# jdcal: auxiliary module to convert between calendars¶

PyHdust jdcal module: third-part functions for converting between Julian dates and calendar dates.

I did not make any modification. The original README is below.

A function for converting Gregorian calendar dates to Julian dates, and another function for converting Julian calendar dates to Julian dates are defined. Two functions for the reverse calculations are also defined.

Different regions of the world switched to Gregorian calendar from Julian calendar on different dates. Having separate functions for Julian and Gregorian calendars allow maximum flexibility in choosing the relevant calendar.

All the above functions are “proleptic”. This means that they work for dates on which the concerned calendar is not valid. For example, Gregorian calendar was not used prior to around October 1582.

Julian dates are stored in two floating point numbers (double). Julian dates, and Modified Julian dates, are large numbers. If only one number is used, then the precision of the time stored is limited. Using two numbers, time can be split in a manner that will allow maximum precision. For example, the first number could be the Julian date for the beginning of a day and the second number could be the fractional day. Calculations that need the latter part can now work with maximum precision.

A function to test if a given Gregorian calendar year is a leap year is defined.

Zero point of Modified Julian Date (MJD) and the MJD of 2000/1/1 12:00:00 are also given.

This module is based on the TPM C library, by Jeffery W. Percival. The idea for splitting Julian date into two floating point numbers was inspired by the IAU SOFA C library.

pyhdust.jdcal.fpart(x)[source]

Return fractional part of given number.

pyhdust.jdcal.gcal2jd(year, month, day)[source]

Gregorian calendar date to Julian date.

The input and output are for the proleptic Gregorian calendar, i.e., no consideration of historical usage of the calendar is made.

year : int
Year as an integer.
month : int
Month as an integer.
day : int
Day as an integer.
jd1, jd2: 2-element tuple of floats
When added together, the numbers give the Julian date for the given Gregorian calendar date. The first number is always MJD_0 i.e., 2451545.5. So the second is the MJD.
>>> gcal2jd(2000,1,1)
(2400000.5, 51544.0)
>>> 2400000.5 + 51544.0 + 0.5
2451545.0
>>> year = [-4699, -2114, -1050, -123, -1, 0, 1, 123, 1678.0, 2000,
....: 2012, 2245]
>>> month = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
>>> day = [1, 12, 23, 14, 25, 16, 27, 8, 9, 10, 11, 31]
>>> x = [gcal2jd(y, m, d) for y, m, d in zip(year, month, day)]
>>> for i in x: print i
(2400000.5, -2395215.0)
(2400000.5, -1451021.0)
(2400000.5, -1062364.0)
(2400000.5, -723762.0)
(2400000.5, -679162.0)
(2400000.5, -678774.0)
(2400000.5, -678368.0)
(2400000.5, -633797.0)
(2400000.5, -65812.0)
(2400000.5, 51827.0)
(2400000.5, 56242.0)
(2400000.5, 141393.0)


Negative months and days are valid. For example, 2000/-2/-4 => 1999/+12-2/-4 => 1999/10/-4 => 1999/9/30-4 => 1999/9/26.

>>> gcal2jd(2000, -2, -4)
(2400000.5, 51447.0)
>>> gcal2jd(1999, 9, 26)
(2400000.5, 51447.0)

>>> gcal2jd(2000, 2, -1)
(2400000.5, 51573.0)
>>> gcal2jd(2000, 1, 30)
(2400000.5, 51573.0)

>>> gcal2jd(2000, 3, -1)
(2400000.5, 51602.0)
>>> gcal2jd(2000, 2, 28)
(2400000.5, 51602.0)


Month 0 becomes previous month.

>>> gcal2jd(2000, 0, 1)
(2400000.5, 51513.0)
>>> gcal2jd(1999, 12, 1)
(2400000.5, 51513.0)


Day number 0 becomes last day of previous month.

>>> gcal2jd(2000, 3, 0)
(2400000.5, 51603.0)
>>> gcal2jd(2000, 2, 29)
(2400000.5, 51603.0)


If day is greater than the number of days in month, then it gets carried over to the next month.

>>> gcal2jd(2000,2,30)
(2400000.5, 51604.0)
>>> gcal2jd(2000,3,1)
(2400000.5, 51604.0)

>>> gcal2jd(2001,2,30)
(2400000.5, 51970.0)
>>> gcal2jd(2001,3,2)
(2400000.5, 51970.0)


The returned Julian date is for mid-night of the given date. To find the Julian date for any time of the day, simply add time as a fraction of a day. For example Julian date for mid-day can be obtained by adding 0.5 to either the first part or the second part. The latter is preferable, since it will give the MJD for the date and time.

BC dates should be given as -(BC - 1) where BC is the year. For example 1 BC == 0, 2 BC == -1, and so on.

Negative numbers can be used for month and day. For example 2000, -1, 1 is the same as 1999, 11, 1.

The Julian dates are proleptic Julian dates, i.e., values are returned without considering if Gregorian dates are valid for the given date.

The input values are truncated to integers.

pyhdust.jdcal.ipart(x)[source]

Return integer part of given number.

pyhdust.jdcal.is_leap(year)[source]

Leap year or not in the Gregorian calendar.

pyhdust.jdcal.jcal2jd(year, month, day)[source]

Julian calendar date to Julian date.

The input and output are for the proleptic Julian calendar, i.e., no consideration of historical usage of the calendar is made.

year : int
Year as an integer.
month : int
Month as an integer.
day : int
Day as an integer.
jd1, jd2: 2-element tuple of floats
When added together, the numbers give the Julian date for the given Julian calendar date. The first number is always MJD_0 i.e., 2451545.5. So the second is the MJD.
>>> jcal2jd(2000, 1, 1)
(2400000.5, 51557.0)
>>> year = [-4699, -2114, -1050, -123, -1, 0, 1, 123, 1678, 2000,
...:  2012, 2245]
>>> month = [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12]
>>> day = [1, 12, 23, 14, 25, 16, 27, 8, 9, 10, 11, 31]
>>> x = [jcal2jd(y, m, d) for y, m, d in zip(year, month, day)]
>>> for i in x: print i
(2400000.5, -2395252.0)
(2400000.5, -1451039.0)
(2400000.5, -1062374.0)
(2400000.5, -723765.0)
(2400000.5, -679164.0)
(2400000.5, -678776.0)
(2400000.5, -678370.0)
(2400000.5, -633798.0)
(2400000.5, -65772.0)
(2400000.5, 51871.0)
(2400000.5, 56285.0)


Unlike gcal2jd, negative months and days can result in incorrect Julian dates.

pyhdust.jdcal.jd2gcal(jd1, jd2)[source]

Julian date to Gregorian calendar date and time of day.

The input and output are for the proleptic Gregorian calendar, i.e., no consideration of historical usage of the calendar is made.

jd1, jd2: int
Sum of the two numbers is taken as the given Julian date. For example jd1 can be the zero point of MJD (MJD_0) and jd2 can be the MJD of the date and time. But any combination will work.
y, m, d, f : int, int, int, float
Four element tuple containing year, month, day and the fractional part of the day in the Gregorian calendar. The first three are integers, and the last part is a float.
>>> jd2gcal(*gcal2jd(2000,1,1))
(2000, 1, 1, 0.0)
>>> jd2gcal(*gcal2jd(1950,1,1))
(1950, 1, 1, 0.0)


Out of range months and days are carried over to the next/previous year or next/previous month. See gcal2jd for more examples.

>>> jd2gcal(*gcal2jd(1999,10,12))
(1999, 10, 12, 0.0)
>>> jd2gcal(*gcal2jd(2000,2,30))
(2000, 3, 1, 0.0)
>>> jd2gcal(*gcal2jd(-1999,10,12))
(-1999, 10, 12, 0.0)
>>> jd2gcal(*gcal2jd(2000, -2, -4))
(1999, 9, 26, 0.0)

>>> gcal2jd(2000,1,1)
(2400000.5, 51544.0)
>>> jd2gcal(2400000.5, 51544.0)
(2000, 1, 1, 0.0)
>>> jd2gcal(2400000.5, 51544.5)
(2000, 1, 1, 0.5)
>>> jd2gcal(2400000.5, 51544.245)
(2000, 1, 1, 0.24500000000261934)
>>> jd2gcal(2400000.5, 51544.1)
(2000, 1, 1, 0.099999999998544808)
>>> jd2gcal(2400000.5, 51544.75)
(2000, 1, 1, 0.75)


The last element of the tuple is the same as

(hh + mm / 60.0 + ss / 3600.0) / 24.0

where hh, mm, and ss are the hour, minute and second of the day.

gcal2jd

pyhdust.jdcal.jd2jcal(jd1, jd2)[source]

Julian calendar date for the given Julian date.

The input and output are for the proleptic Julian calendar, i.e., no consideration of historical usage of the calendar is made.

jd1, jd2: int
Sum of the two numbers is taken as the given Julian date. For example jd1 can be the zero point of MJD (MJD_0) and jd2 can be the MJD of the date and time. But any combination will work.
y, m, d, f : int, int, int, float
Four element tuple containing year, month, day and the fractional part of the day in the Julian calendar. The first three are integers, and the last part is a float.
>>> jd2jcal(*jcal2jd(2000, 1, 1))
(2000, 1, 1, 0.0)
>>> jd2jcal(*jcal2jd(-4000, 10, 11))
(-4000, 10, 11, 0.0)

>>> jcal2jd(2000, 1, 1)
(2400000.5, 51557.0)
>>> jd2jcal(2400000.5, 51557.0)
(2000, 1, 1, 0.0)
>>> jd2jcal(2400000.5, 51557.5)
(2000, 1, 1, 0.5)
>>> jd2jcal(2400000.5, 51557.245)
(2000, 1, 1, 0.24500000000261934)
>>> jd2jcal(2400000.5, 51557.1)
(2000, 1, 1, 0.099999999998544808)
>>> jd2jcal(2400000.5, 51557.75)
(2000, 1, 1, 0.75)