nitorch_fastmath.stochastic

trapprox

trapprox(matvec, shape=None, moments=None, samples=10, method='rademacher', hutchpp=False, **backend)

Stochastic trace approximation (Hutchinson's estimator)

Parameters:

Name	Type	Description	Default
matvec	`sparse tensor or callable(tensor) -> tensor`	Function that computes the matrix-vector product	required
shape	`sequence[int]`	"vector" shape	None
moments	`int`	Number of moments	1
samples	`int`	Number of samples	10
method	`{'rademacher', 'gaussian'}`	Sampling method	'rademacher'
hutchpp	`bool`	Use Hutch++ instead of Hutchinson. /!\ Be aware that it uses more memory.	False

Returns:

Name	Type	Description
trace	`([moments],) tensor`

Reference

1. Hutchinson, M.F., 1989. A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. Communications in Statistics - Simulation and Computation, 18(3), pp.1059-1076.

   @article{hutchinson1989,
     title={A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines},
     author={Hutchinson, Michael F},
     journal={Communications in Statistics-Simulation and Computation},
     volume={18},
     number={3},
     pages={1059--1076},
     year={1989},
     publisher={Taylor \& Francis}
   }
   

2. Meyer, R.A., Musco, C., Musco, C. and Woodruff, D.P., 2021. Hutch++: Optimal stochastic trace estimation. Symposium on Simplicity in Algorithms (SOSA) (pp. 142-155). Society for Industrial and Applied Mathematics.

   @inproceedings{meyer2021,
     title={Hutch++: Optimal stochastic trace estimation},
     author={Meyer, Raphael A and Musco, Cameron and Musco, Christopher and Woodruff, David P},
     booktitle={Symposium on Simplicity in Algorithms (SOSA)},
     pages={142--155},
     year={2021},
     organization={SIAM}
   }
   

vbald

vbald(matvec, shape=None, upper=None, moments=5, samples=5, mc_samples=64, method='rademacher', **backend)

Variational Bayesian Approximation of Log Determinants

Parameters:

Name	Type	Description	Default
matvec	`sparse tensor or callable(tensor) -> tensor`	Function that computes the matrix-vector product	required
shape	`sequence[int]`	"vector" shape	None
upper	`float`	Upper bound on eigenvalues	None
moments	`int`	Number of moments	1
samples	`int`	Number of samples for moment estimation	5
mc_samples	`int`	Number of samples for Monte Carlo integration	64
method	`{'rademacher', 'gaussian'}`	Sampling method	'rademacher'

Returns:

Name	Type	Description
logdet	`scalar tensor`

Reference

1. Granziol, D., Wagstaff, E., Ru, B.X., Osborne, M. and Roberts, S., 2018. VBALD-Variational Bayesian approximation of log determinants. arXiv preprint.

   @article{granziol2018,
     title={VBALD-Variational Bayesian approximation of log determinants},
     author={Granziol, Diego and Wagstaff, Edward and Ru, Bin Xin and Osborne, Michael and Roberts, Stephen},
     journal={arXiv preprint arXiv:1802.08054},
     year={2018}
   }
   

maxeig_power

maxeig_power(matvec, shape=None, max_iter=512, tol=1e-06, **backend)

Estimate the maximum eigenvalue of a matrix by power iteration

Parameters:

Name	Type	Description	Default
matvec	`sparse tensor or callable(tensor) -> tensor`	Function that computes the matrix-vector product	required
shape	`sequence[int]`	"vector" shape	None
max_iter	`int`		512
tol	`float`		1e-6

Returns:

Name	Type	Description
maxeig	`scalar tensor`	Largest eigenvalue