Some new and some improved tensor operations #76
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…t matrix log, exp, and sqrt
Before: the primal output was computed in-line in the custom jvp function. The advantage is that this avoids a second call to the eigendecomposition. The downside is that this in-line computation doesn't itself have a custom jvp, so its derivative can be wrong. After: I re-compute the primal value through the base function (e.g., log_symm), which has the custom jvp defined on it. The eigendecomposition is repeated. We can refactor to eliminate this later if profiling reveals it to be a performance bottleneck.
Put a leading underscore on functions menat for internal use. Most Python tools will ignore these when reporting contents of a module.
Replace all calls except in the new viscoelastic model. Changes are about to merge there and I want to handle the conflicts separately.
tupek2
approved these changes
Feb 27, 2024
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This PR contributes the following:
I changed the matrix log/exp derivative calculations form Mike's very clever implementation that maintains high precision with Taylor and Pade approximations. The version I put in seems to do just as well in the test cases. It doesn't use Pade approximants, it uses the built-in implementations of
log1pandexpm1(which may use the same trick as Mike under the hood, for all I know). I kept Mike's code around in case I'm wrong and these versions are not as accurate.Finally: There are still two calls to the eigenvalue solve when computing the derivative of the matrix functions. I think it's possible to reduce it to one, but it's trickier than I thought. I'll wait until we profile and confirm this is a bottleneck before working on that.