ProductSpaceOperator.derivative

ProductSpaceOperator.derivative(self, x)

Derivative of the product space operator.

Parameters

xdomain element

The point to take the derivative in

Returns

adjointlinear`ProductSpaceOperator`

The derivative

Examples

>>> r3 = odl.rn(3)
>>> pspace = odl.ProductSpace(r3, r3)
>>> I = odl.IdentityOperator(r3)
>>> x = pspace.element([[1, 2, 3], [4, 5, 6]])

Example with linear operator (derivative is itself)

>>> prod_op = ProductSpaceOperator([[0, I], [0, 0]],
...                                domain=pspace, range=pspace)
>>> prod_op(x)
ProductSpace(rn(3), 2).element([
    [ 4.,  5.,  6.],
    [ 0.,  0.,  0.]
])
>>> prod_op.derivative(x)(x)
ProductSpace(rn(3), 2).element([
    [ 4.,  5.,  6.],
    [ 0.,  0.,  0.]
])

Example with affine operator

>>> residual_op = I - r3.element([1, 1, 1])
>>> op = ProductSpaceOperator([[0, residual_op], [0, 0]],
...                           domain=pspace, range=pspace)

Calling operator gives offset by [1, 1, 1]

>>> op(x)
ProductSpace(rn(3), 2).element([
    [ 3.,  4.,  5.],
    [ 0.,  0.,  0.]
])

Derivative of affine operator does not have this offset

>>> op.derivative(x)(x)
ProductSpace(rn(3), 2).element([
    [ 4.,  5.,  6.],
    [ 0.,  0.,  0.]
])