Allow operator + vector in range about odl HOT 12 CLOSED

What would the action of that be?

(op+vec)(x) = op(x) + vec*x

right?

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If we do this we clearly want to add a op - vec aswell.

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I was more thinking of (op+vec)(x) = op(x) + vec, for range elements at least. Actually mostly op-vec, as you wrote, as in residual_op = op - vec.

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If there is no obvious behavior of this operator overload, then it's probably better to just create a class to support it.

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Actually, your proposed action is already covered by op + vec.T, right?

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I dont think we should do what you propose then, simply because it would violate the distributive law.

What you said is equivalent to

(op + vec.T)(x) = op(x) + x.inner(vec)

I think we should implement this as a named operator in default_ops.

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Err, I don't quite follow. This is already supported, or am I missing something? vec.T is an Operator, and that you can add to op as long as op is a functional.

Can you be more specific about the distributive law violation? I don't see it.

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op + vec.T is supported where op is a functional, indeed.

Regarding violating the distributive law, one would expect

(A+B)(x) = A(x) + B(x)

Here A=op so the intepretation is obvious, but with B=vec this is nonobvious. For most of us, one generally inteprets vec as multiplication by the vector. See e.g. our quasi-newton algorithm

(vec * vec.T)(x) = vec * vec.T(x)

The other case doesnt realy make sense to me, then we would have vec(x) = vec, which doesnt realy rhyme for me, and I've never seen this use in the literature (I think).

One option would be to add (and we prolly should do this anyhow) a function called ConstantOperator such that:

ConstantOperator(vec)(x) = vec

That way we could write, very clearly

(A - ConstantOperator(vec))(x) = A(x) - vec

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Any decision on this?

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Dunno. But the expression type operator looks fine to me, and if we want some shortcut later, we can still add it. Or just forget about that this issue ever existed 😉

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Does the ConstantOperator exist? We may want to implement it together with the ResidualOperator.

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Proposal made for that, closing this.

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