def test_sqrt(self):
from pyaudi import gdual_double as gdual
from pyaudi import sqrt
x = gdual(2.3, "x",3);
y = gdual(1.5, "y",3);
p1 = x*x*y - x*y*x*x*x + 3*y*y*y*y*x*y*x; # positive p0
p2 = x*x*y - x*y*x*x*x - 3*y*y*y*y*x*y*x; # negative coefficient
self.assertTrue((sqrt(p1)*sqrt(p1) - p1).is_zero(1e-12))
self.assertTrue((sqrt(p2)*sqrt(p2) - p2).is_zero(1e-12))
def test_sqrt(self):
from pyaudi import gdual_double as gdual
from pyaudi import sqrt
x = gdual(2.3, "x", 3)
y = gdual(1.5, "y", 3)
p1 = x * x * y - x * y * x * x * x + 3 * \
y * y * y * y * x * y * x # positive p0
p2 = x * x * y - x * y * x * x * x - 3 * y * \
y * y * y * x * y * x # negative coefficient
self.assertTrue((sqrt(p1) * sqrt(p1) - p1).is_zero(1e-12))
self.assertTrue((sqrt(p2) * sqrt(p2) - p2).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 = x2.sqrt()
assert (res == pd.sqrt(x2))