/usr/lib/python3/dist-packages/mpl_toolkits/basemap/proj.py is in python3-mpltoolkits.basemap 1.1.0+dfsg-1.
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import pyproj
import math
from matplotlib.cbook import dedent
__version__ = '1.2.2'
_dg2rad = math.radians(1.)
_rad2dg = math.degrees(1.)
_cylproj = ['cyl','merc','mill','gall']
_pseudocyl = ['moll','kav7','eck4','robin','sinu','mbtfpq','vandg','hammer']
_upper_right_out_of_bounds = (
'the upper right corner of the plot is not in the map projection region')
_lower_left_out_of_bounds = (
'the lower left corner of the plot is not in the map projection region')
class Proj(object):
"""
peforms cartographic transformations (converts from longitude,latitude
to native map projection x,y coordinates and vice versa) using proj
(http://proj.maptools.org/)
Uses a pyrex generated C-interface to libproj.
__init__ method sets up projection information.
__call__ method compute transformations.
See docstrings for __init__ and __call__ for details.
Contact: Jeff Whitaker <jeffrey.s.whitaker@noaa.gov>
"""
def __init__(self,projparams,llcrnrlon,llcrnrlat,
urcrnrlon,urcrnrlat,urcrnrislatlon=True):
"""
initialize a Proj class instance.
Input 'projparams' is a dictionary containing proj map
projection control parameter key/value pairs.
See the proj documentation (http://www.remotesensing.org/proj/)
for details.
llcrnrlon,llcrnrlat are lon and lat (in degrees) of lower
left hand corner of projection region.
urcrnrlon,urcrnrlat are lon and lat (in degrees) of upper
right hand corner of projection region if urcrnrislatlon=True
(default). Otherwise, urcrnrlon,urcrnrlat are x,y in projection
coordinates (units meters), assuming the lower left corner is x=0,y=0.
"""
self.projparams = projparams
self.projection = projparams['proj']
# rmajor is the semi-major axis.
# rminor is the semi-minor axis.
# esq is eccentricity squared.
try:
self.rmajor = projparams['a']
self.rminor = projparams['b']
except:
try:
self.rmajor = projparams['R']
except:
self.rmajor = projparams['bR_a']
self.rminor = self.rmajor
if self.rmajor == self.rminor:
self.ellipsoid = False
else:
self.ellipsoid = True
self.flattening = (self.rmajor-self.rminor)/self.rmajor
self.esq = (self.rmajor**2 - self.rminor**2)/self.rmajor**2
self.llcrnrlon = llcrnrlon
self.llcrnrlat = llcrnrlat
if self.projection == 'cyl':
llcrnrx = llcrnrlon
llcrnry = llcrnrlat
elif self.projection == 'ob_tran':
self._proj4 = pyproj.Proj(projparams)
llcrnrx,llcrnry = self(llcrnrlon,llcrnrlat)
llcrnrx = _rad2dg*llcrnrx; llcrnry = _rad2dg*llcrnry
if llcrnrx < 0: llcrnrx = llcrnrx + 360
elif self.projection in 'ortho':
if (llcrnrlon == -180 and llcrnrlat == -90 and
urcrnrlon == 180 and urcrnrlat == 90):
self._fulldisk = True
self._proj4 = pyproj.Proj(projparams)
llcrnrx = -self.rmajor
llcrnry = -self.rmajor
self._width = 0.5*(self.rmajor+self.rminor)
self._height = 0.5*(self.rmajor+self.rminor)
urcrnrx = -llcrnrx
urcrnry = -llcrnry
else:
self._fulldisk = False
self._proj4 = pyproj.Proj(projparams)
llcrnrx, llcrnry = self(llcrnrlon,llcrnrlat)
if llcrnrx > 1.e20 or llcrnry > 1.e20:
raise ValueError(_lower_left_out_of_bounds)
elif self.projection == 'aeqd' and\
(llcrnrlon == -180 and llcrnrlat == -90 and urcrnrlon == 180 and\
urcrnrlat == 90):
self._fulldisk = True
self._proj4 = pyproj.Proj(projparams)
# raise an exception for ellipsoids - there appears to be a bug
# in proj4 that causes the inverse transform to fail for points
# more than 90 degrees of arc away from center point for ellipsoids
# (works fine for spheres) - below is an example
#from pyproj import Proj
#p1 = Proj(proj='aeqd',a=6378137.00,b=6356752.3142,lat_0=0,lon_0=0)
#x,y= p1(91,0)
#lon,lat = p1(x,y,inverse=True) # lon is 89 instead of 91
if self.ellipsoid:
msg = dedent("""
full disk (whole world) Azimuthal Equidistant projection can
only be drawn for a perfect sphere""")
raise ValueError(msg)
llcrnrx = -np.pi*self.rmajor
llcrnry = -np.pi*self.rmajor
self._width = -llcrnrx
self._height = -llcrnry
urcrnrx = -llcrnrx
urcrnry = -llcrnry
elif self.projection == 'geos':
self._proj4 = pyproj.Proj(projparams)
# find major and minor axes of ellipse defining map proj region.
# h is measured from surface of earth at equator.
h = projparams['h'] + self.rmajor
# latitude of horizon on central meridian
lonmax = 90.-(180./np.pi)*np.arcsin(self.rmajor/h)
# longitude of horizon on equator
latmax = 90.-(180./np.pi)*np.arcsin(self.rminor/h)
# truncate to nearest hundredth of a degree (to make sure
# they aren't slightly over the horizon)
latmax = int(100*latmax)/100.
lonmax = int(100*lonmax)/100.
# width and height of visible projection
P = pyproj.Proj(proj='geos',a=self.rmajor,\
b=self.rminor,lat_0=0,lon_0=0,h=projparams['h'])
x1,y1 = P(0.,latmax); x2,y2 = P(lonmax,0.)
width = x2; height = y1
self._height = height
self._width = width
if (llcrnrlon == -180 and llcrnrlat == -90 and
urcrnrlon == 180 and urcrnrlat == 90):
self._fulldisk = True
llcrnrx = -width
llcrnry = -height
urcrnrx = -llcrnrx
urcrnry = -llcrnry
else:
self._fulldisk = False
llcrnrx, llcrnry = self(llcrnrlon,llcrnrlat)
if llcrnrx > 1.e20 or llcrnry > 1.e20:
raise ValueError(_lower_left_out_of_bounds)
elif self.projection == 'nsper':
self._proj4 = pyproj.Proj(projparams)
# find major and minor axes of ellipse defining map proj region.
# h is measured from surface of earth at equator.
h = projparams['h'] + self.rmajor
# latitude of horizon on central meridian
lonmax = 90.-(180./np.pi)*np.arcsin(self.rmajor/h)
# longitude of horizon on equator
latmax = 90.-(180./np.pi)*np.arcsin(self.rmajor/h)
# truncate to nearest hundredth of a degree (to make sure
# they aren't slightly over the horizon)
latmax = int(100*latmax)/100.
lonmax = int(100*lonmax)/100.
# width and height of visible projection
P = pyproj.Proj(proj='nsper',a=self.rmajor,\
b=self.rminor,lat_0=0,lon_0=0,h=projparams['h'])
x1,y1 = P(0.,latmax); x2,y2 = P(lonmax,0.)
width = x2; height = y1
self._height = height
self._width = width
if (llcrnrlon == -180 and llcrnrlat == -90 and
urcrnrlon == 180 and urcrnrlat == 90):
self._fulldisk = True
llcrnrx = -width
llcrnry = -height
urcrnrx = -llcrnrx
urcrnry = -llcrnry
else:
self._fulldisk = False
llcrnrx, llcrnry = self(llcrnrlon,llcrnrlat)
if llcrnrx > 1.e20 or llcrnry > 1.e20:
raise ValueError(_lower_left_out_of_bounds)
elif self.projection in _pseudocyl:
self._proj4 = pyproj.Proj(projparams)
xtmp,urcrnry = self(projparams['lon_0'],90.)
urcrnrx,xtmp = self(projparams['lon_0']+180.,0)
llcrnrx = -urcrnrx
llcrnry = -urcrnry
if self.ellipsoid and self.projection in ['kav7','eck4','mbtfpq']:
msg = "this projection can only be drawn for a perfect sphere"
raise ValueError(msg)
else:
self._proj4 = pyproj.Proj(projparams)
llcrnrx, llcrnry = self(llcrnrlon,llcrnrlat)
if self.projection == 'aeqd': self._fulldisk=False
# compute x_0, y_0 so ll corner of domain is x=0,y=0.
# note that for 'cyl' x,y == lon,lat
if self.projection != 'ob_tran':
self.projparams['x_0']=-llcrnrx
self.projparams['y_0']=-llcrnry
# reset with x_0, y_0.
if self.projection not in ['cyl','ob_tran']:
self._proj4 = pyproj.Proj(projparams)
llcrnry = 0.
llcrnrx = 0.
elif self.projection != 'ob_tran':
llcrnrx = llcrnrlon
llcrnry = llcrnrlat
if urcrnrislatlon:
self.urcrnrlon = urcrnrlon
self.urcrnrlat = urcrnrlat
if self.projection not in ['ortho','geos','nsper','aeqd'] + _pseudocyl:
urcrnrx,urcrnry = self(urcrnrlon,urcrnrlat)
if self.projection == 'ob_tran':
urcrnrx = _rad2dg*urcrnrx; urcrnry = _rad2dg*urcrnry
if urcrnrx < 0: urcrnrx = urcrnrx + 360
elif self.projection in ['ortho','geos','nsper','aeqd']:
if self._fulldisk:
urcrnrx = 2.*self._width
urcrnry = 2.*self._height
else:
urcrnrx,urcrnry = self(urcrnrlon,urcrnrlat)
if urcrnrx > 1.e20 or urcrnry > 1.e20:
raise ValueError(_upper_right_out_of_bounds)
elif self.projection in _pseudocyl:
xtmp,urcrnry = self(projparams['lon_0'],90.)
urcrnrx,xtmp = self(projparams['lon_0']+180.,0)
else:
urcrnrx = urcrnrlon
urcrnry = urcrnrlat
urcrnrlon, urcrnrlat = self(urcrnrx, urcrnry, inverse=True)
self.urcrnrlon = urcrnrlon
self.urcrnrlat = urcrnrlat
# corners of domain.
self.llcrnrx = llcrnrx
self.llcrnry = llcrnry
self.urcrnrx = urcrnrx
self.urcrnry = urcrnry
if urcrnrx > llcrnrx:
self.xmin = llcrnrx
self.xmax = urcrnrx
else:
self.xmax = llcrnrx
self.xmin = urcrnrx
if urcrnry > llcrnry:
self.ymin = llcrnry
self.ymax = urcrnry
else:
self.ymax = llcrnry
self.ymin = urcrnry
def __call__(self, *args, **kw):
# x,y,inverse=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.
For cylindrical equidistant projection ('cyl'), this
does nothing (i.e. x,y == lon,lat).
lon,lat can be either scalar floats or N arrays.
"""
if len(args) == 1:
xy = args[0]
onearray = True
else:
x,y = args
onearray = False
if self.projection == 'cyl': # for cyl x,y == lon,lat
if onearray:
return xy
else:
return x,y
inverse = kw.get('inverse', False)
if onearray:
outxy = self._proj4(xy, inverse=inverse)
else:
outx,outy = self._proj4(x, y, inverse=inverse)
if inverse:
if self.projection in ['merc','mill','gall']:
if self.projection == 'merc':
coslat = math.cos(math.radians(self.projparams['lat_ts']))
sinlat = math.sin(math.radians(self.projparams['lat_ts']))
else:
coslat = 1.
sinlat = 0.
# radius of curvature of the ellipse perpendicular to
# the plane of the meridian.
rcurv = self.rmajor*coslat/math.sqrt(1.-self.esq*sinlat**2)
if onearray:
outxy[:,0] = _rad2dg*(xy[:,0]/rcurv) + self.llcrnrlon
else:
try: # x a scalar or an array
outx = _rad2dg*(x/rcurv) + self.llcrnrlon
except: # x a sequence
outx = [_rad2dg*(xi/rcurv) + self.llcrnrlon for xi in x]
else:
if self.projection in ['merc','mill','gall']:
if self.projection == 'merc':
coslat = math.cos(math.radians(self.projparams['lat_ts']))
sinlat = math.sin(math.radians(self.projparams['lat_ts']))
else:
coslat = 1.
sinlat = 0.
# radius of curvature of the ellipse perpendicular to
# the plane of the meridian.
rcurv = self.rmajor*coslat/math.sqrt(1.-self.esq*sinlat**2)
if onearray:
outxy[:,0] = rcurv*_dg2rad*(xy[:,0]-self.llcrnrlon)
else:
try: # x is a scalar or an array
outx = rcurv*_dg2rad*(x-self.llcrnrlon)
except: # x is a sequence.
outx = [rcurv*_dg2rad*(xi-self.llcrnrlon) for xi in x]
if onearray:
return outxy
else:
return outx, outy
def makegrid(self,nx,ny,returnxy=False):
"""
return arrays of shape (ny,nx) containing lon,lat coordinates of
an equally spaced native projection grid.
if returnxy=True, the x,y values of the grid are returned also.
"""
dx = (self.urcrnrx-self.llcrnrx)/(nx-1)
dy = (self.urcrnry-self.llcrnry)/(ny-1)
x = self.llcrnrx+dx*np.indices((ny,nx),np.float32)[1,:,:]
y = self.llcrnry+dy*np.indices((ny,nx),np.float32)[0,:,:]
lons, lats = self(x, y, inverse=True)
if returnxy:
return lons, lats, x, y
else:
return lons, lats
def makegrid3d(self,nx,ny,returnxy=False):
"""
return array of shape (ny,nx, 2) containing lon,lat coordinates of
an equally spaced native projection grid.
if returnxy=True, the x,y values of the grid are returned also.
"""
dx = (self.urcrnrx-self.llcrnrx)/(nx-1)
dy = (self.urcrnry-self.llcrnry)/(ny-1)
xy = np.empty((ny,nx,2), np.float64)
xy[...,0] = self.llcrnrx+dx*np.indices((ny,nx),np.float32)[1,:,:]
xy[...,1] = self.llcrnry+dy*np.indices((ny,nx),np.float32)[0,:,:]
lonlat = self(xy, inverse=True)
if returnxy:
return lonlat, xy
else:
return lonlat
if __name__ == "__main__":
params = {}
params['proj'] = 'lcc'
params['R'] = 6371200
params['lat_1'] = 50
params['lat_2'] = 50
params['lon_0'] = -107
nx = 349; ny = 277; dx = 32463.41; dy = dx
awips221 = Proj(params,-145.5,1.0,(nx-1)*dx,(ny-1)*dy,urcrnrislatlon=False)
# AWIPS grid 221 parameters
# (from http://www.nco.ncep.noaa.gov/pmb/docs/on388/tableb.html)
llcornerx, llcornery = awips221(-145.5,1.)
# find 4 lon/lat corners of AWIPS grid 221.
llcornerx = 0.; llcornery = 0.
lrcornerx = dx*(nx-1); lrcornery = 0.
ulcornerx = 0.; ulcornery = dy*(ny-1)
urcornerx = dx*(nx-1); urcornery = dy*(ny-1)
llcornerlon, llcornerlat = awips221(llcornerx, llcornery, inverse=True)
lrcornerlon, lrcornerlat = awips221(lrcornerx, lrcornery, inverse=True)
urcornerlon, urcornerlat = awips221(urcornerx, urcornery, inverse=True)
ulcornerlon, ulcornerlat = awips221(ulcornerx, ulcornery, inverse=True)
import sys
sys.stdout.write('4 corners of AWIPS grid 221:\n')
sys.stdout.write('%s %s\n' % llcornerlon, llcornerlat)
sys.stdout.write('%s %s\n' % lrcornerlon, lrcornerlat)
sys.stdout.write('%s %s\n' % urcornerlon, urcornerlat)
sys.stdout.write('%s %s\n' % ulcornerlon, ulcornerlat)
sys.stdout.write('from GRIB docs\n')
sys.stdout.write('(http://www.nco.ncep.noaa.gov/pmb/docs/on388/tableb.html)\n')
sys.stdout.write(' -145.5 1.0\n')
sys.stdout.write(' -68.318 0.897\n')
sys.stdout.write(' -2.566 46.352\n')
sys.stdout.write(' 148.639 46.635\n')
# compute lons and lats for the whole AWIPS grid 221 (377x249).
import time; t1 = time.clock()
lons, lats = awips221.makegrid(nx,ny)
t2 = time.clock()
sys.stdout.write('compute lats/lons for all points on AWIPS 221 grid (%sx%s)\n' %(nx,ny))
sys.stdout.write('max/min lons\n')
sys.stdout.write('%s %s\n' % min(np.ravel(lons)),max(np.ravel(lons)))
sys.stdout.write('max/min lats\n')
sys.stdout.write('%s %s\n' % min(np.ravel(lats)),max(np.ravel(lats)))
sys.stdout.write('took %s secs\n' % t2-t1)
sys.stdout.write('Same thing but with a single 3-D array\n')
t1 = time.clock()
lonlat, xy = awips221.makegrid3d(nx,ny, returnxy=True)
t2 = time.clock()
sys.stdout.write('took %s secs\n' % t2-t1)
assert (lons==lonlat[...,0]).all(), "The longitudes are different"
assert (lats==lonlat[...,1]).all(), "The latitudes are different"
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