.314159265358979323846264338328
>
>
>
> using symbolic math toolbox 5.2  (switch by means of environmental variables)
> digits(30)
> >> vpa(sym('pi'))*.1
>
> ans =
>
> 0.314159265358979323846264338328
>
> >> vpa(sym('pi'))*(.9-.8)
>
> ans =
>
> 0.314159265358979323846264338328

NOTE, I had to use the 32 bit version of Matlab in order to do this as the 64 bit version does not support the symbolic math toolbox :(
``` 0 8/5/2009 6:45:21 PM Similar Artilces:

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Number of column: 5 Vector A: [ 2 4 6 7 8 ] Vector B : [ 5 7 8 10 1] Choice = 1 : Find the highest value Vector A : 8 Vector B: 10 The highest value : 10 Choice = 2 : Find the lowest value Vector A : 2 Vector B: 1 The highest value : 1 Choice = 3 : Find the average value of : Vector A Vector B "Syamil " <syamilsaid@gmail.com> wrote in message <inq3g8\$hhd\$1@fred.mathworks.com>... > Number of column: 5 > Vector A: [ 2 4 6 7 8 ] > Vector B : [ 5 7 8 10 1] > > Choice = 1 : Find the highest value > Vector A : 8 > Vector B: 10 > The highest value : 10 > > Choice = 2 : Find the lowest value > Vector A : 2 > Vector B: 1 > The highest value : 1 > > Choice = 3 : Find the average value of : > Vector A > Vector B Type in matlab: doc min doc max doc mean ...

Why does Matlab do this
What is happening when I type rand(1:10) at the command line? Matlab goes into a 10 minute spin - what's going on? Thanks "Robert" wrote in message <j64asi\$5v4\$1@newscl01ah.mathworks.com>... > What is happening when I type > rand(1:10) > at the command line? > > Matlab goes into a 10 minute spin - what's going on? > Thanks Hi Robert, You're create a 10-D array with that syntax. Do you just want a vector of 10 uniformly distributed random numbers. x = rand(10,1); % or x = rand(1,10); Wayne Hi Wayne, You're right - that's what I was trying to do... but I was just newbie mucking about trying to work out the syntax and I typed that in - then had a looong wait for Matlab to work through it! Thanks for the explanation. Robert "Robert" wrote in message <j64d2h\$dvo\$1@newscl01ah.mathworks.com>... > Hi Wayne, > You're right - that's what I was trying to do... but I was just newbie mucking about trying to work out the syntax and I typed that in - then had a looong wait for Matlab to work through it! > Thanks for the explanation. > Robert That's fine. Welcome to MATLAB!!! If that's the worst memory-intensive mistake you ever make, you'll be fine :) I've done much, much worse. Wayne ...

Problems calling from Matlab a Matlab compiled dll

matlab difference equation
hi, i need help with the matlab code to solve following difference equation: y(t)?0.5y(t ?1) = ?(t), [for t = 0,1,2,3....] with zero initial condition, where ? is the unit pulse ? = 1 for t = 0, otherwise ? = 0 i'll be grateful if someone could help. thanks :) sorry, there were some symbols missing in the earlier post. Here is the correct problem: y(t)-0.5y(t -1) = delta(t), [for t = 0,1,2,3....] with zero initial condition, where delta is the unit pulse delta = 1 for t = 0, otherwise delta = 0 i'll be grateful if someone could help. thanks :) ...

Need help for a matlab mini project
Hello everyone, I have a matlab in class exercise due in few days. I am new to matlab and the instructions provided with the assignment is minimal. Can Someone help me with the basic understanding as in how can I map the problem's solution to matlab script ? I am not able to post question here as it is a jpeg file. Please let me know and then we can discuss further. ...

Matlab automation server and Matlab Compiler Run Time
I did a simple excel macro which runs matlab functions sucessfully in a machine with Matlab installed. Now I want to run it in a computer without matlab, with "MATLAB Compiler Run Time" installed. I can add the Matlb automation server type file (mlapp.tlb) sucessfully, but when I try to run it, I get this error: "ActiveX component can't create object" In this line: Set matlab = New MLApp.MLApp Do you know what is missing? Thanks ...

Develop web application with Matlab (calling matlab from PHP)
Hi all, I am doing a course project. Try to make phone upload some data to server through PHP script and make Matlab read this file (.txt or any file), process, and write a result file on server. After that, my phone can download the result. The key part is that can I use PHP to call matlab function? Or any mechanism I can use to call Matlab through server-end script? My server will be the local hosted server on Mac computer. Also, Matlab is installed on my mac too. Thanks you very much. On Oct 7, 11:54=A0am, Lucas Sun <feng...@gmail.com> wrote: > Hi all, > > I am doing a course project. Try to make phone upload some data to > server through PHP script and make Matlab read this file (.txt or any > file), process, and write a result file on server. After that, my > phone can download the result. > > The key part is that can I use PHP to call matlab function? Or any > mechanism I can use to call Matlab through server-end script? My > server will be the local hosted server on Mac computer. Also, Matlab > is installed on my mac too. > > Thanks you very much. I m also finding this...... ...

Call Matlab m-file from Matlab Scrip Node
My problem with matlab script node is related to calling function in matlab.&nbsp; I created an m-file function that takes an imput temperature (from DAQ) and defines a material property.&nbsp; My matlab script node doesn't seem to recognize my function.&nbsp; I have placed the function in the folder the vi is currently located, but it doesn't read it.&nbsp; How do I get matlab script node to read the functions I create in matlab? Add the directory to matlab path, or call the .m file with it full name ( D:\..... \myfile.m) Let me clarify, &nbsp; I have pasted my matlab code into the matlab scrip node. &nbsp; In this code, I have called a subfunction that I have created. &nbsp; Example k(n)=k_c(T(n)) where k_c is a subfunction I have created. &nbsp; How do I get my code in the node&nbsp;to sucessfully read the subfunction k_c? &nbsp; &nbsp; &nbsp; As indicated, you need to add the directory where the .m file containing the function resides to the list of paths that are read in. This is your startup.m file. The other option is to do a "cd" command prior to calling your function to change to the directory where the .m file containing the function resides. Thanks for reiterating the information.&nbsp; My matlab script node is working properly.&nbsp; I had never used the "cd" command in matlab.&nbsp; I always set the working directory when I open the program, and put all the m files into t...

MatLab Error Of This program has been modified outside MatLab editor
Hi, I am running a MatLab program I've run many times before, and now when I try to run it, I get a message saying : "This program has been modified outside of the MatLab editor. Do you want to reload it?" I've moved the program to a new directory, but I've run MatLab progs from that directory before, so I am perplexed. Can anyone tell me what to do? TIA, Matt In article <972bbd06-3687-4253-9aa0-a08acf91d117@z38g2000hsc.googlegroups.com>, junoexpress <MTBrenneman@gmail.com> wrote: >I am running a MatLab program I've run many times before, and now when >I try to run it, I get a message saying : >"This program has been modified outside of the MatLab editor. Do you >want to reload it?" >I've moved the program to a new directory, but I've run MatLab progs >from that directory before, so I am perplexed. >Can anyone tell me what to do? Use Save As to save the current version under a different name. Then allow Matlab to reload the file. Save that, and then compare the two saved versions to determine what the differences are, and create an appropriately merged version. -- "There is nothing so bad but it can masquerade as moral." -- Walter Lippmann junoexpress <MTBrenneman@gmail.com> wrote in message <972bbd06-3687-4253-9aa0- a08acf91d117@z38g2000hsc.googlegroups.com>... > Hi, >...

Problems calling from Matlab a Matlab compiled dll #3

Problems calling from Matlab a Matlab compiled dll #2

matlab 7.1 use matlab C++ math library
I wanna use matlab C++ math library into VC++6.0, but my matlab is 7.1. if i wanna use matlab C++ math library to programme, how can i setup my VC link?? why matlab7.1 doesn't have "extern->include->cpp" file??? In using matlab C++ math library , what difference between matlab 6.X and matlab7.1??? ... Web resources about - Differences in Digits in Matlab - comp.soft-sys.matlab

Difference - Wikipedia, the free encyclopedia
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