The following are code examples for showing how to use . They are extracted from open source Python projects. You can vote up the examples you like or vote down the exmaples you don’t like. You can also save this page to your account.
Example 1
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 2
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 3
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 4
def age(self, z):
"""
Cosmic time (age) at redshift z.
Parameters
----------
z : `~numpy.ndarray`
Redshift
Returns
-------
age : `~numpy.ndarray`
Age of the universe (cosmic time) at the given redshift.
Unit: [Gyr]
References: Ref.[thomas2000],Eq.(18)
"""
z = np.asarray(z)
t_H = self.hubble_time
t = ((2*t_H / 3 / np.sqrt(1-self.Om0)) *
np.arcsinh(np.sqrt((1/self.Om0 - 1) / (1+z)**3)))
return t Example 5
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 6
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 7
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 8
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 9
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 10
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 11
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 12
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 13
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 14
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 15
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 16
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 17
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 18
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 19
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 20
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 21
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 22
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 23
def asinh(v):
return v.__class__(numpy.arcsinh(v)) Example 24
def age(R):
H0 = 2.3e-18
OmegaM0 = 0.27
yr = 365.25 * 24 * 3600
T0 = 13.7e9
return T0 - (2./3./H0/np.sqrt(1-OmegaM0)) * np.arcsinh(np.sqrt( (1/OmegaM0-1)*R**3 )) / yr
# return the radius of a particle (in kpc) given its mass (in Msun) and density (in Msun/kpc3) Example 25
def age(R):
H0 = 2.3e-18
OmegaM0 = 0.27
yr = 365.25 * 24 * 3600
T0 = 13.7e9
return T0 - (2./3./H0/np.sqrt(1-OmegaM0)) * np.arcsinh(np.sqrt( (1/OmegaM0-1)*R**3 )) / yr
## This private helper function returns the periodicity corrected coordinates input as a (N,3)
# numpy array, and takes the box size (in units of crds) and a test length in units of box size Example 26
def age(R):
H0 = 2.3e-18
OmegaM0 = 0.27
yr = 365.25 * 24 * 3600
T0 = 13.7e9
return T0 - (2./3./H0/np.sqrt(1-OmegaM0)) * np.arcsinh(np.sqrt( (1/OmegaM0-1)*R**3 )) / yr
# return the radius of a particle (in kpc) given its mass (in Msun) and density (in Msun/kpc3) Example 27
def age(R):
H0 = 2.3e-18
OmegaM0 = 0.27
yr = 365.25 * 24 * 3600
T0 = 13.7e9
return T0 - (2./3./H0/np.sqrt(1-OmegaM0)) * np.arcsinh(np.sqrt( (1/OmegaM0-1)*R**3 )) / yr
## This private helper function returns the periodicity corrected coordinates input as a (N,3)
# numpy array, and takes the box size (in units of crds) and a test length in units of box size Example 28
def test_quadratic(self):
self._scipy_skip()
nodes = np.asfortranarray([
[0.0, 0.0],
[1.0, 2.0],
[2.0, 0.0],
])
length = self._call_function_under_test(nodes)
# 2 INT_0^1 SQRT(16 s^2 - 16 s + 5) ds = SQRT(5) + sinh^{-1}(2)/2
arcs2 = np.arcsinh(2.0) # pylint: disable=no-member
expected = np.sqrt(5.0) + 0.5 * arcs2
local_eps = abs(SPACING(expected))
self.assertAlmostEqual(length, expected, delta=local_eps) Example 29
def HybridMag(flux_parameter, band, index=None):
"""Returns a hybrid property describing an asinh magnitude.
``flux_parameter`` must be a column with a flux in nanomaggies. ``band`` is
the band name, to determine the softening parameter. If ``flux_parameter``
is and array, ``index`` defines the position of ``band`` within the array.
"""
@hybrid_property
def hybridMag(self):
if index is not None:
flux = getattr(self, flux_parameter)[index]
else:
flux = getattr(self, flux_parameter)
flux *= 1e-9 # From nanomaggies to maggies
bb_band = bb[band]
asinh_mag = -2.5 / np.log(10) * (np.arcsinh(flux / (2. * bb_band)) + np.log(bb_band))
return asinh_mag
@hybridMag.expression
def hybridMag(cls):
if index is not None:
# It needs to be index + 1 because Postgresql arrays are 1-indexed.
flux = getattr(cls, flux_parameter)[index + 1]
else:
flux = getattr(cls, flux_parameter)
flux *= 1e-9
bb_band = bb[band]
xx = flux / (2. * bb_band)
asinh_mag = (-2.5 / func.log(10) *
(func.log(xx + func.sqrt(func.pow(xx, 2) + 1)) + func.log(bb_band)))
return cast(asinh_mag, Float)
return hybridMag Example 30
def compute_psi(b2, l_eff_a, f_ch, channel_index, interfering_index, rs):
""" compute_psi computes the psi coefficient of the analytical formula.
:param b2: Fiber dispersion coefficient in ps/THz/km. Scalar
:param l_eff_a: Asymptotic effective length in km. Scalar
:param f_ch: Baseband channels center frequencies in THz. Array of size 1xNch
:param channel_index: Index of the channel. Scalar
:param interfering_index: Index of the interfering signal. Scalar
:param rs: Channels' Symbol Rates in TBaud. Array of size 1xNch
:return: psi: the coefficient
"""
b2 = np.abs(b2)
if channel_index == interfering_index: # The signal interfere with itself
rs_sig = rs[channel_index]
psi = np.arcsinh(0.5 * np.pi ** 2 * l_eff_a * b2 * rs_sig ** 2)
else:
f_sig = f_ch[channel_index]
rs_sig = rs[channel_index]
f_int = f_ch[interfering_index]
rs_int = rs[interfering_index]
del_f = f_sig - f_int
psi = np.arcsinh(np.pi ** 2 * l_eff_a * b2 * rs_sig * (del_f + 0.5 * rs_int))
psi -= np.arcsinh(np.pi ** 2 * l_eff_a * b2 * rs_sig * (del_f - 0.5 * rs_int))
return psi Example 31
def _latlon_to_tile(lat, lon, zoom): n = 2 ** zoom x = n * (lon + 180) / 360. y = n * (1 - (np.arcsinh(np.tan(np.deg2rad(lat))) / np.pi)) / 2. return int(x), int(y)
Example 32
def asinhmag(flux, fluxerr, m0 = 22.5, f0=1.0, b=0.01): """ Implements http://ssg.astro.washington.edu/elsst/opsim.shtml?lightcurve_mags """ mag = m0 -(2.5/np.log(10.)) * ( np.arcsinh( flux / (f0 * 2.0 * b)) + np.log(b) ) magplu = m0 -(2.5/np.log(10.)) * ( np.arcsinh( (flux+fluxerr) / (f0 * 2.0 * b)) + np.log(b) ) magmin = m0 -(2.5/np.log(10.)) * ( np.arcsinh( (flux-fluxerr) / (f0 * 2.0 * b)) + np.log(b) ) magerr = 0.5*(magmin - magplu) return (mag, magerr)
Example 33
def adjust(origin):
img = origin.copy()
img[img>4] = 4
img[img < -0.1] = -0.1
MIN = np.min(img)
MAX = np.max(img)
img = np.arcsinh(10*(img - MIN)/(MAX-MIN))/3
return img Example 34
def hz2bark(self, f):
""" Method to compute Bark from Hz.
Args :
f : (ndarray) Array containing frequencies in Hz.
Returns :
Brk : (ndarray) Array containing Bark scaled values.
"""
Brk = 6. * np.arcsinh(f/600.) # Method from RASTA model and computable inverse function.
#Brk = 13. * np.arctan(0.76*f/1000.) + 3.5 * np.arctan(f / (1000 * 7.5)) ** 2.
return Brk Example 35
def test_numpy_method():
# This type of code is used frequently by PyMC3 users
x = tt.dmatrix('x')
data = np.random.rand(5, 5)
x.tag.test_value = data
for fct in [np.arccos, np.arccosh, np.arcsin, np.arcsinh,
np.arctan, np.arctanh, np.ceil, np.cos, np.cosh, np.deg2rad,
np.exp, np.exp2, np.expm1, np.floor, np.log,
np.log10, np.log1p, np.log2, np.rad2deg,
np.sin, np.sinh, np.sqrt, np.tan, np.tanh, np.trunc]:
y = fct(x)
f = theano.function([x], y)
utt.assert_allclose(np.nan_to_num(f(data)),
np.nan_to_num(fct(data))) Example 36
def impl(self, x):
# If x is an int8 or uint8, numpy.arcsinh will compute the result in
# half-precision (float16), where we want float32.
x_dtype = str(getattr(x, 'dtype', ''))
if x_dtype in ('int8', 'uint8'):
return numpy.arcsinh(x, sig='f')
return numpy.arcsinh(x) Example 37
def arcsinh(inp):
if isinstance(inp, ooarray) and inp.dtype == object:
return ooarray([arcsinh(elem) for elem in inp])
if not isinstance(inp, oofun):
return np.arcsinh(inp)
# TODO: move it outside of arcsinh definition
def interval(arg_inf, arg_sup):
raise 'interval for arcsinh is unimplemented yet'
r = oofun(np.arcsinh, inp, d = lambda x: FDmisc.Diag(1.0/sqrt(x**2 + 1)), vectorized = True, interval = interval)
return r Example 38
def t_from_z(self, z):
"""
Compute the age of the Universe from redshift. This is based on Enzo's
CosmologyComputeTimeFromRedshift.C, but altered to use physical units.
Similar to hubble_time, but using an analytical function.
Parameters
----------
z : float
Redshift.
Examples
--------
>>> from yt.utilities.cosmology import Cosmology
>>> co = Cosmology()
>>> print(co.t_from_z(0.).in_units("Gyr"))
See Also
--------
hubble_time
"""
omega_curvature = 1.0 - self.omega_matter - self.omega_lambda
# 1) For a flat universe with omega_matter = 1, things are easy.
if ((self.omega_matter == 1.0) and (self.omega_lambda == 0.0)):
t0 = 2.0/3.0/np.power(1+z, 1.5)
# 2) For omega_matter < 1 and omega_lambda == 0 see
# Peebles 1993, eq. 13-3, 13-10.
if ((self.omega_matter < 1) and (self.omega_lambda == 0)):
eta = np.arccosh(1 +
2*(1-self.omega_matter)/self.omega_matter/(1+z))
t0 = self.omega_matter/ \
(2*np.power(1.0-self.omega_matter, 1.5))*\
(np.sinh(eta) - eta)
# 3) For omega_matter > 1 and omega_lambda == 0, use sin/cos.
if ((self.omega_matter > 1) and (self.omega_lambda == 0)):
eta = np.arccos(1 - 2*(1-self.omega_matter)/self.omega_matter/(1+z))
t0 = self.omega_matter/(2*np.power(1.0-self.omega_matter, 1.5))*\
(eta - np.sin(eta))
# 4) For flat universe, with non-zero omega_lambda, see eq. 13-20.
if ((np.fabs(omega_curvature) < 1.0e-3) and (self.omega_lambda != 0)):
t0 = 2.0/3.0/np.sqrt(1-self.omega_matter)*\
np.arcsinh(np.sqrt((1-self.omega_matter)/self.omega_matter)/ \
np.power(1+z, 1.5))
# Now convert from Time * H0 to time.
my_time = t0 / self.hubble_constant
return my_time.in_base(self.unit_system) Example 39
def test_numpy_ufuncs(self):
# test ufuncs of numpy 1.9.2. see:
# http://docs.scipy.org/doc/numpy/reference/ufuncs.html
# some functions are skipped because it may return different result
# for unicode input depending on numpy version
for name, idx in compat.iteritems(self.indices):
for func in [np.exp, np.exp2, np.expm1, np.log, np.log2, np.log10,
np.log1p, np.sqrt, np.sin, np.cos, np.tan, np.arcsin,
np.arccos, np.arctan, np.sinh, np.cosh, np.tanh,
np.arcsinh, np.arccosh, np.arctanh, np.deg2rad,
np.rad2deg]:
if isinstance(idx, pd.tseries.base.DatetimeIndexOpsMixin):
# raise TypeError or ValueError (PeriodIndex)
# PeriodIndex behavior should be changed in future version
with tm.assertRaises(Exception):
func(idx)
elif isinstance(idx, (Float64Index, Int64Index)):
# coerces to float (e.g. np.sin)
result = func(idx)
exp = Index(func(idx.values), name=idx.name)
self.assert_index_equal(result, exp)
self.assertIsInstance(result, pd.Float64Index)
else:
# raise AttributeError or TypeError
if len(idx) == 0:
continue
else:
with tm.assertRaises(Exception):
func(idx)
for func in [np.isfinite, np.isinf, np.isnan, np.signbit]:
if isinstance(idx, pd.tseries.base.DatetimeIndexOpsMixin):
# raise TypeError or ValueError (PeriodIndex)
with tm.assertRaises(Exception):
func(idx)
elif isinstance(idx, (Float64Index, Int64Index)):
# results in bool array
result = func(idx)
exp = func(idx.values)
self.assertIsInstance(result, np.ndarray)
tm.assertNotIsInstance(result, Index)
else:
if len(idx) == 0:
continue
else:
with tm.assertRaises(Exception):
func(idx) 