freealg.FreeForm.trace#
- FreeForm.trace(size=None, p=1.0, seed=None, **kwargs)#
Estimate the trace of a power.
This function estimates the trace of the matrix power \(\mathbf{A}^p\) of the freeform or that of a larger matrix containing it.
- Parameters:
- sizeint, default=None
The size of the matrix containing \(\mathbf{A}\) to estimate eigenvalues of. If None, returns estimates of the eigenvalues of \(\mathbf{A}\) itself.
- pfloat, default=1.0
The exponent \(p\) in \(\mathbf{A}^p\).
- seedint, default=None
The seed for the Quasi-Monte Carlo sampler.
- **kwargsdict, optional
Pass additional options to the underlying
FreeForm.decompress()function.
- Returns:
- tracefloat
matrix trace
Notes
The trace is highly amenable to subsampling: under free decompression the average eigenvalue is assumed constant, so the trace increases linearly. Traces of powers fall back to
eigvalsh(). All arguments to the .decompress() procedure can be provided.Examples
>>> from freealg import FreeForm