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# * coding:utf8 *


"""Functions for converting between Julian dates and calendar dates.




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.




:author: Prasanth Nair


:contact: prasanthhn@gmail.com


:license: BSD (https://opensource.org/licenses/bsdlicense.php)


"""


from __future__ import division


from __future__ import print_function


import math




__version__ = "1.4.1"




MJD_0 = 2400000.5


MJD_JD2000 = 51544.5






def is_leap(year):


"""Leap year or not in the Gregorian calendar."""


x = year % 4


y = year % 100


z = year % 400




# Divisible by 4 and,


# either not divisible by 100 or divisible by 400.


return not x and (y or not z)






def gcal2jd(year, month, day):


"""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.




Parameters





year : int


Year as an integer.


month : int


Month as an integer.


day : int


Day as an integer.




Returns





jd1, jd2: 2element 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., 2400000.5. So the second is the MJD.




Examples





>>> 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/+122/4 => 1999/10/4 => 1999/9/304 => 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)




Notes





The returned Julian date is for midnight 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 midday 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.




"""


year = int(year)


month = int(month)


day = int(day)




a = int((month  14) / 12.0)


jd = int((1461 * (year + 4800 + a)) / 4.0)


jd += int((367 * (month  2  12 * a)) / 12.0)


x = int((year + 4900 + a) / 100.0)


jd = int((3 * x) / 4.0)


jd += day  2432075.5 # was 32075; add 2400000.5




jd = 0.5 # 0 hours; above JD is for midday, switch to midnight.




return MJD_0, jd






def jd2gcal(jd1, jd2):


"""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.




Parameters





jd1, jd2: float


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.




Returns





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.




Examples





>>> 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)




Notes





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.




See Also





gcal2jd




"""


jd1_f, jd1_i = math.modf(jd1)


jd2_f, jd2_i = math.modf(jd2)




jd_i = jd1_i + jd2_i




f = jd1_f + jd2_f




# Set JD to noon of the current date. Fractional part is the


# fraction from midnight of the current date.


if 0.5 < f < 0.5:


f += 0.5


elif f >= 0.5:


jd_i += 1


f = 0.5


elif f <= 0.5:


jd_i = 1


f += 1.5




ell = jd_i + 68569


n = int((4 * ell) / 146097.0)


ell = int(((146097 * n) + 3) / 4.0)


i = int((4000 * (ell + 1)) / 1461001)


ell = int((1461 * i) / 4.0)  31


j = int((80 * ell) / 2447.0)


day = ell  int((2447 * j) / 80.0)


ell = int(j / 11.0)


month = j + 2  (12 * ell)


year = 100 * (n  49) + i + ell




return int(year), int(month), int(day), f






def jcal2jd(year, month, day):


"""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.




Parameters





year : int


Year as an integer.


month : int


Month as an integer.


day : int


Day as an integer.




Returns





jd1, jd2: 2element 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.




Examples





>>> 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)




Notes





Unlike `gcal2jd`, negative months and days can result in incorrect


Julian dates.




"""


year = int(year)


month = int(month)


day = int(day)




jd = 367 * year


x = int((month  9) / 7.0)


jd = int((7 * (year + 5001 + x)) / 4.0)


jd += int((275 * month) / 9.0)


jd += day


jd += 1729777  2400000.5 # Return 240000.5 as first part of JD.




jd = 0.5 # Convert midday to midnight.




return MJD_0, jd






def jd2jcal(jd1, jd2):


"""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.




Parameters





jd1, jd2: float


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.




Returns





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.




Examples





>>> 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)




"""


jd1_f, jd1_i = math.modf(jd1)


jd2_f, jd2_i = math.modf(jd2)




jd_i = jd1_i + jd2_i




f = jd1_f + jd2_f




# Set JD to noon of the current date. Fractional part is the


# fraction from midnight of the current date.


if 0.5 < f < 0.5:


f += 0.5


elif f >= 0.5:


jd_i += 1


f = 0.5


elif f <= 0.5:


jd_i = 1


f += 1.5




j = jd_i + 1402.0


k = int((j  1) / 1461.0)


ell = j  (1461.0 * k)


n = int((ell  1) / 365.0)  int(ell / 1461.0)


i = ell  (365.0 * n) + 30.0


j = int((80.0 * i) / 2447.0)


day = i  int((2447.0 * j) / 80.0)


i = int(j / 11.0)


month = j + 2  (12.0 * i)


year = (4 * k) + n + i  4716.0




return int(year), int(month), int(day), f


