Thread Subject: datenum: additivity question...

Greetings!

Could you help me please to figure out why the following expressions are not equal to zero:

datenum('00.01.0000 00:00:02', 'dd.mm.yy HH:MM:SS') - 2 * datenum('00.01.0000 00:00:01', 'dd.mm.yy HH:MM:SS')

datenum('00.01.0000 01:00:00', 'dd.mm.yy HH:MM:SS') - 3600 * datenum('00.01.0000 00:00:01', 'dd.mm.yy HH:MM:SS')

datenum('00.01.0001 00:00:00', 'dd.mm.yy HH:MM:SS') - 3600 * 24 * 365 * datenum('00.01.0000 00:00:01', 'dd.mm.yy HH:MM:SS')

etc ...

This has something to do with how MATLAB processes numbers. Basically, the decimal point you see on the screen has many many digits after it that you don't see on the screen. When you multiply by 2 some rounding occurs and therefore, you will end up with a 10^-10 number.

"Kian " <kian.torab@utah.edu> wrote in message <h10of5$56k$1@fred.mathworks.com>...
> This has something to do with how MATLAB processes numbers. Basically, the decimal point you see on the screen has many many digits after it that you don't see on the screen. When you multiply by 2 some rounding occurs and therefore, you will end up with a 10^-10 number.

Does it deal only with rounding error only?
Can I freely make math operations with "serial date numbers"?

"Andrey Kazak" <AK@nospam.ru> wrote in message <h11qgh$mg0$1@fred.mathworks.com>...
> "Kian " <kian.torab@utah.edu> wrote in message <h10of5$56k$1@fred.mathworks.com>...
> > This has something to do with how MATLAB processes numbers. Basically, the decimal point you see on the screen has many many digits after it that you don't see on the screen. When you multiply by 2 some rounding occurs and therefore, you will end up with a 10^-10 number.
>
> Does it deal only with rounding error only?
> Can I freely make math operations with "serial date numbers"?

datenum results are doubles. You can freely make math operations with them just like you can other doubles. But you will have to live with the precision limitations of doubles. Just like you can't represent numbers like 1/3 exactly with a double, you can't in general represent your dates exactly with a double. So don't expect all of your calculations like subtractions etc. to come out exact.

James Tursa

"James Tursa" <aclassyguywithaknotac@hotmail.com> wrote in message <h12489$n7b$1@fred.mathworks.com>...
> "Andrey Kazak" <AK@nospam.ru> wrote in message <h11qgh$mg0$1@fred.mathworks.com>...
> > "Kian " <kian.torab@utah.edu> wrote in message <h10of5$56k$1@fred.mathworks.com>...
> > > This has something to do with how MATLAB processes numbers. Basically, the decimal point you see on the screen has many many digits after it that you don't see on the screen. When you multiply by 2 some rounding occurs and therefore, you will end up with a 10^-10 number.
> >
> > Does it deal only with rounding error only?
> > Can I freely make math operations with "serial date numbers"?
>
> datenum results are doubles. You can freely make math operations with them just like you can other doubles. But you will have to live with the precision limitations of doubles. Just like you can't represent numbers like 1/3 exactly with a double, you can't in general represent your dates exactly with a double. So don't expect all of your calculations like subtractions etc. to come out exact.
>
> James Tursa

Thank you, James!

The final question: what is the precision of doubles in MATLAB? I mean the number of significant digits...

"Andrey Kazak" <AK@nospam.ru> wrote in message <h14hf1$jpk$1@fred.mathworks.com>...
> "James Tursa" <aclassyguywithaknotac@hotmail.com> wrote in message <h12489$n7b$1@fred.mathworks.com>...
> > "Andrey Kazak" <AK@nospam.ru> wrote in message <h11qgh$mg0$1@fred.mathworks.com>...
> > > "Kian " <kian.torab@utah.edu> wrote in message <h10of5$56k$1@fred.mathworks.com>...
> > > > This has something to do with how MATLAB processes numbers. Basically, the decimal point you see on the screen has many many digits after it that you don't see on the screen. When you multiply by 2 some rounding occurs and therefore, you will end up with a 10^-10 number.
> > >
> > > Does it deal only with rounding error only?
> > > Can I freely make math operations with "serial date numbers"?
> >
> > datenum results are doubles. You can freely make math operations with them just like you can other doubles. But you will have to live with the precision limitations of doubles. Just like you can't represent numbers like 1/3 exactly with a double, you can't in general represent your dates exactly with a double. So don't expect all of your calculations like subtractions etc. to come out exact.
> >
> > James Tursa
>
> Thank you, James!
>
> The final question: what is the precision of doubles in MATLAB? I mean the number of significant digits...

About 15 decimal digits in general. For your datenum examples, the best way to see what precision means in terms of datenum results is to use eps. e.g.,

>> format long
>> d = datenum('00.01.0000 00:00:02', 'dd.mm.yy HH:MM:SS')
d =
    2.314813900738955e-005
>> eps(d)*86400
ans =
    2.927345865710862e-016
>> e = datenum('00.01.2009 00:00:02', 'dd.mm.yy HH:MM:SS')
e =
    7.337730000231481e+005
>> eps(e)*86400
ans =
    1.005828380584717e-005

So for your original example, which is very near the MATLAB reference date, the accuracy of the double representation is about 3e-16 seconds. Pretty good, but this is probably not a realistic date to use for this calculation. Using a modern date in 2009 yields an accuracy of the datenum result of about 1e-5 seconds, or 10 microseconds. So that is probably a more realistic number to use for the expected accuracy when using datenum results in calculations. If you need higher accuracy you should probably stick with datevec arrays and write your own custom arithmetic functions that operate on the arrays directly.

James Tursa