This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

power, .^

Element-wise quaternion power

Syntax

C = A.^b

Description

example

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

Examples

collapse all

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

collapse all

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

collapse all

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+bi+cj+dk is given by

A=A(cosθ+u^sinθ)

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=Ab(cos(bθ)+u^sin(bθ))

Extended Capabilities

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

Introduced in R2018b