exp

Exponential of quaternion array

Description

example

B = exp(A) computes the exponential of the elements of the quaternion array A.

Examples

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Create a 4-by-1 quaternion array A.

A = quaternion(magic(4))
A = 4x1 quaternion array
16 +  2i +  3j + 13k
5 + 11i + 10j +  8k
9 +  7i +  6j + 12k
4 + 14i + 15j +  1k

Compute the exponential of A.

B = exp(A)
B = 4x1 quaternion array
5.3525e+06 + 1.0516e+06i + 1.5774e+06j + 6.8352e+06k
-57.359 -     89.189i -     81.081j -     64.865k
-6799.1 +     2039.1i +     1747.8j +     3495.6k
-6.66 +     36.931i +     39.569j +     2.6379k

Input Arguments

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Input quaternion, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

Output Arguments

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Result of quaternion exponential, returned as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

Algorithms

Given a quaternion $A=a+b\text{i}+c\text{j}+d\text{k}=a+\overline{v}$, the exponential is computed by

$\mathrm{exp}\left(A\right)={e}^{a}\left(\mathrm{cos}‖\overline{v}‖+\frac{\overline{v}}{‖\overline{v}‖}\mathrm{sin}‖\overline{v}‖\right)$