curvature -> metric

README.md

@@ -108,7 +108,7 @@ For a quick start, you can browse through the [informal
 introduction](http://ift.pages.mpcdf.de/NIFTy/code.html) or
 dive into NIFTy by running one of the demonstrations, e.g.:
 
-    python demos/wiener_filter_via_curvature.py
+    python demos/getting_started_1.py
 
 
 ### Acknowledgement

demos/getting_started_3.py

@@ -74,7 +74,7 @@ if __name__ == '__main__':
     N_samples = 20
     for i in range(5):
         H = H.at(position)
-        samples = [H.curvature.draw_sample(from_inverse=True)
+        samples = [H.metric.draw_sample(from_inverse=True)
                    for _ in range(N_samples)]
 
         KL = ift.SampledKullbachLeiblerDivergence(H, samples)

docs/source/code.rst

@@ -306,16 +306,16 @@ Energy functionals
 In NIFTy5 such functions are represented by objects of type :class:`Energy`.
 These hold the prescription how to calculate the function's
 :attr:`~Energy.value`, :attr:`~Energy.gradient` and
-(optionally) :attr:`~Energy.curvature` at any given :attr:`~Energy.position`
+(optionally) :attr:`~Energy.metric` at any given :attr:`~Energy.position`
 in parameter space.
 Function values are floating-point scalars, gradients have the form of fields
-living on the energy's position domain, and curvatures are represented by
+living on the energy's position domain, and metrics are represented by
 linear operator objects.
 
 Energies are classes that typically have to be provided by the user when
 tackling new IFT problems.
 Some examples of concrete energy classes delivered with NIFTy5 are
-:class:`QuadraticEnergy` (with position-independent curvature, mainly used with
+:class:`QuadraticEnergy` (with position-independent metric, mainly used with
 conjugate gradient minimization) and :class:`~nifty5.library.WienerFilterEnergy`.
 
 
@@ -367,7 +367,7 @@ This family of algorithms is encapsulated in NIFTy's :class:`DescentMinimizer`
 class, which currently has three concrete implementations:
 :class:`SteepestDescent`, :class:`VL_BFGS`, and :class:`RelaxedNewton`.
 Of these algorithms, only :class:`RelaxedNewton` requires the energy object to
-provide a :attr:`~Energy.curvature` property, the others only need energy
+provide a :attr:`~Energy.metric` property, the others only need energy
 values and gradients.
 
 The flexibility of NIFTy's design allows using externally provided

nifty5/energies/hamiltonian.py

@@ -49,13 +49,13 @@ class Hamiltonian(Energy):
 
     @property
     @memo
-    def curvature(self):
-        prior_curv = self._prior.curvature
+    def metric(self):
+        prior_mtr = self._prior.metric
         if self._ic_samp is None:
-            return self._lh.curvature + prior_curv
+            return self._lh.metric + prior_mtr
         else:
-            return SamplingEnabler(self._lh.curvature, prior_curv.inverse,
-                                   self._ic_samp, prior_curv.inverse)
+            return SamplingEnabler(self._lh.metric, prior_mtr.inverse,
+                                   self._ic_samp, prior_mtr.inverse)
 
     def __str__(self):
         res = 'Likelihood:\t{:.2E}\n'.format(self._lh.value)

nifty5/energies/kl.py

@@ -33,6 +33,6 @@ class SampledKullbachLeiblerDivergence(Energy):
 
     @property
     @memo
-    def curvature(self):
-        return (my_sum(map(lambda v: v.curvature, self._energy_list)) *
+    def metric(self):
+        return (my_sum(map(lambda v: v.metric, self._energy_list)) *
                 (1./len(self._energy_list)))

nifty5/extra/energy_and_model_tests.py

@@ -22,7 +22,7 @@ from ..minimization.energy import Energy
 from ..models.model import Model
 
 __all__ = ["check_value_gradient_consistency",
-           "check_value_gradient_curvature_consistency"]
+           "check_value_gradient_metric_consistency"]
 
 
 def _get_acceptable_model(M):
@@ -100,9 +100,9 @@ def check_value_gradient_consistency(E, tol=1e-8, ntries=100):
         E = Enext
 
 
-def check_value_gradient_curvature_consistency(E, tol=1e-8, ntries=100):
+def check_value_gradient_metric_consistency(E, tol=1e-8, ntries=100):
     if isinstance(E, Model):
-        raise ValueError('Models have no curvature, thus it cannot be tested.')
+        raise ValueError('Models have no metric, thus it cannot be tested.')
     for _ in range(ntries):
         E2 = _get_acceptable_energy(E)
         val = E.value
@@ -112,7 +112,7 @@ def check_value_gradient_curvature_consistency(E, tol=1e-8, ntries=100):
         for i in range(50):
             Emid = E.at(E.position + 0.5*dir)
             dirder = Emid.gradient.vdot(dir)/dirnorm
-            dgrad = Emid.curvature(dir)/dirnorm
+            dgrad = Emid.metric(dir)/dirnorm
             xtol = tol*Emid.gradient_norm
             if abs((E2.value-val)/dirnorm - dirder) < xtol and \
                (abs((E2.gradient-E.gradient)/dirnorm-dgrad) < xtol).all():
@@ -121,5 +121,5 @@ def check_value_gradient_curvature_consistency(E, tol=1e-8, ntries=100):
             dirnorm *= 0.5
             E2 = Emid
         else:
-            raise ValueError("gradient, value and curvature seem inconsistent")
+            raise ValueError("gradient, value and metric seem inconsistent")
         E = Enext

nifty5/library/gaussian_energy.py

@@ -62,7 +62,7 @@ class GaussianEnergy(Energy):
 
     @property
     @memo
-    def curvature(self):
+    def metric(self):
         if self._cov is None:
             return SandwichOperator.make(self._inp.jacobian, None)
         return SandwichOperator.make(self._inp.jacobian, self._cov.inverse)

nifty5/library/poissonian_energy.py

@@ -44,7 +44,7 @@ class PoissonianEnergy(Energy):
 
         # metric = makeOp(d/lamb_val/lamb_val)
         metric = makeOp(1./lamb_val)
-        self._curvature = SandwichOperator.make(self._lamb.jacobian, metric)
+        self._metric = SandwichOperator.make(self._lamb.jacobian, metric)
 
     def at(self, position):
         return self.__class__(self._lamb.at(position), self._d)
@@ -58,5 +58,5 @@ class PoissonianEnergy(Energy):
         return self._gradient
 
     @property
-    def curvature(self):
-        return self._curvature
+    def metric(self):
+        return self._metric

nifty5/minimization/conjugate_gradient.py

@@ -47,7 +47,7 @@ class ConjugateGradient(Minimizer):
         Parameters
         ----------
         energy : Energy object at the starting point of the iteration.
-            Its curvature operator must be independent of position, otherwise
+            Its metric operator must be independent of position, otherwise
             linear conjugate gradient minimization will fail.
         preconditioner : Operator *optional*
             This operator can be provided which transforms the variables of the
@@ -73,7 +73,7 @@ class ConjugateGradient(Minimizer):
             return energy, controller.CONVERGED
 
         while True:
-            q = energy.curvature(d)
+            q = energy.metric(d)
             ddotq = d.vdot(q).real
             if ddotq == 0.:
                 logger.error("Error: ConjugateGradient: ddotq==0.")

nifty5/minimization/descent_minimizer.py

@@ -51,7 +51,7 @@ class DescentMinimizer(Minimizer):
         Parameters
         ----------
         energy : Energy
-           Energy object which provides value, gradient and curvature at a
+           Energy object which provides value, gradient and metric at a
            specific position in parameter space.
 
         Returns

nifty5/minimization/energy.py

@@ -25,7 +25,7 @@ class Energy(NiftyMetaBase()):
     """ Provides the functional used by minimization schemes.
 
    The Energy object is an implementation of a scalar function including its
-   gradient and curvature at some position.
+   gradient and metric at some position.
 
     Parameters
     ----------
@@ -35,11 +35,11 @@ class Energy(NiftyMetaBase()):
     Notes
     -----
     An instance of the Energy class is defined at a certain location. If one
-    is interested in the value, gradient or curvature of the abstract energy
+    is interested in the value, gradient or metric of the abstract energy
     functional one has to 'jump' to the new position using the `at` method.
     This method returns a new energy instance residing at the new position. By
     this approach, intermediate results from computing e.g. the gradient can
-    safely be reused for e.g. the value or the curvature.
+    safely be reused for e.g. the value or the metric.
 
     Memorizing the evaluations of some quantities (using the memo decorator)
     minimizes the computational effort for multiple calls.
@@ -75,7 +75,7 @@ class Energy(NiftyMetaBase()):
         Field : selected location in parameter space.
 
         The Field location in parameter space where value, gradient and
-        curvature are evaluated.
+        metric are evaluated.
         """
         return self._position
 
@@ -104,11 +104,11 @@ class Energy(NiftyMetaBase()):
         return self.gradient.norm()
 
     @property
-    def curvature(self):
+    def metric(self):
         """
-        LinearOperator : implicitly defined curvature.
+        LinearOperator : implicitly defined metric.
             A positive semi-definite operator or function describing the
-            curvature of the potential at the given `position`.
+            metric of the potential at the given `position`.
         """
         raise NotImplementedError
 
@@ -132,7 +132,7 @@ class Energy(NiftyMetaBase()):
         from .iteration_controller import IterationController
         if not isinstance(controller, IterationController):
             raise TypeError
-        return CurvatureInversionEnabler(self, controller, preconditioner)
+        return MetricInversionEnabler(self, controller, preconditioner)
 
     def __mul__(self, factor):
         from .energy_sum import EnergySum
@@ -160,9 +160,9 @@ class Energy(NiftyMetaBase()):
         return EnergySum.make([self], [-1.])
 
 
-class CurvatureInversionEnabler(Energy):
+class MetricInversionEnabler(Energy):
     def __init__(self, ene, controller, preconditioner):
-        super(CurvatureInversionEnabler, self).__init__(ene.position)
+        super(MetricInversionEnabler, self).__init__(ene.position)
         self._energy = ene
         self._controller = controller
         self._preconditioner = preconditioner
@@ -170,7 +170,7 @@ class CurvatureInversionEnabler(Energy):
     def at(self, position):
         if self._position.isSubsetOf(position):
             return self
-        return CurvatureInversionEnabler(
+        return MetricInversionEnabler(
             self._energy.at(position), self._controller, self._preconditioner)
 
     @property
@@ -186,16 +186,16 @@ class CurvatureInversionEnabler(Energy):
         return self._energy.gradient
 
     @property
-    def curvature(self):
+    def metric(self):
         from ..operators.linear_operator import LinearOperator
         from ..operators.inversion_enabler import InversionEnabler
-        curv = self._energy.curvature
+        curv = self._energy.metric
         if self._preconditioner is None:
             precond = None
         elif isinstance(self._preconditioner, LinearOperator):
             precond = self._preconditioner
         elif isinstance(self._preconditioner, Energy):
-            precond = self._preconditioner.at(self.position).curvature
+            precond = self._preconditioner.at(self.position).metric
         return InversionEnabler(curv, self._controller, precond)
 
     def longest_step(self, dir):

nifty5/minimization/energy_sum.py

@@ -67,6 +67,6 @@ class EnergySum(Energy):
 
     @property
     @memo
-    def curvature(self):
-        return my_lincomb(map(lambda v: v.curvature, self._energies),
+    def metric(self):
+        return my_lincomb(map(lambda v: v.metric, self._energies),
                           self._factors)

nifty5/minimization/quadratic_energy.py

@@ -21,7 +21,7 @@ from .energy import Energy
 
 class QuadraticEnergy(Energy):
     """The Energy for a quadratic form.
-    The most important aspect of this energy is that its curvature must be
+    The most important aspect of this energy is that its metric must be
     position-independent.
     """
 
@@ -74,5 +74,5 @@ class QuadraticEnergy(Energy):
         return self._grad
 
     @property
-    def curvature(self):
+    def metric(self):
         return self._A

nifty5/minimization/relaxed_newton.py

@@ -24,7 +24,7 @@ class RelaxedNewton(DescentMinimizer):
     """ Calculates the descent direction according to a Newton scheme.
 
     The descent direction is determined by weighting the gradient at the
-    current parameter position with the inverse local curvature.
+    current parameter position with the inverse local metric.
     """
     def __init__(self, controller, line_searcher=None):
         if line_searcher is None:
@@ -34,4 +34,4 @@ class RelaxedNewton(DescentMinimizer):
                                             line_searcher=line_searcher)
 
     def get_descent_direction(self, energy):
-        return -energy.curvature.inverse_times(energy.gradient)
+        return -energy.metric.inverse_times(energy.gradient)

nifty5/minimization/scipy_minimizer.py

@@ -56,7 +56,7 @@ class _MinHelper(object):
 
     def hessp(self, x, p):
         self._update(x)
-        res = self._energy.curvature(_toField(p, self._domain))
+        res = self._energy.metric(_toField(p, self._domain))
         return _toFlatNdarray(res)
 
 

nifty5/operators/sampling_enabler.py

@@ -32,9 +32,9 @@ class SamplingEnabler(EndomorphicOperator):
     Parameters
     ----------
     likelihood : :class:`EndomorphicOperator`
-        Curvature of the likelihood
+        Metric of the likelihood
     prior : :class:`EndomorphicOperator`
-        Inverse curvature of the prior
+        Inverse metric of the prior
     iteration_controller : :class:`IterationController`
         The iteration controller to use for the iterative numerical inversion
         done by a :class:`ConjugateGradient` object.

test/test_energies/test_map.py

@@ -59,7 +59,7 @@ class Energy_Tests(unittest.TestCase):
         S = ift.create_power_operator(hspace, power_spectrum=_flat_PS)
         energy = ift.WienerFilterEnergy(
             position=s0, d=d, R=R, N=N, S=S, iteration_controller=IC)
-        ift.extra.check_value_gradient_curvature_consistency(
+        ift.extra.check_value_gradient_metric_consistency(
             energy, ntries=10)
 
     @expand(product([ift.GLSpace(15),
@@ -94,7 +94,7 @@ class Energy_Tests(unittest.TestCase):
 
         energy = ift.GaussianEnergy(d_model, d, N)
         if isinstance(nonlinearity(), ift.Linear):
-            ift.extra.check_value_gradient_curvature_consistency(
+            ift.extra.check_value_gradient_metric_consistency(
                 energy, ntries=10)
         else:
             ift.extra.check_value_gradient_consistency(

test/test_minimization/test_minimizers.py

@@ -94,7 +94,7 @@ class Test_Minimizers(unittest.TestCase):
                 return out
 
             @property
-            def curvature(self):
+            def metric(self):
                 class RBCurv(ift.EndomorphicOperator):
                     def __init__(self, loc):
                         self._loc = loc.to_global_data().copy()
@@ -150,7 +150,7 @@ class Test_Minimizers(unittest.TestCase):
                 return ift.Field(self.position.domain, val=2*x*np.exp(-(x**2)))
 
             @property
-            def curvature(self):
+            def metric(self):
                 x = self.position.to_global_data()[0]
                 v = (2 - 4*x*x)*np.exp(-x**2)
                 return ift.DiagonalOperator(
@@ -188,7 +188,7 @@ class Test_Minimizers(unittest.TestCase):
                 return ift.Field(self.position.domain, val=np.sinh(x))
 
             @property
-            def curvature(self):
+            def metric(self):
                 x = self.position.to_global_data()[0]
                 v = np.cosh(x)
                 return ift.DiagonalOperator(