trapz — Trapezoidal numerical integration of sampled data.

trapz(Y) approximates the integral of sampled data in Y using the trapezoidal rule. The integration runs along the first non-singleton dimension unless you specify a different dimension explicitly.

How trapz works

• trapz(Y) assumes unit spacing between adjacent samples.
• trapz(X, Y) accepts a scalar spacing, a vector of coordinates whose length matches the working dimension, or an array X with the same size as Y.
• trapz(..., dim) selects the working dimension explicitly. Dimensions larger than ndims(Y) behave like singleton axes, so the result is zero along those slices.
• Logical inputs are promoted to double precision before integration. Complex-valued Y inputs are integrated component-wise and preserve their complex output type.
• When the selected dimension has length 0 or 1, trapz returns zeros because there are no intervals to integrate.

How RunMat runs trapz on the GPU

RunMat does not yet expose a native provider hook for trapz. When the input is a gpuArray, the runtime gathers the data to host memory, performs the trapezoidal integration with MATLAB-compatible dimension and spacing rules, and re-uploads real-valued outputs so downstream GPU work stays resident.

GPU memory and residency

Manual gpuArray promotion is optional. If sampled data already lives on the GPU, RunMat preserves real-valued outputs as gpuArrays by re-uploading the trapezoidal result after the host fallback path.

Examples

Integrating sampled sine data with explicit coordinates

x = 0:0.01:pi;
y = sin(x);
area = trapz(x, y)

Expected output:

area ≈ 2

Using unit spacing for a row vector

y = [1 2 3];
q = trapz(y)

Expected output:

q = 4

Integrating each row independently

A = [1 2 3; 4 5 6];
q = trapz(A, 2)

Expected output:

q =
     4
    10

Running trapz on GPU data

G = gpuArray([1 2 3]);
q = trapz(G);
result = gather(q)

Expected output:

result = 4

FAQ

What spacing does trapz(Y) assume?

It assumes adjacent samples are one unit apart.

What forms of X are accepted?

A scalar spacing, a vector of coordinates matching the integration dimension, or an array with the same size as Y.

What happens for a scalar or singleton slice?

The integral is zero because there are no trapezoids to sum.

Does trapz support complex inputs?

Yes. RunMat integrates the real and imaginary parts independently and returns a complex result.

Does trapz keep gpuArray residency?

For real-valued results, yes. RunMat currently gathers GPU inputs to the host, computes the trapezoidal integral, and re-uploads the result so downstream GPU code can stay resident.

Related functions to explore

These functions work well alongside trapz. Each page has runnable examples you can try in the browser.

cumtrapz, diff, sum, cumsum, gpuArray, gather

Open-source implementation

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

• View trapz.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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