CODEWITHSUNDEEP
iosmacoslinear-algebraaccelerate-framework
Simplex
Simplex

Reputation: 1000

Eigenvalues of symmetric band matrix using Accelerate framework

In a macOS/iOS code base, I've got a real symmetric band matrix that can be anywhere from 10 × 10 to about 500 × 500, and I need to compute whether all its eigenvalues are greater than (or equal to) a certain threshold. So I only strictly need to know the lowest eigenvalue, in case that helps.

Is there any function or set of functions in Apple's Accelerate framework that can provide a full or partial solution to this? Ideally with a cost proportional to the number of non-zero entries.

Upvotes: 0

Views: 236

Answers (1)

Simplex
Simplex

Reputation: 1000

Based on this, it appears there's a set of LAPACK functions that compute eigenvalues efficiently for banded symmetric matrices. (LAPACK is implemented a part of the Accelerate framework.)

As I understand it, ssbtrd followed by ssterf should do the trick.

SSBTRD reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T.

SSTERF computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm.

Upvotes: 3

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