Python numpy 模块，arccosh() 实例源码
我们从Python开源项目中，提取了以下35个代码示例，用于说明如何使用numpy.arccosh()。
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
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
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))
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
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
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))
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
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
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))
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
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
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))
def _keplerian_to_keplerian_mean(cls, coord, center):
"""Conversion from Keplerian to Keplerian Mean
The difference is the use of Mean anomaly instead of True anomaly
"""
a, e, i, ?, ?, ? = coord
if e < 1:
# Elliptic case
E = arccos((e + cos(?)) / (1 + e * cos(?))) # Eccentric anomaly
M = E - e * sin(E) # Mean anomaly
else:
# Hyperbolic case
H = arccosh((e + cos(?)) / (1 + e * cos(?)))
M = e * sinh(H) - H
return np.array([a, e, i, ?, ?, M], dtype=float)
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
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
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))
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
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
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))
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
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
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))
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
def Dn_plane(l, r, N=20):
alpha = np.arccosh(l/r)
sinh = np.sinh
s = 0.
for n in range(1, N):
n = float(n)
K = n*(n+1)/(2*n-1)/(2*n+3)
s += K*((2*sinh((2*n+1)*alpha)+(2*n+1)*sinh(2*alpha))/(4*(sinh((n+.5)*alpha))**2-(2*n+1)**2*(sinh(alpha))**2) - 1)
return 1./((4./3.)*sinh(alpha)*s)
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
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)))
def impl(self, x):
# If x is an int8 or uint8, numpy.arccosh 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.arccosh(x, sig='f')
return numpy.arccosh(x)
def arccosh(inp):
if isinstance(inp, ooarray) and inp.dtype == object:
return ooarray([arccosh(elem) for elem in inp])
if not isinstance(inp, oofun):
return np.arccosh(inp)
# TODO: move it outside of arccosh definition
def interval(arg_inf, arg_sup):
raise 'interval for arccosh is unimplemented yet'
r = oofun(np.arccosh, inp, d = lambda x: FDmisc.Diag(1.0/sqrt(x**2 - 1)), vectorized = True, interval = interval)
return r
def test_it(self):
for f in self.funcs:
if f is np.arccosh:
x = 1.5
else:
x = .5
fr = f(x)
fz = f(np.complex(x))
assert_almost_equal(fz.real, fr, err_msg='real part %s' % f)
assert_almost_equal(fz.imag, 0., err_msg='imag part %s' % f)
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)
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)