rdivide, ./

Element-wise quaternion right division

Syntax

C = A./B

Description

C = A./B performs quaternion element-wise division by dividing each element of quaternion A by the corresponding element of quaternion B.

Examples

Divide a Quaternion Array by a Real Scalar

Create a 2-by-1 quaternion array, and divide it element-by-element by a real scalar.

A = quaternion([1:4;5:8])

A = 2x1 quaternion array
     1 + 2i + 3j + 4k
     5 + 6i + 7j + 8k

B = 2;
C = A./B

C = 2x1 quaternion array
     0.5 +   1i + 1.5j +   2k
     2.5 +   3i + 3.5j +   4k

Divide a Quaternion Array by Another Quaternion Array

Create a 2-by-2 quaternion array, and divide it element-by-element by another 2-by-2 quaternion array.

q1 = quaternion(magic(4));
A = reshape(q1,2,2)

A = 2x2 quaternion array
     16 +  2i +  3j + 13k      9 +  7i +  6j + 12k
      5 + 11i + 10j +  8k      4 + 14i + 15j +  1k

q2 = quaternion([1:4;3:6;2:5;4:7]);
B = reshape(q2,2,2)

B = 2x2 quaternion array
     1 + 2i + 3j + 4k     2 + 3i + 4j + 5k
     3 + 4i + 5j + 6k     4 + 5i + 6j + 7k

C = A./B

C = 2x2 quaternion array
          2.7 -      0.1i -      2.1j -      1.7k       2.2778 + 0.092593i -  0.46296j -  0.57407k
       1.8256 - 0.081395i +  0.45349j -  0.24419k       1.4524 -      0.5i +   1.0238j -   0.2619k

Input Arguments

A — Dividend

quaternion object | array of quaternion objects | real scalar | array of real numbers

Dividend, specified as a quaternion object, an array of quaternion objects of any dimensionality, a real scalar, or an array of real numbers of any dimensionality. Numeric values must be of data type single or double.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

B — Divisor

quaternion object | array of quaternion objects | real scalar | array of real numbers

Divisor, specified as a quaternion object, an array of quaternion objects of any dimensionality, a real scalar, or an array of real numbers of any dimensionality. Numeric values must be of data type single or double.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

Output Arguments

C — Result

quaternion object | array of quaternion objects

Result of quaternion division, returned as a quaternion object or an array of quaternion objects.

Algorithms

Quaternion Division

Given a quaternion $$A=a_1+a_2\text{i}+a_3\text{j}+a_4\text{k}$$ and a real scalar p,

$$C=A./p=\frac{a_1}{p}+\frac{a_2}{p}\text{i}+\frac{a_3}{p}\text{j}+\frac{a_4}{p}\text{k}$$

Note

For a real scalar p, A./p = A.\p.

Quaternion Division by a Quaternion Scalar

Given two quaternions A and B of compatible sizes,

$$C=A./B=A.*B^{-1}=A.*\left(\frac{conj(B)}{norm{(B)}^2}\right)$$

Extended Capabilities

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