File: __init__.py

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"""
Pyrex wrapper to provide python interfaces to
PROJ.4 (http://proj.maptools.org) functions.

Performs cartographic transformations and geodetic computations.

The Proj class can convert from geographic (longitude,latitude)
to native map projection (x,y) coordinates and vice versa, or
from one map projection coordinate system directly to another.

The Geod class can perform forward and inverse geodetic, or
Great Circle, computations.  The forward computation involves
determining latitude, longitude and back azimuth of a terminus
point given the latitude and longitude of an initial point, plus
azimuth and distance. The inverse computation involves
determining the forward and back azimuths and distance given the
latitudes and longitudes of an initial and terminus point.

Input coordinates can be given as python arrays, lists/tuples,
scalars or numpy/Numeric/numarray arrays. Optimized for objects
that support the Python buffer protocol (regular python and
numpy array objects).

Download: http://code.google.com/p/pyproj/downloads/list

Requirements: python 2.4 or higher.

Example scripts are in 'test' subdirectory of source distribution.
The 'test()' function will run the examples in the docstrings.

Contact:  Jeffrey Whitaker <jeffrey.s.whitaker@noaa.gov

copyright (c) 2006 by Jeffrey Whitaker.

Permission to use, copy, modify, and distribute this software
and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all
copies and that both the copyright notice and this permission
notice appear in supporting documentation. THE AUTHOR DISCLAIMS
ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT
SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT OR
CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. """

from _proj import Proj as _Proj
from _geod import Geod as _Geod
from _proj import _transform
from _proj import __version__
from _proj import set_datapath
from array import array
from types import TupleType, ListType, NoneType
import os
#import numpy as np

pyproj_datadir = "/usr/share/proj/"
set_datapath(pyproj_datadir)

class Proj(_Proj):
    """
    performs cartographic transformations (converts from
    longitude,latitude to native map projection x,y coordinates and
    vice versa) using proj (http://proj.maptools.org/)

    A Proj class instance is initialized with proj map projection
    control parameter key/value pairs. The key/value pairs can
    either be passed in a dictionary, or as keyword arguments,
    or as a proj4 string (compatible with the proj command). See
    http://www.remotesensing.org/geotiff/proj_list for examples of
    key/value pairs defining different map projections.

    Calling a Proj class instance with the arguments lon, lat will
    convert lon/lat (in degrees) to x/y native map projection
    coordinates (in meters).  If optional keyword 'inverse' is True
    (default is False), the inverse transformation from x/y to
    lon/lat is performed. If optional keyword 'radians' is True
    (default is False) lon/lat are interpreted as radians instead of
    degrees. If optional keyword 'errcheck' is True (default is
    False) an exception is raised if the transformation is invalid.
    If errcheck=False and the transformation is invalid, no
    exception is raised and 1.e30 is returned. If the optional keyword
    'preserve_units' is True, the units in map projection coordinates
    are not forced to be meters.

    Works with numpy and regular python array objects, python
    sequences and scalars.
    """

    def __new__(self, projparams=None, preserve_units=False, **kwargs):
        """
        initialize a Proj class instance.

        Proj4 projection control parameters must either be given in a
        dictionary 'projparams' or as keyword arguments. See the proj
        documentation (http://proj.maptools.org) for more information
        about specifying projection parameters.

        Example usage:

        >>> from pyproj import Proj
        >>> p = Proj(proj='utm',zone=10,ellps='WGS84') # use kwargs
        >>> x,y = p(-120.108, 34.36116666)
        >>> print 'x=%9.3f y=%11.3f' % (x,y)
        x=765975.641 y=3805993.134
        >>> print 'lon=%8.3f lat=%5.3f' % p(x,y,inverse=True)
        lon=-120.108 lat=34.361
        >>> # do 3 cities at a time in a tuple (Fresno, LA, SF)
        >>> lons = (-119.72,-118.40,-122.38)
        >>> lats = (36.77, 33.93, 37.62 )
        >>> x,y = p(lons, lats)
        >>> print 'x: %9.3f %9.3f %9.3f' % x
        x: 792763.863 925321.537 554714.301
        >>> print 'y: %9.3f %9.3f %9.3f' % y
        y: 4074377.617 3763936.941 4163835.303
        >>> lons, lats = p(x, y, inverse=True) # inverse transform
        >>> print 'lons: %8.3f %8.3f %8.3f' % lons
        lons: -119.720 -118.400 -122.380
        >>> print 'lats: %8.3f %8.3f %8.3f' % lats
        lats:   36.770   33.930   37.620
        >>> p2 = Proj('+proj=utm +zone=10 +ellps=WGS84') # use proj4 string
        >>> x,y = p2(-120.108, 34.36116666)
        >>> print 'x=%9.3f y=%11.3f' % (x,y)
        x=765975.641 y=3805993.134
        >>> p = Proj(init="epsg:32667")
        >>> print 'x=%12.3f y=%12.3f (meters)' % p(-114.057222, 51.045)
        x=-1783486.760 y= 6193833.196 (meters)
        >>> p = Proj("+init=epsg:32667",preserve_units=True)
        >>> print 'x=%12.3f y=%12.3f (feet)' % p(-114.057222, 51.045)
        x=-5851322.810 y=20320934.409 (feet)
        """
        # if projparams is None, use kwargs.
        if projparams is None:
            if len(kwargs) == 0:
                raise RuntimeError('no projection control parameters specified')
            else:
                projstring = _dict2string(kwargs)
        elif type(projparams) == str:
            # if projparams is a string, interpret as a proj4 init string.
            projstring = projparams
        else: # projparams a dict
            projstring = _dict2string(projparams)
        # make sure units are meters if preserve_units is False.
        if not projstring.count('+units=') and not preserve_units:
            projstring = '+units=m '+projstring
        else:
            kvpairs = []
            for kvpair in projstring.split():
                if kvpair.startswith('+units') and not preserve_units:
                    k,v = kvpair.split('=')
                    kvpairs.append(k+'=m ')
                else:
                    kvpairs.append(kvpair+' ')
            projstring = ''.join(kvpairs)
        return _Proj.__new__(self, projstring)

    def __call__(self, *args, **kw):
    #,lon,lat,inverse=False,radians=False,errcheck=False):
        """
        Calling a Proj class instance with the arguments lon, lat will
        convert lon/lat (in degrees) to x/y native map projection
        coordinates (in meters).  If optional keyword 'inverse' is True
        (default is False), the inverse transformation from x/y to
        lon/lat is performed.  If optional keyword 'radians' is True
        (default is False) the units of lon/lat are radians instead of
        degrees. If optional keyword 'errcheck' is True (default is
        False) an exception is raised if the transformation is invalid.
        If errcheck=False and the transformation is invalid, no
        exception is raised and 1.e30 is returned.

        Instead of calling with lon, lat, a single ndarray of
        shape n,2 may be used, and one of the same shape will
        be returned; this is more efficient.

        Inputs should be doubles (they will be cast to doubles if they
        are not, causing a slight performance hit).

        Works with numpy and regular python array objects, python
        sequences and scalars, but is fastest for array objects.
        """
        inverse = kw.get('inverse', False)
        radians = kw.get('radians', False)
        errcheck = kw.get('errcheck', False)
        #if len(args) == 1:
        #    latlon = np.array(args[0], copy=True,
        #                      order='C', dtype=float, ndmin=2)
        #    if inverse:
        #        _Proj._invn(self, latlon, radians=radians, errcheck=errcheck)
        #    else:
        #        _Proj._fwdn(self, latlon, radians=radians, errcheck=errcheck)
        #    return latlon
        lon, lat = args
        # process inputs, making copies that support buffer API.
        inx, xisfloat, xislist, xistuple = _copytobuffer(lon)
        iny, yisfloat, yislist, yistuple = _copytobuffer(lat)
        # call proj4 functions. inx and iny modified in place.
        if inverse:
            _Proj._inv(self, inx, iny, radians=radians, errcheck=errcheck)
        else:
            _Proj._fwd(self, inx, iny, radians=radians, errcheck=errcheck)
        # if inputs were lists, tuples or floats, convert back.
        outx = _convertback(xisfloat,xislist,xistuple,inx)
        outy = _convertback(yisfloat,yislist,xistuple,iny)
        return outx, outy

    def is_latlong(self):
        """returns True if projection in geographic (lon/lat) coordinates"""
        return _Proj.is_latlong(self)

    def is_geocent(self):
        """returns True if projection in geocentric (x/y) coordinates"""
        return _Proj.is_geocent(self)

def transform(p1, p2, x, y, z=None, radians=False):
    """
    x2, y2, z2 = transform(p1, p2, x1, y1, z1, radians=False)

    Transform points between two coordinate systems defined by the
    Proj instances p1 and p2.

    The points x1,y1,z1 in the coordinate system defined by p1 are
    transformed to x2,y2,z2 in the coordinate system defined by p2.

    z1 is optional, if it is not set it is assumed to be zero (and
    only x2 and y2 are returned).

    In addition to converting between cartographic and geographic
    projection coordinates, this function can take care of datum
    shifts (which cannot be done using the __call__ method of the
    Proj instances). It also allows for one of the coordinate
    systems to be geographic (proj = 'latlong').

    If optional keyword 'radians' is True (default is False) and p1
    is defined in geographic coordinate (pj.is_latlong() is True),
    x1,y1 is interpreted as radians instead of the default degrees.
    Similarly, if p2 is defined in geographic coordinates and
    radians=True, x2, y2 are returned in radians instead of degrees.
    if p1.is_latlong() and p2.is_latlong() both are False, the
    radians keyword has no effect.

    x,y and z can be numpy or regular python arrays, python
    lists/tuples or scalars. Arrays are fastest.  For projections in
    geocentric coordinates, values of x and y are given in meters.
    z is always meters.

    Example usage:

    >>> # projection 1: UTM zone 15, grs80 ellipse, NAD83 datum
    >>> # (defined by epsg code 26915)
    >>> p1 = Proj(init='epsg:26915')
    >>> # projection 2: UTM zone 15, clrk66 ellipse, NAD27 datum
    >>> p2 = Proj(init='epsg:26715')
    >>> # find x,y of Jefferson City, MO.
    >>> x1, y1 = p1(-92.199881,38.56694)
    >>> # transform this point to projection 2 coordinates.
    >>> x2, y2 = transform(p1,p2,x1,y1)
    >>> print '%9.3f %11.3f' % (x1,y1)
    569704.566 4269024.671
    >>> print '%9.3f %11.3f' % (x2,y2)
    569706.333 4268817.680
    >>> print '%8.3f %5.3f' % p2(x2,y2,inverse=True)
     -92.200 38.567
    >>> # process 3 points at a time in a tuple
    >>> lats = (38.83,39.32,38.75) # Columbia, KC and StL Missouri
    >>> lons = (-92.22,-94.72,-90.37)
    >>> x1, y1 = p1(lons,lats)
    >>> x2, y2 = transform(p1,p2,x1,y1)
    >>> xy = x1+y1
    >>> print '%9.3f %9.3f %9.3f %11.3f %11.3f %11.3f' % xy
    567703.344 351730.944 728553.093 4298200.739 4353698.725 4292319.005
    >>> xy = x2+y2
    >>> print '%9.3f %9.3f %9.3f %11.3f %11.3f %11.3f' % xy
    567705.072 351727.113 728558.917 4297993.157 4353490.111 4292111.678
    >>> lons, lats = p2(x2,y2,inverse=True)
    >>> xy = lons+lats
    >>> print '%8.3f %8.3f %8.3f %5.3f %5.3f %5.3f' % xy
     -92.220  -94.720  -90.370 38.830 39.320 38.750
    """
    # process inputs, making copies that support buffer API.
    inx, xisfloat, xislist, xistuple = _copytobuffer(x)
    iny, yisfloat, yislist, yistuple = _copytobuffer(y)
    if z is not None:
        inz, zisfloat, zislist, zistuple = _copytobuffer(z)
    else:
        inz = None
    # call pj_transform.  inx,iny,inz buffers modified in place.
    _transform(p1,p2,inx,iny,inz,radians)
    # if inputs were lists, tuples or floats, convert back.
    outx = _convertback(xisfloat,xislist,xistuple,inx)
    outy = _convertback(yisfloat,yislist,xistuple,iny)
    if inz is not None:
        outz = _convertback(zisfloat,zislist,zistuple,inz)
        return outx, outy, outz
    else:
        return outx, outy

def _copytobuffer(x):
    """
    return a copy of x as an object that supports the python Buffer
    API (python array if input is float, list or tuple, numpy array
    if input is a numpy array). returns copyofx, isfloat, islist,
    istuple (islist is True if input is a list, istuple is true if
    input is a tuple, isfloat is true if input is a float).
    """
    # make sure x supports Buffer API and contains doubles.
    isfloat = False; islist = False; istuple = False
    # first, if it's a numpy array scalar convert to float
    # (array scalars don't support buffer API)
    if hasattr(x,'shape') and x.shape == (): x = float(x)
    try:
        # typecast numpy arrays to double.
        # (this makes a copy - which is crucial
        #  since buffer is modified in place)
        x.dtype.char
        inx = x.astype('d')
    except:
        try: # perhaps they are Numeric/numarrays?
            x.typecode()
            inx = x.astype('d')
        except:
            # perhaps they are regular python arrays?
            try:
                x.typecode
                inx = array('d',x)
            except:
                # try to convert to python array
                # a list.
                if type(x) is ListType:
                    inx = array('d',x)
                    islist = True
                # a tuple.
                elif type(x) is TupleType:
                    inx = array('d',x)
                    istuple = True
                # a scalar?
                else:
                    try:
                        x = float(x)
                        inx = array('d',(x,))
                        isfloat = True
                    except:
                        print 'x is',type(x)
                        raise TypeError, 'input must be an array, list, tuple or scalar'
    return inx,isfloat,islist,istuple

def _convertback(isfloat,islist,istuple,inx):
    # if inputs were lists, tuples or floats, convert back to original type.
    if isfloat:
        return inx[0]
    elif islist:
        return inx.tolist()
    elif istuple:
        return tuple(inx)
    else:
        return inx

def _dict2string(projparams):
    # convert a dict to a proj4 string.
    pjargs = []
    for key,value in projparams.iteritems():
        pjargs.append('+'+key+"="+str(value)+' ')
    return ''.join(pjargs)

class Geod(_Geod):
    """
    performs forward and inverse geodetic, or Great Circle,
    computations.  The forward computation (using the 'fwd' method)
    involves determining latitude, longitude and back azimuth of a
    terminus point given the latitude and longitude of an initial
    point, plus azimuth and distance. The inverse computation (using
    the 'inv' method) involves determining the forward and back
    azimuths and distance given the latitudes and longitudes of an
    initial and terminus point.
    """
    def __new__(self, initparams=None, **kwargs):
        """
        initialize a Geod class instance.

        Geodetic parameters for specifying the ellipsoid
        can be given in a dictionary 'initparams', as keyword arguments, 
        or as as proj4 geod initialization string.
        Following is a list of the ellipsoids that may be defined using the 
        'ellps' keyword:

           MERIT a=6378137.0      rf=298.257       MERIT 1983
           SGS85 a=6378136.0      rf=298.257       Soviet Geodetic System 85
           GRS80 a=6378137.0      rf=298.257222101 GRS 1980(IUGG, 1980)
           IAU76 a=6378140.0      rf=298.257       IAU 1976
            airy a=6377563.396    b=6356256.910    Airy 1830
          APL4.9 a=6378137.0.     rf=298.25        Appl. Physics. 1965
           NWL9D a=6378145.0.     rf=298.25        Naval Weapons Lab., 1965
        mod_airy a=6377340.189    b=6356034.446    Modified Airy
          andrae a=6377104.43     rf=300.0         Andrae 1876 (Den., Iclnd.)
         aust_SA a=6378160.0      rf=298.25        Australian Natl & S. Amer. 1969
           GRS67 a=6378160.0      rf=298.2471674270 GRS 67(IUGG 1967)
          bessel a=6377397.155    rf=299.1528128   Bessel 1841
        bess_nam a=6377483.865    rf=299.1528128   Bessel 1841 (Namibia)
          clrk66 a=6378206.4      b=6356583.8      Clarke 1866
          clrk80 a=6378249.145    rf=293.4663      Clarke 1880 mod.
             CPM a=6375738.7      rf=334.29        Comm. des Poids et Mesures 1799
          delmbr a=6376428.       rf=311.5         Delambre 1810 (Belgium)
         engelis a=6378136.05     rf=298.2566      Engelis 1985
         evrst30 a=6377276.345    rf=300.8017      Everest 1830
         evrst48 a=6377304.063    rf=300.8017      Everest 1948
         evrst56 a=6377301.243    rf=300.8017      Everest 1956
         evrst69 a=6377295.664    rf=300.8017      Everest 1969
         evrstSS a=6377298.556    rf=300.8017      Everest (Sabah & Sarawak)
         fschr60 a=6378166.       rf=298.3         Fischer (Mercury Datum) 1960
        fschr60m a=6378155.       rf=298.3         Modified Fischer 1960
         fschr68 a=6378150.       rf=298.3         Fischer 1968
         helmert a=6378200.       rf=298.3         Helmert 1906
           hough a=6378270.0      rf=297.          Hough
            intl a=6378388.0      rf=297.          International 1909 (Hayford)
           krass a=6378245.0      rf=298.3         Krassovsky, 1942
           kaula a=6378163.       rf=298.24        Kaula 1961
           lerch a=6378139.       rf=298.257       Lerch 1979
           mprts a=6397300.       rf=191.          Maupertius 1738
        new_intl a=6378157.5      b=6356772.2      New International 1967
         plessis a=6376523.       b=6355863.       Plessis 1817 (France)
          SEasia a=6378155.0      b=6356773.3205   Southeast Asia
         walbeck a=6376896.0      b=6355834.8467   Walbeck
           WGS60 a=6378165.0      rf=298.3         WGS 60
           WGS66 a=6378145.0      rf=298.25        WGS 66
           WGS72 a=6378135.0      rf=298.26        WGS 72
           WGS84 a=6378137.0      rf=298.257223563 WGS 84
          sphere a=6370997.0      b=6370997.0      Normal Sphere (r=6370997)

        The parameters of the ellipsoid may also be set directly using
        the 'a' (semi-major or equatorial axis radius) keyword, and
        any one of the following keywords: 'b' (semi-minor,
        or polar axis radius), 'e' (eccentricity), 'es' (eccentricity
        squared), 'f' (flattening), or 'rf' (reciprocal flattening).

        See the proj documentation (http://proj.maptools.org) for more
        information about specifying ellipsoid parameters (specifically,
        the chapter 'Specifying the Earth's figure' in the main Proj
        users manual).

        Example usage:

        >>> from pyproj import Geod
        >>> g = Geod(ellps='clrk66') # Use Clarke 1966 ellipsoid.
        >>> # specify the lat/lons of some cities.
        >>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
        >>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
        >>> newyork_lat = 40.+(47./60.); newyork_lon = -73.-(58./60.)
        >>> london_lat = 51.+(32./60.); london_lon = -(5./60.)
        >>> # compute forward and back azimuths, plus distance
        >>> # between Boston and Portland.
        >>> az12,az21,dist = g.inv(boston_lon,boston_lat,portland_lon,portland_lat)
        >>> print "%7.3f %6.3f %12.3f" % (az12,az21,dist)
        -66.531 75.654  4164192.708
        >>> # compute latitude, longitude and back azimuth of Portland,
        >>> # given Boston lat/lon, forward azimuth and distance to Portland.
        >>> endlon, endlat, backaz = g.fwd(boston_lon, boston_lat, az12, dist)
        >>> print "%6.3f  %6.3f %13.3f" % (endlat,endlon,backaz)
        45.517  -123.683        75.654
        >>> # compute the azimuths, distances from New York to several
        >>> # cities (pass a list)
        >>> lons1 = 3*[newyork_lon]; lats1 = 3*[newyork_lat]
        >>> lons2 = [boston_lon, portland_lon, london_lon]
        >>> lats2 = [boston_lat, portland_lat, london_lat]
        >>> az12,az21,dist = g.inv(lons1,lats1,lons2,lats2)
        >>> for faz,baz,d in zip(az12,az21,dist): print "%7.3f %7.3f %9.3f" % (faz,baz,d)
         54.663 -123.448 288303.720
        -65.463  79.342 4013037.318
         51.254 -71.576 5579916.649
        >>> g2 = Geod('+ellps=clrk66') # use proj4 style initialization string
        >>> az12,az21,dist = g2.inv(boston_lon,boston_lat,portland_lon,portland_lat)
        >>> print "%7.3f %6.3f %12.3f" % (az12,az21,dist)
        -66.531 75.654  4164192.708
        """
        # if initparams is None, use kwargs.
        if initparams is None:
            if len(kwargs) == 0:
                raise RuntimeError('no ellipsoid control parameters specified')
            else:
                initstring = _dict2string(kwargs)
        elif type(initparams) == str:
            # if projparams is a string, interpret as a proj4 init string.
            initstring = initparams
        else: # projparams a dict
            initstring = _dict2string(initparams)
        # make sure units are meters.
        if not  initstring.count('+units='):
            initstring = '+units=m '+initstring
        else:
            kvpairs = []
            for kvpair in initstring.split():
                if kvpair.startswith('+units'):
                    k,v = kvpair.split('=')
                    kvpairs.append(k+'=m ')
                else:
                    kvpairs.append(kvpair+' ')
            initstring = ''.join(kvpairs)
        return _Geod.__new__(self, initstring)

    def fwd(self, lons, lats, az, dist, radians=False):
        """
        forward transformation - Returns longitudes, latitudes and back
        azimuths of terminus points given longitudes (lons) and
        latitudes (lats) of initial points, plus forward azimuths (az)
        and distances (dist).

        Works with numpy and regular python array objects, python
        sequences and scalars.

        if radians=True, lons/lats and azimuths are radians instead of
        degrees. Distances are in meters.
        """
        # process inputs, making copies that support buffer API.
        inx, xisfloat, xislist, xistuple = _copytobuffer(lons)
        iny, yisfloat, yislist, yistuple = _copytobuffer(lats)
        inz, zisfloat, zislist, zistuple = _copytobuffer(az)
        ind, disfloat, dislist, distuple = _copytobuffer(dist)
        # call geod_for function. inputs modified in place.
        _Geod._fwd(self, inx, iny, inz, ind, radians=radians)
        # if inputs were lists, tuples or floats, convert back.
        outx = _convertback(xisfloat,xislist,xistuple,inx)
        outy = _convertback(yisfloat,yislist,xistuple,iny)
        outz = _convertback(zisfloat,zislist,zistuple,inz)
        return outx, outy, outz

    def inv(self, lons1, lats1, lons2, lats2, radians=False):
        """
        inverse transformation - Returns forward and back azimuths, plus
        distances between initial points (specified by lons1, lats1) and
        terminus points (specified by lons2, lats2).

        Works with numpy and regular python array objects, python
        sequences and scalars.

        if radians=True, lons/lats and azimuths are radians instead of
        degrees. Distances are in meters.
        """
        # process inputs, making copies that support buffer API.
        inx, xisfloat, xislist, xistuple = _copytobuffer(lons1)
        iny, yisfloat, yislist, yistuple = _copytobuffer(lats1)
        inz, zisfloat, zislist, zistuple = _copytobuffer(lons2)
        ind, disfloat, dislist, distuple = _copytobuffer(lats2)
        # call geod_inv function. inputs modified in place.
        _Geod._inv(self, inx, iny, inz, ind, radians=radians)
        # if inputs were lists, tuples or floats, convert back.
        outx = _convertback(xisfloat,xislist,xistuple,inx)
        outy = _convertback(yisfloat,yislist,xistuple,iny)
        outz = _convertback(zisfloat,zislist,zistuple,inz)
        return outx, outy, outz

    def npts(self, lon1, lat1, lon2, lat2, npts, radians=False):
        """
        Given a single initial point and terminus point (specified by
        python floats lon1,lat1 and lon2,lat2), returns a list of
        longitude/latitude pairs describing npts equally spaced
        intermediate points along the geodesic between the initial and
        terminus points.

        if radians=True, lons/lats are radians instead of degrees.

        Example usage:

        >>> from pyproj import Geod
        >>> g = Geod(ellps='clrk66') # Use Clarke 1966 ellipsoid.
        >>> # specify the lat/lons of Boston and Portland.
        >>> boston_lat = 42.+(15./60.); boston_lon = -71.-(7./60.)
        >>> portland_lat = 45.+(31./60.); portland_lon = -123.-(41./60.)
        >>> # find ten equally spaced points between Boston and Portland.
        >>> lonlats = g.npts(boston_lon,boston_lat,portland_lon,portland_lat,10)
        >>> for lon,lat in lonlats: print '%6.3f  %7.3f' % (lat, lon)
        43.528  -75.414
        44.637  -79.883
        45.565  -84.512
        46.299  -89.279
        46.830  -94.156
        47.149  -99.112
        47.251  -104.106
        47.136  -109.100
        46.805  -114.051
        46.262  -118.924
        """
        lons, lats = _Geod._npts(self,lon1,lat1,lon2,lat2,npts,radians=radians)
        return zip(lons, lats)

def test():
    """run the examples in the docstrings using the doctest module"""
    import doctest, pyproj
    doctest.testmod(pyproj,verbose=True)

if __name__ == "__main__": test()