def test_exp_log(self):
from pyaudi import gdual_double as gdual
from pyaudi import exp, log
x = gdual(2.3, "x", 5)
y = gdual(1.5, "y", 5)
p1 = x * x * y - x * y * x * x * x + 3 * y * y * y * y * x * y * x
self.assertTrue((exp(log(p1)) - p1).is_zero(1e-10))
def test_function_methods(self):
from pyaudi import gdual_double as gdual
from pyaudi import exp, log, sin, cos
x = gdual(0.5, "x", 11)
self.assertEqual(exp(x), x.exp())
self.assertEqual(log(x), x.log())
self.assertEqual(sin(x), x.sin())
self.assertEqual(cos(x), x.cos())
def test_exp_log(self):
from pyaudi import gdual_double as gdual
from pyaudi import exp, log
x = gdual(2.3, "x",5);
y = gdual(1.5, "y",5);
p1 = x*x*y - x*y*x*x*x + 3*y*y*y*y*x*y*x;
self.assertTrue((exp(log(p1)) - p1).is_zero(1e-10))
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 nn_predict(self, model_input):
vector = model_input
dense_layer_count = 0
for layer_config in self.config:
if layer_config['class_name'] == 'Dense':
wgts, biases = self.weights[dense_layer_count *
2:(dense_layer_count + 1) * 2]
vector = wgts.T.dot(vector) + biases
dense_layer_count += 1
elif layer_config['class_name'] == 'Activation':
if layer_config['config']['activation'] == 'relu':
vector[convert_gdual_to_float(vector) < 0] = 0
elif layer_config['config']['activation'] == 'tanh':
vector = np.vectorize(lambda x: tanh(x))(vector)
elif layer_config['config']['activation'] == 'softplus':
vector = np.vectorize(lambda x: exp(x))(vector) + 1
vector = np.vectorize(lambda x: log(x))(vector)
return vector
def nn_predict(self, model_input):
vector = model_input
dense_layer_count = 0
for layer_config in self.config:
if layer_config['class_name'] == 'Dense':
wgts, biases = self.weights[dense_layer_count *
2:(dense_layer_count + 1) * 2]
vector = wgts.T.dot(vector) + biases
dense_layer_count += 1
elif layer_config['class_name'] == 'Activation':
if layer_config['config']['activation'] == 'relu':
vector[convert_gdual_to_float(vector) < 0] = 0
elif layer_config['config']['activation'] == 'tanh':
vector = np.vectorize(lambda x: tanh(x))(vector)
elif layer_config['config']['activation'] == 'softplus':
# avoiding overflow with exp; | log(1+exp(x)) - x | < 1e-10 for x>=30
floatize = lambda x: x.constant_cf if type(
x) == gdual_double else x
softplus = lambda x: x if floatize(x) > 30.0 else log(
exp(x) + 1)
# softplus = lambda x : log(exp(x)+1)
vector = np.vectorize(softplus)(vector)
return vector
def do(self, x1, x2):
import pyaudi as pd
res = x2.log2()
assert (res == pd.log(x2) / np.log(2.0))
def do(self, x1, x2):
import pyaudi as pd
res = x2.log1p()
assert (res == pd.log(x2 + 1.0))
def __atan2_helper(x1, x2):
return atan(x1 / x2) + (float(x2) < 0) * pi
# gdual_double Definitions
try:
gdual_double.__float__ = lambda self: self.constant_cf
# gdual_double.__int__ = lambda self: int(self.constant_cf)
gdual_double.__abs__ = pyaudi.abs
gdual_double.sqrt = pyaudi.sqrt
gdual_double.exp = pyaudi.exp
gdual_double.expm1 = lambda self: pyaudi.exp(self) - 1.0
gdual_double.log = pyaudi.log
gdual_double.log10 = lambda self: pyaudi.log(self) / pyaudi.log(
gdual_double(10.0))
gdual_double.log1p = lambda self: pyaudi.log(self + 1.0)
gdual_double.log2 = lambda self: pyaudi.log(self) / pyaudi.log(
gdual_double(2.0))
gdual_double.cos = pyaudi.cos
gdual_double.sin = pyaudi.sin
gdual_double.tan = pyaudi.tan
gdual_double.cosh = pyaudi.cosh
gdual_double.sinh = pyaudi.sinh
gdual_double.tanh = pyaudi.tanh
gdual_double.arccos = pyaudi.acos
gdual_double.arcsin = pyaudi.asin
gdual_double.arctan = pyaudi.atan
gdual_double.arctan2 = lambda self, x2: pyaudi.__atan2_helper(self, x2)
gdual_double.erf = pyaudi.erf
from pyaudi import gdual_double as gdual
from pyaudi import exp, log, cbrt
# We want to compute the Taylor expansion of a function f (and thus all derivatives) at x=2, y=3
# 1 - Define the generalized dual numbers (7 is the truncation order, i.e. the maximum order of derivation we will need)
x = gdual(2, "x", 7)
y = gdual(3, "y", 7)
# 2 - Compute your function as usual
f = exp(x * x + cbrt(y) / log(x * y))
# 3 - Inspect the results (this does not require any more computations)
print("Taylor polynomial: " +
str(f)) # This is the Taylor expansion of f (truncated at the 7th order)
print("Derivative value [1,0]: " + str(f.get_derivative(
[1, 0]))) # This is the value of the derivative (d / dx)
print("Derivative value [4,3]: " + str(f.get_derivative(
[4, 3]))) # This is the value of the mixed derivative (d^7 / dx^4dy^3)
# 4 - Using the dictionary interface (note the presence of the "d" before all variables)
print("Derivative value [1,0]: " + str(f.get_derivative(
{"dx": 1}))) # This is the value of the derivative (d / dx)
print("Derivative value [4,3]: " + str(f.get_derivative({
"dx": 4,
"dy": 3
}))) # This is the value of the mixed derivative (d^7 / dx^4dy^3)
from pyaudi import gdual_double as gdual
from pyaudi import exp, log, cbrt
# We want to compute the Taylor expansion of a function f (and thus all derivatives) at x=2, y=3
# 1 - Define the generalized dual numbers (7 is the truncation order, i.e. the maximum order of derivation we will need)
x = gdual(2, "x", 7);
y = gdual(3, "y", 7);
# 2 - Compute your function as usual
f = exp(x*x + cbrt(y) / log(x*y));
# 3 - Inspect the results (this does not require any more computations)
print("Taylor polynomial: " + str(f)) # This is the Taylor expansion of f (truncated at the 7th order)
print("Derivative value [1,0]: " + str(f.get_derivative([1,0]))) # This is the value of the derivative (d / dx)
print("Derivative value [4,3]: " + str(f.get_derivative([4,3]))) # This is the value of the mixed derivative (d^7 / dx^4dy^3)
# 4 - Using the dictionary interface (note the presence of the "d" before all variables)
print("Derivative value [1,0]: " + str(f.get_derivative({"dx":1}))) # This is the value of the derivative (d / dx)
print("Derivative value [4,3]: " + str(f.get_derivative({"dx":4, "dy":3}))) # This is the value of the mixed derivative (d^7 / dx^4dy^3)