Imrpove makefile and flatten the hier a bit

Signed-off-by: Mattias Andrée <maandree@kth.se>

1 files changed, 846 insertions, 0 deletions

diff --git a/solar_python.py b/solar_python.py
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+# solar-python — Solar data calculation and prediction library for Python
+# Copyright © 2014, 2015  Mattias Andrée (maandree@member.fsf.org)
+# 
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Affero General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+# 
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Affero General Public License for more details.
+# 
+# You should have received a copy of the GNU Affero General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+
+
+SOLAR_APPARENT_RADIUS = 32.0 / 60.0
+'''
+:float  Approximate apparent size of the Sun in degrees
+'''
+
+
+SOLAR_ELEVATION_PRESUNSET_POSTSUNRISE = 32.0 / 60.0
+'''
+:float  The Sun's elevation the beginning of sunset and
+        end of sunrise, measured in degrees
+'''
+
+SOLAR_ELEVATION_SUNSET_SUNRISE = -32.0 / 60.0
+'''
+:float  The Sun's elevation the (end of) at sunset and
+        (beginning of) sunrise, measured in degrees
+'''
+
+SOLAR_ELEVATION_CIVIL_DUSK_DAWN = -6.0
+'''
+:float  The Sun's elevation at civil dusk and civil
+        dawn, measured in degrees
+'''
+
+SOLAR_ELEVATION_NAUTICAL_DUSK_DAWN = -12.0
+'''
+:float  The Sun's elevation at nautical dusk and
+        nautical dawn, measured in degrees
+'''
+
+SOLAR_ELEVATION_AMATEUR_ASTRONOMICAL_DUSK_DAWN = -15.0
+'''
+:float  The Sun's elevation at amateur astronomical dusk
+        and amateur astronomical dawn, measured in degrees
+'''
+
+SOLAR_ELEVATION_ASTRONOMICAL_DUSK_DAWN = -18.0
+'''
+:float  The Sun's elevation at astronomical dusk
+        and astronomical dawn, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_TWILIGHT = (-18.0, 0.0)
+'''
+:(float, float)  The Sun's lowest and highest elevation during
+                 all periods of twilight, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_CIVIL_TWILIGHT = (-6.0, SOLAR_ELEVATION_SUNSET_SUNRISE)
+'''
+:(float, float)  The Sun's lowest and highest elevation
+                 during civil twilight, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_NAUTICAL_TWILIGHT = (-12.0, SOLAR_ELEVATION_SUNSET_SUNRISE)
+'''
+:(float, float)  The Sun's lowest and highest elevation
+                 during nautical twilight, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_ASTRONOMICAL_TWILIGHT = (-18.0, SOLAR_ELEVATION_SUNSET_SUNRISE)
+'''
+:(float, float)  The Sun's lowest and highest elevation during
+                 astronomical twilight, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_AMATEUR_ASTRONOMICAL_TWILIGHT = (-18.0, -15.0)
+'''
+:(float, float)  The Sun's lowest and highest elevation during
+                 amateur astronomical twilight, measured in degrees
+'''
+
+SOLAR_ELEVATION_RANGE_GOLDEN_HOUR = (-4.0, 6.0)
+'''
+:(float, float)  The Sun's lowest and highest elevation during
+                 the golden "hour" (also known as magic hour),
+                 measured in degrees. These elevations are
+                 approximate.
+'''
+
+SOLAR_ELEVATION_RANGE_BLUE_HOUR = (-6.0, -4.0)
+'''
+:(float, float)  The Sun's lowest and highest elevation during
+                 the blue "hour", measured in degrees. These
+                 elevations are approximate.
+'''
+
+
+
+# The following functions are used to calculate the result for `sun`
+# (most of them) but could be used for anything else. There name is
+# should tell you enough, `t` (and `noon`) is in Julian Centuries
+# except for in the convertion methods.
+
+
+def julian_day_to_epoch(t):
+    '''
+    Converts a Julian Day timestamp to a POSIX time timestamp
+    
+    @param   t:float  The time in Julian Days
+    @return  :float   The time in POSIX time
+    '''
+    return (t - 2440587.5) * 86400.0
+
+
+def epoch_to_julian_day(t):
+    '''
+    Converts a POSIX time timestamp to a Julian Day timestamp
+    
+    @param   t:float  The time in POSIX time
+    @return  :float   The time in Julian Days
+    '''
+    return t / 86400.0 + 2440587.5
+
+
+def julian_day_to_julian_centuries(t):
+    '''
+    Converts a Julian Day timestamp to a Julian Centuries timestamp
+    
+    @param   t:float  The time in Julian Days
+    @return  :float   The time in Julian Centuries
+    '''
+    return (t - 2451545.0) / 36525.0
+
+
+def julian_centuries_to_julian_day(t):
+    '''
+    Converts a Julian Centuries timestamp to a Julian Day timestamp
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The time in Julian Days
+    '''
+    return t * 36525.0 + 2451545.0
+
+
+def epoch_to_julian_centuries(t):
+    '''
+    Converts a POSIX time timestamp to a Julian Centuries timestamp
+    
+    @param   t:float  The time in POSIX time
+    @return  :float   The time in Julian Centuries
+    '''
+    return julian_day_to_julian_centuries(epoch_to_julian_day(t))
+
+
+def julian_centuries_to_epoch(t):
+    '''
+    Converts a Julian Centuries timestamp to a POSIX time timestamp
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The time in POSIX time
+    '''
+    return julian_day_to_epoch(julian_centuries_to_julian_day(t))
+
+
+def epoch():
+    '''
+    Get current POSIX time
+    
+    @return  :float  The current POSIX time
+    '''
+    import time
+    return time.time()
+
+
+def julian_day():
+    '''
+    Get current Julian Day time
+    
+    @return  :float  The current Julian Day time
+    '''
+    return epoch_to_julian_day(epoch())
+
+
+def julian_centuries():
+    '''
+    Get current Julian Centuries time (100 Julian days since J2000)
+    
+    @return  :float  The current Julian Centuries time
+    '''
+    return epoch_to_julian_centuries(epoch())
+
+
+def radians(deg):
+    '''
+    Convert an angle from degrees to radians
+    
+    @param   deg:float  The angle in degrees
+    @return  :float     The angle in radians
+    '''
+    import math
+    return deg * math.pi / 180
+
+
+def degrees(rad):
+    '''
+    Convert an angle from radians to degrees
+    
+    @param   rad:float  The angle in radians
+    @return  :float     The angle in degrees
+    '''
+    import math
+    return rad * 180 / math.pi
+
+
+def sun_geometric_mean_longitude(t):
+    '''
+    Calculates the Sun's geometric mean longitude
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The Sun's geometric mean longitude in radians
+    '''
+    return radians((0.0003032 * t ** 2 + 36000.76983 * t + 280.46646) % 360)
+    # CANNIBALISERS:
+    #     The result of this function should always be positive, this
+    #     means that after division modulo 360 but before `radians`,
+    #     you will need to add 360 if the value is negative. This can
+    #     only happen if `t` is negative, which can only happen for date
+    #     times before 2000-(01)Jan-01 12:00:00 UTC par division modulo
+    #     implementations with the signess of at least the left operand.
+    #     More precively, it happens between circa 1970-(01)Jan-11
+    #     16:09:02 UTC and circa 374702470660351740 seconds before
+    #     January 1, 1970 00:00 UTC, which is so far back in time
+    #     it cannot be reliable pinned down to the right year, but it
+    #     is without a shadow of a doubt looooong before the Earth
+    #     was formed, is right up there with the age of the Milky Way
+    #     and the universe itself.
+
+
+def sun_geometric_mean_anomaly(t):
+    '''
+    Calculates the Sun's geometric mean anomaly
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The Sun's geometric mean anomaly in radians
+    '''
+    return radians(-0.0001537 * t ** 2 + 35999.05029 * t + 357.52911)
+
+
+def earth_orbit_eccentricity(t):
+    '''
+    Calculates the Earth's orbit eccentricity
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The Earth's orbit eccentricity
+    '''
+    return -0.0000001267 * t ** 2 - 0.000042037 * t + 0.016708634
+
+
+def sun_equation_of_centre(t):
+    '''
+    Calculates the Sun's equation of the centre, the difference between
+    the true anomaly and the mean anomaly
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The Sun's equation of the centre, in radians
+    '''
+    import math
+    a = sun_geometric_mean_anomaly(t)
+    rc = math.sin(1 * a) * (-0.000014 * t ** 2 - 0.004817 * t + 1.914602)
+    rc += math.sin(2 * a) * (-0.000101 * t + 0.019993)
+    rc += math.sin(3 * a) * 0.000289
+    return radians(rc)
+
+
+def sun_real_longitude(t):
+    '''
+    Calculates the Sun's real longitudinal position
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The longitude, in radians
+    '''
+    rc = sun_geometric_mean_longitude(t)
+    return rc + sun_equation_of_centre(t)
+
+
+def sun_apparent_longitude(t):
+    '''
+    Calculates the Sun's apparent longitudinal position
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The longitude, in radians
+    '''
+    import math
+    rc = degrees(sun_real_longitude(t)) - 0.00569
+    rc -= 0.00478 * math.sin(radians(-1934.136 * t + 125.04))
+    return radians(rc)
+
+
+def mean_ecliptic_obliquity(t):
+    '''
+    Calculates the mean ecliptic obliquity of the Sun's
+    apparent motion without variation correction
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The uncorrected mean obliquity, in radians
+    '''
+    rc = 0.001813 * t ** 3 - 0.00059 * t ** 2 - 46.815 * t + 21.448
+    rc = 26 + rc / 60
+    rc = 23 + rc / 60
+    return radians(rc)
+
+
+def corrected_mean_ecliptic_obliquity(t):
+    '''
+    Calculates the mean ecliptic obliquity of the Sun's
+    apparent motion with variation correction
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The mean obliquity, in radians
+    '''
+    import math
+    rc = -1934.136 * t + 125.04
+    rc = 0.00256 * math.cos(radians(rc))
+    rc += degrees(mean_ecliptic_obliquity(t))
+    return radians(rc)
+
+
+def solar_declination(t):
+    '''
+    Calculates the Sun's declination
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The Sun's declination, in radians
+    '''
+    import math
+    rc = math.sin(corrected_mean_ecliptic_obliquity(t))
+    rc *= math.sin(sun_apparent_longitude(t))
+    return math.asin(rc)
+
+
+def equation_of_time(t):
+    '''
+    Calculates the equation of time, the discrepancy
+    between apparent and mean solar time
+    
+    @param   t:float  The time in Julian Centuries
+    @return  :float   The equation of time, in degrees
+    '''
+    import math
+    l = sun_geometric_mean_longitude(t)
+    e = earth_orbit_eccentricity(t)
+    m = sun_geometric_mean_anomaly(t)
+    y = corrected_mean_ecliptic_obliquity(t)
+    y = math.tan(y / 2) ** 2
+    rc = y * math.sin(2 * l)
+    rc += (4 * y * math.cos(2 * l) - 2) * e * math.sin(m)
+    rc -= 0.5 * y ** 2 * math.sin(4 * l)
+    rc -= 1.25 * e ** 2 * math.sin(2 * m)
+    return 4 * degrees(rc)
+
+
+def hour_angle_from_elevation(latitude, declination, elevation):
+    '''
+    Calculates the solar hour angle from the Sun's elevation
+    
+    @param   longitude:float    The longitude in degrees eastwards
+                                from Greenwich, negative for westwards
+    @param   declination:float  The declination, in radians
+    @param   elevation:float    The Sun's elevation, in radians
+    @return  :float             The solar hour angle, in radians
+    '''
+    import math
+    if elevation == 0:
+        return 0
+    rc = math.cos(abs(elevation))
+    rc -= math.sin(radians(latitude)) * math.sin(declination)
+    rc /= math.cos(radians(latitude)) * math.cos(declination)
+    rc = math.acos(rc)
+    return -rc if (rc < 0) == (elevation < 0) else rc
+
+
+def elevation_from_hour_angle(latitude, declination, hour_angle):
+    '''
+    Calculates the Sun's elevation from the solar hour angle
+    
+    @param   longitude:float    The longitude in degrees eastwards
+                                from Greenwich, negative for westwards
+    @param   declination:float  The declination, in radians
+    @param   hour_angle:float   The solar hour angle, in radians
+    @return  :float             The Sun's elevation, in radians
+    '''
+    import math
+    rc = math.cos(radians(latitude))
+    rc *= math.cos(hour_angle) * math.cos(declination)
+    rc += math.sin(radians(latitude)) * math.sin(declination)
+    return math.asin(rc)
+
+
+def time_of_solar_noon(t, longitude):
+    '''
+    Calculates the time of the closest solar noon
+    
+    @param   t:float          A time close to the sought time,
+                              in Julian Centuries
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @return  :float           The time, in Julian Centuries,
+                              of the closest solar noon
+    '''
+    t, rc = julian_centuries_to_julian_day(t), longitude
+    for (k, m) in ((-360, 0), (1440, -0.5)):
+        rc = julian_day_to_julian_centuries(t + m + rc / k)
+        rc = 720 - 4 * longitude - equation_of_time(rc)
+    return rc
+
+
+def time_of_solar_elevation(t, noon, latitude, longitude, elevation):
+    '''
+    Calculates the time the Sun has a specified apparent
+    elevation at a geographical position
+    
+    @param   t:float          A time close to the sought time,
+                              in Julian Centuries
+    @param   noon:float       The time of the closest solar noon
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @param   elevation:float  The solar elevation, in radians
+    @return  :float           The time, in Julian Centuries,
+                              of the specified elevation
+    '''
+    rc = noon
+    rc, et = solar_declination(rc), equation_of_time(rc)
+    rc = hour_angle_from_elevation(latitude, rc, elevation)
+    rc = 720 - 4 * (longitude + degrees(rc)) - et
+    
+    rc = julian_day_to_julian_centuries(julian_centuries_to_julian_day(t) + rc / 1440)
+    rc, et = solar_declination(rc), equation_of_time(rc)
+    rc = hour_angle_from_elevation(latitude, rc, elevation)
+    rc = 720 - 4 * (longitude + degrees(rc)) - et
+    return rc
+
+
+def solar_elevation_from_time(t, latitude, longitude):
+    '''
+    Calculates the Sun's elevation as apparent
+    from a geographical position
+    
+    @param   t:float          The time in Julian Centuries
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @return  :float           The Sun's apparent elevation at the specified
+                              time as seen from the specified position,
+                              measured in radians
+    '''
+    rc = julian_centuries_to_julian_day(t)
+    rc = (rc - float(int(rc + 0.5)) - 0.5) * 1440
+    rc = 720 - rc - equation_of_time(t)
+    rc = radians(rc / 4 - longitude)
+    return elevation_from_hour_angle(latitude, solar_declination(t), rc)
+
+
+def solar_elevation(latitude, longitude, t = None):
+    '''
+    Calculates the Sun's elevation as apparent
+    from a geographical position
+    
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @param   t:float?         The time in Julian Centuries, `None`
+                              for the current time
+    @return  :float           The Sun's apparent elevation at the specified
+                              time as seen from the specified position,
+                              measured in degrees
+    '''
+    rc = julian_centuries() if t is None else t
+    rc = solar_elevation_from_time(rc, latitude, longitude)
+    return degrees(rc)
+
+
+
+def have_sunrise_and_sunset(latitude, t = None):
+    '''
+    Determine whether solar declination currently is
+    so that there can be sunrises and sunsets. If not,
+    you either have 24-hour daytime or 24-hour nighttime.
+    
+    @param   latitude:float  The latitude in degrees northwards from
+                             the equator, negative for southwards
+    @param   t:float?        The time in Julian Centuries, `None`
+                             for the current time
+    @return                  Whether there can be sunrises and
+                             sunsets where you are located
+    '''
+    t = julian_centuries() if t is None else t
+    d = degrees(solar_declination(t))
+    ## Convert everything to the Northern hemisphere
+    latitude = abs(latitude)
+    if d >= 0:
+        ## Northern summer
+        return -90 + d < latitude < 90 - d
+    else:
+        ## Northern winter
+        return -90 - d < latitude < 90 + d
+
+
+def is_summer(latitude, t = None):
+    '''
+    Determine whether it is summer
+    
+    @param   latitude:float  The latitude in degrees northwards from
+                             the equator, negative for southwards
+    @param   t:float?        The time in Julian Centuries, `None`
+                             for the current time
+    @return                  Whether it is summer on the hemisphere
+                             you are located on
+    '''
+    t = julian_centuries() if t is None else t
+    d = solar_declination(t)
+    return (d > 0) == (latitude > 0)
+
+
+def is_winter(latitude, t = None):
+    '''
+    Determine whether it is winter
+    
+    @param   latitude:float  The latitude in degrees northwards from
+                             the equator, negative for southwards
+    @param   t:float?        The time in Julian Centuries, `None`
+                             for the current time
+    @return                  Whether it is winter on the hemisphere
+                             you are located on
+    '''
+    t = julian_centuries() if t is None else t
+    d = solar_declination(t)
+    return not ((d > 0) == (latitude > 0))
+
+
+
+def solar_prediction(delta, requested, fun, epsilon = 0.000001, span = 0.01, t = None):
+    '''
+    Predict the time point of the next or previous
+    time an arbitrary condition is meet
+    
+    @param   delta:float          Iteration step size, negative for past
+                                  event, positive for future event
+    @param   requested:float      The value returned by `fun` for which to
+                                  calculate the time point of occurrence
+    @param   fun:(t:float)→float  Function that calculate the data of interest
+    @param   epsilon:float        The tolerance for the result
+    @param   span:float           The number of Julian Centuries (0,01 for
+                                  one year) to restrict the search to
+    @param   t:float?             The time in Julian Centuries, `None` for
+                                  the current time
+    @return  :float?              The calculated time point, `None` if none
+                                  were found within the specified time span
+    '''
+    fun_ = lambda t : fun(t) - requested
+    t = julian_centuries() if t is None else t
+    t1 = t2 = t
+    v1 = v0 = fun_(t)
+    
+    # Predicate time point to within a small time span
+    while True:
+        if abs(t2 - t) > span:
+            return None
+        t2 += delta
+        v2 = fun_(t2)
+        if (v1 <= 0 <= v2) or ((0 >= v1 >= v2) and (0 <= v0)):
+            break
+        if (v1 >= 0 >= v2) or ((0 <= v1 <= v2) and (0 >= v0)):
+            break
+        t1 = t2
+        v2 = v1
+    
+    # Binary search the small time span for the exact time point
+    for _itr in range(1000):
+        tm = (t1 + t2) / 2
+        v1 = fun_(t1)
+        v2 = fun_(t2)
+        vm = fun_(tm)
+        if abs(v1 - v2) < epsilon:
+            return tm
+        if v1 < v2:
+            if 0 < vm:
+                t2 = tm
+            else:
+                t1 = tm
+        elif v1 > v2:
+            if 0 > vm:
+                t2 = tm
+            else:
+                t1 = tm
+    return tm
+
+
+
+def future_past_equinox(delta, t = None):
+    '''
+    Predict the time point of the next or previous equinox
+    
+    @param   delta:float  Iteration step size, negative for
+                          past event, positive for future event
+    @param   t:float?     The time in Julian Centuries, `None`
+                          for the current time
+    @return  :float       The calculated time point
+    '''
+    return solar_prediction(delta, 0, solar_declination, t = t)
+
+
+def future_equinox(t = None):
+    '''
+    Predict the time point of the next equinox
+    
+    @param   t:float?  The time in Julian Centuries, `None`
+                       for the current time
+    @return  :float    The calculated time point
+    '''
+    return future_past_equinox(0.01 / 2000, t)
+    
+
+def past_equinox(t = None):
+    '''
+    Predict the time point of the previous equinox
+    
+    @param   t:float?  The time in Julian Centuries, `None`
+                       for the current time
+    @return  :float    The calculated time point
+    '''
+    return future_past_equinox(0.01 / -2000, t)
+
+
+
+def future_past_solstice(delta, t = None):
+    '''
+    Predict the time point of the next or previous solstice
+    
+    @param   delta:float  Iteration step size, negative for
+                          past event, positive for future event
+    @param   t:float?     The time in Julian Centuries, `None`
+                          for the current time
+    @return  :float       The calculated time point
+    '''
+    e = 0.00001
+    fun = solar_declination
+    dfun = lambda t : (fun(t + e) - fun(t - e)) / (2 * e)
+    return solar_prediction(delta, 0, dfun, t = t)
+
+
+def future_solstice(t = None):
+    '''
+    Predict the time point of the next solstice
+    
+    @param   t:float?  The time in Julian Centuries,
+                       `None` for the current time
+    @return  :float    The calculated time point
+    '''
+    return future_past_solstice(0.01 / 2000, t)
+    
+
+def past_solstice(t = None):
+    '''
+    Predict the time point of the previous solstice
+    
+    @param   t:float?  The time in Julian Centuries,
+                       `None` for the current time
+    @return  :float    The calculated time point
+    '''
+    return future_past_solstice(0.01 / -2000, t)
+
+
+
+def future_past_elevation(delta, latitude, longitude, elevation, t = None):
+    '''
+    Predict the time point of the next or previous time
+    the Sun reaches or reached a specific elevation
+    
+    @param   delta:float      Iteration step size, negative for past
+                              event, positive for future event
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @param   elevation:float  The elevation of interest
+    @param   t:float?         The time in Julian Centuries, `None`
+                              for the current time
+    @return  :float?          The calculated time point, `None` if
+                              none were found within a year
+    '''
+    fun = lambda t : solar_elevation(latitude, longitude, t)
+    return solar_prediction(delta, elevation, fun, t = t)
+
+
+def future_elevation(latitude, longitude, elevation, t = None):
+    '''
+    Predict the time point of the next time the Sun
+    reaches a specific elevation
+    
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @param   elevation:float  The elevation of interest
+    @param   t:float?         The time in Julian Centuries, `None`
+                              for the current time
+    @return  :float?          The calculated time point, `None` if
+                              none were found within a year
+    '''
+    return future_past_elevation(0.01 / 2000, latitude, longitude, elevation, t)
+    
+
+def past_elevation(latitude, longitude, elevation, t = None):
+    '''
+    Predict the time point of the previous time the Sun
+    reached a specific elevation
+    
+    @param   latitude:float   The latitude in degrees northwards from
+                              the equator, negative for southwards
+    @param   longitude:float  The longitude in degrees eastwards from
+                              Greenwich, negative for westwards
+    @param   elevation:float  The elevation of interest
+    @param   t:float?         The time in Julian Centuries, `None`
+                              for the current time
+    @return  :float?          The calculated time point, `None` if
+                              none were found within a year
+    '''
+    return future_past_elevation(0.01 / -2000, latitude, longitude, elevation, t)
+
+
+
+def future_past_elevation_derivative(delta, latitude, longitude, derivative, t = None):
+    '''
+    Predict the time point of the next or previous time the
+    Sun reaches or reached a specific elevation derivative
+    
+    @param   delta:float       Iteration step size, negative for past
+                               event, positive for future event
+    @param   latitude:float    The latitude in degrees northwards from
+                               the equator, negative for southwards
+    @param   longitude:float   The longitude in degrees eastwards from
+                               Greenwich, negative for westwards
+    @param   derivative:float  The elevation derivative value of interest
+    @param   t:float?          The time in Julian Centuries, `None`
+                               for the current time
+    @return  :float?           The calculated time point, `None` if
+                               none were found within a year
+    '''
+    e = 0.00001
+    fun = lambda t : solar_elevation(latitude, longitude, t)
+    dfun = lambda t : (fun(t + e) - fun(t - e)) / (2 * e)
+    return solar_prediction(delta, derivative, dfun, t = t)
+
+
+def future_elevation_derivative(latitude, longitude, derivative, t = None):
+    '''
+    Predict the time point of the next time the
+    Sun reaches a specific elevation derivative
+    
+    @param   latitude:float    The latitude in degrees northwards from
+                               the equator, negative for southwards
+    @param   longitude:float   The longitude in degrees eastwards from
+                               Greenwich, negative for westwards
+    @param   derivative:float  The elevation derivative value of interest
+    @param   t:float?          The time in Julian Centuries, `None`
+                               for the current time
+    @return  :float?           The calculated time point, `None` if
+                               none were found within a year
+    '''
+    return future_past_elevation_derivative(0.01 / 2000, latitude, longitude, derivative, t)
+    
+
+def past_elevation_derivative(latitude, longitude, derivative, t = None):
+    '''
+    Predict the time point of the previous time
+    the Sun reached a specific elevation derivative
+    
+    @param   latitude:float    The latitude in degrees northwards from
+                               the equator, negative for southwards
+    @param   longitude:float   The longitude in degrees eastwards from
+                               Greenwich, negative for westwards
+    @param   derivative:float  The elevation derivative value of interest
+    @param   t:float?          The time in Julian Centuries, `None`
+                               for the current time
+    @return  :float?           The calculated time point, `None`
+                               if none were found within a year
+    '''
+    return future_past_elevation_derivative(0.01 / -2000, latitude, longitude, derivative, t)
+
+
+
+# TODO: This algorithm is imprecise, gives an incorrent sunrise and I do not fully know its behaviour
+def sunrise_equation(latitude, longitude, t = None):
+    import math
+    # Calculate Julian Cycle
+    j_cent = julian_centuries() if t is None else t
+    j_date = julian_centuries_to_julian_day(j_cent)
+    j_cycle = int(j_date - 2451545.0009 - longitude / 360 + 0.5)
+    
+    # Calculate approximate solar noon and solar man anomaly
+    approx_solar_noon = 451545.0009 + longitude / 360 + j_cycle
+    solar_mean_anomaly = int(357.5291 + 0.98560028 * (j_cycle - 2451545)) % 360
+    
+    # Calculate solar equation of centre
+    equation_of_centre  = 1.9148 * math.sin(1 * solar_mean_anomaly)
+    equation_of_centre += 0.0200 * math.sin(2 * solar_mean_anomaly)
+    equation_of_centre += 0.0003 * math.sin(3 * solar_mean_anomaly)
+    
+    # Calculate solar ecliptic longitude
+    ecliptic_longitude = (solar_mean_anomaly + 102.9372 + equation_of_centre + 180) % 360
+    
+    # Calculate solar transit
+    solar_transit  = approx_solar_noon + 0.0053 * math.sin(solar_mean_anomaly)
+    solar_transit -= 0.0069 * math.sin(2 * ecliptic_longitude)
+    
+    # Calculate solar declination
+    declination = math.asin(math.sin(ecliptic_longitude) * math.sin(radians(23.45)))
+    
+    # Calculate solar hour angle
+    hour_angle  = math.sin(radians(-0.83))
+    hour_angle -= math.sin(latitude) * math.sin(declination)
+    hour_angle /= math.cos(latitude) * math.cos(declination)
+    hour_angle = degrees(math.acos(hour_angle))
+    
+    # Calculate time of sunset and sunrise
+    sunset  = 2451545.0009 + (hour_angle + longitude) / 360
+    sunset += j_cycle + solar_transit - approx_solar_noon
+    sunrise = 2 * solar_transit - sunset
+    
+    # Convert to Julian Centuries
+    return (julian_day_to_julian_centuries(sunset),
+            julian_day_to_julian_centuries(sunrise))
+