dateconv(Y,M,D,from_calend,to_calend) computes bilateral date conversion between Gregorian Common Era ('ce'), Persian Solar Hijri or Jalali ('sh'), and Islamic Lunar Hijri ('lh') calendars. Outputs a 1x3 numeric array vector of [Y,M,D], and a character array with printed date with month names in Persian, Arabic, or English. For Persian and Islamic calendars, the numbers are shown in Eastern Arabic numerals.

For example:
[outdatenum,outdatetxt] = dateconv(2000,1,1,'ce','sh') returns the equivalent date for Jan 1, 2000 in Persian Solar Hijri calendar:

>> [outdatenum,outdatetxt] = dateconv(2000,1,1,'ce','sh')
outdatenum =
1378 10 11
outdatetxt =
'۱۱ دی/جدی ۱۳۷۸'

>> datetoday
Today's date is:
12-Nov-2020
۲۲ آبان/عقرب ۱۳۹۹
۲۶ ربيع-الأول ۱۴۴۲

Conversion takes place through the Julian Day Number. Each calendar is converted to and computed back from the Julian Day Number.

For Gregorian calendar, the algorithm by NASA/Goddard is adopted, which correctly computes the dates for Proleptic era (before 1582).

For Persian/ Jalali calendar, the algorithm is based on the method proposed by Musa Akrami (2014) and implemented by Soroush Rabiei (2017).

Check & tests:

The start of the Persian calendar epoch (1/1/475 SH) per Akrami's 2,820 years cycle starts on Mar 15, 1096 (and NOT on March 21st as other date converter algorithms suggest):
>> dateconv(475,1,1,'sh','ce')
ans =
1096 3 15

The first day of the Persian calendar starts on Mar 19, 622:
>> dateconv(1,1,1,'sh','ce')
ans =
622 3 19

The first day of the Islamic Lunar Hijri starts on July 16, 622:
>> dateconv(1,1,1,'lh','ce')
ans =
622 7 16