freealg.FreeForm.norm#
- FreeForm.norm(size=None, order=2, seed=None, **kwargs)#
Estimate the Schatten norm.
This function estimates the norm of the freeform or a larger matrix containing it using free decompression.
- 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.
- order{float,
''inf,'-inf','fro','nuc'}, default=2 Order of the norm.
float \(p\): Schatten p-norm.
'inf': Largest absolute eigenvalue \(\max \vert \lambda_i \vert)\)'-inf': Smallest absolute eigenvalue \(\min \vert \lambda_i \vert)\)'fro': Frobenius norm corresponding to \(p=2\)'nuc': Nuclear (or trace) norm corresponding to \(p=1\)
- seedint, default=None
The seed for the Quasi-Monte Carlo sampler.
- **kwargsdict, optional
Pass additional options to the underlying
FreeForm.decompress()function.
- Returns:
- normfloat
matrix norm
Notes
Thes Schatten \(p\)-norm is defined by
\[\Vert \mathbf{A} \Vert_p = \left( \sum_{i=1}^N \vert \lambda_i \vert^p \right)^{1/p}.\]Examples
>>> from freealg import FreeForm