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Example 1
def cart2sph(x, y, z):
"""
Converts cartesian coordinates `x`, `y`, `z` into a longitude and latitude.
x=0, y=0, z=0 is assumed to correspond to the center of the globe.
Returns lon and lat in radians.
Parameters
----------
`x`, `y`, `z` : Arrays of cartesian coordinates
Returns
-------
lon : Longitude in radians
lat : Latitude in radians
"""
r = np.sqrt(x**2 + y**2 + z**2)
lat = np.arcsin(z/r)
lon = np.arctan2(y, x)
return lon, lat Example 2
def getTrainTestKernel(self, params, Xtest): self.checkParams(params) ell2 = np.exp(2*params[0]) z = Xtest / np.sqrt(Xtest.shape[1]) S = 1 + self.X_scaled.dot(z.T) sz = 1 + np.sum(z**2, axis=1) sqrtEll2Psx = np.sqrt(ell2+self.sx) sqrtEll2Psz = np.sqrt(ell2+sz) K = S / np.outer(sqrtEll2Psx, sqrtEll2Psz) return np.arcsin(K)
Example 3
def _B_0_function(self, z):
"""
calculate B_0(z) function defined in:
Gould A. 1994 ApJ 421L, 71 "Proper motions of MACHOs
http://adsabs.harvard.edu/abs/1994ApJ...421L..71G
Yoo J. et al. 2004 ApJ 603, 139 "OGLE-2003-BLG-262: Finite-Source
Effects from a Point-Mass Lens"
http://adsabs.harvard.edu/abs/2004ApJ...603..139Y
"""
out = 4. * z / np.pi
function = lambda x: (1.-value**2*np.sin(x)**2)**.5
for (i, value) in enumerate(z):
if value < 1.:
out[i] *= ellipe(value*value)
else:
out[i] *= integrate.quad(function, 0., np.arcsin(1./value))[0]
return out Example 4
def distance(self, lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# convert decimal degrees to radians
lon1 = lon1*pi/180
lat1 = lat1*pi/180
lon2 = lon2*pi/180
lat2 = lat2*pi/180
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = np.sin(dlat/2)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2)**2
c = 2 * np.arcsin(np.sqrt(a))
km = 6371 * c
return km Example 5
def distance(self, lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# convert decimal degrees to radians
lon1 = lon1*pi/180
lat1 = lat1*pi/180
lon2 = lon2*pi/180
lat2 = lat2*pi/180
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = numpy.sin(dlat/2)**2 + numpy.cos(lat1) * numpy.cos(lat2) * numpy.sin(dlon/2)**2
c = 2 * numpy.arcsin(numpy.sqrt(a))
km = 6371 * c
return km Example 6
def distance(lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# convert decimal degrees to radians
lon1 = lon1*pi/180
lat1 = lat1*pi/180
lon2 = lon2*pi/180
lat2 = lat2*pi/180
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = np.sin(dlat/2)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2)**2
c = 2 * np.arcsin(np.sqrt(a))
km = 6371 * c
return km Example 7
def distance(self, lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# convert decimal degrees to radians
lon1 = lon1*pi/180
lat1 = lat1*pi/180
lon2 = lon2*pi/180
lat2 = lat2*pi/180
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = numpy.sin(dlat/2)**2 + numpy.cos(lat1) * numpy.cos(lat2) * numpy.sin(dlon/2)**2
c = 2 * numpy.arcsin(numpy.sqrt(a))
km = 6371 * c
return km Example 8
def distance(self, lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# convert decimal degrees to radians
lon1 = lon1*pi/180
lat1 = lat1*pi/180
lon2 = lon2*pi/180
lat2 = lat2*pi/180
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = numpy.sin(dlat/2)**2 + numpy.cos(lat1) * numpy.cos(lat2) * numpy.sin(dlon/2)**2
c = 2 * numpy.arcsin(numpy.sqrt(a))
km = 6371 * c
return km Example 9
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 10
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 11
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 12
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
@jit(nopython=True)
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + (2 * pi), (2 * pi)))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 13
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
@jit(nopython=True)
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + (2 * pi), (2 * pi)))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 14
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
@jit(nopython=True)
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + (2 * pi), (2 * pi)))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 15
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
@jit(nopython=True)
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + 360, 360))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 16
def sun_elevation(hUTC, dayofyear, year, latitude, longitude):
""" Sun elevation
Args:
hUTC: fractional hour (UTC time)
dayofyear (int):
year (int):
latitude (float): the location latitude (degrees)
longitude (float): the location longitude (degrees)
Returns:
(float) the sun elevation (degrees)
Details:
World Meteorological Organization (2006).Guide to meteorological
instruments and methods of observation. Geneva, Switzerland.
"""
dec = declination(hUTC, dayofyear, year)
lat = numpy.radians(latitude)
ha = numpy.radians(hour_angle(hUTC, dayofyear, year, longitude) * 15)
sinel = numpy.sin(dec) * numpy.sin(lat) + numpy.cos(dec) * numpy.cos(
lat) * numpy.cos(ha)
return numpy.degrees(numpy.arcsin(sinel)) Example 17
def distance(lat1, lon1, lat2, lon2): """ Computes the great circle distance between two points using the haversine formula. Values can be vectors. """ # Convert from degrees to radians pi = 3.14159265 lon1 = lon1 * 2 * pi / 360 lat1 = lat1 * 2 * pi / 360 lon2 = lon2 * 2 * pi / 360 lat2 = lat2 * 2 * pi / 360 dlon = lon2 - lon1 dlat = lat2 - lat1 a = np.sin(dlat / 2)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon / 2)**2 c = 2 * np.arcsin(np.sqrt(a)) distance = 6.367e6 * c return distance
Example 18
def q_to_euler(q):
"""Converts Quaternions to Euler angles.
Parameters
----------
q : array_like
Array holding Quaternions.
Returns
-------
phi : float
`phi` angle in radians.
theta :float
`theta` angle in radians.
psi : float
`psi` angle in radians.
"""
phi = np.arctan2(2*(q[0]*q[1]+q[2]*q[3]),(q[0]**2+q[3]**2-q[1]**2-q[2]**2))
theta = np.arcsin(2*(q[0]*q[2]-q[1]*q[3]))
psi = np.arctan2(2*(q[0]*q[3]+q[1]*q[2]),(q[0]**2+q[1]**2-q[2]**2-q[3]**2))
return phi, theta, psi Example 19
def convert_to_euler(R):
"""Compute the euler angles of this rotation.
Refer to [http://www.staff.city.ac.uk/~sbbh653/publications/euler.pdf]"""
alpha, beta, gamma = 0, 0, 0
if not np.isclose(np.abs(R[2,0]), 1):
beta = - np.arcsin(R[2,0])
alpha = np.arctan2(R[2,1] / np.cos(beta), R[2,2] / np.cos(beta))
gamma = np.arctan2(R[1,0] / np.cos(beta), R[0,0] / np.cos(beta))
else:
gamma = 0
if np.isclose(R[2,0], -1):
beta = np.pi / 2
alpha = gamma + np.arctan2(R[0,1], R[0,2])
else:
beta = - np.pi / 2
alpha = - gamma + np.arctan2(-R[0,1], -R[0,2])
return np.array([alpha, beta, gamma]) Example 20
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
@jit(nopython=True)
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + (2 * pi), (2 * pi)))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 21
def azimuth(_lAz_data):
_inc = _lAz_data[0]
_lat = _lAz_data[1]
velocity_eq = _lAz_data[2]
def _az_calc():
inert_az = np.arcsin(max(min(np.cos(np.deg2rad(_inc)) / np.cos(np.deg2rad(_lat)), 1), -1))
_VXRot = _lAz_data[3] * np.sin(inert_az) - velocity_eq * np.cos(np.deg2rad(_lat))
_VYRot = _lAz_data[3] * np.cos(inert_az)
return np.rad2deg(np.fmod(np.arctan2(_VXRot, _VYRot) + 360, 360))
_az = _az_calc()
if _lAz_data[4] == "Ascending": return _az
if _lAz_data[4] == "Descending":
if _az <= 90: return 180 - _az
elif _az >= 270: return 540 - _az Example 22
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 23
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 24
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 25
def archav(hav):
""" Formula for the inverse haversine
Parameters
-----------
hav : (float)
Haversine of an angle
Returns
---------
alpha : (float)
Angle in radians
"""
alpha = 2.0 * np.arcsin(np.sqrt(hav))
return alpha Example 26
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 27
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 28
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 29
def _to_hpr_single(dcm):
pitch = np.arcsin(dcm[2, 1])
if np.abs(pitch) < 0.5 * np.pi - 1e-3:
heading = np.arctan2(dcm[0, 1], dcm[1, 1])
roll = np.arctan2(-dcm[2, 0], dcm[2, 2])
elif pitch > 0:
roll = 0
heading = np.arctan2(-dcm[0, 2] - dcm[1, 0], dcm[0, 0] - dcm[1, 2])
else:
roll = 0
heading = np.arctan2(dcm[0, 2] - dcm[1, 0], dcm[0, 0] + dcm[1, 2])
if heading < 0:
heading += 2 * np.pi
if heading == 2 * np.pi:
heading = 0
return heading, pitch, roll Example 30
def _to_llw_array(dcm):
lat = np.arcsin(dcm[:, 2, 2])
lon = np.empty(dcm.shape[0])
wan = np.empty(dcm.shape[0])
mask = np.abs(lat) < 0.5 * np.pi - 1e-3
lon[mask] = np.arctan2(dcm[mask, 1, 2], dcm[mask, 0, 2])
wan[mask] = np.arctan2(dcm[mask, 2, 0], dcm[mask, 2, 1])
mask = ~mask
lon[mask] = 0
l_mask = mask & (lat > 0)
wan[l_mask] = np.arctan2(-dcm[l_mask, 0, 0] - dcm[l_mask, 1, 1],
dcm[l_mask, 1, 0] - dcm[l_mask, 0, 1])
l_mask = mask & (lat < 0)
wan[l_mask] = np.arctan2(dcm[l_mask, 0, 0] - dcm[l_mask, 1, 1],
dcm[l_mask, 0, 1] + dcm[l_mask, 1, 0])
return lat, lon, wan Example 31
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 32
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 33
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 34
def apexes(self):
'''Returns the positions of the apexes of HR and AR as a tuple.'''
if self.HRK == 0.:
apex1 = self.HRCenter
else:
theta1 = np.arcsin(self.Dia * self.ARK/2.)\
if np.abs(self.Dia * self.ARK/2.) < 1. else np.pi/2.
apex1 = self.HRCenter - (1-np.cos(theta1))*self.HRNorm/self.HRK
if self.ARK == 0.:
apex2 = self.ARCenter
else:
theta2 = np.arcsin(self.Dia * self.ARK/(2.*np.cos(self.Wedge)))\
if np.abs(self.Dia * self.ARK/(2.*np.cos(self.Wedge))) < 1.\
else np.pi/2.
apex2 = self.ARCenter - (1-np.cos(theta2))*self.ARNorm/self.ARK
return apex1, apex2 Example 35
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 36
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 37
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 38
def galToCel(ll, bb):
"""
Converts Galactic (deg) to Celestial J2000 (deg) coordinates
"""
bb = numpy.radians(bb)
sin_bb = numpy.sin(bb)
cos_bb = numpy.cos(bb)
ll = numpy.radians(ll)
ra_gp = numpy.radians(192.85948)
de_gp = numpy.radians(27.12825)
lcp = numpy.radians(122.932)
sin_lcp_ll = numpy.sin(lcp - ll)
cos_lcp_ll = numpy.cos(lcp - ll)
sin_d = (numpy.sin(de_gp) * sin_bb) \
+ (numpy.cos(de_gp) * cos_bb * cos_lcp_ll)
ramragp = numpy.arctan2(cos_bb * sin_lcp_ll,
(numpy.cos(de_gp) * sin_bb) \
- (numpy.sin(de_gp) * cos_bb * cos_lcp_ll))
dec = numpy.arcsin(sin_d)
ra = (ramragp + ra_gp + (2. * numpy.pi)) % (2. * numpy.pi)
return numpy.degrees(ra), numpy.degrees(dec) Example 39
def celToGal(ra, dec):
"""
Converts Celestial J2000 (deg) to Calactic (deg) coordinates
"""
dec = numpy.radians(dec)
sin_dec = numpy.sin(dec)
cos_dec = numpy.cos(dec)
ra = numpy.radians(ra)
ra_gp = numpy.radians(192.85948)
de_gp = numpy.radians(27.12825)
sin_ra_gp = numpy.sin(ra - ra_gp)
cos_ra_gp = numpy.cos(ra - ra_gp)
lcp = numpy.radians(122.932)
sin_b = (numpy.sin(de_gp) * sin_dec) \
+ (numpy.cos(de_gp) * cos_dec * cos_ra_gp)
lcpml = numpy.arctan2(cos_dec * sin_ra_gp,
(numpy.cos(de_gp) * sin_dec) \
- (numpy.sin(de_gp) * cos_dec * cos_ra_gp))
bb = numpy.arcsin(sin_b)
ll = (lcp - lcpml + (2. * numpy.pi)) % (2. * numpy.pi)
return numpy.degrees(ll), numpy.degrees(bb) Example 40
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 41
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 42
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 43
def ph_dec(m_phs, m_phc, mode='angle'):
if mode == 'sign':
m_bs = np.arcsin(m_phs)
m_bc = np.arccos(m_phc)
m_ph = np.sign(m_bs) * np.abs(m_bc)
elif mode == 'angle':
m_ph = np.angle(m_phc + m_phs * 1j)
return m_ph
#==============================================================================
# From 'analysis_with_del_comp_and_ph_encoding_from_files'
# f0_type: 'f0', 'lf0' Example 44
def refraction_plane(k_vec, n_vec, n1, n2):
'''
k_vec: the directional vector of the incidental ray
n_vec: the normal vector of the incidental plane
n1, n2: the refractive indices
'''
s_vec, p_vec, sin_ins = incident_plane(k_vec, n_vec)
sin_ref = n1*sin_ins /n2 # sin(phi')
a_inc = np.arcsin(sin_ins)
a_ref = np.arcsin(sin_ref)
a_diff = a_inc-a_ref
kr_vec = np.cos(a_diff)*k_vec -np.sin(a_diff)*p_vec
if(kr_vec[2]>0):
print(a_diff, k_vec)
# next, let's calculate the reflectance
cos_inc = np.cos(a_inc)
cos_ref = np.cos(a_ref)
Rs = ((n1*cos_inc - n2*cos_ref)/(n1*cos_inc + n2*cos_ref))**2
Rp = ((n1*cos_ref - n2*cos_inc)/(n1*cos_ref + n2*cos_inc))**2
return kr_vec, Rs, Rp
# done with refraction_plane Example 45
def test_haversine_metric():
def haversine_slow(x1, x2):
return 2 * np.arcsin(np.sqrt(np.sin(0.5 * (x1[0] - x2[0])) ** 2
+ np.cos(x1[0]) * np.cos(x2[0]) *
np.sin(0.5 * (x1[1] - x2[1])) ** 2))
X = np.random.random((10, 2))
haversine = DistanceMetric.get_metric("haversine")
D1 = haversine.pairwise(X)
D2 = np.zeros_like(D1)
for i, x1 in enumerate(X):
for j, x2 in enumerate(X):
D2[i, j] = haversine_slow(x1, x2)
assert_array_almost_equal(D1, D2)
assert_array_almost_equal(haversine.dist_to_rdist(D1),
np.sin(0.5 * D2) ** 2) Example 46
def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1 Example 47
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64 Example 48
def test_against_cmath(self):
import cmath
points = [-1-1j, -1+1j, +1-1j, +1+1j]
name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
atol = 4*np.finfo(np.complex).eps
for func in self.funcs:
fname = func.__name__.split('.')[-1]
cname = name_map.get(fname, fname)
try:
cfunc = getattr(cmath, cname)
except AttributeError:
continue
for p in points:
a = complex(func(np.complex_(p)))
b = cfunc(p)
assert_(abs(a - b) < atol, "%s %s: %s; cmath: %s" % (fname, p, a, b)) Example 49
def transform_non_affine(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:2]
clong = self._center_longitude
clat = self._center_latitude
p = np.sqrt(x*x + y*y)
p = np.where(p == 0.0, 1e-9, p)
c = self._calculate_c(p)
sin_c = np.sin(c)
cos_c = np.cos(c)
lat = np.arcsin(cos_c*np.sin(clat) + ((y*sin_c*np.cos(clat)) / p))
lon = clong + np.arctan(
(x*sin_c) / (p*np.cos(clat)*cos_c - y*np.sin(clat)*sin_c))
return np.concatenate((lon, lat), 1) Example 50
def getTrainKernel(self, params): self.checkParams(params) if (self.sameParams(params)): return self.cache['getTrainKernel'] ell2 = np.exp(2*params[0]) sqrt_ell2PSx = np.sqrt(ell2+self.sx) K = self.S / np.outer(sqrt_ell2PSx, sqrt_ell2PSx) self.cache['K'] = K K_arcsin = np.arcsin(K) self.cache['getTrainKernel'] = K_arcsin self.saveParams(params) return K_arcsin
