log

Natural logarithm of quaternion array

Syntax

B = log(A)

Description

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

Examples

Logarithmic Values of Quaternion Array

Create a 3-by-1 quaternion array A.

A = quaternion(randn(3,4))

A=3×1 quaternion array
     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 quaternion array
      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

A — Input array

scalar | vector | matrix | multidimensional array

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

Data Types: quaternion

Output Arguments

B — Logarithm values

scalar | vector | matrix | multidimensional array

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

$$\log (A)=\log \Vert A\Vert +\frac{\overline{v}}{\Vert \overline{v}\Vert }\text{arccos}\frac{a}{\Vert A\Vert }$$

Extended Capabilities

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