Geografic-Information-System/lib/python/temporal/temporal_granularity.py

"""
Functions to compute the temporal granularity of a map list

Usage:

.. code-block:: python

    import grass.temporal as tgis

    tgis.compute_relative_time_granularity(maps)


(C) 2012-2013 by the GRASS Development Team
This program is free software under the GNU General Public
License (>=v2). Read the file COPYING that comes with GRASS
for details.

:authors: Soeren Gebbert
"""
from abstract_dataset import *
from datetime_math import *

###############################################################################


def check_granularity_string(granularity, temporal_type):
    """Check if the granularity string is valid

        :param granularity: The granularity string
        :param temporal_type: The temporal type of the granularity relative or
                              absolute
        :return: True if valid, False if invalid

        .. code-block:: python

            >>> check_granularity_string("1 year", "absolute")
            True
            >>> check_granularity_string("1 month", "absolute")
            True
            >>> check_granularity_string("1 day", "absolute")
            True
            >>> check_granularity_string("1 minute", "absolute")
            True
            >>> check_granularity_string("1 hour", "absolute")
            True
            >>> check_granularity_string("1 second", "absolute")
            True
            >>> check_granularity_string("5 months", "absolute")
            True
            >>> check_granularity_string("5 days", "absolute")
            True
            >>> check_granularity_string("5 minutes", "absolute")
            True
            >>> check_granularity_string("5 years", "absolute")
            True
            >>> check_granularity_string("5 hours", "absolute")
            True
            >>> check_granularity_string("2 seconds", "absolute")
            True
            >>> check_granularity_string("1 secondo", "absolute")
            False
            >>> check_granularity_string("bla second", "absolute")
            False
            >>> check_granularity_string("bla", "absolute")
            False
            >>> check_granularity_string(1, "relative")
            True
            >>> check_granularity_string("bla", "relative")
            False

    """
    temporal_type

    if granularity is None:
        return False

    if temporal_type == "absolute":
        try:
            num, unit = granularity.split(" ")
        except:
            return False
        if unit not in ["second", "seconds", "minute", "minutes", "hour",
                        "hours", "day", "days", "week", "weeks", "month",
                        "months", "year", "years"]:
            return False

        try:
            integer = int(num)
        except:
            return False
    elif temporal_type == "relative":
        try:
            integer = int(granularity)
        except:
            return False
    else:
        return False

    return True

###############################################################################


def compute_relative_time_granularity(maps):
    """Compute the relative time granularity

        Attention: The computation of the granularity
        is only correct in case of not overlapping intervals.
        Hence a correct temporal topology is required for computation.

        :param maps: a ordered by start_time list of map objects
        :return: An integer


        .. code-block:: python

            >>> import grass.temporal as tgis
            >>> tgis.init()
            >>> maps = []
            >>> for i in range(5):
            ...   map = tgis.RasterDataset("a%i@P"%i)
            ...   check = map.set_relative_time(i,i + 1,"seconds")
            ...   if check:
            ...     maps.append(map)
            >>> tgis.compute_relative_time_granularity(maps)
            1

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,3), (3,6), (6,9))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"years")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            3

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,3), (4,6), (8,11))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"years")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            1

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,8), (2,6), (5,9))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"months")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            4

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,8), (8,12), (12,18))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"days")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            2

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,None), (8,None), (12,None), (24,None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"minutes")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            4

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,None), (8,14), (18,None), (24,None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"hours")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            2

            >>> maps = []
            >>> count = 0
            >>> timelist = ((0,21),)
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_relative_time(t[0],t[1],"hours")
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_relative_time_granularity(maps)
            21

    """

    # The interval time must be scaled to days resolution
    granularity = None
    delta = []
    # First we compute the timedelta of the intervals
    for map in maps:
        start, end = map.get_temporal_extent_as_tuple()
        if (start == 0 or start) and end:
            t = abs(end - start)
            delta.append(int(t))

    # Compute the timedelta of the gaps
    for i in range(len(maps)):
        if i < len(maps) - 1:
            relation = maps[i + 1].temporal_relation(maps[i])
            if relation == "after":
                start1, end1 = maps[i].get_temporal_extent_as_tuple()
                start2, end2 = maps[i + 1].get_temporal_extent_as_tuple()
                # Gaps are between intervals, intervals and
                # points, points and points
                if end1 and start2:
                    t = abs(end1 - start2)
                    delta.append(int(t))
                if not end1 and start2:
                    t = abs(start1 - start2)
                    delta.append(int(t))

    delta.sort()
    ulist = list(set(delta))
    if len(ulist) > 1:
        # Find greatest common divisor
        granularity = gcd_list(ulist)
    elif len(ulist) == 1:
        granularity = ulist[0]
    else:
        granularity = 0

    return granularity

###############################################################################


def compute_absolute_time_granularity(maps):
    """Compute the absolute time granularity

        Attention: The computation of the granularity
        is only correct in case of not overlapping intervals.
        Hence a correct temporal topology is required for computation.

        The computed granularity is returned as number of seconds or minutes
        or hours or days or months or years.

        :param maps: a ordered by start_time list of map objects
        :return: The temporal topology as string "integer unit"

        .. code-block:: python

            >>> import grass.temporal as tgis
            >>> import datetime
            >>> dt = datetime.datetime
            >>> tgis.init()
            >>> maps = []
            >>> count = 0
            >>> timelist = ((dt(2000,01,01),None), (dt(2000,02,01),None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_absolute_time(t[0],t[1])
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_absolute_time_granularity(maps)
            '1 month'

            >>> maps = []
            >>> count = 0
            >>> timelist = ((dt(2000,01,01),None), (dt(2000,01,02),None), (dt(2000,01,03),None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_absolute_time(t[0],t[1])
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_absolute_time_granularity(maps)
            '1 day'

            >>> maps = []
            >>> count = 0
            >>> timelist = ((dt(2000,01,01),None), (dt(2000,01,02),None), (dt(2000,05,04,0,5,30),None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_absolute_time(t[0],t[1])
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_absolute_time_granularity(maps)
            '30 seconds'

            >>> maps = []
            >>> count = 0
            >>> timelist = ((dt(2000,01,01),dt(2000,05,02)), (dt(2000,05,04,2),None))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_absolute_time(t[0],t[1])
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_absolute_time_granularity(maps)
            '2 hours'

            >>> maps = []
            >>> count = 0
            >>> timelist = ((dt(2000,01,01),dt(2000,02,01)), (dt(2005,05,04,12),dt(2007,05,20,6)))
            >>> for t in timelist:
            ...   map = tgis.RasterDataset("a%i@P"%count)
            ...   check = map.set_absolute_time(t[0],t[1])
            ...   if check:
            ...     maps.append(map)
            ...   count += 1
            >>> tgis.compute_absolute_time_granularity(maps)
            '6 hours'

    """

    has_seconds = False
    has_minutes = False
    has_hours = False
    has_days = False
    has_months = False
    has_years = False

    use_seconds = False
    use_minutes = False
    use_hours = False
    use_days = False
    use_months = False
    use_years = False

    delta = []
    datetime_delta = []
    # First we compute the timedelta of the intervals
    for map in maps:
        start, end = map.get_temporal_extent_as_tuple()
        if start and end:
            delta.append(end - start)
            datetime_delta.append(compute_datetime_delta(start, end))

    # Compute the timedelta of the gaps
    for i in range(len(maps)):
        if i < len(maps) - 1:
            relation = maps[i + 1].temporal_relation(maps[i])
            if relation == "after":
                start1, end1 = maps[i].get_temporal_extent_as_tuple()
                start2, end2 = maps[i + 1].get_temporal_extent_as_tuple()
                # Gaps are between intervals, intervals and
                # points, points and points
                if end1 and start2:
                    delta.append(end1 - start2)
                    datetime_delta.append(compute_datetime_delta(end1, start2))
                if not end1 and start2:
                    delta.append(start2 - start1)
                    datetime_delta.append(compute_datetime_delta(
                        start1, start2))
    # Check what changed
    dlist = []
    for d in datetime_delta:
        if "second" in d and d["second"] > 0:
            has_seconds = True
            #print "has second"
        if "minute" in d and d["minute"] > 0:
            has_minutes = True
            #print "has minute"
        if "hour" in d and d["hour"] > 0:
            has_hours = True
            #print "has hour"
        if "day" in d and d["day"] > 0:
            has_days = True
            #print "has day"
        if "month" in d and d["month"] > 0:
            has_months = True
            #print "has month"
        if "year" in d and d["year"] > 0:
            has_years = True
            #print "has year"

    # Create a list with a single time unit only
    if has_seconds:
        for d in datetime_delta:
            if "second" in d and d["second"] > 0:
                dlist.append(d["second"])
            elif "minute" in d and d["minute"] > 0:
                dlist.append(d["minute"] * 60)
            elif "hour" in d and d["hour"] > 0:
                dlist.append(d["hour"] * 3600)
            elif "day" in d and d["day"] > 0:
                dlist.append(d["day"] * 24 * 3600)
            else:
                dlist.append(d["max_days"] * 24 * 3600)
        use_seconds = True
    elif has_minutes:
        for d in datetime_delta:
            if "minute" in d and d["minute"] > 0:
                dlist.append(d["minute"])
            elif "hour" in d and d["hour"] > 0:
                dlist.append(d["hour"] * 60)
            elif "day" in d:
                dlist.append(d["day"] * 24 * 60)
            else:
                dlist.append(d["max_days"] * 24 * 60)
        use_minutes = True
    elif has_hours:
        for d in datetime_delta:
            if "hour" in d and d["hour"] > 0:
                dlist.append(d["hour"])
            elif "day" in d and d["day"] > 0:
                dlist.append(d["day"] * 24)
            else:
                dlist.append(d["max_days"] * 24)
        use_hours = True
    elif has_days:
        for d in datetime_delta:
            if "day" in d and d["day"] > 0:
                dlist.append(d["day"])
            else:
                dlist.append(d["max_days"])
        use_days = True
    elif has_months:
        for d in datetime_delta:
            if "month" in d and d["month"] > 0:
                dlist.append(d["month"])
            elif "year" in d and d["year"] > 0:
                dlist.append(d["year"] * 12)
        use_months = True
    elif has_years:
        for d in datetime_delta:
            if "year" in d:
                dlist.append(d["year"])
        use_years = True

    dlist.sort()
    ulist = list(set(dlist))

    if len(ulist) == 0:
        return None

    if len(ulist) > 1:
        # Find greatest common divisor
        granularity = gcd_list(ulist)
    else:
        granularity = ulist[0]

    if use_seconds:
        if granularity == 1:
            return "%i second" % granularity
        else:
            return "%i seconds" % granularity
    elif use_minutes:
        if granularity == 1:
            return "%i minute" % granularity
        else:
            return "%i minutes" % granularity
    elif use_hours:
        if granularity == 1:
            return "%i hour" % granularity
        else:
            return "%i hours" % granularity
    elif use_days:
        if granularity == 1:
            return "%i day" % granularity
        else:
            return "%i days" % granularity
    elif use_months:
        if granularity == 1:
            return "%i month" % granularity
        else:
            return "%i months" % granularity
    elif use_years:
        if granularity == 1:
            return "%i year" % granularity
        else:
            return "%i years" % granularity

    return None

###############################################################################

def compute_common_relative_time_granularity(gran_list):
	"""Compute the greatest common granule from a list of relative time granules
    
        .. code-block:: python

            >>> import grass.temporal as tgis
            >>> tgis.init()
            >>> grans = [1,2,30]
            >>> tgis.compute_common_relative_time_granularity(grans)
            1
            
            >>> import grass.temporal as tgis
            >>> tgis.init()
            >>> grans = [10,20,30]
            >>> tgis.compute_common_relative_time_granularity(grans)
            10
    """
	return gcd_list(gran_list)

###############################################################################

def compute_common_absolute_time_granularity(gran_list,
                                             start_date_list = None):
    """ Compute the greatest common granule from a list of absolute time granules,
        considering the start times of the related space time datasets in the
        common granularity computation.

        :param gran_list: List of granularities
        :param start_date_list: List of the start times of related space time datasets
        :return: The common granularity

        .. code-block:: python

            from datetime import datetime
            >>> import grass.temporal as tgis
            >>> tgis.init()
            >>> grans = ["20 second", "10 minutes", "2 hours"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '20 seconds'

            >>> grans = ["20 second", "10 minutes", "2 hours"]
            >>> dates = [datetime(2001,1,1,0,0,20),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 second'

            >>> grans = ["7200 second", "240 minutes", "1 year"]
            >>> dates = [datetime(2001,1,1,0,0,10),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 second'

            >>> grans = ["7200 second", "89 minutes", "1 year"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '60 seconds'

            >>> grans = ["120 minutes", "2 hours"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '60 minutes'

            >>> grans = ["120 minutes", "2 hours"]
            >>> dates = [datetime(2001,1,1,0,30,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 minute'

            >>> grans = ["360 minutes", "3 hours"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '60 minutes'

            >>> grans = ["2 hours", "4 hours", "8 hours"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '2 hours'

            >>> grans = ["2 hours", "4 hours", "8 hours"]
            >>> dates = [datetime(2001,1,1,2,0,0),
            ...          datetime(2001,1,1,4,0,0),
            ...          datetime(2001,1,1,8,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 hour'

            >>> grans = ["8 hours", "2 days"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '8 hours'

            >>> grans = ["8 hours", "2 days"]
            >>> dates = [datetime(2001,1,1,10,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 hour'

            >>> grans = ["120 months", "360 months", "4 years"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '12 months'

            >>> grans = ["30 days", "10 days", "5 days"]
            >>> dates = [datetime(2001,2,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '5 days'

            >>> grans = ["30 days", "10 days", "5 days"]
            >>> dates = [datetime(2001,2,2,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 day'

            >>> grans = ["2 days", "360 months", "4 years"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '2 days'

            >>> grans = ["2 days", "360 months", "4 years"]
            >>> dates = [datetime(2001,1,2,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 day'

            >>> grans = ["120 months", "360 months", "4 years"]
            >>> dates = [datetime(2001,2,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 month'

            >>> grans = ["120 months", "361 months", "4 years"]
            >>> dates = [datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),
            ...          datetime(2001,1,1,0,0,0),]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '1 month'

            >>> grans = ["120 months", "360 months", "4 years"]
            >>> tgis.compute_common_absolute_time_granularity(grans, dates)
            '12 months'

        ..

    """

    common_granule = compute_common_absolute_time_granularity_simple(gran_list)

    if start_date_list is None:
        return common_granule

    num, granule = common_granule.split()

    if granule in ["seconds",  "second"]:
        # If the start seconds are different between the start dates
        # set the granularity to one second
        for start_time in start_date_list:
            if start_time.second != start_date_list[0].second:
                return "1 second"
        # Make sure the granule does not exceed the hierarchy limit
        if int(num) > 60:
            if int(num)%60 == 0:
                return "60 seconds"
            else:
                return "1 second"

    if granule in ["minutes",  "minute"]:
        # If the start minutes are different between the start dates
        # set the granularity to one minute
        for start_time in start_date_list:
            if start_time.minute != start_date_list[0].minute:
                return "1 minute"
        # Make sure the granule does not exceed the hierarchy limit
        if int(num) > 60:
            if int(num)%60 == 0:
                return "60 minutes"
            else:
                return "1 minute"

    if granule in ["hours",  "hour"]:
        # If the start hours are different between the start dates
        # set the granularity to one hour
        for start_time in start_date_list:
            if start_time.hour != start_date_list[0].hour:
                return "1 hour"
        # Make sure the granule does not exceed the hierarchy limit
        if int(num) > 24:
            if int(num)%24 == 0:
                return "24 hours"
            else:
                return "1 hour"

    if granule in ["days",  "day"]:
        # If the start days are different between the start dates
        # set the granularity to one day
        for start_time in start_date_list:
            if start_time.day != start_date_list[0].day:
                return "1 day"
        # Make sure the granule does not exceed the hierarchy limit
        if int(num) > 365:
            if int(num)%365 == 0:
                return "365 days"
            else:
                return "1 day"

    if granule in ["months",  "month"]:
        # If the start months are different between the start dates
        # set the granularity to one month
        for start_time in start_date_list:
            if start_time.month != start_date_list[0].month:
                return "1 month"
        # Make sure the granule does not exceed the hierarchy limit
        if int(num) > 12:
            if int(num)%12 == 0:
                return "12 months"
            else:
                return "1 month"

    return common_granule

###############################################################################

def compute_common_absolute_time_granularity_simple(gran_list):
    """ Compute the greatest common granule from a list of absolute time granules

        :param gran_list: List of granularities
        :param start_date_list:
        :return: The common granularity

        .. code-block:: python

            >>> import grass.temporal as tgis
            >>> tgis.init()
            >>> grans = ["1 second", "2 seconds", "30 seconds"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '1 second'
            
            >>> grans = ["3 second", "6 seconds", "30 seconds"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '3 seconds'
            
            >>> grans = ["12 second", "18 seconds", "30 seconds", "10 minutes"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '6 seconds'
            
            >>> grans = ["20 second", "10 minutes", "2 hours"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '20 seconds'
            
            >>> grans = ["7200 second", "240 minutes", "1 year"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '7200 seconds'
            
            >>> grans = ["7200 second", "89 minutes", "1 year"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '60 seconds'

            >>> grans = ["10 minutes", "20 minutes", "30 minutes", "40 minutes", "2 hours"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '10 minutes'

            >>> grans = ["120 minutes", "2 hours"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '120 minutes'

            >>> grans = ["360 minutes", "3 hours"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '180 minutes'

            >>> grans = ["2 hours", "4 hours", "8 hours"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '2 hours'

            >>> grans = ["8 hours", "2 days"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '8 hours'

            >>> grans = ["48 hours", "1 month"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '24 hours'

            >>> grans = ["48 hours", "1 year"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '24 hours'

            >>> grans = ["2 months", "4 months", "1 year"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '2 months'

            >>> grans = ["120 months", "360 months", "4 years"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '24 months'

            >>> grans = ["120 months", "361 months", "4 years"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '1 month'

            >>> grans = ["2 years", "3 years", "4 years"]
            >>> tgis.compute_common_absolute_time_granularity(grans)
            '1 year'
    """
    
    has_seconds = False # 0
    has_minutes = False # 1
    has_hours = False     # 2
    has_days = False      # 3
    has_months = False  # 4
    has_years = False     # 5
    
    seconds = []
    minutes = []
    hours = []
    days = []
    months = []
    years = []
    
    min_gran = 6
    max_gran = -1
    
    for entry in gran_list:
        if not check_granularity_string(entry, "absolute"):
            return False

        num,  gran = entry.split()
        
        if gran in ["seconds",  "second"]:
            has_seconds = True
            if min_gran > 0:
                min_gran = 0
            if max_gran < 0:
                max_gran = 0
                
            seconds.append(int(num))

        if gran in ["minutes",  "minute"]:
            has_minutes = True
            if min_gran > 1:
                min_gran = 1
            if max_gran < 1:
                max_gran = 1
                
            minutes.append(int(num))

        if gran in ["hours",  "hour"]:
            has_hours = True
            if min_gran > 2:
                min_gran = 2
            if max_gran < 2:
                max_gran = 2
                
            hours.append(int(num))

        if gran in ["days",  "day"]:
            has_days = True
            if min_gran > 3:
                min_gran = 3
            if max_gran < 3:
                max_gran = 3
                
            days.append(int(num))

        if gran in ["months",  "month"]:
            has_months = True
            if min_gran > 4:
                min_gran = 4
            if max_gran < 4:
                max_gran = 4
                
            months.append(int(num))

        if gran in ["years",  "year"]:
            has_years = True
            if min_gran > 5:
                min_gran = 5
            if max_gran < 5:
                max_gran = 5
                
            years.append(int(num))
            
    if has_seconds:
        if has_minutes:
            minutes.sort()
            seconds.append(minutes[0]*60)
        if has_hours:
            hours.sort()
            seconds.append(hours[0]*60*60)
        if has_days:
            days.sort()
            seconds.append(days[0]*60*60*24)
        if has_months:
            months.sort()
            seconds.append(months[0]*60*60*24*28)
            seconds.append(months[0]*60*60*24*29)
            seconds.append(months[0]*60*60*24*30)
            seconds.append(months[0]*60*60*24*31)
        if has_years:
            years.sort()
            seconds.append(years[0]*60*60*24*365)
            seconds.append(years[0]*60*60*24*366)

        num = gcd_list(seconds)
        gran = "second"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)
        
    elif has_minutes:
        if has_hours:
            hours.sort()
            minutes.append(hours[0]*60)
        if has_days:
            days.sort()
            minutes.append(days[0]*60*24)
        if has_months:
            months.sort()
            minutes.append(months[0]*60*24*28)
            minutes.append(months[0]*60*24*29)
            minutes.append(months[0]*60*24*30)
            minutes.append(months[0]*60*24*31)
        if has_years:
            years.sort()
            minutes.append(years[0]*60*24*365)
            minutes.append(years[0]*60*24*366)
        num = gcd_list(minutes)
        gran = "minute"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)
        
    elif has_hours:
        if has_days:
            days.sort()
            hours.append(days[0]*24)
        if has_months:
            months.sort()
            hours.append(months[0]*24*28)
            hours.append(months[0]*24*29)
            hours.append(months[0]*24*30)
            hours.append(months[0]*24*31)
        if has_years:
            years.sort()
            hours.append(years[0]*24*365)
            hours.append(years[0]*24*366)
        num = gcd_list(hours)
        gran = "hour"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)

    elif has_days:
        if has_months:
            months.sort()
            days.append(months[0]*28)
            days.append(months[0]*29)
            days.append(months[0]*30)
            days.append(months[0]*31)
        if has_years:
            years.sort()
            days.append(years[0]*365)
            days.append(years[0]*366)
        num = gcd_list(days)
        gran = "day"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)

    elif has_months:
        if has_years:
            years.sort()
            months.append(years[0]*12)
        num = gcd_list(months)
        gran = "month"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)
        
    elif has_years:
        num = gcd_list(years)
        gran = "year"
        if num > 1:
            gran += "s"
        return "%i %s"%(num,  gran)
        

###############################################################################
# http://akiscode.com/articles/gcd_of_a_list.shtml
# Copyright (c) 2010 Stephen Akiki
# MIT License (Means you can do whatever you want with this)
#  See http://www.opensource.org/licenses/mit-license.php
# Error Codes:
#   None


def gcd(a, b):
    """The Euclidean Algorithm """
    a = abs(a)
    b = abs(b)
    while a:
        a, b = b % a, a
    return b

###############################################################################


def gcd_list(list):
    """Finds the GCD of numbers in a list.

    :param list: List of numbers you want to find the GCD of
                 E.g. [8, 24, 12]
    :return: GCD of all numbers

    """
    return reduce(gcd, list)

###############################################################################

if __name__ == "__main__":
    import doctest
    doctest.testmod()