def quadrf(ev, y):
L = ev[1] # length
k = ev[4] # quadrupole strength
if k == 0:
R = drift(ev, y)
else:
wrzlk = sqrt(abs(k))
Omega = wrzlk*L
coshom = cosh(Omega)
sinhom = sinh(Omega)
cosom = cos(Omega)
sinom = sin(Omega)
R = array([
[cosom, sinom/wrzlk, 0., 0., 0., 0.],
[-wrzlk*sinom, cosom, 0., 0., 0., 0.],
[0., 0., coshom, sinhom/wrzlk, 0., 0.],
[0., 0., wrzlk*sinhom, coshom, 0., 0.],
[0., 0., 0., 0., 1., L/(y**2)],
[0., 0., 0., 0., 0., 1.]
])
return R
python类sinh()的实例源码
def quadaf(ev, y):
L = ev[1] # length
k = ev[4] # quadrupole strength
if k == 0:
R = drift(ev, y)
else:
wrzlk = sqrt(abs(k))
Omega = wrzlk*L
coshom = cosh(Omega)
sinhom = sinh(Omega)
cosom = cos(Omega)
sinom = sin(Omega)
R = array([
[coshom, sinhom/wrzlk, 0., 0., 0., 0],
[wrzlk*sinhom, coshom, 0., 0., 0., 0],
[0., 0., cosom, sinom/wrzlk, 0., 0],
[0., 0., -wrzlk*sinom, cosom, 0., 0],
[0., 0., 0., 0., 1., L/(y**2)],
[0., 0., 0., 0., 0., 1.]
])
return R
def redshift(self, age):
"""
Invert the above ``self.age(z)`` formula analytically, to calculate
the redshift corresponding to the given cosmic time (age).
Parameters
----------
age : `~numpy.ndarray`
Age of the universe (i.e., cosmic time)
Unit: [Gyr]
Returns
-------
z : `~numpy.ndarray`
Redshift corresponding to the specified age.
"""
age = np.asarray(age)
t_H = self.hubble_time
term1 = (1/self.Om0) - 1
term2 = np.sinh(3*age * np.sqrt(1-self.Om0) / (2*t_H)) ** 2
z = (term1 / term2) ** (1/3) - 1
return z
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 sinh(self, out=None):
assert out is None
return self.elemwise(np.sinh)
def Dm(self, z, cm=False, meter=False, pc=False, kpc=False, mpc=False):
Ok = self.Ok()
sOk = num.sqrt(num.abs(Ok))
Dc = self.Dc(z)
Dh = self.Dh()
conversion = self.lengthConversion(cm=cm, meter=meter, pc=pc, kpc=kpc, mpc=mpc)
if Ok > 0:
return Dh / sOk * num.sinh(sOk * Dc / Dh) * conversion
elif Ok == 0:
return Dc * conversion
else:
return Dh / sOk * num.sin(sOk * Dc / Dh) * conversion
# Angular diameter distance
# Ratio of an objects physical transvserse size to its angular size in radians
def test_basic_ufuncs(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf) = self.d
assert_equal(np.cos(x), cos(xm))
assert_equal(np.cosh(x), cosh(xm))
assert_equal(np.sin(x), sin(xm))
assert_equal(np.sinh(x), sinh(xm))
assert_equal(np.tan(x), tan(xm))
assert_equal(np.tanh(x), tanh(xm))
assert_equal(np.sqrt(abs(x)), sqrt(xm))
assert_equal(np.log(abs(x)), log(xm))
assert_equal(np.log10(abs(x)), log10(xm))
assert_equal(np.exp(x), exp(xm))
assert_equal(np.arcsin(z), arcsin(zm))
assert_equal(np.arccos(z), arccos(zm))
assert_equal(np.arctan(z), arctan(zm))
assert_equal(np.arctan2(x, y), arctan2(xm, ym))
assert_equal(np.absolute(x), absolute(xm))
assert_equal(np.angle(x + 1j*y), angle(xm + 1j*ym))
assert_equal(np.angle(x + 1j*y, deg=True), angle(xm + 1j*ym, deg=True))
assert_equal(np.equal(x, y), equal(xm, ym))
assert_equal(np.not_equal(x, y), not_equal(xm, ym))
assert_equal(np.less(x, y), less(xm, ym))
assert_equal(np.greater(x, y), greater(xm, ym))
assert_equal(np.less_equal(x, y), less_equal(xm, ym))
assert_equal(np.greater_equal(x, y), greater_equal(xm, ym))
assert_equal(np.conjugate(x), conjugate(xm))
def test_testUfuncRegression(self):
# Tests new ufuncs on MaskedArrays.
for f in ['sqrt', 'log', 'log10', 'exp', 'conjugate',
'sin', 'cos', 'tan',
'arcsin', 'arccos', 'arctan',
'sinh', 'cosh', 'tanh',
'arcsinh',
'arccosh',
'arctanh',
'absolute', 'fabs', 'negative',
'floor', 'ceil',
'logical_not',
'add', 'subtract', 'multiply',
'divide', 'true_divide', 'floor_divide',
'remainder', 'fmod', 'hypot', 'arctan2',
'equal', 'not_equal', 'less_equal', 'greater_equal',
'less', 'greater',
'logical_and', 'logical_or', 'logical_xor',
]:
try:
uf = getattr(umath, f)
except AttributeError:
uf = getattr(fromnumeric, f)
mf = getattr(numpy.ma.core, f)
args = self.d[:uf.nin]
ur = uf(*args)
mr = mf(*args)
assert_equal(ur.filled(0), mr.filled(0), f)
assert_mask_equal(ur.mask, mr.mask, err_msg=f)
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
self.assertTrue(eq(np.cos(x), cos(xm)))
self.assertTrue(eq(np.cosh(x), cosh(xm)))
self.assertTrue(eq(np.sin(x), sin(xm)))
self.assertTrue(eq(np.sinh(x), sinh(xm)))
self.assertTrue(eq(np.tan(x), tan(xm)))
self.assertTrue(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
self.assertTrue(eq(np.sqrt(abs(x)), sqrt(xm)))
self.assertTrue(eq(np.log(abs(x)), log(xm)))
self.assertTrue(eq(np.log10(abs(x)), log10(xm)))
self.assertTrue(eq(np.exp(x), exp(xm)))
self.assertTrue(eq(np.arcsin(z), arcsin(zm)))
self.assertTrue(eq(np.arccos(z), arccos(zm)))
self.assertTrue(eq(np.arctan(z), arctan(zm)))
self.assertTrue(eq(np.arctan2(x, y), arctan2(xm, ym)))
self.assertTrue(eq(np.absolute(x), absolute(xm)))
self.assertTrue(eq(np.equal(x, y), equal(xm, ym)))
self.assertTrue(eq(np.not_equal(x, y), not_equal(xm, ym)))
self.assertTrue(eq(np.less(x, y), less(xm, ym)))
self.assertTrue(eq(np.greater(x, y), greater(xm, ym)))
self.assertTrue(eq(np.less_equal(x, y), less_equal(xm, ym)))
self.assertTrue(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
self.assertTrue(eq(np.conjugate(x), conjugate(xm)))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((xm, ym))))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((x, y))))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((xm, y))))
self.assertTrue(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def test_testUfuncRegression(self):
f_invalid_ignore = [
'sqrt', 'arctanh', 'arcsin', 'arccos',
'arccosh', 'arctanh', 'log', 'log10', 'divide',
'true_divide', 'floor_divide', 'remainder', 'fmod']
for f in ['sqrt', 'log', 'log10', 'exp', 'conjugate',
'sin', 'cos', 'tan',
'arcsin', 'arccos', 'arctan',
'sinh', 'cosh', 'tanh',
'arcsinh',
'arccosh',
'arctanh',
'absolute', 'fabs', 'negative',
'floor', 'ceil',
'logical_not',
'add', 'subtract', 'multiply',
'divide', 'true_divide', 'floor_divide',
'remainder', 'fmod', 'hypot', 'arctan2',
'equal', 'not_equal', 'less_equal', 'greater_equal',
'less', 'greater',
'logical_and', 'logical_or', 'logical_xor']:
try:
uf = getattr(umath, f)
except AttributeError:
uf = getattr(fromnumeric, f)
mf = getattr(np.ma, f)
args = self.d[:uf.nin]
with np.errstate():
if f in f_invalid_ignore:
np.seterr(invalid='ignore')
if f in ['arctanh', 'log', 'log10']:
np.seterr(divide='ignore')
ur = uf(*args)
mr = mf(*args)
self.assertTrue(eq(ur.filled(0), mr.filled(0), f))
self.assertTrue(eqmask(ur.mask, mr.mask))
def sinh(x: Number = 0.0) -> Number:
return np.sinh(x)
def bark2freq(b):
return 650.*np.sinh(b/7.)
def bark2freq(b):
return 650.*np.sinh(b/7.)
def bark2freq(b):
return 650*np.sinh(b/7)
def Dn_plane(l, r, N=10):
alpha = acosh(l/r)
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 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 Dn_plane(l, r, N=100):
alpha = acosh(l/r)
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 Dn_plane(l, r, N=100):
alpha = acosh(l/r)
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 sinh(v):
return v.__class__(numpy.sinh(v))
def cir_int_rt_chf(u, t, k, theta, sigma, r0):
r = np.sqrt(k ** 2 - 1j * u * 2 * sigma ** 2)
cosh_fun = np.cosh(r * t / 2)
sinh_fun = np.sinh(r * t / 2)
coth_fun = cosh_fun / sinh_fun
a_t_v = np.exp(t * theta * (k ** 2) / (sigma ** 2)) / (cosh_fun + (k / r) * sinh_fun) ** (
2 * k * theta / (sigma ** 2))
b_t_v = 2 * 1j * u / (k + r * coth_fun)
return a_t_v * np.exp(b_t_v * r0)
def test_basic_ufuncs(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf) = self.d
assert_equal(np.cos(x), cos(xm))
assert_equal(np.cosh(x), cosh(xm))
assert_equal(np.sin(x), sin(xm))
assert_equal(np.sinh(x), sinh(xm))
assert_equal(np.tan(x), tan(xm))
assert_equal(np.tanh(x), tanh(xm))
assert_equal(np.sqrt(abs(x)), sqrt(xm))
assert_equal(np.log(abs(x)), log(xm))
assert_equal(np.log10(abs(x)), log10(xm))
assert_equal(np.exp(x), exp(xm))
assert_equal(np.arcsin(z), arcsin(zm))
assert_equal(np.arccos(z), arccos(zm))
assert_equal(np.arctan(z), arctan(zm))
assert_equal(np.arctan2(x, y), arctan2(xm, ym))
assert_equal(np.absolute(x), absolute(xm))
assert_equal(np.angle(x + 1j*y), angle(xm + 1j*ym))
assert_equal(np.angle(x + 1j*y, deg=True), angle(xm + 1j*ym, deg=True))
assert_equal(np.equal(x, y), equal(xm, ym))
assert_equal(np.not_equal(x, y), not_equal(xm, ym))
assert_equal(np.less(x, y), less(xm, ym))
assert_equal(np.greater(x, y), greater(xm, ym))
assert_equal(np.less_equal(x, y), less_equal(xm, ym))
assert_equal(np.greater_equal(x, y), greater_equal(xm, ym))
assert_equal(np.conjugate(x), conjugate(xm))
def test_testUfuncRegression(self):
# Tests new ufuncs on MaskedArrays.
for f in ['sqrt', 'log', 'log10', 'exp', 'conjugate',
'sin', 'cos', 'tan',
'arcsin', 'arccos', 'arctan',
'sinh', 'cosh', 'tanh',
'arcsinh',
'arccosh',
'arctanh',
'absolute', 'fabs', 'negative',
'floor', 'ceil',
'logical_not',
'add', 'subtract', 'multiply',
'divide', 'true_divide', 'floor_divide',
'remainder', 'fmod', 'hypot', 'arctan2',
'equal', 'not_equal', 'less_equal', 'greater_equal',
'less', 'greater',
'logical_and', 'logical_or', 'logical_xor',
]:
try:
uf = getattr(umath, f)
except AttributeError:
uf = getattr(fromnumeric, f)
mf = getattr(numpy.ma.core, f)
args = self.d[:uf.nin]
ur = uf(*args)
mr = mf(*args)
assert_equal(ur.filled(0), mr.filled(0), f)
assert_mask_equal(ur.mask, mr.mask, err_msg=f)
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
self.assertTrue(eq(np.cos(x), cos(xm)))
self.assertTrue(eq(np.cosh(x), cosh(xm)))
self.assertTrue(eq(np.sin(x), sin(xm)))
self.assertTrue(eq(np.sinh(x), sinh(xm)))
self.assertTrue(eq(np.tan(x), tan(xm)))
self.assertTrue(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
self.assertTrue(eq(np.sqrt(abs(x)), sqrt(xm)))
self.assertTrue(eq(np.log(abs(x)), log(xm)))
self.assertTrue(eq(np.log10(abs(x)), log10(xm)))
self.assertTrue(eq(np.exp(x), exp(xm)))
self.assertTrue(eq(np.arcsin(z), arcsin(zm)))
self.assertTrue(eq(np.arccos(z), arccos(zm)))
self.assertTrue(eq(np.arctan(z), arctan(zm)))
self.assertTrue(eq(np.arctan2(x, y), arctan2(xm, ym)))
self.assertTrue(eq(np.absolute(x), absolute(xm)))
self.assertTrue(eq(np.equal(x, y), equal(xm, ym)))
self.assertTrue(eq(np.not_equal(x, y), not_equal(xm, ym)))
self.assertTrue(eq(np.less(x, y), less(xm, ym)))
self.assertTrue(eq(np.greater(x, y), greater(xm, ym)))
self.assertTrue(eq(np.less_equal(x, y), less_equal(xm, ym)))
self.assertTrue(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
self.assertTrue(eq(np.conjugate(x), conjugate(xm)))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((xm, ym))))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((x, y))))
self.assertTrue(eq(np.concatenate((x, y)), concatenate((xm, y))))
self.assertTrue(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def test_testUfuncRegression(self):
f_invalid_ignore = [
'sqrt', 'arctanh', 'arcsin', 'arccos',
'arccosh', 'arctanh', 'log', 'log10', 'divide',
'true_divide', 'floor_divide', 'remainder', 'fmod']
for f in ['sqrt', 'log', 'log10', 'exp', 'conjugate',
'sin', 'cos', 'tan',
'arcsin', 'arccos', 'arctan',
'sinh', 'cosh', 'tanh',
'arcsinh',
'arccosh',
'arctanh',
'absolute', 'fabs', 'negative',
'floor', 'ceil',
'logical_not',
'add', 'subtract', 'multiply',
'divide', 'true_divide', 'floor_divide',
'remainder', 'fmod', 'hypot', 'arctan2',
'equal', 'not_equal', 'less_equal', 'greater_equal',
'less', 'greater',
'logical_and', 'logical_or', 'logical_xor']:
try:
uf = getattr(umath, f)
except AttributeError:
uf = getattr(fromnumeric, f)
mf = getattr(np.ma, f)
args = self.d[:uf.nin]
with np.errstate():
if f in f_invalid_ignore:
np.seterr(invalid='ignore')
if f in ['arctanh', 'log', 'log10']:
np.seterr(divide='ignore')
ur = uf(*args)
mr = mf(*args)
self.assertTrue(eq(ur.filled(0), mr.filled(0), f))
self.assertTrue(eqmask(ur.mask, mr.mask))
def comoving_transverse_distance(self, z_i, z_f):
r"""
When multiplied by some angle, the distance between two objects
observed at redshift, z_f, with an angular separation given by that
angle, viewed by an observer at redshift, z_i (Hogg 1999).
Parameters
----------
z_i : float
The redshift of the observer.
z_f : float
The redshift of the observed object.
Examples
--------
>>> from yt.utilities.cosmology import Cosmology
>>> co = Cosmology()
>>> print(co.comoving_transverse_distance(0., 1.).in_units("Mpccm"))
"""
if (self.omega_curvature > 0):
return (self.hubble_distance() / np.sqrt(self.omega_curvature) *
np.sinh(np.sqrt(self.omega_curvature) *
self.comoving_radial_distance(z_i, z_f) /
self.hubble_distance())).in_base(self.unit_system)
elif (self.omega_curvature < 0):
return (self.hubble_distance() /
np.sqrt(np.fabs(self.omega_curvature)) *
np.sin(np.sqrt(np.fabs(self.omega_curvature)) *
self.comoving_radial_distance(z_i, z_f) /
self.hubble_distance())).in_base(self.unit_system)
else:
return self.comoving_radial_distance(z_i, z_f)
def __init__(self, generator: Generator=Autoincrement()):
super().__init__(numpy.sinh, generator)
def test_sinh():
fun = lambda x : 3.0 * np.sinh(x)
d_fun = grad(fun)
check_grads(fun, npr.randn())
check_grads(d_fun, npr.randn())
def integrate_fip(p, v, z, dt, omega2):
"""
Integrate the equation of motion of the Floating-base Inverted Pendulum.
Parameters
----------
p : array, shape=(3,)
Initial position.
v : array, shape=(3,)
Initial velocity.
z : array, shape=(3,)
ZMP location throughout the integration.
dt : scalar
Integration step.
omega2 : scalar
FIP constant.
Returns
-------
p_next : array, shape=(3,)
Position at the end of the integration step.
v_next : array, shape=(3,)
Velocity at the end of the integration step.
Note
----
The Linear Inverted Pendulum Mode (LIPM) is a special case of the FIP, so
this function also applies to COP-based controllers.
"""
omega = sqrt(omega2)
a = omega2 * (p - z) + gravity
p_next = p + v / omega * sinh(omega * dt) \
+ a / omega2 * (cosh(omega * dt) - 1.)
v_next = v * cosh(omega * dt) + a / omega * sinh(omega * dt)
return p_next, v_next
test_core.py 文件源码
项目：PyDataLondon29-EmbarrassinglyParallelDAWithAWSLambda
作者: SignalMedia
项目源码
文件源码
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def test_basic_ufuncs(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf) = self.d
assert_equal(np.cos(x), cos(xm))
assert_equal(np.cosh(x), cosh(xm))
assert_equal(np.sin(x), sin(xm))
assert_equal(np.sinh(x), sinh(xm))
assert_equal(np.tan(x), tan(xm))
assert_equal(np.tanh(x), tanh(xm))
assert_equal(np.sqrt(abs(x)), sqrt(xm))
assert_equal(np.log(abs(x)), log(xm))
assert_equal(np.log10(abs(x)), log10(xm))
assert_equal(np.exp(x), exp(xm))
assert_equal(np.arcsin(z), arcsin(zm))
assert_equal(np.arccos(z), arccos(zm))
assert_equal(np.arctan(z), arctan(zm))
assert_equal(np.arctan2(x, y), arctan2(xm, ym))
assert_equal(np.absolute(x), absolute(xm))
assert_equal(np.angle(x + 1j*y), angle(xm + 1j*ym))
assert_equal(np.angle(x + 1j*y, deg=True), angle(xm + 1j*ym, deg=True))
assert_equal(np.equal(x, y), equal(xm, ym))
assert_equal(np.not_equal(x, y), not_equal(xm, ym))
assert_equal(np.less(x, y), less(xm, ym))
assert_equal(np.greater(x, y), greater(xm, ym))
assert_equal(np.less_equal(x, y), less_equal(xm, ym))
assert_equal(np.greater_equal(x, y), greater_equal(xm, ym))
assert_equal(np.conjugate(x), conjugate(xm))
test_core.py 文件源码
项目：PyDataLondon29-EmbarrassinglyParallelDAWithAWSLambda
作者: SignalMedia
项目源码
文件源码
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def test_testUfuncRegression(self):
# Tests new ufuncs on MaskedArrays.
for f in ['sqrt', 'log', 'log10', 'exp', 'conjugate',
'sin', 'cos', 'tan',
'arcsin', 'arccos', 'arctan',
'sinh', 'cosh', 'tanh',
'arcsinh',
'arccosh',
'arctanh',
'absolute', 'fabs', 'negative',
# 'nonzero', 'around',
'floor', 'ceil',
# 'sometrue', 'alltrue',
'logical_not',
'add', 'subtract', 'multiply',
'divide', 'true_divide', 'floor_divide',
'remainder', 'fmod', 'hypot', 'arctan2',
'equal', 'not_equal', 'less_equal', 'greater_equal',
'less', 'greater',
'logical_and', 'logical_or', 'logical_xor',
]:
try:
uf = getattr(umath, f)
except AttributeError:
uf = getattr(fromnumeric, f)
mf = getattr(numpy.ma.core, f)
args = self.d[:uf.nin]
ur = uf(*args)
mr = mf(*args)
assert_equal(ur.filled(0), mr.filled(0), f)
assert_mask_equal(ur.mask, mr.mask, err_msg=f)
