Merge branch 'master' into 'mpitests'

Master

See merge request !174

demos/critical_filtering.py

-from nifty import *
-from nifty.library.wiener_filter import WienerFilterEnergy
+import numpy as np
+from nifty import (VL_BFGS, DiagonalOperator, FFTOperator, Field,
+                   LinearOperator, PowerSpace, RelaxedNewton, RGSpace,
+                   SteepestDescent, create_power_operator, exp, log, sqrt)
 from nifty.library.critical_filter import CriticalPowerEnergy
-import plotly.offline as pl
-import plotly.graph_objs as go
+from nifty.library.wiener_filter import WienerFilterEnergy
 
+import plotly.graph_objs as go
+import plotly.offline as pl
 from mpi4py import MPI
+
 comm = MPI.COMM_WORLD
 rank = comm.rank
 
 np.random.seed(42)
 
 
-def plot_parameters(m,t,p, p_d):
+def plot_parameters(m, t, p, p_d):
 
     x = log(t.domain[0].kindex)
     m = fft.adjoint_times(m)
@@ -20,7 +24,8 @@ def plot_parameters(m,t,p, p_d):
     p = p.val.get_full_data().real
     p_d = p_d.val.get_full_data().real
     pl.plot([go.Heatmap(z=m)], filename='map.html')
-    pl.plot([go.Scatter(x=x,y=t), go.Scatter(x=x ,y=p), go.Scatter(x=x, y=p_d)], filename="t.html")
+    pl.plot([go.Scatter(x=x, y=t), go.Scatter(x=x, y=p),
+             go.Scatter(x=x, y=p_d)], filename="t.html")
 
 
 class AdjointFFTResponse(LinearOperator):
@@ -36,6 +41,7 @@ class AdjointFFTResponse(LinearOperator):
 
     def _adjoint_times(self, x, spaces=None):
         return self.FFT(self.R.adjoint_times(x))
+
     @property
     def domain(self):
         return self._domain
@@ -48,41 +54,40 @@ class AdjointFFTResponse(LinearOperator):
     def unitary(self):
         return False
 
+
 if __name__ == "__main__":
 
     distribution_strategy = 'not'
 
     # Set up position space
-    s_space = RGSpace([128,128])
+    s_space = RGSpace([128, 128])
     # s_space = HPSpace(32)
 
     # Define harmonic transformation and associated harmonic space
     fft = FFTOperator(s_space)
     h_space = fft.target[0]
 
-    # Setting up power space
+    # Set up power space
     p_space = PowerSpace(h_space, logarithmic=True,
                          distribution_strategy=distribution_strategy)
 
-    # Choosing the prior correlation structure and defining correlation operator
+    # Choose the prior correlation structure and defining correlation operator
     p_spec = (lambda k: (.5 / (k + 1) ** 3))
     S = create_power_operator(h_space, power_spectrum=p_spec,
                               distribution_strategy=distribution_strategy)
 
-    # Drawing a sample sh from the prior distribution in harmonic space
+    # Draw a sample sh from the prior distribution in harmonic space
     sp = Field(p_space,  val=p_spec,
                distribution_strategy=distribution_strategy)
     sh = sp.power_synthesize(real_signal=True)
 
-
-    # Choosing the measurement instrument
+    # Choose the measurement instrument
     # Instrument = SmoothingOperator(s_space, sigma=0.01)
     Instrument = DiagonalOperator(s_space, diagonal=1.)
     # Instrument._diagonal.val[200:400, 200:400] = 0
-    #Instrument._diagonal.val[64:512-64, 64:512-64] = 0
+    # Instrument._diagonal.val[64:512-64, 64:512-64] = 0
 
-
-    #Adding a harmonic transformation to the instrument
+    # Add a harmonic transformation to the instrument
     R = AdjointFFTResponse(fft, Instrument)
 
     noise = 1.
@@ -92,7 +97,7 @@ if __name__ == "__main__":
                           std=sqrt(noise),
                           mean=0)
 
-    # Creating the mock data
+    # Create mock data
     d = R(sh) + n
 
     # The information source
@@ -103,52 +108,49 @@ if __name__ == "__main__":
     if rank == 0:
         pl.plot([go.Heatmap(z=d_data)], filename='data.html')
 
-    #  minimization strategy
-
+    #  Minimization strategy
     def convergence_measure(a_energy, iteration):  # returns current energy
         x = a_energy.value
-        print (x, iteration)
-
+        print(x, iteration)
 
-    minimizer1 = RelaxedNewton(convergence_tolerance=1e-2,
-                              convergence_level=2,
-                              iteration_limit=3,
+    minimizer1 = RelaxedNewton(convergence_tolerance=1e-4,
+                               convergence_level=1,
+                               iteration_limit=5,
                                callback=convergence_measure)
-
-    minimizer2 = VL_BFGS(convergence_tolerance=0,
-                       iteration_limit=7,
+    minimizer2 = VL_BFGS(convergence_tolerance=1e-4,
+                         convergence_level=1,
+                         iteration_limit=20,
                          callback=convergence_measure,
-                       max_history_length=3)
+                         max_history_length=20)
+    minimizer3 = SteepestDescent(convergence_tolerance=1e-4,
+                                 iteration_limit=100,
+                                 callback=convergence_measure)
 
-    # Setting starting position
-    flat_power = Field(p_space,val=1e-8)
+    # Set starting position
+    flat_power = Field(p_space, val=1e-8)
     m0 = flat_power.power_synthesize(real_signal=True)
 
     t0 = Field(p_space, val=log(1./(1+p_space.kindex)**2))
 
-
-
     for i in range(500):
         S0 = create_power_operator(h_space, power_spectrum=exp(t0),
                                    distribution_strategy=distribution_strategy)
 
-        # Initializing the  nonlinear Wiener Filter energy
+        # Initialize non-linear Wiener Filter energy
         map_energy = WienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S0)
-        # Solving the Wiener Filter analytically
+        # Solve the Wiener Filter analytically
         D0 = map_energy.curvature
         m0 = D0.inverse_times(j)
-        # Initializing the power energy with updated parameters
-        power_energy = CriticalPowerEnergy(position=t0, m=m0, D=D0, smoothness_prior=10., samples=3)
-
-        (power_energy, convergence) = minimizer1(power_energy)
+        # Initialize power energy with updated parameters
+        power_energy = CriticalPowerEnergy(position=t0, m=m0, D=D0,
+                                           smoothness_prior=10., samples=3)
 
+        (power_energy, convergence) = minimizer2(power_energy)
 
-        # Setting new power spectrum
+        # Set new power spectrum
         t0.val = power_energy.position.val.real
 
-        # Plotting current estimate
-        print i
-        if i%50 == 0:
-            plot_parameters(m0,t0,log(sp), data_power)
-
-
+        # Plot current estimate
+        print(i)
+        if i % 5 == 0:
+            plot_parameters(m0, t0, log(sp), data_power)

nifty/energies/line_energy.py

@@ -16,10 +16,8 @@
 # NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
 # and financially supported by the Studienstiftung des deutschen Volkes.
 
-from .energy import Energy
 
-
-class LineEnergy(Energy):
+class LineEnergy(object):
     """ Evaluates an underlying Energy along a certain line direction.
 
     Given an Energy class and a line direction, its position is parametrized by
@@ -27,34 +25,31 @@ class LineEnergy(Energy):
 
     Parameters
     ----------
-    position : float
-        The step length parameter along the given line direction.
+    line_position : float
+        Defines the full spatial position of this energy via
+        self.energy.position = zero_point + line_position*line_direction
     energy : Energy
         The Energy object which will be evaluated along the given direction.
     line_direction : Field
-        Direction used for line evaluation.
-    zero_point :  Field *optional*
-        Fixing the zero point of the line restriction. Used to memorize this
-        position in new initializations. By the default the current position
-        of the supplied `energy` instance is used (default : None).
+        Direction used for line evaluation. Does not have to be normalized.
+    offset :  float *optional*
+        Indirectly defines the zero point of the line via the equation
+        energy.position = zero_point + offset*line_direction
+        (default : 0.).
 
     Attributes
     ----------
-    position : float
+    line_position : float
         The position along the given line direction relative to the zero point.
     value : float
-        The value of the energy functional at given `position`.
-    gradient : float
-        The gradient of the underlying energy instance along the line direction
-        projected on the line direction.
-    curvature : callable
-        A positive semi-definite operator or function describing the curvature
-        of the potential at given `position`.
+        The value of the energy functional at the given position
+    directional_derivative : float
+        The directional derivative at the given position
     line_direction : Field
         Direction along which the movement is restricted. Does not have to be
         normalized.
     energy : Energy
-        The underlying Energy at the `position` along the line direction.
+        The underlying Energy at the given position
 
     Raises
     ------
@@ -72,45 +67,49 @@ class LineEnergy(Energy):
 
     """
 
-    def __init__(self, position, energy, line_direction, zero_point=None):
-        super(LineEnergy, self).__init__(position=position)
-        self.line_direction = line_direction
-
-        if zero_point is None:
-            zero_point = energy.position
-        self._zero_point = zero_point
+    def __init__(self, line_position, energy, line_direction, offset=0.):
+        self._line_position = float(line_position)
+        self._line_direction = line_direction
 
-        position_on_line = self._zero_point + self.position*line_direction
-        self.energy = energy.at(position=position_on_line)
+        pos = energy.position \
+            + (self._line_position-float(offset))*self._line_direction
+        self.energy = energy.at(position=pos)
 
-    def at(self, position):
+    def at(self, line_position):
         """ Returns LineEnergy at new position, memorizing the zero point.
 
         Parameters
         ----------
-        position : float
+        line_position : float
             Parameter for the new position on the line direction.
 
         Returns
         -------
-        out : LineEnergy
             LineEnergy object at new position with same zero point as `self`.
 
         """
 
-        return self.__class__(position,
+        return self.__class__(line_position,
                               self.energy,
                               self.line_direction,
-                              zero_point=self._zero_point)
+                              offset=self.line_position)
 
     @property
     def value(self):
         return self.energy.value
 
     @property
-    def gradient(self):
-        return self.energy.gradient.vdot(self.line_direction)
+    def line_position(self):
+        return self._line_position
+
+    @property
+    def line_direction(self):
+        return self._line_direction
 
     @property
-    def curvature(self):
-        return self.energy.curvature
+    def directional_derivative(self):
+        res = self.energy.gradient.vdot(self.line_direction)
+        if abs(res.imag) / max(abs(res.real), 1.) > 1e-12:
+            print "directional derivative has non-negligible " \
+                  "imaginary part:", res
+        return res.real

nifty/field.py

@@ -112,7 +112,6 @@ class Field(Loggable, Versionable, object):
 
     def __init__(self, domain=None, val=None, dtype=None,
                  distribution_strategy=None, copy=False):
-
         self.domain = self._parse_domain(domain=domain, val=val)
         self.domain_axes = self._get_axes_tuple(self.domain)
 
@@ -128,6 +127,7 @@ class Field(Loggable, Versionable, object):
         else:
             self.set_val(new_val=val, copy=copy)
 
+
     def _parse_domain(self, domain, val=None):
         if domain is None:
             if isinstance(val, Field):
@@ -466,7 +466,7 @@ class Field(Loggable, Versionable, object):
         return result_obj
 
     def power_synthesize(self, spaces=None, real_power=True, real_signal=True,
-                         mean=None, std=None):
+                         mean=None, std=None, distribution_strategy=None):
         """ Yields a sampled field with `self`**2 as its power spectrum.
 
         This method draws a Gaussian random field in the harmonic partner
@@ -541,13 +541,16 @@ class Field(Loggable, Versionable, object):
         else:
             result_list = [None, None]
 
+        if distribution_strategy is None:
+            distribution_strategy = gc['default_distribution_strategy']
+
         result_list = [self.__class__.from_random(
                              'normal',
                              mean=mean,
                              std=std,
                              domain=result_domain,
                              dtype=np.complex,
-                             distribution_strategy=self.distribution_strategy)
+                             distribution_strategy=distribution_strategy)
                        for x in result_list]
 
         # from now on extract the values from the random fields for further
@@ -609,39 +612,47 @@ class Field(Loggable, Versionable, object):
 
         # correct variance
         if preserve_gaussian_variance:
+            assert issubclass(val.dtype.type, np.complexfloating),\
+                    "complex input field is needed here"
             h *= np.sqrt(2)
             a *= np.sqrt(2)
 
-            if not issubclass(val.dtype.type, np.complexfloating):
-                # in principle one must not correct the variance for the fixed
-                # points of the hermitianization. However, for a complex field
-                # the input field loses half of its power at its fixed points
-                # in the `hermitian` part. Hence, here a factor of sqrt(2) is
-                # also necessary!
-                # => The hermitianization can be done on a space level since
-                # either nothing must be done (LMSpace) or ALL points need a
-                # factor of sqrt(2)
-                # => use the preserve_gaussian_variance flag in the
-                # hermitian_decomposition method above.
-
-                # This code is for educational purposes:
-                fixed_points = [domain[i].hermitian_fixed_points()
-                                for i in spaces]
-                fixed_points = [[fp] if fp is None else fp
-                                for fp in fixed_points]
-
-                for product_point in itertools.product(*fixed_points):
-                    slice_object = np.array((slice(None), )*len(val.shape),
-                                            dtype=np.object)
-                    for i, sp in enumerate(spaces):
-                        point_component = product_point[i]
-                        if point_component is None:
-                            point_component = slice(None)
-                        slice_object[list(domain_axes[sp])] = point_component
-
-                    slice_object = tuple(slice_object)
-                    h[slice_object] /= np.sqrt(2)
-                    a[slice_object] /= np.sqrt(2)
+#            The code below should not be needed in practice, since it would
+#            only ever be called when hermitianizing a purely real field.
+#            However it might be of educational use and keep us from forgetting
+#            how these things are done ...
+
+#            if not issubclass(val.dtype.type, np.complexfloating):
+#                # in principle one must not correct the variance for the fixed
+#                # points of the hermitianization. However, for a complex field
+#                # the input field loses half of its power at its fixed points
+#                # in the `hermitian` part. Hence, here a factor of sqrt(2) is
+#                # also necessary!
+#                # => The hermitianization can be done on a space level since
+#                # either nothing must be done (LMSpace) or ALL points need a
+#                # factor of sqrt(2)
+#                # => use the preserve_gaussian_variance flag in the
+#                # hermitian_decomposition method above.
+#
+#                # This code is for educational purposes:
+#                fixed_points = [domain[i].hermitian_fixed_points()
+#                                for i in spaces]
+#                fixed_points = [[fp] if fp is None else fp
+#                                for fp in fixed_points]
+#
+#                for product_point in itertools.product(*fixed_points):
+#                    slice_object = np.array((slice(None), )*len(val.shape),
+#                                            dtype=np.object)
+#                    for i, sp in enumerate(spaces):
+#                        point_component = product_point[i]
+#                        if point_component is None:
+#                            point_component = slice(None)
+#                        slice_object[list(domain_axes[sp])] = point_component
+#
+#                    slice_object = tuple(slice_object)
+#                    h[slice_object] /= np.sqrt(2)
+#                    a[slice_object] /= np.sqrt(2)
+
         return (h, a)
 
     def _spec_to_rescaler(self, spec, result_list, power_space_index):
@@ -657,7 +668,7 @@ class Field(Loggable, Versionable, object):
                 result_list[0].domain_axes[power_space_index])
 
         if pindex.distribution_strategy is not local_distribution_strategy:
-            self.logger.warn(
+            raise AttributeError(
                 "The distribution_strategy of pindex does not fit the "
                 "slice_local distribution strategy of the synthesized field.")
 
@@ -764,14 +775,14 @@ class Field(Loggable, Versionable, object):
         dim
 
         """
-
+        if not hasattr(self, '_shape'):
             shape_tuple = tuple(sp.shape for sp in self.domain)
             try:
                 global_shape = reduce(lambda x, y: x + y, shape_tuple)
             except TypeError:
                 global_shape = ()
-
-        return global_shape
+            self._shape = global_shape
+        return self._shape
 
     @property
     def dim(self):

nifty/library/critical_filter/critical_power_curvature.py

@@ -21,7 +21,7 @@ class CriticalPowerCurvature(InvertibleOperatorMixin, EndomorphicOperator):
 
     # ---Overwritten properties and methods---
 
-    def __init__(self, theta, T, inverter=None, preconditioner=None):
+    def __init__(self, theta, T, inverter=None, preconditioner=None, **kwargs):
 
         self.theta = DiagonalOperator(theta.domain, diagonal=theta)
         self.T = T
@@ -30,7 +30,8 @@ class CriticalPowerCurvature(InvertibleOperatorMixin, EndomorphicOperator):
         self._domain = self.theta.domain
         super(CriticalPowerCurvature, self).__init__(
                                                  inverter=inverter,
-                                                 preconditioner=preconditioner)
+                                                 preconditioner=preconditioner,
+                                                 **kwargs)
 
     def _times(self, x, spaces):
         return self.T(x) + self.theta(x)

nifty/library/critical_filter/critical_power_energy.py

@@ -53,24 +53,28 @@ class CriticalPowerEnergy(Energy):
         default : None
     """
 
+    # ---Overwritten properties and methods---
+
     def __init__(self, position, m, D=None, alpha=1.0, q=0.,
                  smoothness_prior=0., logarithmic=True, samples=3, w=None):
         super(CriticalPowerEnergy, self).__init__(position=position)
         self.m = m
         self.D = D
         self.samples = samples
-        self.smoothness_prior = np.float(smoothness_prior)
         self.alpha = Field(self.position.domain, val=alpha)
         self.q = Field(self.position.domain, val=q)
         self.T = SmoothnessOperator(domain=self.position.domain[0],
-                                    strength=self.smoothness_prior,
+                                    strength=smoothness_prior,
                                     logarithmic=logarithmic)
         self.rho = self.position.domain[0].rho
         self._w = w if w is not None else None
 
+    # ---Mandatory properties and methods---
+
     def at(self, position):
         return self.__class__(position, self.m, D=self.D, alpha=self.alpha,
                               q=self.q, smoothness_prior=self.smoothness_prior,
+                              logarithmic=self.logarithmic,
                               w=self.w, samples=self.samples)
 
     @property
@@ -94,6 +98,16 @@ class CriticalPowerEnergy(Energy):
                                            T=self.T)
         return curvature
 
+    # ---Added properties and methods---
+
+    @property
+    def logarithmic(self):
+        return self.T.logarithmic
+
+    @property
+    def smoothness_prior(self):
+        return self.T.strength
+
     @property
     def w(self):
         if self._w is None:

nifty/library/wiener_filter/wiener_filter_curvature.py

@@ -22,7 +22,7 @@ class WienerFilterCurvature(InvertibleOperatorMixin, EndomorphicOperator):
 
     """
 
-    def __init__(self, R, N, S, inverter=None, preconditioner=None):
+    def __init__(self, R, N, S, inverter=None, preconditioner=None, **kwargs):
 
         self.R = R
         self.N = N
@@ -32,7 +32,8 @@ class WienerFilterCurvature(InvertibleOperatorMixin, EndomorphicOperator):
         self._domain = self.S.domain
         super(WienerFilterCurvature, self).__init__(
                                                  inverter=inverter,
-                                                 preconditioner=preconditioner)
+                                                 preconditioner=preconditioner,
+                                                 **kwargs)
 
     @property
     def domain(self):

nifty/library/wiener_filter/wiener_filter_energy.py

@@ -23,7 +23,7 @@ class WienerFilterEnergy(Energy):
         The prior signal covariance in harmonic space.
     """
 
-    def __init__(self, position, d, R, N, S, inverter=None):
+    def __init__(self, position, d, R, N, S):
         super(WienerFilterEnergy, self).__init__(position=position)
         self.d = d
         self.R = R
@@ -32,7 +32,7 @@ class WienerFilterEnergy(Energy):
 
     def at(self, position):
         return self.__class__(position=position, d=self.d, R=self.R, N=self.N,
-                              S=self.S, inverter=self.inverter)
+                              S=self.S)
 
     @property
     @memo
@@ -49,6 +49,7 @@ class WienerFilterEnergy(Energy):
     def curvature(self):
         return WienerFilterCurvature(R=self.R, N=self.N, S=self.S)
 
+    @property
     @memo
     def _Dx(self):
         return self.curvature(self.position)

nifty/minimization/descent_minimizer.py

@@ -137,7 +137,7 @@ class DescentMinimizer(Loggable, object):
 
             # compute the the gradient for the current location
             gradient = energy.gradient
-            gradient_norm = gradient.vdot(gradient)
+            gradient_norm = gradient.norm()
 
             # check if position is at a flat point
             if gradient_norm == 0:
@@ -147,7 +147,6 @@ class DescentMinimizer(Loggable, object):
 
             # current position is encoded in energy object
             descent_direction = self.get_descent_direction(energy)
-
             # compute the step length, which minimizes energy.value along the
             # search direction
             step_length, f_k, new_energy = \
@@ -155,8 +154,12 @@ class DescentMinimizer(Loggable, object):
                                                energy=energy,
                                                pk=descent_direction,
                                                f_k_minus_1=f_k_minus_1)
+            if f_k_minus_1 is None:
+                delta=1e30
+            else:
+                delta = abs(f_k -f_k_minus_1)/max(abs(f_k),abs(f_k_minus_1),1.)
             f_k_minus_1 = energy.value
-
+            tx1=energy.position-new_energy.position
             # check if new energy value is bigger than old energy value
             if (new_energy.value - energy.value) > 0:
                 self.logger.info("Line search algorithm returned a new energy "
@@ -165,7 +168,6 @@ class DescentMinimizer(Loggable, object):
 
             energy = new_energy
             # check convergence
-            delta = abs(gradient).max() * (step_length/np.sqrt(gradient_norm))
             self.logger.debug("Iteration:%08u step_length=%3.1E "
                               "delta=%3.1E energy=%3.1E" %
                               (iteration_number, step_length, delta,

nifty/minimization/line_searching/line_search.py

@@ -63,7 +63,7 @@ class LineSearch(Loggable, object):
             iteration of the line search procedure. (Default: None)
 
         """
-        self.line_energy = LineEnergy(position=0.,
+        self.line_energy = LineEnergy(line_position=0.,
                                       energy=energy,
                                       line_direction=pk)
         if f_k_minus_1 is not None:

nifty/minimization/line_searching/line_search_strong_wolfe.py

@@ -62,8 +62,8 @@ class LineSearchStrongWolfe(LineSearch):
     """
 
     def __init__(self, c1=1e-4, c2=0.9,
-                 max_step_size=50, max_iterations=10,
-                 max_zoom_iterations=10):
+                 max_step_size=1000000000, max_iterations=100,
+                 max_zoom_iterations=30):