nifty8.operators.scaling_operator module

class ScalingOperator(domain, factor, sampling_dtype=None)

Bases: EndomorphicOperator

Operator which multiplies a Field with a scalar.

Parameters:

• domain (Domain or tuple of Domain or DomainTuple) – The domain on which the Operator’s input Field is defined.

• factor (scalar) – The multiplication factor

• sampling_dtype – If this operator represents the covariance of a Gaussian probabilty distribution, sampling_dtype specifies if it is real or complex Gaussian. If sampling_dtype is None, the operator cannot be used as a covariance, i.e. no samples can be drawn. Default: None.

Notes

Operator supports the multiplication with a scalar. So one does not need instantiate ScalingOperator explicitly in most cases.

Formally, this operator always supports all operation modes (times, adjoint_times, inverse_times and inverse_adjoint_times), even if factor is 0 or infinity. It is the user’s responsibility to apply the operator only in appropriate ways (e.g. call inverse_times only if factor is nonzero).

Along with this behaviour comes the feature that it is possible to draw an inverse sample from a ScalingOperator (which is a zero-field). This occurs if one draws an inverse sample of a positive definite sum of two operators each of which are only positive semi-definite. However, it is unclear whether this beviour does not lead to unwanted effects somewhere else.

__call__(other)

Same as times()

__init__(domain, factor, sampling_dtype=None)

__repr__()

Return repr(self).

apply(x, mode)

Applies the Operator to a given x, in a specified mode.

Parameters:

• x (nifty8.field.Field) – The input Field, defined on the Operator’s domain or target, depending on mode.

• mode (int) –

  • TIMES: normal application

  • ADJOINT_TIMES: adjoint application

  • INVERSE_TIMES: inverse application

  • ADJOINT_INVERSE_TIMES or INVERSE_ADJOINT_TIMES: adjoint inverse application

Returns:

The processed Field defined on the Operator’s target or domain, depending on mode.

Return type:

nifty8.field.Field

draw_sample(from_inverse=False)

Generates a sample from a Gaussian distribution with zero mean and covariance given by the operator.

May or may not be implemented. Only optional.

Parameters:

from_inverse (bool (default : False)) – if True, the sample is drawn from the inverse of the operator

Returns:

A sample from the Gaussian of given covariance.

Return type:

nifty8.field.Field or nifty8.multi_field.MultiField

get_sqrt()

Return operator op which obeys self == op.adjoint @ op.

Note that this function is only implemented for operators with real spectrum.

Returns:

Operator which is the square root of self

Return type:

EndomorphicOperator