trapz — Approximate integrals of sampled data using the trapezoidal rule with MATLAB-compatible dimension handling.

trapz(Y) approximates integrals of single- or double-precision sampled data using trapezoidal segments. By default integration runs along the first non-singleton dimension, with MATLAB-compatible explicit-dimension forms supported. Typed-integer sample data and spacing are available in RunMat mode when every value can enter the binary64 integration domain exactly.

Syntax

Q = trapz(Y)
Q = trapz(Y, dim)
Q = trapz(X, Y)
Q = trapz(X, Y, dim)

Inputs

Returns

Errors

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.
• Single-precision sample data produces single-precision output; typed-integer sample data is a RunMat extension and produces double output.
• Native typed-integer Y and X roles are independently compatibility-gated and require exact binary64 conversion. Native typed-integer dim is an ordinary exact structural selector.
• When the selected dimension has length 0 or 1, trapz returns zeros because there are no intervals to integrate.

Does RunMat run trapz on the GPU?

Real, logical, and complex-interleaved gpuArray sample inputs use provider-backed trapezoidal integration for unit spacing, scalar spacing, coordinate-vector spacing, and same-size coordinate-tensor spacing.

Spacing inputs must be real-valued. Provider-missing cases use the host fallback path to preserve MATLAB-compatible semantics.

GPU memory and residency

Manual gpuArray promotion is optional. If real, logical, or complex-interleaved sampled data already lives on the GPU, RunMat preserves the output as a gpuArray through the provider trapz_dim 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

Using trapz with coding agents

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

FAQ

Related Math functions

Open-source implementation

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

• View the source for trapz 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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