d = eigs(A)
d = eigs(A, k)
d = eigs(A, k, which)
d = eigs(A, k, sigma)
[V, D] = eigs(...)
| Parameter | Description |
|---|---|
| A | a sparse double, single, complex double, or complex single square matrix. |
| k | a positive integer smaller than the matrix dimension. Default is 6. |
| which | a string selecting eigenvalues: 'lm', 'sm', 'lr', 'sr', 'li', 'si', 'la', or 'sa'. |
| sigma | a finite scalar. Eigenvalues nearest to sigma are computed by shift-invert mode. Complex sigma values are supported for complex sparse matrices. |
| Parameter | Description |
|---|---|
| d | selected eigenvalues returned as a dense column vector. |
| V | dense matrix whose columns are the selected eigenvectors. |
| D | dense diagonal matrix containing the selected eigenvalues. |
eigs computes a subset of eigenvalues and, optionally, the corresponding eigenvectors of a sparse floating-point square matrix.
For a matrix A, the returned eigenpairs satisfy:
$$A\mathbf{v} = \lambda\mathbf{v}$$eigs(A, k, which) selects eigenvalues by magnitude, real part, or imaginary part. The values 'la' and 'sa' are accepted as aliases for largest and smallest algebraic values on symmetric real matrices.
eigs(A, k, sigma) selects eigenvalues nearest to the scalar sigma.
When the optional ARPACK backend is not available, eigs uses a dense fallback for small sparse matrices. Larger sparse matrices still require ARPACK to avoid excessive memory use.
Sparse single and sparse single-complex inputs are accepted. The selected eigenproblem is computed through the double-precision sparse backend, and dense outputs are converted back to single or single-complex when applicable.
A = sparse([4 1 0; 1 3 0; 0 0 2]);
d = eigs(A, 2)
[V, D] = eigs(A, 2)A = sparse(diag([1 2 4 8 16]));
d = eigs(A, 2, 3.5)A = sparse(diag([1 + 1i, 2 - 1i, 4 + 2i]));
d = eigs(A, 2, 2 + 0.5i)A = sparse(single(diag([1 + 1i, 2 - 1i, 4 + 2i])));
d = eigs(A, 2)| Version | Description |
|---|---|
| 2.0.0 | dense fallback added for small sparse matrices when ARPACK is unavailable. |
| 2.0.0 | sparse single and sparse single-complex inputs supported through the sparse double-precision backend. |