ReductionOperator.derivative

ReductionOperator.derivative(x)[source]

Derivative of the reduction operator.

Parameters

xdomain element: The point to take the derivative in.

Returns

derivative : linear BroadcastOperator

Examples

>>> r3 = odl.rn(3)
>>> I = odl.IdentityOperator(r3)
>>> x = [1.0, 2.0, 3.0]
>>> y = [4.0, 6.0, 8.0]

Example with linear operator (derivative is itself)

>>> op = ReductionOperator(I, 2 * I)
>>> op([x, y])
rn(3).element([  9.,  14.,  19.])
>>> op.derivative([x, y])([x, y])
rn(3).element([  9.,  14.,  19.])

Example with affine operator

>>> residual_op = I - r3.element([1, 1, 1])
>>> op = ReductionOperator(residual_op, 2 * residual_op)

Calling operator gives offset by [3, 3, 3]

>>> op([x, y])
rn(3).element([  6.,  11.,  16.])

Derivative of affine operator does not have this offset

>>> op.derivative([x, y])([x, y])
rn(3).element([  9.,  14.,  19.])