eigs — Compute selected eigenvalues and eigenvectors with MATLAB-compatible dense-fallback signatures.

eigs(A) returns a subset of eigenvalues. RunMat accepts dense, complex, logical, and small sparse or gpuArray compatibility inputs by materializing them on the host, computes the exact full eigendecomposition through the shared eig path, and selects the requested subset.

Syntax

eigs(A)

How eigs works

• eigs(A) returns up to six eigenvalues with largest magnitude.
• eigs(A,k) clamps k to size(A,2) when larger than the matrix order.
• eigs(A,k,sigma) supports numeric sigma and the documented text selectors largestabs, smallestabs, largestreal, smallestreal, bothendsreal, largestimag, smallestimag, and bothendsimag, plus documented short aliases.
• eigs(A,B,...) solves the generalized problem by reusing eig(A,B) and then selecting the requested subset.
• Two outputs return selected right eigenvectors and a diagonal eigenvalue matrix. Three outputs append convergence flag 0 because the current exact fallback either succeeds fully or raises an error.
• Options supplied as a struct or name-value pairs are validated for MATLAB-compatible field names, value shapes, subspace-dimension minimums, and generalized-problem sigma constraints. Iterative controls such as tolerance, maximum iterations, subspace dimension, start vector, display, and failure treatment do not change the exact fallback result.
• Function-handle Afun forms are intentionally rejected with a deterministic unsupported-form error until RunMat has iterative operator eigensolver support.
• Sparse inputs are materialized to dense host tensors for compatibility only. Very large sparse problems are not a completed high-performance eigs path and should be queued for a future sparse/provider implementation.

Does RunMat run eigs on the GPU?

eigs currently gathers gpuArray inputs and returns host tensors because subset eigenvalue selection needs host-side ordering.

The builtin is explicitly marked ResidencyPolicy::GatherImmediately so the runtime does not imply a false GPU fast path.

A future provider implementation should add a true partial eigensolver hook in runmat-accelerate and parity tests against this exact fallback.

Examples

Largest magnitude eigenvalues

A = diag([1 8 -3 4]);
d = eigs(A, 2)

Expected output:

d = [8; 4]

Smallest magnitude eigenvalues from sparse input

S = sparse(diag([10 2 -4]));
d = eigs(S, 2, 'smallestabs')

Expected output:

d = [2; -4]

Generalized eigenvalue subset

A = [2 0; 0 9];
B = [1 0; 0 3];
d = eigs(A, B, 1, 'smallestreal')

Expected output:

d = 2

Using eigs with coding agents

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

FAQ

Related Linalg functions

Open-source implementation

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

• View the source for eigs 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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