num_dual.Dual2_64

class num_dual.Dual2_64

Second order dual number using 64-bit-floats as fields.

A second order dual number consists of f_0 + f_1 ε_1 + f_2 ε_1^2 where f_0 is the function value, f_1 the first derivative and f_2 the second derivative.

Examples

>>> from num_dual import Dual2_64 as D264
>>> x = D264(1.0, 0.0, 0.0)
>>> y = D264.from_re(2.0)
>>> x + y
3 + [0]ε1 + [0]ε1²

First and second derivative of a function.

>>> from num_dual import second_derivative
>>> import numpy as np
>>> f, df, d2f = second_derivative(lambda x: x * x + np.sqrt(x), 4.0)
>>> f
18.0
>>> df
8.25
>>> d2f
1.96875

__init__()

Methods

__init__()
arccos()	Computes the arccosine of a (hyper) dual number.
arccosh()	Computes the inverse hyperbolic cosine of a (hyper) dual number.
arcsin()	Computes the arcsine of a (hyper) dual number.
arcsinh()	Computes the inverse hyperbolic sine of a (hyper) dual number.
arctan()	Computes the arctangent of a (hyper) dual number.
arctanh()	Computes the inverse hyperbolic tangent of a (hyper) dual number.
cbrt()	Cubic root.
cos()	Hyperbolic cosine function.
cosh()	Computes the hyperbolic cosine of a (hyper) dual number.
exp()	Calculate the exponential of (hyper) dual number.
exp2()	Calculate 2**x of (hyper) dual number x.
expm1()	Calculate exp(x) - 1.
from_re(re)	(Hyper) dual number from real part, setting all other parts to zero.
log()	Calculate natural logarithm.
log10()	Calculate logarithm with base 10.
log1p()	Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.
log2()	Calculate logarithm with base 2.
log_base(base)	Calculate logarithm with given base.
mul_add(a, b)	Fused multiply-add.
powd(n)	Power using self (hyper) dual number as exponent.
powf(n)	Power using 64-bin float as exponent.
powi(n)	Power using 32-bit integer as exponent.
recip()	Reciprocal value of self.
sin()	Hyperbolic sine function.
sin_cos()	Simultaneously computes the sine and cosine of the (hyper) dual number, x.
sinh()	Computes the hyperbolic sine of a (hyper) dual number.
sph_j0()	Computes the first spherical bessel function.
sph_j1()	Computes the second spherical bessel function.
sph_j2()	Computes the third spherical bessel function.
sqrt()	Sqaure root.
tan()	Computes the tangent of a (hyper) dual number (in radians).
tanh()	Computes the hyperbolic tangent of a (hyper) dual number.

Attributes

first_derivative
second_derivative
value	Real part.