atan2
Four-quadrant inverse tangent
Syntax
Description
P = atan2(
returns the
four-quadrant inverse
tangent (tan-1) of Y
,X
)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
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) |
|
|
atan2(-0,-0) |
|
|
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 R2006aR2023a: 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.
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)