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############################################################################## |
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# |
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# Copyright (c) 2003-2012 by University of Queensland |
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# http://www.uq.edu.au |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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# Development until 2012 by Earth Systems Science Computational Center (ESSCC) |
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# Development since 2012 by School of Earth Sciences |
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# |
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############################################################################## |
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"""General cost functions for minimization""" |
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__copyright__="""Copyright (c) 2003-2012 by University of Queensland |
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http://www.uq.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="https://launchpad.net/escript-finley" |
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|
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__all__ = ['CostFunction', 'MeteredCostFunction' ] |
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class CostFunction(object): |
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""" |
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A function *f(x)* that can be minimized (base class). |
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|
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Example of usage:: |
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|
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cf=DerivedCostFunction() |
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# ... calculate x ... |
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args=cf.getArguments(x) # this could be potentially expensive! |
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f=cf.getValue(x, *args) |
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# ... it could be required to update x without using the gradient... |
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# ... but then ... |
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gf=cf.getGradient(x, *args) |
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|
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The class makes a difference for the representation of the solution x (x-type) and |
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the gradients (r-type). |
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""" |
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|
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def __init__(self): |
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""" |
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the base constructor initializes the counters so subclasses should |
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ensure the super class constructor is called. |
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""" |
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self.provides_inverse_Hessian_approximation=True |
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|
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def getDualProduct(self, x, r): |
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""" |
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returns the dual product of ``x`` and ``r`` |
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|
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:type x: x-type |
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:type r: r-type |
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:rtype: ```float``` |
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""" |
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raise NotImplementedError |
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|
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def getValue(self, x, *args): |
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""" |
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returns the value *f(x)* using the precalculated values for *x*. |
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|
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:param x: a solution approximation |
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:type x: x-type |
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:rtype: ```float``` |
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""" |
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raise NotImplementedError |
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|
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def __call__(self, x, *args): |
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""" |
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short for ``getValue(x, *args)``. |
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""" |
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return self.getValue(x, *args) |
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|
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def getGradient(self, x, *args): |
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""" |
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returns the gradient of *f* at *x* using the precalculated values for |
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*x*. |
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|
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:param x: location of derivative |
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:type x: x-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype r: r-type |
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""" |
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raise NotImplementedError |
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|
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def getArguments(self, x): |
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""" |
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returns precalculated values that are shared in the calculation of |
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*f(x)* and *grad f(x)* and the Hessian operator |
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|
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:param x: location of derivative |
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:type x: x-type |
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""" |
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return () |
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|
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def getInverseHessianApproximation(self, x, r, *args): |
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""" |
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returns an approximative evaluation *p* of the inverse of the Hessian operator of the costfunction |
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for a given gradient type *r* at a given location *x*: *H(x) p = r* |
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|
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:param x: location of Hessian operator to be evaluated. |
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:type x: x-type |
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:param r: a given gradient |
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:type r: r-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype x: x-type |
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:note: In general it is assumed that the Hessian *H(x)* needs to be calculate in each call for a new |
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location *x*. However, the solver may suggest that this is not required, typically when the iteration |
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is close to completeness. |
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:note: class attribute provides_inverse_Hessian_approximation need to be set to True to encourage |
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the solver to call this method. |
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|
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""" |
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raise NotImplementedError |
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def updateHessian(self): |
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""" |
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notifies the class that the Hessian operator needs to be updated. This method is |
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called by the solver method. |
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""" |
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pass |
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|
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class MeteredCostFunction(CostFunction): |
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""" |
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This an intrumented version of the ``CostFunction`` class. The function calls update statistical information. |
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The actual work is done by the methods with corresponding name and a leading underscore. These functions |
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need to be overwritten for a particular cost function implementation. |
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""" |
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|
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def __init__(self): |
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""" |
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the base constructor initializes the counters so subclasses should |
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ensure the super class constructor is called. |
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""" |
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super(MeteredCostFunction, self).__init__() |
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self.resetCounters() |
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|
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def resetCounters(self): |
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""" |
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resets all statistical counters |
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""" |
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self.DualProduct_calls=0 |
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self.Value_calls=0 |
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self.Gradient_calls=0 |
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self.Arguments_calls=0 |
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self.InverseHessianApproximation_calls=0 |
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|
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def getDualProduct(self, x, r): |
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""" |
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returns the dual product of ``x`` and ``r`` |
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|
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:type x: x-type |
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:type r: r-type |
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:rtype: ```float``` |
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""" |
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self.DualProduct_calls+=1 |
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return self._getDualProduct(x, r) |
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|
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def _getDualProduct(self, x, r): |
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""" |
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returns the dual product of ``x`` and ``r`` |
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:type x: x-type |
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:type r: r-type |
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:rtype: ```float``` |
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:note: This is the worker for `getDualProduct()`, needs to be overwritten. |
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""" |
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raise NotImplementedError |
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|
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def getValue(self, x, *args): |
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""" |
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returns the value *f(x)* using the precalculated values for *x*. |
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|
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:param x: a solution approximation |
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:type x: x-type |
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:rtype: ```float``` |
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""" |
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self.Value_calls+=1 |
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return self._getValue(x, *args) |
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|
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def _getValue(self, x, *args): |
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""" |
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returns the value *f(x)* using the precalculated values for *x*. |
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|
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:param x: a solution approximation |
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:type x: x-type |
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:rtype: ```float``` |
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:note: This is the worker for ``getValue()`, needs to be overwritten. |
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""" |
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raise NotImplementedError |
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|
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def getGradient(self, x, *args): |
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""" |
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returns the gradient of *f* at *x* using the precalculated values for |
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*x*. |
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:param x: location of derivative |
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:type x: x-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype r: r-type |
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""" |
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self.Gradient_calls+=1 |
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return self._getGradient(x, *args) |
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def _getGradient(self, x, *args): |
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""" |
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returns the gradient of *f* at *x* using the precalculated values for |
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*x*. |
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|
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:param x: location of derivative |
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:type x: x-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype r: r-type |
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:note: This is the worker for `getGradient()`, needs to be overwritten. |
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""" |
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raise NotImplementedError |
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|
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|
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|
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def getArguments(self, x): |
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""" |
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returns precalculated values that are shared in the calculation of |
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*f(x)* and *grad f(x)* and the Hessian operator |
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|
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:param x: location of derivative |
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:type x: x-type |
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""" |
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self.Arguments_calls+=1 |
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return self._getArguments(x) |
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|
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def _getArguments(self, x): |
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""" |
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returns precalculated values that are shared in the calculation of |
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*f(x)* and *grad f(x)* and the Hessian operator |
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:param x: location of derivative |
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:type x: x-type |
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:note: Overwrite this function to implement a specific cost function |
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""" |
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return () |
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|
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def getInverseHessianApproximation(self, x, r,*args): |
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""" |
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returns an approximative evaluation *p* of the inverse of the Hessian operator of the costfunction |
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for a given gradient type *r* at a given location *x*: *H(x) p = r* |
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|
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:param x: location of Hessian operator to be evaluated. |
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:type x: x-type |
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:param r: a given gradient |
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:type r: r-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype x: x-type |
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:note: In general it is assumed that the Hessian *H(x)* needs to be calculate in each call for a new |
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location *x*. However, the solver may suggest that this is not required, typically when the iteration |
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ius close to completness. |
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""" |
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self.InverseHessianApproximation_calls+=1 |
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return self._getInverseHessianApproximation(x, r, *args) |
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|
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def _getInverseHessianApproximation(self, x, r, *args): |
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""" |
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returns an approximative evaluation *p* of the inverse of the Hessian operator of the costfunction |
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for a given gradient type *r* at a given location *x*: *H(x) p = r* |
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|
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:param x: location of Hessian operator to be evaluated. |
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:type x: x-type |
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:param r: a given gradient |
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:type r: r-type |
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:param args: pre-calculated values for ``x`` from ``getArguments()`` |
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:rtype x: x-type |
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:note: In general it is assumed that the Hessian *H(x)* needs to be calculate in each call for a new |
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location *x*. However, the solver may suggest that this is not required, typically when the iteration |
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ius close to completness. |
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:note: :note: This is the worker for getInverseHessianApproximation()`, needs to be overwritten. |
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""" |
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raise NotImplementedError |
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