#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# Gramps - a GTK+/GNOME based genealogy program
#
# Copyright (C) 2007-2009  B. Malengier
# Copyright (C) 2009  Swoon on bug tracker
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
#


#-------------------------------------------------------------------------
#
# Standard python modules
#
#-------------------------------------------------------------------------
from ..const import GRAMPS_LOCALE as glocale
_ = glocale.translation.gettext
import math

#-------------------------------------------------------------------------
#
# Gramps modules
#
#-------------------------------------------------------------------------


#-------------------------------------------------------------------------
#
# begin localisation part
#
#-------------------------------------------------------------------------

# translation of N/S/E/W, make sure translator understands
degrees = "1"
North = _("%(north_latitude)s N") % {'north_latitude' : degrees}
South = _("%(south_latitude)s S") % {'south_latitude' : degrees}
East = _("%(east_longitude)s E") % {'east_longitude' : degrees}
West = _("%(west_longitude)s W") % {'west_longitude' : degrees}

# extract letters we really need
North = North.replace("1", " ").strip()
South = South.replace("1", " ").strip()
East = East.replace("1", " ").strip()
West = West.replace("1", " ").strip()

# build dictionary with translation en to local language
translate_en_loc = {}
translate_en_loc['N'] = North
translate_en_loc['S'] = South
translate_en_loc['E'] = East
translate_en_loc['W'] = West

# keep translation only if it does not conflict with english
if 'N' == South or 'S' == North or 'E' == West or 'W' == East:
    translate_en_loc['N'] = 'N'
    translate_en_loc['S'] = 'S'
    translate_en_loc['E'] = 'E'
    translate_en_loc['W'] = 'W'
# end localisation part


#------------------
#
# helper functions
#
#------------------

def __convert_structure_to_float(sign, degs, mins=0, secs=0.0):
    """helper function which converts a structure to a nice
    representation
    """
    v = float(degs)
    if mins is not None:
        v += float(mins) / 60.
    if secs is not None:
        v += secs / 3600.
    return -v if sign == "-" else v

def __convert_using_float_repr(stringValue):
    """ helper function that tries to convert the string using the float
    representation
    """
    try:
        v = float(stringValue)
        return v
    except ValueError:
        return None

def __convert_using_colon_repr(stringValue):
    """ helper function that tries to convert the string using the colon
    representation
    """
    if stringValue.find(r':') == -1:
        return None

    l = stringValue.split(':')
    if len(l) < 2 or len(l) > 3:
        return None
    l[0] = l[0].strip()
    # if no characters before ':' nothing useful is input!
    if len(l[0]) == 0:
        return None
    if l[0][0] in ['+', '-']:
        sign = l[0][0]
        l[0] = l[0][1:].strip()
        # regard a second sign as an error
        if l[0][0] in ['+', '-']:
            return None
    else:
        sign = '+'
    try:
        degs = int(l[0])
        if degs < 0:
            return None
    except:
        return None
    try:
        mins = int(l[1])
        if mins < 0 or mins >= 60:
            return None
    except:
        return None
    secs = 0.
    if len(l) == 3:
        try:
            secs = float(l[2])
            if secs < 0. or secs >= 60.:
                return None
        except:
            return None

    return __convert_structure_to_float(sign, degs, mins, secs)

def __convert_using_classic_repr(stringValue, typedeg):
    """helper function that tries to convert the string using the colon
    representation
    """
    if stringValue.find(r'_') != -1:
        return None    # not a valid lat or lon

    #exchange some characters
    stringValue = stringValue.replace('°', r'_')
    #allow to input ° as #, UTF-8 code c2b00a
    stringValue = stringValue.replace('º', r'_')
    #allow to input º as #, UTF-8 code c2b a0a
    stringValue = stringValue.replace(r'#', r'_')
    #allow to input " as ''
    stringValue = stringValue.replace(r"''", r'"')
    #allow some special unicode symbols
    stringValue = stringValue.replace('\u2033', r'"')
    stringValue = stringValue.replace('\u2032', r"'")
    #ignore spaces, a regex with \s* would be better here...
    stringValue = stringValue.replace(r' ', r'')
    stringValue = stringValue.replace(r'\t', r'')

    # get the degrees, must be present
    if stringValue.find(r'_') == -1:
        return None
    l = stringValue.split(r'_')
    if len(l) != 2:
        return None

    try:
        degs = int(l[0])  #degrees must be integer value
        if degs < 0:
            return None
    except:
        return None
    # next: minutes might be present once
    l2 = l[1].split(r"'")
    l3 = l2
    mins = 0
    # See if minutes might be decimal?
    # Then no seconds is supposed to be given
    if l2[0].find(r'.') > 0:
        # Split in integer and decimal parts
        l4 = l2[0].split(r".")
        # Set integer minutes
        l2[0] = l4[0]
        # Convert the decimal part of minutes to seconds
        try:
            lsecs = float('0.' + l4[1]) * 60.0
            # Set the seconds followed by direction letter N/S/W/E
            l2[1] = str(lsecs) +  '"' + l2[1]
        except:
            return None

    if len(l2) > 2:
        return None
    if len(l2) == 2:
        l3 = [l2[1],]
        try:
            mins = int(l2[0]) #minutes must be integer value
            if mins < 0 or mins >= 60:
                return None
        except:
            return None
    # next: seconds might be present once
    l3 = l3[0].split(r'"')
    last = l3[0]
    secs = 0.
    if len(l3) > 2:
        return None
    if len(l3) == 2:
        last = l3[1]
        try:
            secs = float(l3[0])
            if secs < 0. or secs >= 60.:
                return None
        except:
            return None
    # last entry should be the direction
    if typedeg == 'lat':
        if last == 'N':
            sign = '+'
        elif last == 'S':
            sign = '-'
        else:
            return None
    elif typedeg == 'lon':
        if last == 'E':
            sign = '+'
        elif last == 'W':
            sign = '-'
        else:
            return None
    else:
        return None

    return __convert_structure_to_float(sign, degs, mins, secs)

def __convert_using_modgedcom_repr(val, typedeg):
    """ helper function that tries to convert the string using the
    modified GEDCOM representation where direction [NSEW] is appended
    instead of prepended. This particular representation is the result
    of value normalization done on values passed to this function
    """
    if typedeg == 'lat':
        pos = val.find('N')
        if pos >= 0:
            stringValue = val[:pos]
        else:
            pos = val.find('S')
            if pos >= 0:
                stringValue = '-' + val[:pos]
            else:
                return None
    else:
        pos = val.find('E')
        if pos >= 0:
            stringValue = val[:pos]
        else:
            pos = val.find('W')
            if pos >= 0:
                stringValue = '-' + val[:pos]
            else:
                return None
    try:
        v = float(stringValue)
        return v
    except ValueError:
        return None

def __convert_float_val(val, typedeg="lat"):
    # function converting input to float, recognizing decimal input, or
    # degree notation input. Only english input
    # There is no check on maximum/minimum of degree
    # In case of degree minutes seconds direction input,
    # it is checked that degree >0, 0<= minutes <= 60,
    # 0<= seconds <= 60, direction is in the directions dic.

    # format: XX.YYYY
    v = __convert_using_float_repr(val)
    if v is not None:
        return v

    # format: XX:YY:ZZ
    v = __convert_using_colon_repr(val)
    if v is not None:
        return v

    # format: XX° YY' ZZ" [NSWE]
    v = __convert_using_classic_repr(val, typedeg)
    if v is not None:
        return v

    # format XX.YYYY[NSWE]
    v = __convert_using_modgedcom_repr(val, typedeg)
    if v is not None:
        return v

    # no format succeeded
    return None

#-------------------------------------------------------------------------
#
# conversion function
#
#-------------------------------------------------------------------------

def conv_lat_lon(latitude, longitude, format="D.D4"):
    """
    Convert given string latitude and longitude to a required format.

    :param latitude: Latitude
    :type latitude: string
    :param longitude: Longitude
    :type longitude: string
    :param format: Ouput format
    :type format: string
    :returns: a tuple of 2 strings, or a string (for ISO formats). If
              conversion fails: returns: (None, None)  or None (for ISO formats)

    Possible formats:

    =========   ============================================================
    Format      Description
    =========   ============================================================
    'D.D4'      degree notation, 4 decimals
                eg +12.0154 , -124.3647
    'D.D8'      degree notation, 8 decimals (precision like ISO-DMS)
                eg +12.01543265 , -124.36473268
    'DEG'       degree, minutes, seconds notation
                eg 50°52'21.92''N , 124°52'21.92''E ° has UTF-8 code c2b00a
                or N50º52'21.92" , E14º52'21.92"   º has UTF-8 code c2ba0a
                or N50º52.3456' , E14º52.9876' ; decimal minutes, no seconds
    'DEG-:'     degree, minutes, seconds notation with :
                eg -50:52:21.92 , 124:52:21.92
    'ISO-D'     ISO 6709 degree notation i.e. ±DD.DDDD±DDD.DDDD
    'ISO-DM'    ISO 6709 degree, minutes notation
                i.e. ±DDMM.MMM±DDDMM.MMM
    'ISO-DMS'   ISO 6709 degree, minutes, seconds notation
                i.e. ±DDMMSS.SS±DDDMMSS.SS
    'RT90'      Output format for the Swedish coordinate system RT90
    =========   ============================================================

    Some generalities:

    * -90 <= latitude <= +90 with +00 the equator
    * -180 <= longitude < +180 with +000 prime meridian and -180 the 180th
      meridian
    """

    # we start the function changing latitude/longitude in english
    if latitude.find('N') == -1 and latitude.find('S') == -1:
        # entry is not in english, convert to english
        latitude = latitude.replace(translate_en_loc['N'], 'N')
        latitude = latitude.replace(translate_en_loc['S'], 'S')
    if longitude.find('E') == -1 and longitude.find('W') == -1:
        # entry is not in english, convert to english
        longitude = longitude.replace(translate_en_loc['W'], 'W')
        longitude = longitude.replace(translate_en_loc['E'], 'E')

    # take away leading spaces
    latitude = latitude.lstrip()
    longitude = longitude.lstrip()
    # check if first character is alpha i.e. N or S, put it last
    if len(latitude) > 1 and latitude[0].isalpha():
        latitude = latitude[1:] + latitude[0]
    # check if first character is alpha i.e. E or W, put it last
    if len(longitude) > 1 and longitude[0].isalpha():
        longitude = longitude[1:] + longitude[0]

    # convert to float
    lat_float = __convert_float_val(latitude, 'lat')
    lon_float = __convert_float_val(longitude, 'lon')

    # give output (localized if needed)
    if lat_float is None or lon_float is None:
        if format == "ISO-D" or format == "ISO-DM" or format == "ISO-DMS":
            return None
        else:
            return (None, None)
    if lat_float > 90. or lat_float < -90. \
           or lon_float >= 180. or lon_float < -180.:
        if format == "ISO-D" or format == "ISO-DM" or format == "ISO-DMS":
            return None
        else:
            return (None, None)

    if format == "D.D4":
        # correct possible roundoff error
        str_lon = "%.4f" % (lon_float)
        if str_lon == "180.0000":
            str_lon = "-180.0000"
        return ("%.4f" % lat_float, str_lon)

    if format == "D.D8" or format == "RT90":
        # correct possible roundoff error
        str_lon = "%.8f" % (lon_float)
        if str_lon == "180.00000000":
            str_lon = "-180.00000000"
        if format == "RT90":
            tx = __conv_WGS84_SWED_RT90(lat_float, lon_float)
            return ("%i" %  tx[0], "%i" % tx[1])
        else:
            return ("%.8f" % lat_float, str_lon)

    if format == "GEDCOM":
        # The 5.5.1 spec is inconsistent.  Length is supposedly 5 to 8 chars,
        # but the sample values are longer, using up to 6 fraction digits.
        # As a compromise, we will produce up to 6 fraction digits, but only
        # if necessary
        # correct possible roundoff error
        if lon_float >= 0:
            str_lon = "%.6f" % (lon_float)
            if str_lon == "180.000000":
                str_lon = "W180.000000"
            else:
                str_lon = "E" + str_lon
        else:
            str_lon = "W" + "%.6f" % (-lon_float)
        str_lon = str_lon[:-5] + str_lon[-5:].rstrip("0")
        str_lat = ("%s%.6f" % (("N", lat_float) if lat_float >= 0
                               else ("S", -lat_float)))
        str_lat = str_lat[:-5] + str_lat[-5:].rstrip("0")
        return (str_lat, str_lon)

    deg_lat = int(lat_float)
    deg_lon = int(lon_float)
    min_lat = int(60. * (lat_float - float(deg_lat)))
    min_lon = int(60. * (lon_float - float(deg_lon)))
    sec_lat = 3600. * (lat_float - float(deg_lat) - float(min_lat) / 60.)
    sec_lon = 3600. * (lon_float - float(deg_lon) - float(min_lon) / 60.)

    # dump minus sign on all, store minus sign. Carefull: int(-0.8)=0 !!
    if (deg_lat) < 0:
        deg_lat = -1 * deg_lat
    if (min_lat) < 0:
        min_lat = -1 * min_lat
    if (sec_lat) < 0.:
        sec_lat = -1. * sec_lat
    if (deg_lon) < 0:
        deg_lon = -1 * deg_lon
    if (min_lon) < 0:
        min_lon = -1 * min_lon
    if (sec_lon) < 0.:
        sec_lon = -1. * sec_lon
    # keep sign as -1* 0 = +0, so 0°2'S is given correct sign in ISO
    sign_lat = "+"
    dir_lat = ""
    if lat_float >= 0.:
        dir_lat = translate_en_loc['N']
    else:
        dir_lat = translate_en_loc['S']
        sign_lat = "-"
    sign_lon = "+"
    dir_lon = ""
    if lon_float >= 0.:
        dir_lon = translate_en_loc['E']
    else:
        dir_lon = translate_en_loc['W']
        sign_lon = "-"

    if format == "DEG":
        str_lat = ("%d°%02d'%05.2f\"" % (deg_lat, min_lat, sec_lat)) + dir_lat
        str_lon = ("%d°%02d'%05.2f\"" % (deg_lon, min_lon, sec_lon)) + dir_lon
        # correct possible roundoff error in seconds
        if str_lat[-6-len(dir_lat)] == '6':
            if min_lat == 59:
                str_lat = ("%d°%02d'%05.2f\"" % (deg_lat+1, 0, 0.)) + dir_lat
            else:
                str_lat = ("%d°%02d'%05.2f\"" % (deg_lat, min_lat+1, 0.)) \
                          + dir_lat
        if str_lon[-6-len(dir_lon)] == '6':
            if min_lon == 59:
                if deg_lon == 179 and sign_lon == "+":
                    str_lon = ("%d°%02d'%05.2f\"" % (180, 0, 0.)) \
                              + translate_en_loc['W']
                else:
                    str_lon = ("%d°%02d'%05.2f\"" % (deg_lon+1, 0, 0.)) \
                              + dir_lon
            else:
                str_lon = ("%d°%02d'%05.2f\"" % (deg_lon, min_lon+1, 0.)) \
                          + dir_lon

        return  (str_lat, str_lon)

    if format == "DEG-:":
        if sign_lat == "+":
            sign_lat = ""
        sign_lon_h = sign_lon
        if sign_lon == "+":
            sign_lon_h = ""
        str_lat = sign_lat + ("%d:%02d:%05.2f" % (deg_lat, min_lat, sec_lat))
        str_lon = sign_lon_h + ("%d:%02d:%05.2f" % (deg_lon, min_lon, sec_lon))

        # correct possible roundoff error in seconds

        if str_lat[-5] == '6':
            if min_lat == 59:
                str_lat = sign_lat + ("%d:%02d:%05.2f" % (deg_lat+1, 0, 0.))
            else:
                str_lat = sign_lat + \
                          ("%d:%02d:%05.2f" % (deg_lat, min_lat+1, 0.))
        if str_lon[-5] == '6':
            if min_lon == 59:
                if deg_lon == 179 and sign_lon == "+":
                    str_lon = '-' + ("%d:%02d:%05.2f" % (180, 0, 0.))
                else:
                    str_lon = sign_lon_h + \
                              ("%d:%02d:%05.2f" % (deg_lon+1, 0, 0.))
            else:
                str_lon = sign_lon_h + \
                          ("%d:%02d:%05.2f" % (deg_lon, min_lon+1, 0.))

        return (str_lat, str_lon)

    if format == "ISO-D":  # ±DD.DDDD±DDD.DDDD
        str_lon = "%+09.4f" % (lon_float)
        # correct possible roundoff error
        if str_lon == "+180.0000":
            str_lon = "-180.0000"
        return ("%+08.4f" % lat_float) + str_lon

    if format == "ISO-DM":  # ±DDMM.MMM±DDDMM.MMM
        min_fl_lat = float(min_lat)+ sec_lat/60.
        min_fl_lon = float(min_lon)+ sec_lon/60.
        str_lat = sign_lat + ("%02d%06.3f" % (deg_lat, min_fl_lat))
        str_lon = sign_lon + ("%03d%06.3f" % (deg_lon, min_fl_lon))
        # correct possible roundoff error
        if str_lat[3:] == "60.000":
            str_lat = sign_lat + ("%02d%06.3f" % (deg_lat+1, 0.))
        if str_lon[4:] == "60.000":
            if deg_lon == 179 and sign_lon == "+":
                str_lon = "-" + ("%03d%06.3f" % (180, 0.))
            else:
                str_lon = sign_lon + ("%03d%06.3f" % (deg_lon+1, 0.))
        return str_lat + str_lon

    if format == "ISO-DMS":  # ±DDMMSS.SS±DDDMMSS.SS
        str_lat = sign_lat + ("%02d%02d%06.3f" % (deg_lat, min_lat, sec_lat))
        str_lon = sign_lon + ("%03d%02d%06.3f" % (deg_lon, min_lon, sec_lon))
        # correct possible roundoff error
        if str_lat[5:] == "60.000":
            if min_lat == 59:
                str_lat = sign_lat + ("%02d%02d%06.3f" % (deg_lat+1, 0, 0.))
            else:
                str_lat = sign_lat + \
                          ("%02d%02d%06.3f" % (deg_lat, min_lat +1, 0.))
        if str_lon[6:] == "60.000":
            if min_lon == 59:
                if deg_lon == 179 and sign_lon == "+":
                    str_lon = "-" + ("%03d%02d%06.3f" % (180, 0, 0))
                else:
                    str_lon = sign_lon + \
                              ("%03d%02d%06.3f" % (deg_lon+1, 0, 0.))
            else:
                str_lon = sign_lon + \
                          ("%03d%02d%06.3f" % (deg_lon, min_lon+1, 0.))
        return str_lat + str_lon



def atanh(x):
    """arctangent hyperbolicus"""
    return 1.0/2.0*math.log((1.0 + x)/(1.0 -x))


def __conv_WGS84_SWED_RT90(lat, lon):
    """
    Input is lat and lon as two float numbers
    Output is X and Y coordinates in RT90
    as a tuple of float numbers

    The code below converts to/from the Swedish RT90 koordinate
    system. The converion functions use "Gauss Conformal Projection
    (Transverse Marcator)" Krüger Formulas.
    The constanst are for the Swedish RT90-system.
    With other constants the conversion should be useful for
    other geographical areas.

    """
    # Some constants used for conversion to/from Swedish RT90
    f = 1.0/298.257222101
    e2 = f*(2.0-f)
    n = f/(2.0-f)
    L0 = math.radians(15.8062845294)   # 15 deg 48 min 22.624306 sec
    k0 = 1.00000561024
    a = 6378137.0   # meter
    at = a/(1.0+n)*(1.0+ 1.0/4.0* pow(n, 2)+1.0/64.0*pow(n, 4))
    FN = -667.711 # m
    FE = 1500064.274 # m

    #the conversion
    lat_rad = math.radians(lat)
    lon_rad = math.radians(lon)
    A = e2
    B = 1.0/6.0*(5.0*pow(e2, 2) - pow(e2, 3))
    C = 1.0/120.0*(104.0*pow(e2, 3) - 45.0*pow(e2, 4))
    D = 1.0/1260.0*(1237.0*pow(e2, 4))
    DL = lon_rad - L0
    E = A + B*pow(math.sin(lat_rad), 2) + \
            C*pow(math.sin(lat_rad), 4) + \
            D*pow(math.sin(lat_rad), 6)
    psi = lat_rad - math.sin(lat_rad)*math.cos(lat_rad)*E
    xi = math.atan2(math.tan(psi), math.cos(DL))
    eta = atanh(math.cos(psi)*math.sin(DL))
    B1 = 1.0/2.0*n - 2.0/3.0*pow(n, 2) + 5.0/16.0*pow(n, 3) + \
                     41.0/180.0*pow(n, 4)
    B2 = 13.0/48.0*pow(n, 2) - 3.0/5.0*pow(n, 3) + 557.0/1440.0*pow(n, 4)
    B3 = 61.0/240.0*pow(n, 3) - 103.0/140.0*pow(n, 4)
    B4 = 49561.0/161280.0*pow(n, 4)
    X = xi + B1*math.sin(2.0*xi)*math.cosh(2.0*eta) + \
             B2*math.sin(4.0*xi)*math.cosh(4.0*eta) + \
             B3*math.sin(6.0*xi)*math.cosh(6.0*eta) + \
             B4*math.sin(8.0*xi)*math.cosh(8.0*eta)
    Y = eta + B1*math.cos(2.0*xi)*math.sinh(2.0*eta) + \
              B2*math.cos(4.0*xi)*math.sinh(4.0*eta) + \
              B3*math.cos(6.0*xi)*math.sinh(6.0*eta) + \
              B4*math.cos(8.0*xi)*math.sinh(8.0*eta)
    X = X*k0*at + FN
    Y = Y*k0*at + FE
    return (X, Y)

def __conv_SWED_RT90_WGS84(X, Y):
    """
    Input is X and Y coordinates in RT90 as float
    Output is lat and long in degrees, float as tuple
    """
    # Some constants used for conversion to/from Swedish RT90
    f = 1.0/298.257222101
    e2 = f*(2.0-f)
    n = f/(2.0-f)
    L0 = math.radians(15.8062845294)   # 15 deg 48 min 22.624306 sec
    k0 = 1.00000561024
    a = 6378137.0   # meter
    at = a/(1.0+n)*(1.0+ 1.0/4.0* pow(n, 2)+1.0/64.0*pow(n, 4))
    FN = -667.711 # m
    FE = 1500064.274 # m

    xi = (X - FN)/(k0*at)
    eta = (Y - FE)/(k0*at)
    D1 = 1.0/2.0*n - 2.0/3.0*pow(n, 2) + 37.0/96.0*pow(n, 3) - \
         1.0/360.0*pow(n, 4)
    D2 = 1.0/48.0*pow(n, 2) + 1.0/15.0*pow(n, 3) - 437.0/1440.0*pow(n, 4)
    D3 = 17.0/480.0*pow(n, 3) - 37.0/840.0*pow(n, 4)
    D4 = 4397.0/161280.0*pow(n, 4)
    xip = xi - D1*math.sin(2.0*xi)*math.cosh(2.0*eta) - \
               D2*math.sin(4.0*xi)*math.cosh(4.0*eta) - \
               D3*math.sin(6.0*xi)*math.cosh(6.0*eta) - \
               D4*math.sin(8.0*xi)*math.cosh(8.0*eta)
    etap = eta - D1*math.cos(2.0*xi)*math.sinh(2.0*eta) - \
                 D2*math.cos(4.0*xi)*math.sinh(4.0*eta) - \
                 D3*math.cos(6.0*xi)*math.sinh(6.0*eta) - \
                 D4*math.cos(8.0*xi)*math.sinh(8.0*eta)
    psi = math.asin(math.sin(xip)/math.cosh(etap))
    DL = math.atan2(math.sinh(etap), math.cos(xip))
    LON = L0 + DL
    A = e2 + pow(e2, 2) + pow(e2, 3) + pow(e2, 4)
    B = -1.0/6.0*(7.0*pow(e2, 2) + 17*pow(e2, 3) + 30*pow(e2, 4))
    C = 1.0/120.0*(224.0*pow(e2, 3) + 889.0*pow(e2, 4))
    D = 1.0/1260.0*(4279.0*pow(e2, 4))
    E = A + B*pow(math.sin(psi), 2) + \
            C*pow(math.sin(psi), 4) + \
            D*pow(math.sin(psi), 6)
    LAT = psi + math.sin(psi)*math.cos(psi)*E
    LAT = math.degrees(LAT)
    LON = math.degrees(LON)
    return LAT, LON


#-------------------------------------------------------------------------
#
# For Testing the convert function in this module, apply it as a script:
#     ==> in command line do "python PlaceUtils.py"
#
#-------------------------------------------------------------------------

if __name__ == '__main__':
    def test_formats_success(lat1, lon1, text=''):
        format0 = "D.D4"
        format1 = "D.D8"
        format2 = "DEG"
        format3 = "DEG-:"
        format4 = "ISO-D"
        format5 = "ISO-DM"
        format6 = "ISO-DMS"
        format7 = "RT90"
        format8 = "GEDCOM"
        print("Testing conv_lat_lon function, "+text+':')
        res1, res2 = conv_lat_lon(lat1, lon1, format0)
        print(lat1, lon1, "in format", format0, "is   ", res1, res2)
        res1, res2 = conv_lat_lon(lat1, lon1, format1)
        print(lat1, lon1, "in format", format1, "is   ", res1, res2)
        res1, res2 = conv_lat_lon(lat1, lon1, format2)
        print(lat1, lon1, "in format", format2, "is    ", res1, res2)
        res1, res2 = conv_lat_lon(lat1, lon1, format3)
        print(lat1, lon1, "in format", format3, "is  ", res1, res2)
        res = conv_lat_lon(lat1, lon1, format4)
        print(lat1, lon1, "in format", format4, "is ", res)
        res = conv_lat_lon(lat1, lon1, format5)
        print(lat1, lon1, "in format", format5, "is", res)
        res = conv_lat_lon(lat1, lon1, format6)
        print(lat1, lon1, "in format", format6, "is", res)
        res1, res2 = conv_lat_lon(lat1, lon1, format7)
        print(lat1, lon1, "in format", format7, "is", res1, res2, "\n")
        res1, res2 = conv_lat_lon(lat1, lon1, format8)
        print(lat1, lon1, "in format", format8, "is", res1, res2, "\n")

    def test_formats_fail(lat1, lon1, text=''):
        print("This test should make conv_lat_lon function fail, %s:") % text
        res1, res2 = conv_lat_lon(lat1, lon1)
        print(lat1, lon1, " fails to convert, result=", res1, res2, "\n")

    def test_RT90_conversion():
        """
        a given lat/lon is converted to RT90 and back as a test:
        """
        la = 59.0 + 40.0/60. + 9.09/3600.0
        lo = 12.0 + 58.0/60.0 + 57.74/3600.0
        x, y = __conv_WGS84_SWED_RT90(la, lo)
        lanew, lonew = __conv_SWED_RT90_WGS84(x, y)
        assert math.fabs(lanew - la) < 1e-6, math.fabs(lanew - la)
        assert math.fabs(lonew - lo) < 1e-6, math.fabs(lonew - lo)

    lat, lon = '50.849888888888', '2.885897222222'
    test_formats_success(lat, lon)
    lat, lon = ' 50°50\'59.60"N', '  2°53\'9.23"E'
    test_formats_success(lat, lon)
    lat, lon = ' 50 : 50 : 59.60 ', ' -2:53 : 9.23   '
    test_formats_success(lat, lon)
    lat, lon = ' dummy', '  2#53 \' 9.23  "  E '
    test_formats_fail(lat, lon)
    lat, lon = ' 50:50: 59.60', '  d u m my'
    test_formats_fail(lat, lon)
    lat, lon = ' 50°59.60"N', '  2°53\'E'
    test_formats_success(lat, lon)
    lat, lon = ' 11° 11\' 11" N, 11° 11\' 11" O', ' '
    test_formats_fail(lat, lon)
    # very small negative
    lat, lon = '-0.00006', '-0.00006'
    test_formats_success(lat, lon)
    # missing direction N/S
    lat, lon = ' 50°59.60"', '  2°53\'E'
    test_formats_fail(lat, lon)
    # wrong direction on latitude
    lat, lon = ' 50°59.60"E', '  2°53\'N'
    test_formats_fail(lat, lon)
    # same as above
    lat, lon = ' 50°59.99"E', '  2°59\'59.99"N'
    test_formats_fail(lat, lon)
    # test precision
    lat, lon = ' 50°59.99"S', '  2°59\'59.99"E'
    test_formats_success(lat, lon)
    lat, lon = 'N50.849888888888', 'E2.885897222222'
    test_formats_success(lat, lon)
    # to large value of lat
    lat, lon = '90.849888888888', '2.885897222222'
    test_formats_fail(lat, lon)
    # extreme values allowed
    lat, lon = '90', '-180'
    test_formats_success(lat, lon)
    # extreme values allowed
    lat, lon = '90° 00\' 00.00" S ', '179° 59\'59.99"W'
    test_formats_success(lat, lon)
    # extreme value not allowed
    lat, lon = '90° 00\' 00.00" N', '180° 00\'00.00" E'
    test_formats_fail(lat, lon)
    # extreme values allowed
    lat, lon = '90: 00: 00.00 ', '-179: 59:59.99'
    test_formats_success(lat, lon)
    # extreme value not allowed
    lat, lon = '90° 00\' 00.00" N', '180:00:00.00'
    test_formats_fail(lat, lon)
    # extreme values not allowed
    lat, lon = '90', '180'
    test_formats_fail(lat, lon)
    lat, lon = ' 89°59\'60"N', '  2°53\'W'
    test_formats_fail(lat, lon)
    lat, lon = ' 89°60\'00"N', '  2°53\'W'
    test_formats_fail(lat, lon)
    lat, lon = ' 89.1°40\'00"N', '  2°53\'W'
    test_formats_fail(lat, lon)
    lat, lon = ' 89°40\'00"N', '  2°53.1\'W'
    test_formats_fail(lat, lon)
    lat, lon = '0', '0'
    test_formats_success(lat, lon,
                         "Special 0 value, crossing 0-meridian and equator")
    # small values close to equator
    lat, lon = ' 1°1"N', '  1°1\'E'
    test_formats_success(lat, lon)
    # roundoff
    lat, lon = ' 1°59.999"N', '  1°59.999"E'
    test_formats_success(lat, lon, 'Examples of round off and how it behaves')
    lat, lon = ' 1°59\'59.9999"N', '  1°59\'59.9999"E'
    test_formats_success(lat, lon, 'Examples of round off and how it behaves')
    lat, lon = '89°59\'59.9999"S', '179°59\'59.9999"W'
    test_formats_success(lat, lon, 'Examples of round off and how it behaves')
    lat, lon = '89°59\'59.9999"N', '179°59\'59.9999"E'
    test_formats_success(lat, lon, 'Examples of round off and how it behaves')
    #insane number of decimals:
    lat, lon = '89°59\'59.99999999"N', '179°59\'59.99999999"E'
    test_formats_success(lat, lon, 'Examples of round off and how it begaves')
    #recognise '' as seconds "
    lat, lon = '89°59\'59.99\'\' N', '179°59\'59.99\'\'E'
    test_formats_success(lat, lon, "input \" as ''")
    #test localisation of , and . as delimiter
    lat, lon = '50.849888888888', '2,885897222222'
    test_formats_success(lat, lon, 'localisation of . and , ')
    lat, lon = '89°59\'59.9999"S', '179°59\'59,9999"W'
    test_formats_success(lat, lon, 'localisation of . and , ')
    lat, lon = '89°59\'1.599,999"S', '179°59\'59,9999"W'
    test_formats_fail(lat, lon, 'localisation of . and , ')
    #rest
    lat, lon = '81.2', '-182.3'
    test_formats_fail(lat, lon)
    lat, lon = '-91.2', '-1'
    test_formats_fail(lat, lon)
    lat, lon = '++50:10:1', '2:1:2'
    test_formats_fail(lat, lon)
    lat, lon = '-50:10:1', '-+2:1:2'
    test_formats_success(lat, lon)
    lat, lon = '-50::1', '-2:1:2'
    test_formats_fail(lat, lon)
    lat, lon = '- 50  : 2 : 1 ', '-2:1:2'
    test_formats_success(lat, lon)
    lat, lon = '+ 50:2 :  1', '-2:1:2'
    test_formats_success(lat, lon)
    lat, lon = '+50:', '-2:1:2'
    test_formats_fail(lat, lon)
    lat, lon = '+50:1', '-2:1:2'
    test_formats_success(lat, lon)
    lat, lon = '+50: 0 : 1 : 1', '-2:1:2'
    test_formats_fail(lat, lon)
    lat, lon = '+61° 43\' 60.00"', '+17° 7\' 60.00"'
    test_formats_fail(lat, lon)
    lat, lon = '+61° 44\' 00.00"N', '+17° 8\' 00.00"E'
    test_formats_success(lat, lon)
    lat, lon = ': 0 : 1 : 1', ':1:2'
    test_formats_fail(lat, lon)
    lat, lon = 'N 50º52\'21.92"', 'E 124º52\'21.92"'
    test_formats_success(lat, lon,
                         'New format with N/E first and another º - character')
    lat, lon = 'S 50º52\'21.92"', 'W 124º52\'21.92"'
    test_formats_success(lat, lon,
                         'New format with S/W first and another º - character')

    test_RT90_conversion()
