atan — Element-wise inverse tangent in MATLAB and RunMat.

Y = atan(X) computes the inverse tangent (in radians) of each element in X. It supports real and complex values, and "like" options control output class/residency in MATLAB- and RunMat-compatible forms.

Syntax

Y = atan(X)
Y = atan(X, "like", P)

Inputs

Returns

Errors

How atan works

• Works on scalars, vectors, matrices, and N-D tensors, including logical and integer inputs (which are promoted to double precision before evaluation).
• Character arrays are interpreted as their Unicode code points and return dense double arrays of identical shape.
• Complex inputs follow MATLAB's analytic extension atan(z) = (1/(2i)) * (log(1 + i z) - log(1 - i z)), ensuring identical branch behavior and NaN/Inf propagation.
• Returns results in radians for real inputs and complex numbers for complex inputs.
• Empty arrays and already scalar values pass straight through while preserving shape.

Does RunMat run atan on the GPU?

When RunMat Accelerate is active and the selected provider implements unary_atan, the runtime keeps tensors on the GPU and executes the kernel entirely on-device.

If the provider lacks unary_atan (or declines the request), RunMat gathers the data to the host, computes the result with the reference implementation, and then reapplies residency requests such as 'like' prototypes automatically.

Fusion planning groups neighboring elementwise operations so downstream kernels can stay on the GPU even if atan itself fell back to the CPU.

GPU memory and residency

Usually you do not need to call gpuArray. When a provider exposes unary_atan, the runtime keeps data on the GPU automatically. If the hook is missing (or if you supply a host 'like' prototype), RunMat gathers and computes on the CPU, then honors the requested residency so you do not have to manage transfers manually.

Examples

Arctangent of a scalar

y = atan(1)

Expected output:

y = 0.7854

Element-wise arctangent of a vector

x = linspace(-2, 2, 5);
angles = atan(x)

Expected output:

angles = [-1.1071  -0.7854         0    0.7854    1.1071]

Computing inverse tangent of every entry in a matrix

A = [-2 -1 0; 1 2 3];
Y = atan(A)

Expected output:

Y =
   -1.1071   -0.7854         0
    0.7854    1.1071    1.2490

Evaluating atan on a complex number

z = 1 + 2i;
w = atan(z)

Expected output:

w = 1.3390 + 0.4024i

Keeping the result on the GPU with 'like'

proto = gpuArray.zeros(1, 1);
G = gpuArray([-3 -1 0 1 3]);
deviceResult = atan(G, 'like', proto);
result = gather(deviceResult)

Expected output:

result =
   -1.2490   -0.7854         0    0.7854    1.2490

Inspecting character codes via inverse tangent

codes = atan('RUN')

Expected output:

codes =
    1.5586    1.5590    1.5580

Using atan with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how atan changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how atan is executed, line by line, in Rust.

• View the source for atan in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

• RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
• Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing