karana.py

#!/usr/bin/python3

# A programme to convert between Julian Days and the ancient Tibetan calendar described in the Tantra Karaṇa

from math import floor, ceil
from fractions import Fraction
from numpy import sign
from months import NUM_TIBETAN as MONTHS, TIBETAN_NUM as MONTHNO
import tibetan

def dayof(mcount, tithi):
    '''Compute the Julian Day corresponding to a given tithi in a given month'''
    mcount = floor(mcount)
    tithi = int(tithi)

    t = tibetan.tibetan.karana(mcount, tithi)
    ans = t[0] + sign(sum(t) - t[0])
    return ans

# astronomical constants
epoch = 2015531 + Fraction(30,60) # nominal epoch corresponding to the new moon that fell on 23 March 806 AD (Julian)
sid_year = Fraction(3731481, 10216) # Svante Janson, Tibetan Calendar Mathematics, section A.5

def tojd(tithi, month, year):
    '''Convert a date in the Karaṇa system to a Julian Day.'''
    tithi = int(tithi) - 1 # subtract 1 because computers count from 0
    month = str(month)
    year = int(year) + 221

    if (month[:4] == "Leap"):
        leap = True
        month = month[5:]
    else:
        leap = False

    mcount = (((year * 12) - 2) * Fraction(67,65)) # months since the epoch
    if (mcount % 1 > Fraction(1,65)):
        mcount += Fraction(67,65)
    # we are now at approximately Losar. next, step through the months until we get to the specified month.
    m = 0
    while (MONTHS[m] != month):
        if (mcount % 1 in (Fraction(0,65), Fraction(1,65))):
            m += 0
        else:
            m += 1
        mcount += Fraction(67,65)
    if ( (leap == True) and (mcount % 1 in (Fraction(63,68), Fraction(64,65)))):
        mcount += 1

    jday = dayof(mcount, tithi)
    return jday

def fromjd(jday):
    '''Given a Julian Day, compute a date in the Karaṇa system'''
    jday = Fraction(jday)

    # compute the year
    year = round((jday - epoch) / sid_year)
    mcount = (((year * 12) - 2) * Fraction(67,65))
    if (mcount % 1 > Fraction(1,65)):
        mcount += Fraction(67,65)
    while(dayof(  (mcount + (12 * Fraction(67,65))), 0) <= jday):
        year += 1
        mcount += (12 * Fraction(67,65))
    while(dayof(mcount, 0) > jday):
        year -= 1
        mcount -= (12 * Fraction(67,65))
    year -= 221

    # compute the month
    m = 0
    while( dayof( (mcount + Fraction(67,65)), 0) <= jday):
        if (mcount % 1 in ( Fraction(63,65), Fraction(64,65) )):
            m += 0
        else:
            m += 1
        mcount += Fraction(67,65)
    if (mcount % 1 in (Fraction(0,65), Fraction(1,65))):
        month = "Leap " + MONTHS[m]
    else:
        month = MONTHS[m]

    # compute the tithi
    tithi = 0
    while( dayof( mcount, (tithi + 1)) <= jday):
        tithi += 1

    return((tithi + 1), month, year)