pyrtid.regularization.TVRegularizator#

class pyrtid.regularization.TVRegularizator(grid: ~pyrtid.utils.grid.RectilinearGrid, eps: float = 1e-20, preconditioner: ~pyrtid.utils.preconditioner.Preconditioner = <pyrtid.utils.preconditioner.NoTransform object>)[source]#

Bases: Regularizator

Apply a Total Variation (sharpening) regularization.

Attributes

  • grid (RectilinearGrid) – RectilinearGrid of the field.

  • eps (float) – Small factor added in the square root to deal with the singularity at $nabla u = 0$ when computing the gradient. The default is 1e-20.

  • preconditioner (Preconditioner) – Parameter pre-transformation operator (variable change for the solver). The default is the identity function: f(x) = x, which means no change is made.

__init__(grid: ~pyrtid.utils.grid.RectilinearGrid, eps: float = 1e-20, preconditioner: ~pyrtid.utils.preconditioner.Preconditioner = <pyrtid.utils.preconditioner.NoTransform object>) → None#

Initialize the instance.

Parameters

preconditioner (Preconditioner) – Whether the regularization is applied to the preconditioned values or not, by default False.

Methods definition

_eval_loss(values: ndarray[Any, dtype[float64]]) → float[source]#

Compute the gradient of the regularization loss function analytically.

\[\]

mathcal{R}_{TN}(u) = frac{1}{2} sum_{j=1}^{M} sum_{i=1}^{N} left( dfrac{u_{i+1, j} - u_{i,j}}{dx} right)^{2}

Parameters

values (NDArrayFloat) – The parameter for which the regularization is computed.

Return type

float

_eval_loss_gradient_analytical(values: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]][source]#

Compute the gradient of the regularization loss function analytically.

Parameters

values (NDArrayFloat) – The parameter for which the regularization is computed.

Returns

The regularization gradient.

Return type

NDArrayFloat

eval_loss(values: ndarray[Any, dtype[float64]]) → float#

Compute the regularization loss function.

Parameters

values (NDArrayFloat) – The parameter for which the regularization is computed.

Returns

The regularization gradient.

Return type

NDArrayFloat

eval_loss_gradient(values: ndarray[Any, dtype[float64]], is_finite_differences: bool = False, max_workers: int = 1) → ndarray[Any, dtype[float64]]#

Compute the gradient of the regularization loss function.

Parameters

  • values (NDArrayFloat) – The parameter for which the regularization is computed.

  • is_finite_differences (bool) – If true, a numerical approximation by 2nd order finite difference is returned. Cost twice the values dimensions in terms of loss function calls. The default is False.

  • max_workers (int) – Number of workers used if the gradient is approximated by finite differences. If different from one, the calculation relies on multi-processing to decrease the computation time. The default is 1.

Returns

The regularization gradient (not preconditioned).

Return type

NDArrayFloat

eval_loss_gradient_analytical(values: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]]#

Compute the gradient of the regularization loss function analytically.

Parameters

values (NDArrayFloat) – The parameter for which the regularization is computed.

Returns

The regularization gradient.

Return type

NDArrayFloat