gradient — Compute numerical gradients in MATLAB and RunMat.

gradient(F) computes numerical derivatives using central differences in the interior and one-sided differences at boundaries. Default dimension behavior and multi-output ordering follow MATLAB semantics.

Syntax

G = gradient(F)
G = gradient(F, h)
[G1, G2, ...] = gradient(F)
[G1, G2, ...] = gradient(F, h1, h2, ...)

Inputs

Returns

Returned values from gradient depend on how many outputs the caller requests.

Errors

How gradient works

• gradient(F) chooses the first non-singleton dimension for vectors and returns the column-direction derivative for matrices.
• [FX, FY] = gradient(F) on a matrix returns FX for dimension 2 (across columns) and FY for dimension 1 (down rows), matching MATLAB.
• gradient(F, h) applies the same scalar spacing to every returned dimension.
• gradient(F, hx, hy, ...) accepts one scalar spacing per output dimension. In v1, each spacing must be scalar.
• Interior points use central differences (f(i+1) - f(i-1)) / (2*h), while the first and last points use one-sided differences.
• Real, logical, and scalar numeric inputs promote through the standard tensor conversion path. Complex host inputs are supported by differentiating the real and imaginary parts independently.
• When a GPU tensor is passed and the active provider implements gradient_dim, scalar-spacing gradients stay resident on the device. Real and complex-interleaved GPU tensors are supported; coordinate-vector spacing currently gathers to the host.

Does RunMat run gradient on the GPU?

The WGPU backend implements gradient_dim for real and complex-interleaved tensors, so scalar-spacing gradients execute on the device and return GPU tensors for both single-output and multi-output calls.

The simple in-process provider also exposes real and complex gradient_dim, allowing provider-level parity tests without requiring a physical GPU.

Coordinate-vector spacing is intentionally out of scope for this version and falls back to host evaluation.

GPU memory and residency

Manual gpuArray promotion is optional. When a scalar-spacing gradient starts with GPU-resident data and the active provider implements gradient_dim, RunMat keeps the result on the device. Complex-interleaved GPU tensors preserve complex residency. If the provider lacks the hook, or if spacing is specified with coordinate vectors, RunMat gathers to the host and preserves MATLAB-compatible results.

Examples

Differentiating a row vector

v = [1 4 9];
g = gradient(v)

Expected output:

g = [3 4 5]

Requesting both matrix gradient components

A = [1 2; 3 4];
[FX, FY] = gradient(A)

Expected output:

FX =
     1     1
     1     1

FY =
     2     2
     2     2

Using scalar spacing on GPU data

G = gpuArray(single([1 4 9]));
D = gradient(G, 2);
out = gather(D)

Expected output:

out = single([1.5 2.0 2.5])

Feeding gradient into a vector-field plot

[X, Y] = meshgrid(linspace(-2, 2, 25), linspace(-2, 2, 25));
Z = X .* exp(-X.^2 - Y.^2);
[DX, DY] = gradient(Z, X(1,2)-X(1,1), Y(2,1)-Y(1,1));
quiver(X, Y, DX, DY)

Using gradient with coding agents

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

FAQ

Related Math functions

Open-source implementation

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

• View the source for gradient 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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