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 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 do(self, x1, x2):
import pyaudi as pd
res = x1.arcsin()
assert (res == pd.asin(x1))