How to convert a MATLAB serial date number to a calendar date?

Question

This is not so much a programming question as it is a desire for clarification to understand the way the Matlab serial date number format works. I'm referencing Matlab serial date numbers and I would like to know how to convert them into calendar dates using the simplest means possible. Many of the references out there only instruct how to work with these numbers within Matlab itself, but I want to be able to make sense of these by hand using arithmetic to derive the dates they represent without the use of Matlab (if this is even possible).

From the research I have done already, I do understand that a Matlab timestamp is essentially a count of the number of days since January 1, 0000 and that the floating point numbers appended to it further represent specific hours, minutes, etc. I'm not as clear on how these break down however. The reference information out there is not very informative nor comprehensive and I'm struggling to understand how it works.

Say I have the timestamp 735071.64930556. Could anybody provide me with a formula to be able to derive the calendar date that this represents, or guide me through the process to convert it? From a programming standpoint, my purpose for wanting to understand this is so I can eventually write a converter to be able to handle this format within the application I'm developing. For now though, I simply wish to understand how the process works.

Thanks

Answer 1

Use datevec or datestr :

>> datevec(735071.64930556)
ans =
  1.0e+003 *
    2.0120    0.0070    0.0210    0.0150    0.0350    0.0000

>> datestr(735071.64930556)
ans =
21-Jul-2012 15:35:00

Answer 2

What makes your question a little bit difficult to answer is mostly the leap year / leap second problem. If you expect date values to exist only over a limited range of values, the problem is somewhat simpler (actually I am not sure how Matlab deals with the "lost days" when the world went from Julian to Gregorian calendars, for example - see http://en.wikipedia.org/wiki/Conversion_between_Julian_and_Gregorian_calendars for a hint of what I am talking about).

The hours-minutes-seconds part is relatively easy. When you have

datevalue = 735071.64930556;

You can compute:

rem = datevalue - floor(datevalue);
hours = floor(24*rem);
rem = 24 * rem - hours;
minutes = floor( 60 * rem );
rem = 60 * rem - minutes;
seconds = 60 * rem;

To get the year / month / day, your best bet is to use some built in function in the language of your choice (for many examples, see http://www.epochconverter.com/epoch/daynumbers.php ), or knock yourself out and create some lookup tables. If you have the date of the first of every month, the lookup would be fast; and from 0 CE until today, that would be only 2013 * 12 entries - not a very large table. Such a table could be created in Matlab and exported...