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
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
Y | Any | Yes | — | Sample values. |
dim | Any | Yes | — | Integration dimension. |
X | Any | Yes | — | Sample points or spacing. |
Returns
| Name | Type | Description |
|---|---|---|
Q | NumericArray | Cumulative trapezoidal integral output. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:cumtrapz:InvalidArgument | Input argument count, dimension selector, or spacing arguments are invalid. | cumtrapz: invalid argument |
RunMat:cumtrapz:InvalidInput | Input values cannot be converted to supported numeric integration domains. | cumtrapz: invalid input |
RunMat:cumtrapz:Internal | Integration execution fails during gather, allocation, or provider promotion. | cumtrapz: internal integration failure |
How cumtrapz works
cumtrapz(Y)assumes unit spacing between adjacent samples.cumtrapz(X, Y)accepts a scalar spacing, a vector of coordinates whose length matches the working dimension, or an arrayXwith the same size asY.cumtrapz(..., dim)selects the working dimension explicitly. Dimensions larger thanndims(Y)behave like singleton axes, so the result stays zero along those slices.- Logical inputs are promoted to double precision before integration. Complex-valued
Yinputs are integrated component-wise and preserve their complex output type. - 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?
RunMat does not yet expose a native provider hook for cumtrapz. When the input is a gpuArray, the runtime gathers the data to host memory, performs the cumulative 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 cumulative results as gpuArrays by re-uploading the output after the host fallback path.
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 10Running 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.
Run a small cumtrapz example, explain the result, then change one input and compare the output.
FAQ
How is cumtrapz different from trapz?⌄
trapz returns the final integrated value, while cumtrapz returns the running integral at every sample.
Why is the first element zero?⌄
There is no interval before the first sample, so the cumulative integral begins at zero.
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.
Does cumtrapz support complex inputs?⌄
Yes. RunMat accumulates the real and imaginary components independently and returns a complex result.
Does cumtrapz keep gpuArray residency?⌄
For real-valued results, yes. RunMat currently gathers GPU inputs to the host, computes the cumulative trapezoidal integral, and re-uploads the result so downstream GPU code can stay resident.
Related Math functions
Reduction
all · any · cummax · cummin · cumprod · cumsum · diff · gradient · max · mean · median · min · nnz · prod · std · sum · trapz · var
Elementwise
abs · angle · complex · conj · double · exp · expm1 · factorial · gamma · hypot · imag · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · sign · single · sqrt · times
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · deg2rad · rad2deg · sin · sind · sinh · tan · tand · tanh
Structure
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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