Python math.acosh() Examples

def get(self):
        self.x += self.config.get('dx', 0.1)

        val = eval(self.config.get('function', 'sin(x)'), {
            'sin': math.sin,
            'sinh': math.sinh,
            'cos': math.cos,
            'cosh': math.cosh,
            'tan': math.tan,
            'tanh': math.tanh,
            'asin': math.asin,
            'acos': math.acos,
            'atan': math.atan,
            'asinh': math.asinh,
            'acosh': math.acosh,
            'atanh': math.atanh,
            'log': math.log,
            'abs': abs,
            'e': math.e,
            'pi': math.pi,
            'x': self.x
        })

        return self.createEvent('ok', 'Sine wave', val) 

def Cn(l):
    alpha = acosh(l/r)
    s = 0.
    for n in range(1, 100):
        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 asech(x):
	if type(x) in dtypes:
		return math.acosh(1. / x)

	return functor1(asech, x) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * (1024**2))
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall, b"x" * (1024**2))
        finally:
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not strictly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * test_support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * test_support.SOCK_MAX_SIZE)
        finally:
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not strictly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * test_support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * test_support.SOCK_MAX_SIZE)
        finally:
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * support.SOCK_MAX_SIZE)
        finally:
            signal.alarm(0)
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def acosh(node): return merge([node], math.acosh) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * test_support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * test_support.SOCK_MAX_SIZE)
        finally:
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * support.SOCK_MAX_SIZE)
        finally:
            signal.alarm(0)
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * (1024**2))
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall, b"x" * (1024**2))
        finally:
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def check_sendall_interrupted(self, with_timeout):
        # socketpair() is not stricly required, but it makes things easier.
        if not hasattr(signal, 'alarm') or not hasattr(socket, 'socketpair'):
            self.skipTest("signal.alarm and socket.socketpair required for this test")
        # Our signal handlers clobber the C errno by calling a math function
        # with an invalid domain value.
        def ok_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
        def raising_handler(*args):
            self.assertRaises(ValueError, math.acosh, 0)
            1 // 0
        c, s = socket.socketpair()
        old_alarm = signal.signal(signal.SIGALRM, raising_handler)
        try:
            if with_timeout:
                # Just above the one second minimum for signal.alarm
                c.settimeout(1.5)
            with self.assertRaises(ZeroDivisionError):
                signal.alarm(1)
                c.sendall(b"x" * support.SOCK_MAX_SIZE)
            if with_timeout:
                signal.signal(signal.SIGALRM, ok_handler)
                signal.alarm(1)
                self.assertRaises(socket.timeout, c.sendall,
                                  b"x" * support.SOCK_MAX_SIZE)
        finally:
            signal.alarm(0)
            signal.signal(signal.SIGALRM, old_alarm)
            c.close()
            s.close() 

def testAcosh(self):
        self.assertRaises(TypeError, math.acosh)
        self.ftest('acosh(1)', math.acosh(1), 0)
        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
        self.assertRaises(ValueError, math.acosh, 0)
        self.assertRaises(ValueError, math.acosh, -1)
        self.assertEqual(math.acosh(INF), INF)
        self.assertRaises(ValueError, math.acosh, NINF)
        self.assertTrue(math.isnan(math.acosh(NAN))) 

def test_acosh(self):
        self.assertEqual(session.source("Test", x=real(3.14, 6.5)).type("acosh(x)"), real(math.acosh(3.14), math.acosh(6.5)))
        self.assertEqual(session.source("Test", x=real(almost(1), 6.5)).type("acosh(x)"), real(almost(0), math.acosh(6.5)))
        self.assertEqual(session.source("Test", x=real(1, 6.5)).type("acosh(x)"), real(0, math.acosh(6.5)))
        self.assertRaises(FemtocodeError, lambda: session.source("Test", x=real(0, 6.5)).type("acosh(x)"))
        self.assertRaises(FemtocodeError, lambda: session.source("Test", x=real(0, 0.5)).type("acosh(x)"))
        self.assertRaises(FemtocodeError, lambda: session.source("Test", x=real(0, almost(0.5))).type("acosh(x)"))
        for entry in numerical.toPython(ylim = "ylim", a = "acosh(ylim + 1)").submit():
            self.assertEqual(entry.a, math.acosh(entry.ylim + 1)) 

def acosh(arg):
    return generate_intrinsic_function_expression(arg, 'acosh', math.acosh) 

def __init__(self):
        ParameterCell.__init__(self)
        self.a = None
        self.b = None
        self.c = None
        self.d = None
        self.formula = ""
        self._previous_values = [None, None, None, None]
        self._formula_globals = globals();
        self._formula_locals = {
            "exp":math.exp,
            "pow":math.pow,
            "log":math.log,
            "log10":math.log10,
            "acos":math.acos,
            "asin":math.asin,
            "atan":math.atan,
            "atan2":math.atan2,
            "cos":math.cos,
            "hypot":math.hypot,
            "sin":math.sin,
            "tan":math.tan,
            "degrees":math.degrees,
            "radians":math.radians,
            "acosh":math.acosh,
            "asinh":math.asinh,
            "atanh":math.atanh,
            "cosh":math.cosh,
            "sinh":math.sinh,
            "tanh":math.tanh,
            "pi":math.pi,
            "e":math.e,
            "ceil":math.ceil,
            "sign":ParameterMathFun.signum,
            "abs":math.fabs,
            "floor":math.floor,
            "mod":math.fmod,
            "sqrt":math.sqrt,
            "curt":ParameterMathFun.curt,
            "str":str,
            "int":int,
            "float":float
        } 

def test_one():
    from math import sin, cos, tan, asin, acos, atan
    from math import sinh, cosh, tanh, asinh, acosh, atanh
    from math import exp, expm1, log, log10, log1p, sqrt, lgamma
    from math import fabs, ceil, floor, trunc, erf, erfc
    try:
        from math import log2
    except ImportError:
        def log2(x):
            return log(x) / log(2)

    def wrapper(f, v):
        try:
            return f(v)
        except ValueError:
            if f == sqrt:
                return float('nan')
            if v >= 0:
                return float('inf')
            else:
                return -float('inf')

    def compare(a, b):
        if isfinite(a) and isfinite(b):
            return assert_almost_equals(a, b)
        return str(a) == str(b)

    for f in [sin, cos, tan, asin, acos, atan,
              sinh, cosh, tanh, asinh, acosh, atanh,
              exp, expm1, log, log2, log10, log1p, sqrt,
              lgamma,
              fabs, ceil, floor, trunc,
              erf, erfc]:
        for p in [0.5, 1]:
            a = random_lst(p=p)
            b = SparseArray.fromlist(a)
            c = getattr(b, f.__name__)()
            res = [wrapper(f, x) for x in a]
            index = [k for k, v in enumerate(res) if v != 0]
            res = [x for x in res if x != 0]
            print(f, p, c.non_zero, len(res))
            assert c.non_zero == len(res)
            [assert_almost_equals(v, w) for v, w in zip(index,
                                                        c.index)]
            [compare(v, w) for v, w in zip(res,
                                           c.data)] 

def V_horiz_conical(D, L, a, h, headonly=False):
    r'''Calculates volume of a tank with conical ends, according to [1]_.

    .. math::
        V_f = A_fL + \frac{2aR^2}{3}K, \;\;0 \le h < R\\

        V_f = A_fL + \frac{2aR^2}{3}\pi/2,\;\; h = R\\

        V_f = A_fL + \frac{2aR^2}{3}(\pi-K), \;\; R< h \le 2R

        K = \cos^{-1} M + M^3\cosh^{-1} \frac{1}{M} - 2M\sqrt{1 - M^2}

        M = \left|\frac{R-h}{R}\right|

        Af = R^2\cos^{-1}\frac{R-h}{R} - (R-h)\sqrt{2Rh - h^2}

    Parameters
    ----------
    D : float
        Diameter of the main cylindrical section, [m]
    L : float
        Length of the main cylindrical section, [m]
    a : float
        Distance the cone head extends on one side, [m]
    h : float
        Height, as measured up to where the fluid ends, [m]
    headonly : bool, optional
        Function returns only the volume of a single head side if True

    Returns
    -------
    V : float
        Volume [m^3]

    Examples
    --------
    Matching example from [1]_, with inputs in inches and volume in gallons.

    >>> V_horiz_conical(D=108., L=156., a=42., h=36)/231
    2041.1923581273443

    References
    ----------
    .. [1] Jones, D. "Calculating Tank Volume." Text. Accessed December 22, 2015.
       http://www.webcalc.com.br/blog/Tank_Volume.PDF'''
    R = D/2.
    Af = R*R*acos((R-h)/R) - (R-h)*(2*R*h - h*h)**0.5
    M = abs((R-h)/R)
    if h == R:
        Vf = a*R*R/3.*pi
    else:
        K = acos(M) + M*M*M*acosh(1./M) - 2.*M*(1.-M*M)**0.5
        if 0. <= h < R:
            Vf = 2.*a*R*R/3*K
        elif R < h <= 2*R:
            Vf = 2.*a*R*R/3*(pi - K)
    if headonly:
        Vf = 0.5*Vf
    else:
        Vf += Af*L
    return Vf