def test11_hyp():
for i in range(-5, 5):
for j in range(-5, 5):
a = ek.sinh(C(i, j))
b = C(cmath.sinh(complex(i, j)))
assert ek.allclose(a, b)
a = ek.cosh(C(i, j))
b = C(cmath.cosh(complex(i, j)))
assert ek.allclose(a, b)
sa, ca = ek.sincosh(C(i, j))
sb = C(cmath.sinh(complex(i, j)))
cb = C(cmath.cosh(complex(i, j)))
assert ek.allclose(sa, sb)
assert ek.allclose(ca, cb)
# Python appears to handle the branch cuts
# differently from Enoki, C, and Mathematica..
a = ek.asinh(C(i + 0.1, j))
b = C(cmath.asinh(complex(i + 0.1, j)))
assert ek.allclose(a, b)
a = ek.acosh(C(i, j))
b = C(cmath.acosh(complex(i, j)))
assert ek.allclose(a, b, atol=1e-7)
if abs(i) != 1 or j != 0:
a = ek.atanh(C(i, j))
b = C(cmath.atanh(complex(i, j)))
assert ek.allclose(a, b, atol=1e-7)
def test_areal_inverses():
assert asin(mpf(0)) == 0
assert asinh(mpf(0)) == 0
assert acosh(mpf(1)) == 0
assert isinstance(asin(mpf(0.5)), mpf)
assert isinstance(asin(mpf(2.0)), mpc)
assert isinstance(acos(mpf(0.5)), mpf)
assert isinstance(acos(mpf(2.0)), mpc)
assert isinstance(atanh(mpf(0.1)), mpf)
assert isinstance(atanh(mpf(1.1)), mpc)
random.seed(1)
for i in range(50):
x = random.uniform(0, 1)
assert asin(mpf(x)).ae(math.asin(x))
assert acos(mpf(x)).ae(math.acos(x))
x = random.uniform(-10, 10)
assert asinh(mpf(x)).ae(cmath.asinh(x).real)
assert isinstance(asinh(mpf(x)), mpf)
x = random.uniform(1, 10)
assert acosh(mpf(x)).ae(cmath.acosh(x).real)
assert isinstance(acosh(mpf(x)), mpf)
x = random.uniform(-10, 0.999)
assert isinstance(acosh(mpf(x)), mpc)
x = random.uniform(-1, 1)
assert atanh(mpf(x)).ae(cmath.atanh(x).real)
assert isinstance(atanh(mpf(x)), mpf)
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9 * j * 10**k + 0.8 * one * 10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2 * 10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9 * 10**k + j * 0.8 * one * 10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_areal_inverses():
assert asin(mpf(0)) == 0
assert asinh(mpf(0)) == 0
assert acosh(mpf(1)) == 0
assert isinstance(asin(mpf(0.5)), mpf)
assert isinstance(asin(mpf(2.0)), mpc)
assert isinstance(acos(mpf(0.5)), mpf)
assert isinstance(acos(mpf(2.0)), mpc)
assert isinstance(atanh(mpf(0.1)), mpf)
assert isinstance(atanh(mpf(1.1)), mpc)
random.seed(1)
for i in range(50):
x = random.uniform(0, 1)
assert asin(mpf(x)).ae(math.asin(x))
assert acos(mpf(x)).ae(math.acos(x))
x = random.uniform(-10, 10)
assert asinh(mpf(x)).ae(cmath.asinh(x).real)
assert isinstance(asinh(mpf(x)), mpf)
x = random.uniform(1, 10)
assert acosh(mpf(x)).ae(cmath.acosh(x).real)
assert isinstance(acosh(mpf(x)), mpf)
x = random.uniform(-10, 0.999)
assert isinstance(acosh(mpf(x)), mpc)
x = random.uniform(-1, 1)
assert atanh(mpf(x)).ae(cmath.atanh(x).real)
assert isinstance(atanh(mpf(x)), mpf)
def Zin(Zl, Zo, B, l, a=0):
"""
Impedância de entrada (Meios com ou sem perdas)
Obs : Para meios sem perdas, o valor de a é definido em 0
e pode ser deixado em branco
Parâmetros
----------
Zl : Imp. característica do meio 2
Zo : Imp. característica do meio 1
B : Constante de fase da onda
l : Distância do ponto de encontro entre os dois
meios e o ponto de visão relativo da impedância
a : Constante de atenuação da onda
Retorna a impedância de entrada no formato cartesiano (alfa + jBeta)
"""
z = a + B * 1j
x = cmath.atanh(z * l)
x = Zo * (Zl + Zo * x) / (Zo + Zl * x)
helper.prettyPrint(x, ["Impedância de entrada"])
return x
def op_atanh(x):
"""Returns the inverse hyperbolic tangent of this mathematical object."""
if isinstance(x, list):
return [op_atanh(a) for a in x]
elif isinstance(x, complex):
return cmath.atanh(x)
else:
return math.atanh(x)
def atan_impl(z):
"""cmath.atan(z) = -j * cmath.atanh(z j)"""
r = cmath.atanh(complex(-z.imag, z.real))
if math.isinf(z.real) and math.isnan(z.imag):
# XXX this is odd but necessary
return complex(r.imag, r.real)
else:
return complex(r.imag, -r.real)
def atan_impl(z):
"""cmath.atan(z) = -j * cmath.atanh(z j)"""
r = cmath.atanh(complex(-z.imag, z.real))
if math.isinf(z.real) and math.isnan(z.imag):
# XXX this is odd but necessary
return complex(r.imag, r.real)
else:
return complex(r.imag, -r.real)
def p_sine(t):
'''e : SINE LP e RP
| COSINE LP e RP
| SECANT LP e RP
| COSECANT LP e RP
| TANGENT LP e RP
| COTANGENT LP e RP
| LOG LP e COMMA e RP
| LN LP e RP
| EXP POW LP e RP
| ARCSINE LP e RP
| ARCCOSINE LP e RP
| ARCTANGENT LP e RP
| SINEH LP e RP
| COSINEH LP e RP
| TANGENTH LP e RP
| ARCSINEH LP e RP
| ARCCOSINEH LP e RP
| ARCTANGENTH LP e RP
'''
if t[1] == 'sin':
t[0] = cmath.sin(t[3])
elif t[1] == 'cos':
t[0] = cmath.cos(t[3])
elif t[1] == 'sec':
t[0] = 1/cmath.cos(t[3])
elif t[1] == 'cosec':
t[0] = 1/cmath.sin(t[3])
elif t[1] == 'tan':
t[0] = cmath.tan(t[3])
elif t[1] == 'cot':
t[0] = 1/cmath.tan(t[3])
elif t[1] == 'log':
t[0] = cmath.log(t[3], t[5])
elif t[1] == 'ln':
t[0] = cmath.log(t[3], cmath.e)
elif t[1] == 'e':
t[0] = cmath.exp(t[4])
elif t[1] == 'asin':
t[0] = cmath.asin(t[3])
elif t[1] == 'acos':
t[0] = cmath.acos(t[3])
elif t[1] == 'atan':
t[0] = cmath.atan(t[3])
elif t[1] == 'sinh':
t[0] = cmath.sinh(t[3])
elif t[1] == 'cosh':
t[0] = cmath.cosh(t[3])
elif t[1] == 'tanh':
t[0] = cmath.tanh(t[3])
elif t[1] == 'asinh':
t[0] = cmath.asinh(t[3])
elif t[1] == 'acosh':
t[0] = cmath.acosh(t[3])
elif t[1] == 'atanh':
t[0] = cmath.atanh(t[3])
def ATANH(df, price='Close'):
"""
Inverse Hyperbolic Tangent
"""
atanh_list = []
i = 0
while i < len(df[price]):
atanh = cmath.atanh(df[price][i]).real
atanh_list.append(atanh)
i += 1
return atanh_list
def atanh(z):
""" An AlComplex compatible hyperbolic arctangent function. It gets the main value.
Parameters
----------
z : Python numeric type or AlComplex
Returns
-------
AlComplex
"""
return AlComplex.from_python_complex(cm.atanh(z.to_python_complex()))
def rescaling( x, n , c = 0.9999999999, W = [0,255] ):
D = [-n*2**15,n*2**15]
w = W[1]-W[0] # lengthe of range
d = D[1]-D[0] # length of domain
T = 2 * atanh(2*c-1) # upper bound where 100*c % of the limit can theoretically be achieved
t = (x-D[0])/d * 2*T - T # rescaling the domain, so it matches to [-T,T]
y = ((exp(t)/(1+exp(t))) * w + W[0])/c
return real(y)
def oneArgFuncEval(function, value):
# Evaluates functions that take a complex number input
if function == "sin":
return cmath.sin(value)
elif function == "cos":
return cmath.cos(value)
elif function == "tan":
return cmath.tan(value)
elif function == "asin":
return cmath.asin(value)
elif function == "acos":
return cmath.acos(value)
elif function == "atan":
return cmath.atan(value)
elif function == "csc":
return 1.0 / cmath.sin(value)
elif function == "sec":
return 1.0 / cmath.cos(value)
elif function == "cot":
return 1.0 / cmath.tan(value)
elif function == "ln":
return cmath.log(value)
elif function == "sqr":
return cmath.sqrt(value)
elif function == "abs":
return cmath.sqrt((value.real ** 2) + (value.imag ** 2))
elif function == "exp":
return cmath.exp(value)
if function == "sinh":
return cmath.sinh(value)
elif function == "cosh":
return cmath.cosh(value)
elif function == "tanh":
return cmath.tanh(value)
elif function == "asinh":
return cmath.asinh(value)
elif function == "acosh":
return cmath.acosh(value)
elif function == "atanh":
return cmath.atanh(value)
elif function == "ceil":
return math.ceil(value.real) + complex(0, 1) * math.ceil(value.imag)
elif function == "floor":
return math.floor(value.real) + complex(0, 1) * math.floor(value.imag)
elif function == "trunc":
return math.trunc(value.real) + complex(0, 1) * math.trunc(value.imag)
elif function == "fac":
if value.imag == 0 and value < 0 and value.real == int(value.real):
return "Error: The factorial function is not defined on the negative integers."
return gamma(value + 1)
elif function == "log":
return cmath.log10(value)
def oneArgFuncEval(function, value):
# Evaluates functions that take a complex number input
if function == "sin":
return cmath.sin(value)
elif function == "cos":
return cmath.cos(value)
elif function == "tan":
return cmath.tan(value)
elif function == "asin":
return cmath.asin(value)
elif function == "acos":
return cmath.acos(value)
elif function == "atan":
return cmath.atan(value)
elif function == "csc":
return 1.0 / cmath.sin(value)
elif function == "sec":
return 1.0 / cmath.cos(value)
elif function == "cot":
return 1.0 / cmath.tan(value)
elif function == "ln":
return cmath.log(value)
elif function == "sqr":
return cmath.sqrt(value)
elif function == "abs":
return cmath.sqrt((value.real**2) + (value.imag**2))
elif function == "exp":
return cmath.exp(value)
if function == "sinh":
return cmath.sinh(value)
elif function == "cosh":
return cmath.cosh(value)
elif function == "tanh":
return cmath.tanh(value)
elif function == "asinh":
return cmath.asinh(value)
elif function == "acosh":
return cmath.acosh(value)
elif function == "atanh":
return cmath.atanh(value)
elif function == "ceil":
return math.ceil(value.real) + complex(0, 1) * math.ceil(value.imag)
elif function == "floor":
return math.floor(value.real) + complex(0, 1) * math.floor(value.imag)
elif function == "trunc":
return math.trunc(value.real) + complex(0, 1) * math.trunc(value.imag)
elif function == "fac":
if value.imag == 0 and value < 0 and value.real == int(value.real):
return "Error: The factorial function is not defined on the negative integers."
return gamma(value + 1)
elif function == "log":
return cmath.log10(value)
def do_func(self, funcstr, x):
return eval(
funcstr, {
"x": x,
"e": cmath.e,
"pi": cmath.pi,
"i": 1j,
"exp": cmath.exp,
"sin": cmath.sin,
"cos": cmath.cos,
"tan": cmath.tan,
"sinh": cmath.sinh,
"cosh": cmath.cosh,
"tanh": cmath.tanh,
"sec": lambda x: 1 / cmath.cos(x),
"csc": lambda x: 1 / cmath.sin(x),
"cot": lambda x: cmath.cos(x) / cmath.sin(x),
"sech": lambda x: 1 / cmath.cosh(x),
"csch": lambda x: 1 / cmath.sinh(x),
"coth": lambda x: cmath.cosh(x) / cmath.sinh(x),
"arcsin": cmath.asin,
"arccos": cmath.acos,
"arctan": cmath.atan,
"arsinh": cmath.asinh,
"arcosh": cmath.acosh,
"artanh": cmath.atanh,
"arcsec": lambda x: cmath.acos(1 / x),
"arccsc": lambda x: cmath.asin(1 / x),
"arccot": lambda x: cmath.atan(1 / x),
"arsech": lambda x: cmath.acosh(1 / x),
"arcsch": lambda x: cmath.asinh(1 / x),
"arcoth": lambda x: cmath.atanh(1 / x),
"abs": abs,
"sgn": sign,
"arg": cmath.phase,
"cis": lambda x: cmath.cos(x) + 1j * cmath.sin(x),
"pow": pow,
"sqrt": cmath.sqrt,
"nrt": lambda x, n: x**(1 / n),
"log": cmath.log,
"ln": lambda x: cmath.log(x),
"floor": math.floor,
"ceil": math.ceil,
"trunc": math.trunc,
"round": round,
"gamma": math_gamma,
"weierstrauss": math_weierstrauss,
"choose": math_choose,
"max": max,
"min": min
}, {})
def atanh(x):
"""
Return the inverse hyperbolic tangent of x.
"""
if isinstance(x,ADF):
ad_funcs = list(map(to_auto_diff,[x]))
x = ad_funcs[0].x
########################################
# Nominal value of the constructed ADF:
f = atanh(x)
########################################
variables = ad_funcs[0]._get_variables(ad_funcs)
if not variables or isinstance(f, bool):
return f
########################################
# Calculation of the derivatives with respect to the arguments
# of f (ad_funcs):
lc_wrt_args = [-1./(x**2 - 1)]
qc_wrt_args = [2*x/(x**4 - 2*x**2 + 1)]
cp_wrt_args = 0.0
########################################
# Calculation of the derivative of f with respect to all the
# variables (Variable) involved.
lc_wrt_vars,qc_wrt_vars,cp_wrt_vars = _apply_chain_rule(
ad_funcs,variables,lc_wrt_args,qc_wrt_args,
cp_wrt_args)
# The function now returns an ADF object:
return ADF(f, lc_wrt_vars, qc_wrt_vars, cp_wrt_vars)
else:
# try: # pythonic: fails gracefully when x is not an array-like object
# return [atanh(xi) for xi in x]
# except TypeError:
if x.imag:
return cmath.atanh(x)
else:
return math.atanh(x.real)
def atanh(x):
"""
Return the inverse hyperbolic tangent of x.
"""
if isinstance(x, ADF):
ad_funcs = list(map(to_auto_diff, [x]))
x = ad_funcs[0].x
########################################
# Nominal value of the constructed ADF:
f = atanh(x)
########################################
variables = ad_funcs[0]._get_variables(ad_funcs)
if not variables or isinstance(f, bool):
return f
########################################
# Calculation of the derivatives with respect to the arguments
# of f (ad_funcs):
lc_wrt_args = [-1. / (x**2 - 1)]
qc_wrt_args = [2 * x / (x**4 - 2 * x**2 + 1)]
cp_wrt_args = 0.0
########################################
# Calculation of the derivative of f with respect to all the
# variables (Variable) involved.
lc_wrt_vars, qc_wrt_vars, cp_wrt_vars = _apply_chain_rule(
ad_funcs, variables, lc_wrt_args, qc_wrt_args, cp_wrt_args)
# The function now returns an ADF object:
return ADF(f, lc_wrt_vars, qc_wrt_vars, cp_wrt_vars)
else:
# try: # pythonic: fails gracefully when x is not an array-like object
# return [atanh(xi) for xi in x]
# except TypeError:
if x.imag:
return cmath.atanh(x)
else:
return math.atanh(x.real)
def atanh(x):
"""
Uncertain number hyperbolic arctangent function
.. note::
In the complex case there are two branch cuts:
one extends from 1 along the real axis to :math:`\infty`,
continuous from below; the other extends from -1
along the real axis to :math:`-\infty`, continuous
from above.
"""
try:
return x._atanh()
except AttributeError:
if isinstance(x, numbers.Real):
return math.atanh(x)
elif isinstance(x, numbers.Complex):
return cmath.atanh(x)
else:
raise TypeError("illegal argument: {!r}".format(x))
def atanh_usecase(x):
return cmath.atanh(x)
def atanh(x):
if is_complex(x):
return cmath.atanh(x)
return math.atanh(x)
def test_atanh(self):
self.assertAlmostEqual(complex(0.11750, 1.40992),
cmath.atanh(complex(3, 4)))
def testAtanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atanh(z), z)
assert abs(cosh(x) - math.cosh(x)) < 1e-14 assert abs(sinh(x) - math.sinh(x)) < 1e-14 assert abs(tanh(x) - math.tanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Hyperbolic functions - complex version x = 0.5j assert abs(cosh(x) - cmath.cosh(x)) < 1e-14 assert abs(sinh(x) - cmath.sinh(x)) < 1e-14 assert abs(tanh(x) - cmath.tanh(x)) < 1e-14 assert abs(acosh(x) - cmath.acosh(x)) < 1e-14 assert abs(asinh(x) - cmath.asinh(x)) < 1e-14 assert abs(atanh(x) - cmath.atanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Rounding operations. assert type(round(0.5)) is mpf assert type(round(mpq(1,2))) is mpf assert type(floor(0.5)) is mpf assert type(ceil(0.5)) is mpf assert round(0.5) == 1 assert round(-0.5) == -1 assert round(1.5) == 2 assert round(-1.5) == -2 assert abs(round(0.25,1) - 0.3) < 1e-14 assert abs(round(1.123456789,4) - 1.1235) < 1e-14
assert abs(cosh(x) - math.cosh(x)) < 1e-14 assert abs(sinh(x) - math.sinh(x)) < 1e-14 assert abs(tanh(x) - math.tanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Hyperbolic functions - complex version x = 0.5j assert abs(cosh(x) - cmath.cosh(x)) < 1e-14 assert abs(sinh(x) - cmath.sinh(x)) < 1e-14 assert abs(tanh(x) - cmath.tanh(x)) < 1e-14 assert abs(acosh(x) - cmath.acosh(x)) < 1e-14 assert abs(asinh(x) - cmath.asinh(x)) < 1e-14 assert abs(atanh(x) - cmath.atanh(x)) < 1e-14 #------------------------------------------------------------------------------ # Rounding operations. assert type(round(0.5)) is mpf assert type(round(mpq(1, 2))) is mpf assert type(floor(0.5)) is mpf assert type(ceil(0.5)) is mpf assert round(0.5) == 1 assert round(-0.5) == -1 assert round(1.5) == 2 assert round(-1.5) == -2 assert abs(round(0.25, 1) - 0.3) < 1e-14 assert abs(round(1.123456789, 4) - 1.1235) < 1e-14
def atanh(x):
if isinstance(x, complex):
return cmath.atanh(x)
else:
return math.atanh(x)
# trigonometric functions
c = 2 + 2j
print('arc sine =', cmath.asin(c))
print('arc cosine =', cmath.acos(c))
print('arc tangent =', cmath.atan(c))
print('sine =', cmath.sin(c))
print('cosine =', cmath.cos(c))
print('tangent =', cmath.tan(c))
# hyperbolic functions
c = 2 + 2j
print('inverse hyperbolic sine =', cmath.asinh(c))
print('inverse hyperbolic cosine =', cmath.acosh(c))
print('inverse hyperbolic tangent =', cmath.atanh(c))
print('hyperbolic sine =', cmath.sinh(c))
print('hyperbolic cosine =', cmath.cosh(c))
print('hyperbolic tangent =', cmath.tanh(c))
# classification functions
print(cmath.isfinite(2 + 2j)) # True
print(cmath.isfinite(cmath.inf + 2j)) # False
print(cmath.isinf(2 + 2j)) # False
print(cmath.isinf(cmath.inf + 2j)) # True
print(cmath.isinf(cmath.nan + 2j)) # False
print(cmath.isnan(2 + 2j)) # False
print(cmath.isnan(cmath.inf + 2j)) # False
print("The tangent value of complex number is : ")
print(cmath.tan(z))
print("The arc sine value of complex number is : ")
print(cmath.asin(z))
print("The arc cosine value of complex number is : ")
print(cmath.acos(z))
print("The arc tangent value of complex number is : ")
print(cmath.atan(z))
print("The hyperbolic sine value of complex number is : ")
print(cmath.sinh(z))
print("The hyperbolic cosine value of complex number is : ")
print(cmath.cosh(z))
print("The hyperbolic tangent value of complex number is : ")
print(cmath.tanh(z))
print("The inverse hyperbolic sine value of complex number is : ")
print(cmath.asinh(z))
print("The inverse hyperbolic cosine value of complex number is : ")
print(cmath.acosh(z))
print("The inverse hyperbolic tangent value of complex number is : ")
print(cmath.atanh(z))
def atanh_usecase(x):
return cmath.atanh(x)
def ATANH(df, price='Close'):
"""
Inverse Hyperbolic Tangent
Returns: list of floats = jhta.ATANH(df, price='Close')
"""
return [cmath.atanh(df[price][i]).real for i in range(len(df[price]))]
def p(self, q, w):
q = abs(q)
x = w/(self.nu_max*q) # dimensionless constant
#return 3j*x**2/(2*w)*( (1j*pi-2*atanh(x))*(1/x-x) - 2 )
return 3j/(2*(self.nu_max*q))*( (1j*pi-2*cmath.atanh(x))*(1-x**2) - 2*x) # nicer form for w=0
# trigonometric functions
c = 2 + 2j
print('arc sine =', cmath.asin(c))
print('arc cosine =', cmath.acos(c))
print('arc tangent =', cmath.atan(c))
print('sine =', cmath.sin(c))
print('cosine =', cmath.cos(c))
print('tangent =', cmath.tan(c))
# hyperbolic functions
c = 2 + 2j
print('inverse hyperbolic sine =', cmath.asinh(c))
print('inverse hyperbolic cosine =', cmath.acosh(c))
print('inverse hyperbolic tangent =', cmath.atanh(c))
print('hyperbolic sine =', cmath.sinh(c))
print('hyperbolic cosine =', cmath.cosh(c))
print('hyperbolic tangent =', cmath.tanh(c))
# classification functions
print(cmath.isfinite(2 + 2j)) # True
print(cmath.isfinite(cmath.inf + 2j)) # False
print(cmath.isinf(2 + 2j)) # False
print(cmath.isinf(cmath.inf + 2j)) # True
print(cmath.isinf(cmath.nan + 2j)) # False
print(cmath.isnan(2 + 2j)) # False
'fact': lambda x: factorial(int(x)),
'asin': lambda x: cmath.asin(x),
'acos': lambda x: cmath.acos(x),
'atan': lambda x: cmath.atan(x),
'acsc': lambda x: cmath.asin(1/x),
'asec': lambda x: cmath.acos(1/x),
'acot': lambda x: cmath.atan(1/x),
'sinh': lambda x: cmath.sinh(x),
'cosh': lambda x: cmath.cosh(x),
'tanh': lambda x: cmath.tanh(x),
'csch': lambda x: 1/cmath.sinh(x),
'sech': lambda x: 1/cmath.cosh(x),
'coth': lambda x: 1/cmath.tanh(x),
'asinh': lambda x: cmath.asinh(x),
'acosh': lambda x: cmath.acosh(x),
'atanh': lambda x: cmath.atanh(x),
'acsch': lambda x: cmath.asinh(1/x),
'asech': lambda x: cmath.acosh(1/x),
'acoth': lambda x: cmath.atanh(1/x)
}
def replace_variables(phrase, replacement, var = 'x'):
"""Replaces all instances of a named variable in a phrase with a
replacement, 'x' by default."""
i = 0
while i < len(phrase):
match = re.match('((sum.+?,).+,.+?\))', phrase[i:])
if match:
i += len(match.groups(0)[1]) - 1
match = re.match(function_pattern, phrase[i:])
if match:
def arctanh(self):
comp_value = cmath.atanh(self.comp_value)
dx1 = 1 - self.comp_value**2
dxr = 1 / dx1
comp_unc = self.comp_unc * dxr # if y = atanh(x) than U(y) = U(x) 1/1-x^2
return Ucom(comp_value, comp_unc, self.name, self.dep)
def nfwshear(theta, nfwpars, zcluster, zsource, cc):
"""
return the tangential shear of a source galaxy at z=zsource expected
assuming a NFW profile with parameters=nfwpars when the galaxy is at
radial angular distance=theta (in arcmin) from the center of a galaxy
cluster at z=zcluster
Assumes a circularly symmetric NFW profile with parameters in dictionary
variable nfwpars, and a cosmology
(number, dict, number, number, cosmologyCalculator) -> number
(list|array|number, dict, number, list|array|number, cosmologyCalculator)
-> list|array|number
theta: angular distance in arcmin
nfwpars: dictionary containing M200 and concentration
zcluster: redshift of cluster
zsource: redshift of background source
cc: cosmology calculator class
Assumes flat universe and LCDM
Checked against Sarah's matlab code
"""
# unpack cosmological model, only implemented OmegaM for now
if (cc.isClosed() or cc.isOpen()):
print 'SIS shear model not implemented for non-flat universes yet!',
print 'OmegaK = ',cc.omegaCurv
return -99
if (not cc.isLambda):
print 'SIS shear model not implemented for non-LCDM universes yet!',
print 'w0 = ',cc.wX,'wa =',cc.wXa
return -99
# unpack NFW model
m200 = nfwpars["M200"]
conc = nfwpars["c"]
#print 'NFW model: m200 =',m200,' c =',conc
# unpack cosmological model, only implemented OmegaM for now
OmegaM = cc.omegamat
OmegaQ = 1. - OmegaM
w0 = -1.
wa = 0.
h = 1.
cc.sethubble(h) # all in h units
# mean density at cluster redshift
z_plus1_cubed = (1.+zcluster)*(1.+zcluster)*(1.+zcluster)
rho_m_zclust = const.rho_crit*OmegaM*z_plus1_cubed
#print 'rho_crit =',const.rho_crit,', zcluster =',zcluster
#print 'rho_m(z_clust) =',rho_m_zclust
# return Hubble distance c/H0 in Mpc/h
Dh = cc.DH()
# LENS QUANITITES
cc.setEmissionRedShift(zcluster)
# angular diameter distance etc to lens Mpc/h
Dd = cc.AngularDiameterDistanceMpc()
# transverse comoving distance to lens Mpc/h
Dm_lens = cc.TransComovDistanceMpc()
# NFW model
delta_c = 200./3.*conc*conc*conc / (math.log(1.+conc) - conc/(1.+conc))
rho_s = delta_c*rho_m_zclust
r200 = math.pow(m200/(200.*rho_m_zclust*4./3.*const.pi),1./3.)
theta200 = (r200/Dd) *180./const.pi*60 # r200 in theta in arcmin
r_s = r200/conc
#print 'NFW model parameters: delta_c =',delta_c,' rho_s =',rho_s,'r200 =',r200,
#print 'theta200 =',theta200,'r_s =',r_s
wasNum = False
if (isinstance(zsource, (int, long, float, complex))): # if single z
# SOURCE QUANTITIES
cc.setEmissionRedShift(zsource)
# angular diameter distance etc to source Mpc/h (don't actually need this)
Ds = cc.AngularDiameterDistanceMpc()
# transverse comoving distance to source Mpc/h
Dm_source = cc.TransComovDistanceMpc()
# Angular diameter distance between lens and source
sqrt1 = Dm_source*math.sqrt(1.+cc.omegaCurv*Dm_lens*Dm_lens/(Dh*Dh))
sqrt2 = Dm_lens*math.sqrt(1.+cc.omegaCurv*Dm_source*Dm_source/(Dh*Dh))
Dds = (sqrt1 - sqrt2)/(1.+zsource)
wasNum = True
else: # if list/array of z
Ds = np.zeros([len(zsource)])
Dds = np.zeros([len(zsource)])
theta_hold = np.zeros([len(zsource)])
i = 0
for zs in zsource:
# SOURCE QUANTITIES
cc.setEmissionRedShift(zs)
# angular diameter distance etc to source Mpc/h
Ds[i] = cc.AngularDiameterDistanceMpc()
# transverse comoving distance to source Mpc/h
Dm_source = cc.TransComovDistanceMpc()
# Angular diameter distance between lens and source
sqrt1 = Dm_source*math.sqrt(1.+cc.omegaCurv*Dm_lens*Dm_lens/(Dh*Dh))
sqrt2 = Dm_lens*math.sqrt(1.+cc.omegaCurv*Dm_source*Dm_source/(Dh*Dh))
Dds[i] = (sqrt1 - sqrt2)/(1.+zs)
theta_hold[i] = theta[i]
i+=1
theta = theta_hold
# sigma crit in Msolar/Mpc^2
sig_crit = cosmocalcs.Sigma_crit_Msolar_Mpcsq(zcluster, zsource, cc)
#sig_crit = cosmocalcs.Sigma_crit(zcluster, zsource, 100., OmegaM, OmegaQ, w0, wa)/const.msolarKg
#print 'Sigma_crit =',sig_crit
# dimensionless lens parameter
x = theta*(1./60.)*(const.pi/180.)*(Dd/r_s)
#print 'x =',x
#print 'If x=1: kappa =',2.*r_s*rho_s/sig_crit/3.
#print 'If x=1: mod_gamma =', r_s*rho_s/sig_crit*(10./3. + 4.*math.log(0.5))
if (wasNum):
xvals = np.zeros([1])
kappa = np.zeros([1])
mod_gamma = np.zeros([1])
xvals[0] = x
sc = sig_crit
sig_crit = np.zeros([1])
sig_crit[0] = sc
else:
xvals = x
kappa = np.zeros([len(x)])
mod_gamma = np.zeros([len(x)])
#print type(xvals)
i=0
for x in xvals:
# kappa and gamma
if (x<1.):
#print 'x<1'
kappa[i] = 2.*r_s*rho_s/sig_crit[i]/(x*x-1.)*(1. - 2./math.sqrt(1 - x*x) \
*math.atanh(math.sqrt( (1-x)/(1+x) )) )
mod_gamma[i] = r_s*rho_s/sig_crit[i]*(4./(x*x)*math.log(x/2.) - 2./(x*x-1) \
+ 4.*math.atanh(math.sqrt((1-x)/(1+x)))*(2 - 3*x*x) \
/ (x*x*math.sqrt((1-x*x)*(1-x*x)*(1-x*x))) )
elif (x == 1.):
#print 'x=1'
kappa[i] = 2.*r_s*rho_s/sig_crit[i]/3.
mod_gamma[i] = r_s*rho_s/sig_crit[i]*(10./3. + 4.*math.log(0.5))
elif (x>1.):
#print 'x>1'
k = 2.*r_s*rho_s/sig_crit[i]/(x*x - 1.)*(1. - 2./math.sqrt(x*x - 1) \
*math.atan(math.sqrt((x-1.)/(1.+x) )) )
kappa[i] = k
mod_gamma_atan = (r_s*rho_s/sig_crit[i]*(4./(x*x)*math.log(x/2.) - 2./(x*x-1) \
+ 4.*math.atan(math.sqrt((x-1.)/(1.+x)))*(2. - 3.*x*x) \
/ (x*x*math.sqrt(pow(x*x-1.,3))) ) )
# something doesn't seem to work right with atan, so use atanh
# and take real part (imaginary parts of the below are zero anyway).
mod_gamma_complex = r_s*rho_s/sig_crit[i]*(4./(x*x)*math.log(x/2.) - 2./(x*x-1) \
+ 4.*cmath.atanh(cmath.sqrt((1.-x)/(1.+x)))*(2. - 3.*x*x) \
/ ( x*x*cmath.exp(1.5*cmath.log(1.-x*x))) )
if (abs(mod_gamma_complex.imag))>1e-6:
print 'WARNING! Complex part might be large',abs(mod_gamma_complex.imag)
mod_gamma[i] = mod_gamma_complex.real
i+=1
#print mod_gamma,type(mod_gamma),mod_gamma_atan,type(mod_gamma_atan)
if (wasNum):
mod_gamma = mod_gamma[0]
kappa = kappa[0]
# NB. this agrees with numerical integration of kappa values too
return mod_gamma, kappa
Power and Log Functions
The cmath() module provides some useful functions for logarithmic
and power operations.
"""
c = 1+2j
print('e^c = ', cmath.exp(c))
print('log2(c) = ', cmath.log(c,2))
print('log10(c) = ', cmath.log10(c))
print('sqrt(c) = ', cmath.sqrt(c))
"""
Trigonometric Functions
"""
c = 2+4j
print('arc sine value:\n ', cmath.asin(c))
print('arc cosine value:\n ', cmath.acos(c))
print('arc tangent value:\n ', cmath.atan(c))
print('sine value:\n ', cmath.sin(c))
print('cosine value:\n ', cmath.cos(c))
print('tangent value:\n ', cmath.tan(c))
"""
Hyperbolic Functions
"""
c = 2+4j
print('Inverse hyperbolic sine value: \n', cmath.asinh(c))
print('Inverse hyperbolic cosine value: \n', cmath.acosh(c))
print('Inverse hyperbolic tangent value: \n', cmath.atanh(c))
print('Inverse sine value: \n', cmath.sinh(c))
print('Inverse cosine value: \n', cmath.cosh(c))
print('Inverse tangent value: \n', cmath.tanh(c))
def testAtanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atanh(z), z)
def rpn_calc(input, angle_mode = 0):
global stack
single_arg_funcs = ['exp','sqrt','sin','asin','cos','acos','tan','atan', 'sinh','asinh','cosh','acosh','tanh',
'atanh','!', 'polar']
num, arg, option = parse(input)
#print(num, arg, option)
#print('\n')
if arg == None and (num != None or num != 'Error'):
config.stack.append(num)
history.append('Entered number: ' + str(num) )
return config.stack
# Simple arithmatic-----------------------------------------------------------------------
if option == None and num != None:
if arg not in single_arg_funcs:
last = config.stack.pop()
if arg == '+':
try:
result = Decimal(last) + Decimal(num)
hist = str(last) + '+' + str(num) + '=' + str(result)
except TypeError:
result = last + num
hist = str(last) + '+' + str(num) + '=' + str(result)
if arg == '-':
try:
result = Decimal(last) - Decimal(num)
hist = str(last) + '-' + str(num) + '=' + str(result)
except TypeError:
result = last - num
hist = str(last) + '-' + str(num) + '=' + str(result)
if arg == '*':
try:
result = Decimal(last) * Decimal(num)
hist = str(last) + '*' + str(num) + '=' + str(result)
except TypeError:
result = last * num
hist = str(last) + '*' + str(num) + '=' + str(result)
if arg == '/':
try:
result = Decimal(last) / Decimal(num)
hist = str(last) + '/' + str(num) + '=' + str(result)
except TypeError:
result = last / num
hist = str(last) + '/' + str(num) + '=' + str(result)
if arg == '**':
try:
result = pow(Decimal(last), Decimal(num) )
hist = str(last) + '**' + str(num) + '=' + str(result)
except TypeError:
result = last ** num
hist = str(last) + '**' + str(num) + '=' + str(result)
if arg == 'rt':
try:
result = root(Decimal(last), Decimal(num) )
hist = str(last) + 'raised to 1 over ' + str(num) + '=' + str(result)
except TypeError:
result = root(last + num)
hist = str(last) + 'raised to 1 over ' + str(num) + '=' + str(result)
if arg == '%':
try:
result = Decimal(last) % Decimal(num)
hist = str(last) + '%' + str(num) + '=' + str(result)
except TypeError:
result = last % num
hist = str(last) + '%' + str(num) + '=' + str(result)
if arg == '!':
try:
result = Decimal(math.factorial(num))
hist = str(num) + '!' + '=' + str(result)
except TypeError:
result = math.factorial(num)
hist = str(num) + '!' + '=' + str(result)
if arg == 'exp':
try:
result = math.exp(Decimal(num))
hist = str(num) + 'exp' + '=' + str(result)
except ValueError:
result = cmath.exp(Decimal(num))
hist = str(num) + 'exp' + '=' + str(result)
except TypeError:
result = cmath.exp(num)
hist = str(num) + 'exp' + '=' + str(result)
if arg == 'sqrt':
try:
result = math.sqrt(Decimal(num))
hist = str(num) + 'sqrt' + '=' + str(result)
except ValueError:
result = cmath.sqrt(Decimal(num))
hist = str(num) + 'sqrt' + '=' + str(result)
except TypeError:
result = cmath.sqrt(num)
hist = str(num) + 'sqrt' + '=' + str(result)
if arg == 'log':
try:
result = math.log10(Decimal(num))
hist = str(num) + 'log10' + '=' + str(result)
except ValueError:
result = cmath.log10(Decimal(num))
hist = str(num) + 'log10' + '=' + str(result)
except TypeError:
result = cmath.log10(num)
hist = str(num) + 'log10' + '=' + str(result)
#=================================
if arg == 'ln':
try:
result = math.log(Decimal(num))
hist = str(num) + 'ln' + '=' + str(result)
except ValueError:
result = cmath.log(Decimal(num))
hist = str(num) + 'ln' + '=' + str(result)
except TypeError:
result = cmath.log(num)
hist = str(num) + 'ln' + '=' + str(result)
#--------TRIG--------------------------------
if arg == 'sin':
if angle_mode == 1:
try:
result = math.sin(Decimal(num))
hist = 'sin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sin(num)
hist = 'sin' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.sin(math.radians(Decimal(num)))
hist = 'sin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sin(num)
hist = 'sin' + str(num) + '=' + str(result)
if arg == 'cos':
if angle_mode == 1:
try:
result = math.cos(Decimal(num))
hist = 'cos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cos(num)
hist = 'cos' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.cos(math.radians(Decimal(num)))
hist = 'cos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cos(num)
hist = 'cos' + str(num) + '=' + str(result)
if arg == 'tan':
if angle_mode == 1:
try:
result = math.tan(Decimal(num))
hist = 'tan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tan(num)
hist = 'tan' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.tan(math.radians(Decimal(num)))
hist = 'tan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tan(num)
hist = 'tan' + str(num) + '=' + str(result)
if arg == 'asin':
if angle_mode == 1:
try:
result = math.asin(Decimal(num))
hist = 'asin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asin(num)
hist = 'asin' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.asin(math.radians(Decimal(num)))
hist = 'asin' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asin(num)
hist = 'asin' + str(num) + '=' + str(result)
if arg == 'acos':
if angle_mode == 1:
try:
result = math.acos(Decimal(num))
hist = 'acos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acos(num)
hist = 'acos' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.acos(math.radians(Decimal(num)))
hist = 'acos' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acos(num)
hist = 'acos' + str(num) + '=' + str(result)
if arg == 'atan':
if angle_mode == 1:
try:
result = math.atan(Decimal(num))
hist = 'atan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atan(num)
hist = 'atan' + str(num) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.atan(math.radians(Decimal(num)))
hist = 'atan' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atan(num)
hist = 'atan' + str(num) + '=' + str(result)
if arg == 'sinh':
try:
result = math.sinh(Decimal(num))
hist = 'sinh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.sinh(num)
hist = 'sinh' + str(num) + '=' + str(result)
if arg == 'cosh':
try:
result = math.cosh(Decimal(num))
hist = 'cosh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.cosh(num)
hist = 'cosh' + str(num) + '=' + str(result)
if arg == 'tanh':
try:
result = math.tanh(Decimal(num))
hist = 'tanh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.tanh(num)
hist = 'tanh' + str(num) + '=' + str(result)
if arg == 'asinh':
try:
result = math.asinh(Decimal(num))
hist = 'asinh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.asinh(num)
hist = 'asinh' + str(num) + '=' + str(result)
if arg == 'acosh':
try:
result = math.acosh(Decimal(num))
hist = 'acosh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.acosh(num)
hist = 'acosh' + str(num) + '=' + str(result)
if arg == 'atanh':
try:
result = math.atanh(Decimal(num))
hist = 'atanh' + str(num) + '=' + str(result)
except TypeError:
result = cmath.atanh(num)
hist = 'atanh' + str(num) + '=' + str(result)
if arg == 'rect': #continue here....
try:
result = rect(last, num)
hist = 'Convert ' + str(last) + ',' + str(num) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to rectangular coords. No result.'
if arg == 'polar':
try:
result = polar(num)
hist = 'Convert ' + str(num) + ' to polar coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to polar coords. No result.'
config.stack.append(result)
history.append(hist)
return config.stack
#=======================================================================================================================
#----Only argument passed-----------------------------------------------------------------------------------------------
#=======================================================================================================================
elif option == None and num == None:
last = config.stack.pop()
if arg not in single_arg_funcs:
try:
n_minus1 = config.stack.pop()
except IndexError:
try:
config.stack.append(Decimal(last))
except TypeError:
config.stack.append(last)
except TypeError:
config.stack.append(last)
except Exception as e:
return 'Error'
if arg == '+':
try:
result = Decimal(n_minus1) + Decimal(last)
hist = str(n_minus1) + '+' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 + last
hist = str(n_minus1) + '+' + str(last) + '=' + str(result)
if arg == '-':
try:
result = Decimal(n_minus1) - Decimal(last)
hist = str(n_minus1) + '-' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 - last
hist = str(n_minus1) + '-' + str(last) + '=' + str(result)
if arg == '*':
try:
result = Decimal(n_minus1) * Decimal(last)
hist = str(n_minus1) + '*' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 * last
hist = str(n_minus1) + '*' + str(last) + '=' + str(result)
if arg == '/':
try:
result = Decimal(n_minus1) / Decimal(last)
hist = str(n_minus1) + '/' + str(last) + '=' + str(result)
except TypeError:
result = n_minus1 / last
hist = str(n_minus1) + '/' + str(last) + '=' + str(result)
if arg == '!':
try:
result = Decimal(math.factorial(last))
hist = str(last) + '!' '=' + str(result)
except TypeError:
result = math.factorial(last)
hist = str(last) + '!' '=' + str(result)
except OverflowError:
config.stack.append(last)
hist = str('Factorial overflow error, no result.')
return 'Error'
if arg == '**':
try:
result = pow(Decimal(last), Decimal(last))
hist = str(n_minus1) + '**' + str(last) + '=' + str(result)
except TypeError:
result = last ** last
hist = str(n_minus1) + '**' + str(last) + '=' + str(result)
if arg == 'log':
try:
result = math.log10(Decimal(last))
hist = str(last) +'log10' + '=' + str(result)
except ValueError:
result = cmath.log10(Decimal(last))
hist = str(last) +'log10' + '=' + str(result)
except TypeError:
result = cmath.log10(last)
hist = str(last) +'log10' + '=' + str(result)
if arg == 'ln':
try:
result = math.log(Decimal(last))
hist = str(last) +'ln' + '=' + str(result)
except ValueError:
result = cmath.log(Decimal(last))
hist = str(last) +'ln' + '=' + str(result)
except TypeError:
result = cmath.log(last)
hist = str(last) +'ln' + '=' + str(result)
if arg == 'rt':
try:
result = root(Decimal(last), Decimal(n_minus1))
hist = str(n_minus1) + 'root' + str(last) + '=' + str(result)
except TypeError:
result = root(last), (n_minus1)
hist = str(n_minus1) + 'root' + str(last) + '=' + str(result)
if arg == 'exp':
try:
result = math.exp(Decimal(last))
hist = str(last) +'exp' + '=' + str(result)
except TypeError:
result = cmath.exp(last)
hist = str(last) +'exp' + '=' + str(result)
if arg == 'sqrt':
try:
result = math.sqrt(Decimal(last))
hist = 'Square root of ' + str(last) + '=' + str(result)
except ValueError:
result = cmath.sqrt(Decimal(last))
hist = 'Square root of ' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sqrt(last)
hist = 'Square root of ' + str(last) + '=' + str(result)
#----------Trig----------------------------------------
#--------TRIG--------------------------------
if arg == 'sin':
if angle_mode == 1:
try:
result = math.sin(Decimal(last))
hist = 'sin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sin(last)
hist = 'sin' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.sin(math.radians(Decimal(last)))
hist = 'sin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.sin(last)
hist = 'sin' + str(last) + '=' + str(result)
if arg == 'cos':
if angle_mode == 1:
try:
result = math.cos(Decimal(last))
hist = 'cos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.cos(last)
hist = 'cos' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.cos(math.radians(Decimal(last)))
hist = 'cos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.cos(last)
hist = 'cos' + str(last) + '=' + str(result)
if arg == 'tan':
if angle_mode == 1:
try:
result = math.tan(Decimal(last))
hist = 'tan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.tan(last)
hist = 'tan' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.tan(math.radians(Decimal(last)))
hist = 'tan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.tan(last)
hist = 'tan' + str(last) + '=' + str(result)
if arg == 'asin':
if angle_mode == 1:
try:
result = math.asin(Decimal(last))
hist = 'asin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.asin(last)
hist = 'asin' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.asin(math.radians(Decimal(last)))
hist = 'asin' + str(last) + '=' + str(result)
except TypeError:
result = cmath.asin(last)
hist = 'asin' + str(last) + '=' + str(result)
if arg == 'acos':
if angle_mode == 1:
try:
result = math.acos(Decimal(last))
hist = 'acos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.acos(last)
hist = 'acos' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.acos(math.radians(Decimal(last)))
hist = 'acos' + str(last) + '=' + str(result)
except TypeError:
result = cmath.acos(last)
hist = 'acos' + str(last) + '=' + str(result)
if arg == 'atan':
if angle_mode == 1:
try:
result = math.atan(Decimal(last))
hist = 'atan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.atan(last)
hist = 'atan' + str(last) + '=' + str(result)
elif angle_mode == 0:
try:
result = math.atan(math.radians(Decimal(last)))
hist = 'atan' + str(last) + '=' + str(result)
except TypeError:
result = cmath.atan(last)
hist = 'atan' + str(last) + '=' + str(result)
if arg == 'sinh':
try:
result = math.sinh(Decimal(last))
hist = 'sinh' + str(last) + '=' + str(result)
except TypeError:
result = math.sinh(last)
hist = 'sinh' + str(last) + '=' + str(result)
if arg == 'cosh':
try:
result = math.cosh(Decimal(last))
hist = 'cosh' + str(last) + '=' + str(result)
except TypeError:
result = math.cosh(last)
hist = 'cosh' + str(last) + '=' + str(result)
if arg == 'tanh':
try:
result = math.tanh(Decimal(last))
hist = 'tanh' + str(last) + '=' + str(result)
except TypeError:
result = math.tanh(last)
hist = 'tanh' + str(last) + '=' + str(result)
if arg == 'asinh':
try:
result = math.asinh(Decimal(last))
hist = 'asinh' + str(last) + '=' + str(result)
except TypeError:
result = math.asinh(last)
hist = 'asinh' + str(last) + '=' + str(result)
if arg == 'acosh':
try:
result = math.acosh(Decimal(last))
hist = 'acosh' + str(last) + '=' + str(result)
except TypeError:
result = math.acosh(last)
hist = 'acosh' + str(last) + '=' + str(result)
if arg == 'atanh':
try:
result = math.atanh(Decimal(last))
hist = 'atanh' + str(last) + '=' + str(result)
except TypeError:
result = math.atanh(last)
hist = 'atanh' + str(last) + '=' + str(result)
if arg == 'rect': #continue here....
try:
result = rect(n_minus1, last)
hist = 'Convert ' + str(n_minus1) + ',' + str(last) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to rectangular coords. No result.'
if arg == 'polar':
try:
result = polar(last)
hist = 'Convert complex value ' + str(last) + ' to rectangular coords.'
except TypeError:
result = 'Error'
hist = 'Error in attempted conversion to polar coords. No result.'
config.stack.append(result)
history.append(hist)
return config.stack
