Python cmath.atanh方法代碼示例

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def testTanhSign(self):
        for z in complex_zeros:
            self.assertComplexIdentical(cmath.tanh(z), z)

    # The algorithm used for atan and atanh makes use of the system
    # log1p function; If that system function doesn't respect the sign
    # of zero, then atan and atanh will also have difficulties with
    # the sign of complex zeros. 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def testAtanhSign(self):
        for z in complex_zeros:
            self.assertComplexIdentical(cmath.atanh(z), z) 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
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]))] 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def test_atanh(self):
        self.assertAlmostEqual(complex(0.11750, 1.40992),
                               cmath.atanh(complex(3, 4))) 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def main_derivatives_and_departures(T, P, V, b, delta, epsilon, a_alpha,
                                        da_alpha_dT, d2a_alpha_dT2, quick=True):
        if quick:
            x0 = V - b
            x1 = V*V + V*delta + epsilon
            x3 = R*T
            x4 = 1./(x0*x0)
            x5 = 2.*V + delta
            x6 = 1./(x1*x1)
            x7 = a_alpha*x6
            x8 = P*V
            x9 = delta*delta
            x10 = -4.*epsilon + x9
            x11 = x10**-0.5
            x12 = 2.*x11*catanh(x11*x5).real
            x13 = x10**-0.5 
            x14 = V + delta*0.5
            x15 = 2.*epsilon*x13
            x16 = x13*x9*0.5
            dP_dT = R/x0 - da_alpha_dT/x1
            dP_dV = -x3*x4 + x5*x7
            d2P_dT2 = -d2a_alpha_dT2/x1
            d2P_dV2 = -2.*a_alpha*x5*x5*x6/x1 + 2.*x7 + 2.*x3*x4/x0
            d2P_dTdV = -R*x4 + da_alpha_dT*x5*x6
            H_dep = x12*(T*da_alpha_dT - a_alpha) - x3 + x8
            S_dep = -R*log((V*x3/(x0*x8))**2)*0.5 + da_alpha_dT*x12  # Consider Real part of the log only via log(x**2)/2 = Re(log(x))
            Cv_dep = -T*d2a_alpha_dT2*x13*(-log(((x14 - x15 + x16)/(x14 + x15 - x16))**2)*0.5) # Consider Real part of the log only via log(x**2)/2 = Re(log(x))
        else:
            dP_dT = R/(V - b) - da_alpha_dT/(V**2 + V*delta + epsilon)
            dP_dV = -R*T/(V - b)**2 - (-2*V - delta)*a_alpha/(V**2 + V*delta + epsilon)**2
            d2P_dT2 = -d2a_alpha_dT2/(V**2 + V*delta + epsilon)
            d2P_dV2 = 2*(R*T/(V - b)**3 - (2*V + delta)**2*a_alpha/(V**2 + V*delta + epsilon)**3 + a_alpha/(V**2 + V*delta + epsilon)**2)
            d2P_dTdV = -R/(V - b)**2 + (2*V + delta)*da_alpha_dT/(V**2 + V*delta + epsilon)**2
            H_dep = P*V - R*T + 2*(T*da_alpha_dT - a_alpha)*catanh((2*V + delta)/sqrt(delta**2 - 4*epsilon)).real/sqrt(delta**2 - 4*epsilon)
            S_dep = -R*log(V) + R*log(P*V/(R*T)) + R*log(V - b) + 2*da_alpha_dT*catanh((2*V + delta)/sqrt(delta**2 - 4*epsilon)).real/sqrt(delta**2 - 4*epsilon)
            Cv_dep = -T*(sqrt(1/(delta**2 - 4*epsilon))*log(V - delta**2*sqrt(1/(delta**2 - 4*epsilon))/2 + delta/2 + 2*epsilon*sqrt(1/(delta**2 - 4*epsilon))) - sqrt(1/(delta**2 - 4*epsilon))*log(V + delta**2*sqrt(1/(delta**2 - 4*epsilon))/2 + delta/2 - 2*epsilon*sqrt(1/(delta**2 - 4*epsilon))))*d2a_alpha_dT2
        return [dP_dT, dP_dV, d2P_dT2, d2P_dV2, d2P_dTdV, H_dep, S_dep, Cv_dep] 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
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)

    dps = mp.dps
    mp.dps = 300
    assert isinstance(asin(0.5), mpf)
    mp.dps = 1000
    assert asin(1).ae(pi/2)
    assert asin(-1).ae(-pi/2)
    mp.dps = dps 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def test_invhyperb_inaccuracy():
    mp.dps = 15
    assert (asinh(1e-5)*10**5).ae(0.99999999998333333)
    assert (asinh(1e-10)*10**10).ae(1)
    assert (asinh(1e-50)*10**50).ae(1)
    assert (asinh(-1e-5)*10**5).ae(-0.99999999998333333)
    assert (asinh(-1e-10)*10**10).ae(-1)
    assert (asinh(-1e-50)*10**50).ae(-1)
    assert asinh(10**20).ae(46.744849040440862)
    assert asinh(-10**20).ae(-46.744849040440862)
    assert (tanh(1e-10)*10**10).ae(1)
    assert (tanh(-1e-10)*10**10).ae(-1)
    assert (atanh(1e-10)*10**10).ae(1)
    assert (atanh(-1e-10)*10**10).ae(-1) 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def test_complex_inverse_functions():
    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) 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def test_atanh():
    mp.dps = 15
    assert atanh(0) == 0
    assert atanh(0.5).ae(0.54930614433405484570)
    assert atanh(-0.5).ae(-0.54930614433405484570)
    assert atanh(1) == inf
    assert atanh(-1) == -inf
    assert isnan(atanh(nan))
    assert isinstance(atanh(1), mpf)
    assert isinstance(atanh(-1), mpf)
    # Limits at infinity
    jpi2 = j*pi/2
    assert atanh(inf).ae(-jpi2)
    assert atanh(-inf).ae(jpi2)
    assert atanh(mpc(inf,-1)).ae(-jpi2)
    assert atanh(mpc(inf,0)).ae(-jpi2)
    assert atanh(mpc(inf,1)).ae(jpi2)
    assert atanh(mpc(1,inf)).ae(jpi2)
    assert atanh(mpc(0,inf)).ae(jpi2)
    assert atanh(mpc(-1,inf)).ae(jpi2)
    assert atanh(mpc(-inf,1)).ae(jpi2)
    assert atanh(mpc(-inf,0)).ae(jpi2)
    assert atanh(mpc(-inf,-1)).ae(-jpi2)
    assert atanh(mpc(-1,-inf)).ae(-jpi2)
    assert atanh(mpc(0,-inf)).ae(-jpi2)
    assert atanh(mpc(1,-inf)).ae(-jpi2) 

# 需要導入模塊: import cmath [as 別名]
# 或者: from cmath import atanh [as 別名]
def test_perturbation_rounding():
    mp.dps = 100
    a = pi/10**50
    b = -pi/10**50
    c = 1 + a
    d = 1 + b
    mp.dps = 15
    assert exp(a) == 1
    assert exp(a, rounding='c') > 1
    assert exp(b, rounding='c') == 1
    assert exp(a, rounding='f') == 1
    assert exp(b, rounding='f') < 1
    assert cos(a) == 1
    assert cos(a, rounding='c') == 1
    assert cos(b, rounding='c') == 1
    assert cos(a, rounding='f') < 1
    assert cos(b, rounding='f') < 1
    for f in [sin, atan, asinh, tanh]:
        assert f(a) == +a
        assert f(a, rounding='c') > a
        assert f(a, rounding='f') < a
        assert f(b) == +b
        assert f(b, rounding='c') > b
        assert f(b, rounding='f') < b
    for f in [asin, tan, sinh, atanh]:
        assert f(a) == +a
        assert f(b) == +b
        assert f(a, rounding='c') > a
        assert f(b, rounding='c') > b
        assert f(a, rounding='f') < a
        assert f(b, rounding='f') < b
    assert ln(c) == +a
    assert ln(d) == +b
    assert ln(c, rounding='c') > a
    assert ln(c, rounding='f') < a
    assert ln(d, rounding='c') > b
    assert ln(d, rounding='f') < b
    assert cosh(a) == 1
    assert cosh(b) == 1
    assert cosh(a, rounding='c') > 1
    assert cosh(b, rounding='c') > 1
    assert cosh(a, rounding='f') == 1
    assert cosh(b, rounding='f') == 1