PointwiseInnerAdjoint

class odl.operator.tensor_ops.PointwiseInnerAdjoint(*args, **kwargs)

Bases: PointwiseInnerBase

Adjoint of the point-wise inner product operator.

The adjoint of the inner product operator is a mapping

A^* : X --> X^d

If the vector field space X^d is weighted by a vector v, the adjoint, applied to a function h from X is the vector field

x --> h(x) * (w / v) * G(x),

where G and w are the vector field and weighting from the inner product operator, resp., and all multiplications are understood component-wise.

Attributes:

adjoint

Adjoint of this operator.

base_space

Base space X of this operator's domain and range.

domain

Set of objects on which this operator can be evaluated.

inverse

Return the operator inverse.

is_functional

True if this operator's range is a Field.

is_linear

True if this operator is linear.

is_weighted

True if weighting is not 1 or all ones.

range

Set in which the result of an evaluation of this operator lies.

vecfield

Fixed vector field G of this inner product.

weights

Weighting array of this operator.

Methods

__call__(x[, out])	Return self(x[, out, **kwargs]).
derivative(point)	Return the operator derivative at point.
norm([estimate])	Return the operator norm of this operator.

__init__(sspace, vecfield, vfspace=None, weighting=None)

Initialize a new instance.

Parameters:

sspaceLinearSpace

"Scalar" space on which the operator acts

vecfieldrange element-like

Vector field of the point-wise inner product operator

vfspaceProductSpace, optional

Space of vector fields to which the operator maps. It must be a power space with sspace as base space. This option is intended to enforce an operator range with a certain weighting. Default: ProductSpace(space, len(vecfield), weighting=weighting)

weightingarray-like or float, optional

Weighting array or constant of the inner product operator. If an array is given, its length must be equal to len(vecfield). By default, the weights are is taken from range.weighting if applicable. Note that this excludes unusual weightings with custom inner product, norm or dist.