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Allow computing functions of matrices with methods beyond eigenvalues #196

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pnkraemer opened this issue May 27, 2024 · 1 comment · Fixed by #212
Closed

Allow computing functions of matrices with methods beyond eigenvalues #196

pnkraemer opened this issue May 27, 2024 · 1 comment · Fixed by #212
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enhancement New feature or request

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@pnkraemer
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Currently, all Lanczos-based functions of matrices use an eigenvalue decomposition to evaluate f(H)v.

For some functions, e.g. log and exp, alternatives may be more reliable.

I propose either providing a matfun_dense: Callable option to matrix-function-vector products, or hard-code log, exp, sqrt, and perhaps others in funm.
To decide which ones to hard-code, we could refer to what jax.scipy.linalg offers in terms of dense matrix-functions.

@pnkraemer pnkraemer added the enhancement New feature or request label May 27, 2024
@pnkraemer
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pnkraemer commented May 31, 2024

#201 takes care of most of this, but leaves some open todos for applications in trace estimation (which is why this issue remains open for a bit longer).

Edit: the open todo is extending e.g. integrand_funm_sym to expect different dense matrix functions. Currently, this is not the case.

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