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                # -*- coding: utf-8 -*-  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """This module contains helper functions used by :class:`~apexpy.Apex`."""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import datetime as dt  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import numpy as np  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import time  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def set_array_float(in_val):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """Set array data type to float.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    in_val : any  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        Input value, only modified if it is a np.ndarray  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Returns  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    -------  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    out_val : any  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        Output value, if `in_val` was an array, `out_val` will be an array of  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        type `np.float64`.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    if isinstance(in_val, np.ndarray):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        out_val = in_val.astype(np.float64)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    else:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        out_val = in_val  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    return out_val  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def checklat(lat, name='lat'):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """Makes sure the latitude is inside [-90, 90], clipping close values  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    (tolerance 1e-4).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    lat : array-like  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        latitude  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    name : str, optional  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        parameter name to use in the exception message  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    lat : ndarray or float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Same as input where values just outside the range have been  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        clipped to [-90, 90]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Raises  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ValueError  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        if any values are too far outside the range [-90, 90]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    if np.any(np.abs(lat) > 90 + 1e-5):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        raise ValueError('{:} must be in [-90, 90]'.format(name)) | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return np.clip(lat, -90.0, 90.0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def getsinIm(alat):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """Computes sinIm from modified apex latitude.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    alat : array-like  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Modified apex latitude  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    sinIm : ndarray or float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    alat = np.float64(alat)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return 2 * np.sin(np.radians(alat)) / np.sqrt(4 - 3  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                                                  * np.cos(np.radians(alat))**2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def getcosIm(alat):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """Computes cosIm from modified apex latitude.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    alat : array-like  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Modified apex latitude  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    cosIm : ndarray or float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    alat = np.float64(alat)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return np.cos(np.radians(alat)) / np.sqrt(4 - 3  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                                              * np.cos(np.radians(alat))**2)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def toYearFraction(date):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """Converts :class:`datetime.date` or :class:`datetime.datetime` to decimal  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    year.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    date : :class:`datetime.date` or :class:`datetime.datetime`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Input date or datetime object  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    year : float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Decimal year  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Notes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    -----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    The algorithm is taken from http://stackoverflow.com/a/6451892/2978652  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    def sinceEpoch(date):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        """returns seconds since epoch"""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return time.mktime(date.timetuple())  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    year = date.year  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    startOfThisYear = dt.datetime(year=year, month=1, day=1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    startOfNextYear = dt.datetime(year=year + 1, month=1, day=1)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    yearElapsed = sinceEpoch(date) - sinceEpoch(startOfThisYear)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    yearDuration = sinceEpoch(startOfNextYear) - sinceEpoch(startOfThisYear)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    fraction = yearElapsed / yearDuration  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    year += fraction  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return year  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def gc2gdlat(gclat):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                                     | 
                
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                    """Converts geocentric latitude to geodetic latitude using WGS84.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                    ---------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                    gclat : array-like  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                        Geocentric latitude  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                    gdlat : ndarray or float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                        Geodetic latitude  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                    WGS84_e2 = 0.006694379990141317  # WGS84 first eccentricity squared  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                    return np.rad2deg(-np.arctan(np.tan(np.deg2rad(gclat)) / (WGS84_e2 - 1)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                def subsol(datetime):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                    """Finds subsolar geocentric latitude and longitude.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                    datetime : :class:`datetime.datetime` or :class:`numpy.ndarray[datetime64]`  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                        Date and time in UTC (naive objects are treated as UTC)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                    -------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                    sbsllat : float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                        Latitude of subsolar point  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                    sbsllon : float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                        Longitude of subsolar point  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    Notes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                    -----  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                    Based on formulas in Astronomical Almanac for the year 1996, p. C24.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                    (U.S. Government Printing Office, 1994). Usable for years 1601-2100,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                    inclusive. According to the Almanac, results are good to at least 0.01  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                    degree latitude and 0.025 degrees longitude between years 1950 and 2050.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                    Accuracy for other years has not been tested. Every day is assumed to have  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                    exactly 86400 seconds; thus leap seconds that sometimes occur on December  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                    31 are ignored (their effect is below the accuracy threshold of the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                    algorithm).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                    After Fortran code by A. D. Richmond, NCAR. Translated from IDL  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                    by K. Laundal.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                    # Convert to year, day of year and seconds since midnight  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                    if isinstance(datetime, dt.datetime):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                        year = np.asanyarray([datetime.year])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                        doy = np.asanyarray([datetime.timetuple().tm_yday])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                        ut = np.asanyarray([datetime.hour * 3600 + datetime.minute * 60  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                                            + datetime.second + datetime.microsecond / 1.0e6])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                    elif isinstance(datetime, np.ndarray):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                        # This conversion works for datetime of wrong precision or unit epoch  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                        times = datetime.astype('datetime64[us]') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                        year_floor = times.astype('datetime64[Y]') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                        day_floor = times.astype('datetime64[D]') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                        year = year_floor.astype(int) + 1970  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                        doy = (day_floor - year_floor).astype(int) + 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                        ut = (times.astype('datetime64[us]') - day_floor).astype(float) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                        ut /= 1e6  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                    else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                        raise ValueError("input must be datetime.datetime or numpy array") | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                    if not (np.all(1601 <= year) and np.all(year <= 2100)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                        raise ValueError('Year must be in [1601, 2100]') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                    yr = year - 2000  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                    nleap = np.floor((year - 1601.0) / 4.0).astype(int)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                    nleap -= 99  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                    mask_1900 = year <= 1900  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                    if np.any(mask_1900):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                        ncent = np.floor((year[mask_1900] - 1601.0) / 100.0).astype(int)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                        ncent = 3 - ncent  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                        nleap[mask_1900] = nleap[mask_1900] + ncent  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                    l0 = -79.549 + (-0.238699 * (yr - 4.0 * nleap) + 3.08514e-2 * nleap)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                    g0 = -2.472 + (-0.2558905 * (yr - 4.0 * nleap) - 3.79617e-2 * nleap)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                    # Days (including fraction) since 12 UT on January 1 of IYR:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                    df = (ut / 86400.0 - 1.5) + doy  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    224
                 | 
                                    
                                                     | 
                
                 | 
                    # Mean longitude of Sun:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                    lmean = l0 + 0.9856474 * df  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
                 | 
                                    
                                                     | 
                
                 | 
                    # Mean anomaly in radians:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                    grad = np.radians(g0 + 0.9856003 * df)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                    # Ecliptic longitude:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                    lmrad = np.radians(lmean + 1.915 * np.sin(grad)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                                       + 0.020 * np.sin(2.0 * grad))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                    sinlm = np.sin(lmrad)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                    # Obliquity of ecliptic in radians:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                    epsrad = np.radians(23.439 - 4e-7 * (df + 365 * yr + nleap))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                    # Right ascension:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                    alpha = np.degrees(np.arctan2(np.cos(epsrad) * sinlm, np.cos(lmrad)))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                    # Declination, which is also the subsolar latitude:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                    sslat = np.degrees(np.arcsin(np.sin(epsrad) * sinlm))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                    # Equation of time (degrees):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                    etdeg = lmean - alpha  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                    nrot = np.round(etdeg / 360.0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                    etdeg = etdeg - 360.0 * nrot  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                    # Subsolar longitude calculation. Earth rotates one degree every 240 s.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                    sslon = 180.0 - (ut / 240.0 + etdeg)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                    nrot = np.round(sslon / 360.0)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                    sslon = sslon - 360.0 * nrot  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                    # Return a single value from the output if the input was a single value  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    255
                 | 
                                    
                                                     | 
                
                 | 
                    if isinstance(datetime, dt.datetime):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                        return sslat[0], sslon[0]  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    257
                 | 
                                    
                                                     | 
                
                 | 
                    return sslat, sslon  | 
            
            
                                                        
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                 |