exp

Exponential of quaternion array

Since R2023b

Syntax

B = exp(A)

Description

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

Examples

Exponential of Quaternion Array

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

A — Input quaternion

quaternion object | array of quaternion objects

Input quaternion, specified as a quaternion object or an array of quaternion objects of any dimensionality.

Output Arguments

B — Result

quaternion object | array of quaternion objects

Result of quaternion exponential, returned as a quaternion object or an array of quaternion objects of the same size as A.

Algorithms

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

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

Extended Capabilities

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

Version History

Introduced in R2023b