power, .^

Element-wise quaternion power

Description

example

C = A.^b raises each element of A to the corresponding power in b.

Examples

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Create a quaternion and raise it to a real scalar power.

A = quaternion(1,2,3,4)
A = quaternion
1 + 2i + 3j + 4k

b = 3;
C = A.^b
C = quaternion
-86 -  52i -  78j - 104k

Create a 2-by-1 quaternion array and raise it to powers from a 2-D array.

A = quaternion([1:4;5:8])
A = 2x1 quaternion array
1 + 2i + 3j + 4k
5 + 6i + 7j + 8k

b = [1 0 2; 3 2 1]
b = 2×3

1     0     2
3     2     1

C = A.^b
C = 2x3 quaternion array
1 +    2i +    3j +    4k        1 +    0i +    0j +    0k      -28 +    4i +    6j +    8k
-2110 -  444i -  518j -  592k     -124 +   60i +   70j +   80k        5 +    6i +    7j +    8k

Input Arguments

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Base, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion | single | double

Exponent, specified as a real scalar, vector, matrix, or multidimensional array.

Data Types: single | double

Output Arguments

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Each element of quaternion A raised to the corresponding power in b, returned as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

Algorithms

The polar representation of a quaternion $A=a+b\text{i}+c\text{j}+d\text{k}$ is given by

$A=‖A‖\left(\mathrm{cos}\theta +\stackrel{^}{u}\mathrm{sin}\theta \right)$

where θ is the angle of rotation, and û is the unit quaternion.

Quaternion A raised by a real exponent b is given by

$P=A.^b={‖A‖}^{b}\left(\mathrm{cos}\left(b\theta \right)+\stackrel{^}{u}\mathrm{sin}\left(b\theta \right)\right)$