def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
python类cosh()的实例源码
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def cosh(a):
"""Elementwise hyperbolic cosine."""
if not isSparseVector(a):
raise TypeError("Argument must be a SparseVector")
rv = SparseVector(a.n, {})
for k in a.values.keys():
rv.values[k] = math.cosh(a.values[k])
return rv
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def T(a,b,d):
T = (math.cosh(a+b) - math.cosh(a-b))/(math.cosh(a+b) + math.cosh(d))
return T
#Calculation of SINH function of Kappa
def toGeographic(self, x, y):
x = x/(self.k * self.radius)
y = y/(self.k * self.radius)
D = y + self.latInRadians
lon = math.atan(math.sinh(x)/math.cos(D))
lat = math.asin(math.sin(D)/math.cosh(x))
lon = self.lon + math.degrees(lon)
lat = math.degrees(lat)
return (lat, lon)
def cosh(node): return merge([node], math.cosh)
def toGeographic(self, x, y):
x /= self.radius
y /= self.radius
D = y + self.lat_rad
lon = atan(sinh(x) / cos(D))
lat = asin(sin(D) / cosh(x))
lon = self.lon + degrees(lon)
lat = degrees(lat)
return lat, lon
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def cos(x):
z = _make_complex(x)
return cosh(complex(-z.imag, z.real))
def cosh(x):
_cosh_special = [
[inf+nanj, None, inf, complex(float("inf"), -0.0), None, inf+nanj, inf+nanj],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[nan, None, 1, complex(1, -0.0), None, nan, nan],
[nan, None, complex(1, -0.0), 1, None, nan, nan],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[inf+nanj, None, complex(float("inf"), -0.0), inf, None, inf+nanj, inf+nanj],
[nan+nanj, nan+nanj, nan, nan, nan+nanj, nan+nanj, nan+nanj]
]
z = _make_complex(x)
if not isfinite(z):
if math.isinf(z.imag) and not math.isnan(z.real):
raise ValueError
if math.isinf(z.real) and math.isfinite(z.imag) and z.imag != 0:
if z.real > 0:
return complex(math.copysign(inf, math.cos(z.imag)),
math.copysign(inf, math.sin(z.imag)))
return complex(math.copysign(inf, math.cos(z.imag)),
-math.copysign(inf, math.sin(z.imag)))
return _cosh_special[_special_type(z.real)][_special_type(z.imag)]
if abs(z.real) > _LOG_LARGE_DOUBLE:
x_minus_one = z.real - math.copysign(1, z.real)
ret = complex(e * math.cos(z.imag) * math.cosh(x_minus_one),
e * math.sin(z.imag) * math.sinh(x_minus_one))
else:
ret = complex(math.cos(z.imag) * math.cosh(z.real),
math.sin(z.imag) * math.sinh(z.real))
if math.isinf(ret.real) or math.isinf(ret.imag):
raise OverflowError
return ret
def sinh(x):
_sinh_special = [
[inf+nanj, None, complex(-float("inf"), -0.0), -inf, None, inf+nanj, inf+nanj],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[nanj, None, complex(-0.0, -0.0), complex(-0.0, 0.0), None, nanj, nanj],
[nanj, None, complex(0.0, -0.0), complex(0.0, 0.0), None, nanj, nanj],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[inf+nanj, None, complex(float("inf"), -0.0), inf, None, inf+nanj, inf+nanj],
[nan+nanj, nan+nanj, complex(float("nan"), -0.0), nan, nan+nanj, nan+nanj, nan+nanj]
]
z = _make_complex(x)
if not isfinite(z):
if math.isinf(z.imag) and not math.isnan(z.real):
raise ValueError
if math.isinf(z.real) and math.isfinite(z.imag) and z.imag != 0:
if z.real > 0:
return complex(math.copysign(inf, math.cos(z.imag)),
math.copysign(inf, math.sin(z.imag)))
return complex(-math.copysign(inf, math.cos(z.imag)),
math.copysign(inf, math.sin(z.imag)))
return _sinh_special[_special_type(z.real)][_special_type(z.imag)]
if abs(z.real) > _LOG_LARGE_DOUBLE:
x_minus_one = z.real - math.copysign(1, z.real)
return complex(math.cos(z.imag) * math.sinh(x_minus_one) * e,
math.sin(z.imag) * math.cosh(x_minus_one) * e)
return complex(math.cos(z.imag) * math.sinh(z.real),
math.sin(z.imag) * math.cosh(z.real))
def tanh(x):
_tanh_special = [
[-1, None, complex(-1, -0.0), -1, None, -1, -1],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[nan+nanj, None, complex(-0.0, -0.0), complex(-0.0, 0.0), None, nan+nanj, nan+nanj],
[nan+nanj, None, complex(0.0, -0.0), 0.0, None, nan+nanj, nan+nanj],
[nan+nanj, None, None, None, None, nan+nanj, nan+nanj],
[1, None, complex(1, -0.0), 1, None, 1, 1],
[nan+nanj, nan+nanj, complex(float("nan"), -0.0), nan, nan+nanj, nan+nanj, nan+nanj]
]
z = _make_complex(x)
if not isfinite(z):
if math.isinf(z.imag) and math.isfinite(z.real):
raise ValueError
if math.isinf(z.real) and math.isfinite(z.imag) and z.imag != 0:
if z.real > 0:
return complex(1, math.copysign(0.0, math.sin(z.imag)
* math.cos(z.imag)))
return complex(-1, math.copysign(0.0, math.sin(z.imag)
* math.cos(z.imag)))
return _tanh_special[_special_type(z.real)][_special_type(z.imag)]
if abs(z.real) > _LOG_LARGE_DOUBLE:
return complex(
math.copysign(1, z.real),
4*math.sin(z.imag)*math.cos(z.imag)*math.exp(-2*abs(z.real))
)
tanh_x = math.tanh(z.real)
tan_y = math.tan(z.imag)
cx = 1/math.cosh(z.real)
denom = 1 + tanh_x * tanh_x * tan_y * tan_y
return complex(tanh_x * (1 + tan_y*tan_y)/denom,
((tan_y / denom) * cx) * cx)
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def test_trig_hyperb_basic():
for x in (list(range(100)) + list(range(-100,0))):
t = x / 4.1
assert cos(mpf(t)).ae(math.cos(t))
assert sin(mpf(t)).ae(math.sin(t))
assert tan(mpf(t)).ae(math.tan(t))
assert cosh(mpf(t)).ae(math.cosh(t))
assert sinh(mpf(t)).ae(math.sinh(t))
assert tanh(mpf(t)).ae(math.tanh(t))
assert sin(1+1j).ae(cmath.sin(1+1j))
assert sin(-4-3.6j).ae(cmath.sin(-4-3.6j))
assert cos(1+1j).ae(cmath.cos(1+1j))
assert cos(-4-3.6j).ae(cmath.cos(-4-3.6j))
def test_complex_functions():
for x in (list(range(10)) + list(range(-10,0))):
for y in (list(range(10)) + list(range(-10,0))):
z = complex(x, y)/4.3 + 0.01j
assert exp(mpc(z)).ae(cmath.exp(z))
assert log(mpc(z)).ae(cmath.log(z))
assert cos(mpc(z)).ae(cmath.cos(z))
assert sin(mpc(z)).ae(cmath.sin(z))
assert tan(mpc(z)).ae(cmath.tan(z))
assert sinh(mpc(z)).ae(cmath.sinh(z))
assert cosh(mpc(z)).ae(cmath.cosh(z))
assert tanh(mpc(z)).ae(cmath.tanh(z))
