angle

Phase angle

Syntax

P = angle(Z)


Description

P = angle(Z) returns the phase angles, in radians, for each element of complex array Z. The angles lie between ±π.

For complex Z, the magnitude R and phase angle theta are given by

R = abs(Z)
theta = angle(Z)

and the statement

Z = R.*exp(i*theta)

converts back to the original complex Z.

Examples

Phase Angles of Matrix Elements

Create a matrix of complex values and compute the phase angle of each element.

Z = [1 - 1i   2 + 1i   3 - 1i   4 + 1i
     1 + 2i   2 - 2i   3 + 2i   4 - 2i
     1 - 3i   2 + 3i   3 - 3i   4 + 3i
     1 + 4i   2 - 4i   3 + 4i   4 - 4i];

P = angle(Z)

P = 4×4

   -0.7854    0.4636   -0.3218    0.2450
    1.1071   -0.7854    0.5880   -0.4636
   -1.2490    0.9828   -0.7854    0.6435
    1.3258   -1.1071    0.9273   -0.7854

Algorithms

The angle function takes a complex number z = x + iy and calculates atan2(y,x) to find the angle formed in the xy-plane between the positive x-axis and a ray from the origin to the point (x,y). This phase angle is also the imaginary part of the complex logarithm, since

$$\begin{array}{l}z=r{e}^{i\theta }\\ \log \left(z\right)=\log \left(r\right)+i\theta .\end{array}$$

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).