cov — Compute covariance matrices in MATLAB and RunMat.

cov returns covariance matrices for numeric data with columns as variables and rows as observations. Single-matrix, paired-input, weighting, and row-handling forms follow MATLAB semantics.

Syntax

C = cov(X)
C = cov(X, Y_or_w)
C = cov(X, normalization)
C = cov(X, rows_option)
C = cov(X, Y, opt)
C = cov(X, Y, w)
C = cov(X, Y, w, opt)

Inputs

Returns

Errors

How cov works

• cov(X) treats each column of X as a variable and returns a square covariance matrix.
• cov(X, Y) concatenates X and Y column-wise (they must have the same number of rows) before computing the covariance.
• The second argument can be the normalization flag 0 (default) or 1, matching MATLAB's unbiased and biased estimators.
• You can pass a weight vector to obtain frequency-weighted covariance.
• 'omitrows' drops rows containing NaN or Inf before the covariance is computed.
• 'partialrows' performs pairwise deletion: each covariance entry uses only the rows that contain finite values for that column pair.

Does RunMat run cov on the GPU?

RunMat invokes provider-specific GPU kernels when:

1. Data inputs already reside on the GPU; 2. The rows option is 'all'; 3. Any weight vector is either a host numeric/logical vector that can be uploaded temporarily or a real gpuArray vector on the same provider; and 4. The active provider exposes the custom covariance hook.

If any of these conditions is not met, RunMat gathers the data to the host, evaluates the reference implementation, and returns a dense host tensor. This guarantees MATLAB-compatible behaviour regardless of GPU support.

GPU memory and residency

You usually do not need to call gpuArray. Expressions such as cov(sin(X)) keep temporary results on the GPU as long as the active provider handles the operation. For rows='all', observation weight vectors can also stay on the provider path: host weights are uploaded temporarily and resident real gpuArray row or column vectors are used directly when they belong to the same provider. The builtin gathers to the CPU for 'omitrows', 'partialrows', unsupported complex/provider-mismatched resident weights, or when the provider does not implement the covariance hook. Explicitly calling gpuArray remains supported for MATLAB compatibility and to seed GPU residency when you are unsure about planner decisions.

Examples

Computing covariance of columns in a matrix

X = [4.0 2.0 0.60;
     4.2 2.1 0.59;
     3.9 2.0 0.58;
     4.3 2.1 0.62;
     4.1 2.2 0.63];
C = cov(X)

Expected output:

C =
    0.0250    0.0075    0.0018
    0.0075    0.0070    0.0014
    0.0018    0.0014    0.0004

Covariance between two vectors

x = [1 2 3 4]';
y = [10 11 9 12]';
C = cov(x, y)

Expected output:

C =
    1.6667    0.6667
    0.6667    1.6667

Weighted covariance with observation weights

X = [4.0 2.0;
     4.2 2.1;
     3.9 2.0;
     4.3 2.1;
     4.1 2.2];
w = [1 1 1 2 2];
Cw = cov(X, w)

Expected output:

Cw =
    0.0224    0.0050
    0.0050    0.0067

Ignoring rows that contain missing values

X = [1   NaN 2;
     3   4   5;
     NaN 6   7;
     8   9   10];
C = cov(X, 'omitrows')

Expected output:

C =
   12.5000   12.5000   12.5000
   12.5000   12.5000   12.5000
   12.5000   12.5000   12.5000

Pairwise covariance with staggered NaNs

X = [ 1   2   NaN;
      4   NaN 6;
      7   8   9];
C = cov(X, 'partialrows')

Expected output:

C =
    9.0000   18.0000    4.5000
   18.0000   18.0000       NaN
    4.5000       NaN    4.5000

Running covariance on gpuArray inputs

X = [4.0 2.0 0.60;
     4.2 2.1 0.59;
     3.9 2.0 0.58;
     4.3 2.1 0.62;
     4.1 2.2 0.63];
G = gpuArray(X);
CG = cov(G);
CG_host = gather(CG)

Expected output:

CG_host =
    0.0250    0.0075    0.0018
    0.0075    0.0070    0.0014
    0.0018    0.0014    0.0004

Using cov with coding agents

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

FAQ

Related Stats functions

Open-source implementation

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

• View the source for cov 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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• RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
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