hypot — Compute element-wise Euclidean norms with hypot in MATLAB and RunMat.

z = hypot(x, y) computes sqrt(|x|.^2 + |y|.^2) element-wise using overflow-resistant arithmetic. Implicit expansion, complex handling, and output shape follow MATLAB semantics.

Syntax

R = hypot(X, Y)

Inputs

Returns

Errors

How hypot works

• Real inputs return non-negative doubles even when the operands are negative.
• Complex arguments are converted to their magnitudes before forming sqrt(|x|.^2 + |y|.^2), matching MATLAB's definition since R2020b.
• Scalars broadcast across the other operand when shapes are compatible; otherwise an error is raised.
• Empty inputs propagate emptiness according to MATLAB's size rules.
• Inf operands return Inf; NaN operands propagate NaN.

Does RunMat run hypot on the GPU?

Hook available and shapes match: the Euclidean norm executes in a single fused GPU kernel.

Hook missing or implicit expansion required: RunMat gathers the data to the host, computes the MATLAB-compatible result, and reuses the host tensor downstream.

Fusion-enabled expressions: the fusion planner can emit a WGSL hypot(a, b) node so long as the active provider marks the group as supported; otherwise the execution seamlessly falls back to the host path.

Providers can implement elem_hypot by emitting a single WGSL/compute shader that calls hypot(a, b); the included WGPU backend demonstrates this pattern.

GPU memory and residency

Manual gpuArray calls are typically unnecessary. RunMat's planner keeps tensors on the GPU when profitable and automatically gathers data when the active provider lacks elem_hypot. You can still force residency with explicit gpuArray/gather to mirror MATLAB workflows or when interoperating with custom kernels.

Examples

Computing the hypotenuse of two scalars

result = hypot(3, 4)

Expected output:

result = 5

Using hypot with vectors and implicit expansion

x = [-3, 0, 4];
y = 4;
norms = hypot(x, y)

Expected output:

norms = [5 4 5]

Calculating per-element distances between two matrices

X = [1 2; 3 4];
Y = [0 1; 1 0];
dist = hypot(X, Y)

Expected output:

dist = [1.0000 2.2361; 3.1623 4.0000]

Working with complex numbers

a = [1+2i, 3-4i];
b = [2-1i, -1+1i];
mag = hypot(a, b)

Expected output:

mag = [3.1623 5.1962]

Applying hypot to character data

codes = hypot('A', zeros(1, 1))

Expected output:

codes = 65.0000

Executing hypot on GPU arrays

Gx = gpuArray([3 4; 5 12]);
Gy = gpuArray([4 3; 12 5]);
distance_gpu = hypot(Gx, Gy);
distance = gather(distance_gpu)

Expected output:

distance = [5 5; 13 13]

Using hypot with coding agents

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

FAQ

Related Math functions

Open-source implementation

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

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

About RunMat

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