opts.issym in eigs() - meaning

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Ingo 2012-1-2

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回答： Christine Tobler 2016-8-30

Hello everyone,

I'm having trouble understanding the meaning of an option. In eigs(), one can set the option opts.issym, which by default is 0.

Am I right to understand, that using opts.issym=1 will tell Matlab that the matrix is symmetrical? If so, will this significantly increase the speed for large matrices or what effects does using this have?

Greetings

Ingo Bürk

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Ingo 2012-1-2

I tried it for 3000-by-3000 matrices and if anything, it made eigs() a little bit slower. Makes me wonder what this option is good for at all?

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Answer 1

Christine Tobler 2016-8-30

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The options opts.issym and opts.isreal are only meant to be used when passing in a function handle for A.

When a matrix A is passed in, the options opts.issym and opts.isreal are ignored, and instead issymmetric(A) and isreal(A) are used.

For symmetric matrices, there a better algorithm is used if issymmetric(A) is true. This means that if a matrix is symmetric up to round-off error (check issymmetric(A)), it can be better to call eigs( (A + A')/2, ...) instead, as this will use the symmetric algorithm.

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Answer 2

Walter Roberson 2012-1-2

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You get the 'la', 'sa', 'be' options for real symmetric.

I recall from my research last year that there are algorithms that depend upon the matrix being real and symmetric. I have not, however, checked out the references to figure out which algorithm is used.

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Ingo 2012-1-2

Thanks.

I am looking for smallest eigenvalues, but instead of 'la' and so on I'm using sigma=eps, following Example 4 on the Matlab help to correctly get several identical eigenvalues. Therefore, I can't use one of those options.

But even if I used them, I'd still be wondering what opts.issym does?

Greetings

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