s = svds(A)
s = svds(A, k)
s = svds(A, k, which)
[U, S, V] = svds(...)
| Parameter | Description |
|---|---|
| A | a sparse double, single, complex double, or complex single matrix. |
| k | a positive integer smaller than the smaller matrix dimension. Default is 6. |
| which | a string: 'largest' or 'lm' for largest singular values, 'smallest' or 'sm' for smallest singular values. |
| Parameter | Description |
|---|---|
| s | selected singular values returned as a dense column vector in decreasing order. |
| U | dense matrix whose columns are the selected left singular vectors. |
| S | dense diagonal matrix containing the selected singular values. |
| V | dense matrix whose columns are the selected right singular vectors. |
svds computes selected singular values and, optionally, the corresponding singular vectors of a sparse floating-point matrix.
For a matrix A, the returned factors satisfy:
$$A V = U S$$Tall matrices use the smaller normal problem when possible, and wide matrices use the corresponding transposed normal problem.
When the optional ARPACK backend is not available, svds 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 singular-value problem is computed through the double-precision sparse backend, and dense outputs are converted back to single or single-complex when applicable.
A = sparse([1 0 0; 0 2 0; 3 0 0; 0 4 0; 0 0 5]);
s = svds(A, 2)
[U, S, V] = svds(A, 2, 'smallest')A = sparse([1 + 1i 0 0; 0 2i 0; 3 0 0; 0 4 0; 0 0 5i]);
s = svds(A, 2)A = sparse(single([1 + 1i 0 0; 0 2i 0; 3 0 0; 0 4 0; 0 0 5i]));
s = svds(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. |