dualnum.HyperDual64¶

class dualnum.HyperDual64¶

Hyper dual number using 64-bit-floats as fields.

A hyper dual number consists of a + b ε1 + c ε2 + d ε1ε2

Examples

>>> from dualnum import HyperDual64 as HD64
>>> x = HD64(1.0, 0.0, 0.0, 0.0) # constructor
>>> y = HD64.from_re(2.0)        # from real value
>>> x + y
3 + [0]ε1 + [0]ε2 + [0]ε1ε2

Compute partial derivatives of a function.

>>> from dualnum import HyperDual64 as HD64, derive2
>>> x, y = derive2(3.0, 4.0)
>>> # the above is equal to
>>> x = HD64(3.0, 1.0, 0.0, 0.0)
>>> y = HD64(4.0, 0.0, 1.0, 0.0)
>>> fxy = x**2 * y - y**3
>>> fxy.value
-28
>>> fxy.first_derivative
(24.0, -39.0) # df/dx, df/dy
fxy.second_derivative
6.0

__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`	(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`	Calculate logarithm with given base.
`mul_add`	Fused multiply-add.
`powd`	Power using self (hyper) dual number as exponent.
`powf`	Power using 64-bin float as exponent.
`powi`	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`	First hyperdual part.
`second_derivative`	Third hyperdual part.
`value`	Real part.