pdhg_stepsize¶

odl.solvers.nonsmooth.primal_dual_hybrid_gradient.pdhg_stepsize(L, tau=None, sigma=None)[source]¶

Default step sizes for pdhg.

Parameters:

LOperator or float: Operator or norm of the operator that are used in the pdhg method. If it is an Operator, the norm is computed with Operator.norm(estimate=True).
taupositive float, optional: Use this value for tau instead of computing it from the operator norms, see Notes.
sigmapositive float, optional: The sigma step size parameters for the dual update.

Returns:

taufloat: The tau step size parameter for the primal update.
sigmatuple of float: The sigma step size parameter for the dual update.

Notes

To guarantee convergence, the parameters $\tau$ , $\sigma$ and $L$ need to satisfy

$\tau \sigma \|L\|^2 < 1$

This function has 4 options, $\tau$ / $\sigma$ given or not given.

Neither $\tau$ nor $\sigma$ are given, they are chosen as

$\tau = \sigma = \frac{\sqrt{0.9}}{\|L\|}$
If only $\sigma$ is given, $\tau$ is set to

$\tau = \frac{0.9}{\sigma \|L\|^2}$
If only $\tau$ is given, $\sigma$ is set to

$\sigma = \frac{0.9}{\tau \|L\|^2}$
If both are given, they are returned as-is without further validation.