def test_inverse_functions(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, tanh
from pyaudi import asinh, acosh, atanh
from pyaudi import sin, cos, tan
from pyaudi import asin, acos, atan
x = gdual(1.1, "x",6);
y = gdual(1.2, "y",6);
p1 = 1. / (x + y);
self.assertTrue((cos(acos(p1))-p1).is_zero(1e-12))
self.assertTrue((acos(cos(p1))-p1).is_zero(1e-12))
self.assertTrue((sin(asin(p1))-p1).is_zero(1e-12))
self.assertTrue((asin(sin(p1))-p1).is_zero(1e-12))
self.assertTrue((tan(atan(p1))-p1).is_zero(1e-12))
self.assertTrue((atan(tan(p1))-p1).is_zero(1e-12))
self.assertTrue((cosh(acosh(p1))-p1).is_zero(1e-12))
self.assertTrue((acosh(cosh(p1))-p1).is_zero(1e-12))
self.assertTrue((sinh(asinh(p1))-p1).is_zero(1e-12))
self.assertTrue((asinh(sinh(p1))-p1).is_zero(1e-12))
self.assertTrue((tanh(atanh(p1))-p1).is_zero(1e-12))
self.assertTrue((atanh(tanh(p1))-p1).is_zero(1e-12))
def test_inverse_functions(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, tanh
from pyaudi import asinh, acosh, atanh
from pyaudi import sin, cos, tan
from pyaudi import asin, acos, atan
x = gdual(1.1, "x", 6)
y = gdual(1.2, "y", 6)
p1 = 1. / (x + y)
self.assertTrue((cos(acos(p1)) - p1).is_zero(1e-12))
self.assertTrue((acos(cos(p1)) - p1).is_zero(1e-12))
self.assertTrue((sin(asin(p1)) - p1).is_zero(1e-12))
self.assertTrue((asin(sin(p1)) - p1).is_zero(1e-12))
self.assertTrue((tan(atan(p1)) - p1).is_zero(1e-12))
self.assertTrue((atan(tan(p1)) - p1).is_zero(1e-12))
self.assertTrue((cosh(acosh(p1)) - p1).is_zero(1e-12))
self.assertTrue((acosh(cosh(p1)) - p1).is_zero(1e-12))
self.assertTrue((sinh(asinh(p1)) - p1).is_zero(1e-12))
self.assertTrue((asinh(sinh(p1)) - p1).is_zero(1e-12))
self.assertTrue((tanh(atanh(p1)) - p1).is_zero(1e-12))
self.assertTrue((atanh(tanh(p1)) - p1).is_zero(1e-12))
def test_tanh(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, tanh
x = gdual(2.3, "x", 10)
y = gdual(1.5, "y", 10)
p1 = x + y
self.assertTrue((tanh(p1) - sinh(p1) / cosh(p1)).is_zero(1e-12))
def test_tanh(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, tanh
x = gdual(2.3, "x",10);
y = gdual(1.5, "y",10);
p1 = x + y;
self.assertTrue((tanh(p1) - sinh(p1) / cosh(p1)).is_zero(1e-12))
def test_sinh_and_cosh(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, sinh_and_cosh
x = gdual(2.3, "x",8);
y = gdual(1.5, "y",8);
p1 = x + y;
self.assertTrue((sinh(2*p1) - 2 * sinh(p1) * cosh(p1)).is_zero(1e-12))
self.assertTrue((cosh(2*p1) - 1 - 2*sinh(p1)*sinh(p1)).is_zero(1e-12))
self.assertTrue((cosh(2*p1) + 1 - 2*cosh(p1)*cosh(p1)).is_zero(1e-12))
self.assertTrue((cosh(2*p1) - cosh(p1)*cosh(p1) - sinh(p1) * sinh(p1)).is_zero(1e-12))
self.assertTrue((- sinh(p1)*sinh(p1) + cosh(p1)*cosh(p1) - 1).is_zero(1e-12))
res = sinh_and_cosh(p1);
self.assertTrue((res[0] - sinh(p1)).is_zero(1e-12))
self.assertTrue((res[1] - cosh(p1)).is_zero(1e-12))
def some_complex_irrational_f(x, y, z):
from pyaudi import exp, log, cos, sin, tan, sqrt, cbrt, cos, sin, tan, acos, asin, atan, cosh, sinh, tanh, acosh, asinh, atanh
from pyaudi import abs as gd_abs
from pyaudi import sin_and_cos, sinh_and_cosh
f = (x + y + z) / 10.
retval = exp(f) + log(f) + f**2 + sqrt(f) + cbrt(f) + cos(f) + sin(f)
retval += tan(f) + acos(f) + asin(f) + atan(f) + cosh(f) + sinh(f)
retval += tanh(f) + acosh(f) + asinh(f) + atanh(f)
a = sin_and_cos(f)
b = sinh_and_cosh(f)
retval += a[0] + a[1] + b[0] + b[1]
return retval
def some_complex_irrational_f(x,y,z):
from pyaudi import exp, log, cos, sin, tan, sqrt, cbrt, cos, sin, tan, acos, asin, atan, cosh, sinh, tanh, acosh, asinh, atanh
from pyaudi import abs as gd_abs
from pyaudi import sin_and_cos, sinh_and_cosh
f = (x+y+z) / 10.
retval = exp(f) + log(f) + f**2 + sqrt(f) + cbrt(f) + cos(f) + sin(f)
retval += tan(f) + acos(f) + asin(f) + atan(f) + cosh(f) + sinh(f)
retval += tanh(f) + acosh(f) + asinh(f) + atanh(f)
a = sin_and_cos(f)
b = sinh_and_cosh(f)
retval+=a[0]+a[1]+b[0]+b[1]
return retval
def test_sinh_and_cosh(self):
from pyaudi import gdual_double as gdual
from pyaudi import sinh, cosh, sinh_and_cosh
x = gdual(2.3, "x", 8)
y = gdual(1.5, "y", 8)
p1 = x + y
self.assertTrue(
(sinh(2 * p1) - 2 * sinh(p1) * cosh(p1)).is_zero(1e-12))
self.assertTrue(
(cosh(2 * p1) - 1 - 2 * sinh(p1) * sinh(p1)).is_zero(1e-12))
self.assertTrue(
(cosh(2 * p1) + 1 - 2 * cosh(p1) * cosh(p1)).is_zero(1e-12))
self.assertTrue((cosh(2 * p1) - cosh(p1) * cosh(p1) -
sinh(p1) * sinh(p1)).is_zero(1e-12))
self.assertTrue(
(-sinh(p1) * sinh(p1) + cosh(p1) * cosh(p1) - 1).is_zero(1e-12))
res = sinh_and_cosh(p1)
self.assertTrue((res[0] - sinh(p1)).is_zero(1e-12))
self.assertTrue((res[1] - cosh(p1)).is_zero(1e-12))
def do(self, x1, x2):
import pyaudi as pd
res = x1.sinh()
assert (res == pd.sinh(x1))