From c1a9b35ba59afa0f765b4a4f4891d7c93a4465ab Mon Sep 17 00:00:00 2001
From: Theo Steininger <theo.steininger@ipt.ai>
Date: Sat, 29 Jul 2017 18:24:17 +0200
Subject: [PATCH] First draft of log-normal energy and curvature.

---
 nifty/library/__init__.py                     |  1 +
 .../log_normal_wiener_filter/__init__.py      |  4 ++
 .../log_normal_wiener_filter_curvature.py     | 59 +++++++++++++++
 .../log_normal_wiener_filter_energy.py        | 71 +++++++++++++++++++
 4 files changed, 135 insertions(+)
 create mode 100644 nifty/library/log_normal_wiener_filter/__init__.py
 create mode 100644 nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_curvature.py
 create mode 100644 nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_energy.py

diff --git a/nifty/library/__init__.py b/nifty/library/__init__.py
index 9e45d0fb..dce7e6b2 100644
--- a/nifty/library/__init__.py
+++ b/nifty/library/__init__.py
@@ -1,2 +1,3 @@
 from critical_filter import *
+from log_normal_wiener_filter import *
 from wiener_filter import *
diff --git a/nifty/library/log_normal_wiener_filter/__init__.py b/nifty/library/log_normal_wiener_filter/__init__.py
new file mode 100644
index 00000000..8e43d246
--- /dev/null
+++ b/nifty/library/log_normal_wiener_filter/__init__.py
@@ -0,0 +1,4 @@
+# -*- coding: utf-8 -*-
+
+from log_normal_wiener_filter_curvature import LogNormalWienerFilterCurvature
+from log_normal_wiener_filter_energy import LogNormalWienerFilterEnergy
diff --git a/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_curvature.py b/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_curvature.py
new file mode 100644
index 00000000..9d6f82a2
--- /dev/null
+++ b/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_curvature.py
@@ -0,0 +1,59 @@
+from nifty.operators import EndomorphicOperator,\
+                            InvertibleOperatorMixin
+from nifty.basic_arithmetics import exp
+
+class WienerFilterCurvature(InvertibleOperatorMixin, EndomorphicOperator):
+    """The curvature of the LogNormalWienerFilterEnergy.
+
+    This operator implements the second derivative of the
+    LogNormalWienerFilterEnergy used in some minimization algorithms or for
+    error estimates of the posterior maps. It is the inverse of the propagator
+    operator.
+
+    Parameters
+    ----------
+    R: LinearOperator,
+        The response operator of the Wiener filter measurement.
+    N : EndomorphicOperator
+        The noise covariance.
+    S: DiagonalOperator,
+        The prior signal covariance
+
+    """
+
+    def __init__(self, R, N, S, inverter=None, preconditioner=None, **kwargs):
+
+        self.R = R
+        self.N = N
+        self.S = S
+        if preconditioner is None:
+            preconditioner = self.S.times
+        self._domain = self.S.domain
+        super(WienerFilterCurvature, self).__init__(
+                                                 inverter=inverter,
+                                                 preconditioner=preconditioner,
+                                                 **kwargs)
+
+    @property
+    def domain(self):
+        return self._domain
+
+    @property
+    def self_adjoint(self):
+        return True
+
+    @property
+    def unitary(self):
+        return False
+
+    # ---Added properties and methods---
+
+    def _times(self, x, spaces):
+        expx = exp(x)
+        expxx = expx*x
+        part1 = self.S.inverse_times(x)
+        part2 = (expx *   # is an adjoint necessary here?
+                 self.R.adjoint_times(self.N.inverse_times(self.R(expxx))))
+        part3 = (expxx *  # is an adjoint necessary here?
+                 self.R.adjoint_times(self.N.inverse_times(self.R(expx))))
+        return part1 + part2 + part3
diff --git a/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_energy.py b/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_energy.py
new file mode 100644
index 00000000..3a51a948
--- /dev/null
+++ b/nifty/library/log_normal_wiener_filter/log_normal_wiener_filter_energy.py
@@ -0,0 +1,71 @@
+from nifty.energies.energy import Energy
+from nifty.energies.memoization import memo
+from nifty.library.wiener_filter import WienerFilterCurvature
+from nifty.basic_arithmetics import exp
+
+class LogNormalWienerFilterEnergy(Energy):
+    """The Energy for the log-normal Wiener filter.
+
+    It covers the case of linear measurement with
+    Gaussian noise and Gaussain signal prior with known covariance.
+
+    Parameters
+    ----------
+    position: Field,
+        The current position.
+    d : Field,
+        the data.
+    R : Operator,
+        The response operator, describtion of the measurement process.
+    N : EndomorphicOperator,
+        The noise covariance in data space.
+    S : EndomorphicOperator,
+        The prior signal covariance in harmonic space.
+    """
+
+    def __init__(self, position, d, R, N, S):
+        super(WienerFilterEnergy, self).__init__(position=position)
+        self.d = d
+        self.R = R
+        self.N = N
+        self.S = S
+
+    def at(self, position):
+        return self.__class__(position=position, d=self.d, R=self.R, N=self.N,
+                              S=self.S)
+
+    @property
+    @memo
+    def value(self):
+        return (0.5*self.position.vdot(self._Sx) -
+                self._Rexpxd.vdot(self._NRexpxd))
+
+    @property
+    @memo
+    def gradient(self):
+        return self._Sx + self._expx * self.R.adjoint_times(self._NRexpxd)
+
+    @property
+    @memo
+    def curvature(self):
+        return WienerFilterCurvature(R=self.R, N=self.N, S=self.S)
+
+    @property
+    @memo
+    def _expx(self):
+        return exp(self.position)
+
+    @property
+    @memo
+    def _Rexpxd(self):
+        return self.R(self._expx) - self.d
+
+    @property
+    @memo
+    def _NRexpxd(self):
+        return self.N.inverse_times(self._Rexpxd)
+
+    @property
+    @memo
+    def _Sx(self):
+        return self.S.inverse_times(self.position)
-- 
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