ldivide, .\

Element-wise quaternion left division

Since R2023b

Syntax

C = A.\B

Description

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

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

B = 2;
C = A.\B

C = 2×1 quaternion array
     0.066667 -  0.13333i -      0.2j -  0.26667k
     0.057471 - 0.068966i -  0.08046j - 0.091954k

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([1:4;2:5;4:7;5:8]);
A = reshape(q1,2,2)

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

q2 = quaternion(magic(4));
B = reshape(q2,2,2)

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

C = A.\B

C = 2×2 quaternion array
          2.7 -      1.9i -      0.9j -      1.7k       1.5159 -  0.37302i -  0.15079j -  0.02381k
       2.2778 +  0.46296i -  0.57407j + 0.092593k       1.2471 +  0.91379i -  0.33908j -   0.1092k

Input Arguments

A — 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.

B — 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.

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,

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

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, then

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

Extended Capabilities

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

Version History

Introduced in R2023b