autodiff.Dual.__pow__

Dual.__pow__(other)

Return self to the power of other.

Parameters

selfDual

otherint, float

Returns

outDual

Notes

If other is a non-integer scalar and self.val is less than zero, the derivative is a complex number. This will raise a ValueError. Only integer powers are supported if the base is negative.

If self.val is equal to zero and other is less than one, we cannot compute the derivative of the result due to a ZeroDivisionError.

If other is a Dual and self.val is less than or equal to zero, we cannot compute the derivative of the result since the log of a negative number is not defined. This will raise a ValueError.

Examples

Dual number and scalar:

>>> ad.Dual(2) ** 5
Dual(32, array([80]))

Two dual numbers (univariate):

>>> ad.Dual(2, [1]) ** ad.Dual(3, [2])
Dual(8, array([23.09035489]))

Two dual numbers (multivariate):

>>> ad.Dual(3, [1, 2]) ** ad.Dual(2, [3, 4])
Dual(9, array([35.66253179, 51.55004239]))

Example of errors raised (see notes above):

>>> ad.Dual(-1) ** 1.2
Traceback (most recent call last):
...
ValueError: -1 cannot be raised to the power of 1.2; only integer powers are allowed if base is negative

>>> ad.Dual(0) ** -2
Traceback (most recent call last):
...
ZeroDivisionError: 0.0 cannot be raised to a negative power

>>> ad.Dual(0) ** ad.Dual(1)
Traceback (most recent call last):
...
ValueError: 0 cannot be raised to the power of 1; log is undefined for x = 0

previous

autodiff.Dual.__rtruediv__

next

autodiff.Dual.__rpow__