atan2

Four-quadrant inverse tangent

Syntax

P = atan2(Y,X)

Description

P = atan2(Y,X) returns the four-quadrant inverse tangent (tan^-1) of Y and X, which must be real. The atan2 function follows the convention that atan2(x,x) returns 0 when x is mathematically zero (either 0 or -0).

Examples

Find Four-Quadrant Inverse Tangent of a Point

Find the four-quadrant inverse tangent of the point y = 4, x = -3.

atan2(4,-3)

ans = 
2.2143

Convert Complex Number to Polar Coordinates

Convert 4 + 3i into polar coordinates.

z = 4 + 3i;
r = abs(z)

r = 
5

theta = atan2(imag(z),real(z))

theta = 
0.6435

The radius r and the angle theta are the polar coordinate representation of 4 + 3i.

Alternatively, use angle to calculate theta.

theta = angle(z)

theta = 
0.6435

Convert r and theta back into the original complex number.

z = r*exp(i*theta)

z = 
4.0000 + 3.0000i

Plot Four-Quadrant Inverse Tangent

Plot atan2(Y,X) for -4<Y<4 and -4<X<4.

Define the interval to plot over.

[X,Y] = meshgrid(-4:0.1:4,-4:0.1:4);

Find atan2(Y,X) over the interval.

P = atan2(Y,X);

Use surf to generate a surface plot of the function. Note that plot plots the discontinuity that exists at Y=0 for all X<0.

surf(X,Y,P);
view(45,45);

Input Arguments

Y — y-coordinates

scalar | vector | matrix | multidimensional array | table | timetable

y-coordinates, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. Inputs Y and X must either be the same size or have sizes that are compatible (for example, Y is an M-by-N matrix and X is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | table | timetable

X — x-coordinates

scalar | vector | matrix | multidimensional array | table | timetable

x-coordinates, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. Inputs Y and X must either be the same size or have sizes that are compatible (for example, Y is an M-by-N matrix and X is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | table | timetable

More About

Four-Quadrant Inverse Tangent

The four-quadrant inverse tangent, atan2(Y,X), returns values in the closed interval [–π, π] based on the values of Y and X, as shown in the graphic.

In contrast, atan(Y/X) returns results that are limited to the interval [–π/2, π/2], shown on the right side of the diagram.

IEEE Compliance

For real inputs, atan2 has a few behaviors that differ from those recommended in the IEEE^®-754 Standard.

	MATLAB®	IEEE
atan2(0,-0)	0	pi
atan2(-0,-0)	0	-pi

Extended Capabilities

Tall Arrays

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

The atan2 function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you use atan2 with single type and double type operands, the generated code might not produce the same result as MATLAB. See Binary Element-Wise Operations with Single and Double Operands (MATLAB Coder).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The atan2 function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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).

Version History

Introduced before R2006a

R2023a: Perform calculations directly on tables and timetables

The atan2 function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.