cumtrapz — Compute cumulative trapezoidal integration in MATLAB and RunMat.

cumtrapz(Y) computes cumulative trapezoidal integrals of sampled data in Y. The output matches Y in size, with zero at the first element of the integration dimension and running integral values thereafter.

Syntax

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

Inputs

Returns

Errors

How cumtrapz works

• cumtrapz(Y) assumes unit spacing between adjacent samples.
• cumtrapz(X, Y) accepts documented single- or double-precision scalar spacing or a coordinate vector whose length matches the working dimension. A same-size coordinate tensor is an explicitly gated RunMat extension.
• cumtrapz(..., dim) selects the working dimension explicitly. Dimensions larger than ndims(Y) behave like singleton axes, so the result stays zero along those slices.
• Documented Y classes are single and double, real or complex, and output preserves single versus double. Typed-integer and logical Y, typed-integer or logical X, and typed-integer dim are separate RunMat-only extensions.
• Typed-integer Y and X cross the binary64 integration boundary only when every authoritative integer value is exactly representable; otherwise RunMat reports an error instead of silently rounding.
• When the selected dimension has length 0 or 1, the output is zero along that dimension because there are no intervals to accumulate.

Does RunMat run cumtrapz on the GPU?

Floating real and complex-interleaved resident Y can use provider-backed cumulative trapezoidal integration with real unit, scalar, coordinate-vector, or gated same-size coordinate-tensor spacing.

Mixed-provider spacing does not cross-dispatch. Integer or logical resident values, missing hooks, provider errors, and contract-invalid results use the exactness-checked host fallback path.

GPU memory and residency

Resident floating input dispatch is resolved from the input handle's owner, not the ambient active provider. Native results are validated for shape, storage, precision, device, and owner; invalid native results are freed before host fallback. Fallback returns to the first resident owner when provider precision permits.

Examples

Computing a cumulative integral with explicit coordinates

x = [0 1 3];
y = [0 1 2];
q = cumtrapz(x, y)

Expected output:

q = [0 0.5 3.5]

Using unit spacing for sampled data

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

Expected output:

q = [0 1.5 4]

Accumulating across rows in a matrix

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

Expected output:

q =
     0    1.5    4
     0    4.5   10

Running cumtrapz on GPU data

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

Expected output:

result = [0 1.5 4]

Using cumtrapz with coding agents

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

FAQ

Related Math functions

Open-source implementation

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

• View the source for cumtrapz 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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