Documentation

log

Natural logarithm of quaternion array

Description

B = log(A) computes the natural logarithm of the elements of the quaternion array A.

Examples

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Create a 3-by-1 quaternion array A.

A = quaternion(randn(3,4))
A=3×1 object
0.53767 + 0.86217i - 0.43359j +  2.7694k
1.8339 + 0.31877i + 0.34262j -  1.3499k
-2.2588 -  1.3077i +  3.5784j +  3.0349k

Compute the logarithmic values of A.

B = log(A)
B=3×1 object
1.0925 + 0.40848i - 0.20543j +  1.3121k
0.8436 + 0.14767i + 0.15872j - 0.62533k
1.6807 - 0.53829i +   1.473j +  1.2493k

Input Arguments

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

Data Types: quaternion

Output Arguments

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Quaternion natural logarithm values, returned as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

Algorithms

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

$\mathrm{log}\left(A\right)=\mathrm{log}‖A‖+\frac{\overline{v}}{‖\overline{v}‖}\text{arccos}\frac{a}{‖A‖}$

Extended Capabilities

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