power, .^

Element-wise quaternion power

Syntax

C = A.^b

Description

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

Examples

Raise a Quaternion to a Real Scalar Power

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

Raise a Quaternion Array to Powers from a Multidimensional Array

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

A = quaternion([1:4;5:8])

A=2×1 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=2×3 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

A — Base

scalar | vector | matrix | multidimensional array

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

Data Types: quaternion | single | double

b — Exponent

scalar | vector | matrix | multidimensional array

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

Data Types: single | double

Output Arguments

C — Result

scalar | vector | matrix | multidimensional array

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

$$A=\Vert A\Vert \left(\cos \theta +\widehat{u}\sin \theta \right)$$

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

Quaternion A raised by a real exponent b is given by

$$P=A.^b={\Vert A\Vert }^b\left(\cos \left(b\theta \right)+\widehat{u}\sin \left(b\theta \right)\right)$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.