ENH: Add rosenbrock functional, see #600 #602
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| class RosenbrockFunctional(Functional): | ||
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| """The famous Rosenbrock funciton on ``R^n``. |
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I don't like the word "famous", "well-known" is more adequate.
| >>> import odl | ||
| >>> r2 = odl.rn(2) | ||
| >>> functional = RosenbrockFunctional(r2) | ||
| >>> functional([1, 1]) # optimum is 0 at [0, 0] |
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| class RosenbrockFunctional(Functional): | ||
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| """The famous Rosenbrock funciton on ``R^n``. |
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The Rosenbrock function seems to have two different versions. Should we clarify this?
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Perhaps we should, but the first one is not feasible for a general implementation since it only works for spaces of even dimension. I'll write this in the notes
odl/solvers/functional/__init__.py
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| __all__ += default_functionals.__all__ | ||
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| from . import example_functionals | ||
| __all__ += ('example_functionals',) |
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In light of the restructuring effort in #52: I find these names very long, especially since they repeat the word "functional" while lying in the functional subpackage. They could easily be abbreviated to ..._funcs.
| # You should have received a copy of the GNU General Public License | ||
| # along with ODL. If not, see <http://www.gnu.org/licenses/>. | ||
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| """Example functions used in optimization.""" |
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| class RosenbrockFunctional(Functional): | ||
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| """The famous Rosenbrock funciton on ``R^n``. |
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I don't like the word "famous", "well-known" is more adequate.
| \sum_{i=1}^{n - 1} c (x_{i+1} - x_i^2)^2 + (1 - x_i)^2 | ||
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| Where :math:`c` is a constant usually set to 100 which determines how ill- | ||
| posed the function should be. |
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The function is not ill-posed, rather the minimization problem. Alternatively, you could write "ill-behaved" in quotation marks.
| space : `FnBase` | ||
| Domain of the functional. | ||
| scale : positive float, optional | ||
| The scale ``c`` in the functional, determines how ill posed the |
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See above comment about "ill-posed".
This style "Main clause, main clause without subject" reads poorly in general. Here it's trivially possible to improve the flow of the sentence by writing "... in the functional determining how ill-...".
| if not isinstance(space, FnBase): | ||
| raise ValueError('`space` must be a `FnBase`') | ||
| if space.size < 2: | ||
| raise ValueError('`space` must be at least two dimensional') |
| raise ValueError('`space` must be a `FnBase`') | ||
| if space.size < 2: | ||
| raise ValueError('`space` must be at least two dimensional') | ||
| super().__init__(space=space, linear=False, grad_lipschitz=np.nan) |
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No estimate for the Lipschitz constant?
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It's infinite on all of R^n since the function is Quartic.
Edit: Should probably say infinity then
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Right, I keep forgetting that we're on the whole space.
| def derivative(self, x): | ||
| """The derivative of the gradient. | ||
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| This is also known as the hessian. |
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Even worse than the gradient, for these things I think it's better to just let users read the code (it is readily available) if they are interested. Easier to maintain as well.
Adding it would only be helpfull (imo) if we also added a deriviation of the result, which would take way too much space.
| result = 0 | ||
| for i in range(0, self.domain.size - 1): | ||
| result += self.scale * ((x[i + 1] - x[i] ** 2) ** 2 + | ||
| (x[i] - 1) ** 2) |
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The most common case will be R2 and such, there it only makes this harder to read and slower, I doubt it's worth it. Any performance gains would be in improving the hessian to be more diagonal.
| Where :math:`c` is a constant usually set to 100 which determines how ill- | ||
| posed the function should be. | ||
| It has a minimum at :math:`x = [1, \\dots, 1]`, independent of :math:`c`. | ||
| """ |
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It's a mess and I doubt anyone would read it, users can open the code if they are truly interested.
adler-j
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Updated according to comments and rebased. |
kohr-h
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Looks very good, one final request before merge.
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| """The well-known Rosenbrock function on ``R^n``. | ||
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| This function is usually used as a test problem in smooth optimization. |
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Please add a link to Wikipedia here.
adler-j
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Merge after CI |
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Minor yet probably useful addition. We could add more examples if we want.