working on laplace

demos/critical_filtering.py

@@ -8,33 +8,33 @@ from mpi4py import MPI
 comm = MPI.COMM_WORLD
 rank = comm.rank
 
-np.random.seed(62)
+np.random.seed(232)
 
-class NonlinearResponse(LinearOperator):
-    def __init__(self, FFT, Instrument, function, derivative, default_spaces=None):
-        super(NonlinearResponse, self).__init__(default_spaces)
+
+def plot_parameters(m,t,t_true, t_real, t_d):
+    m = fft.adjoint_times(m)
+    m_data = m.val.get_full_data().real
+    t_data = t.val.get_full_data().real
+    t_d_data = t_d.val.get_full_data().real
+    t_true_data = t_true.val.get_full_data().real
+    t_real_data = t_real.val.get_full_data().real
+    pl.plot([go.Heatmap(z=m_data)], filename='map.html')
+    pl.plot([go.Scatter(y=t_data), go.Scatter(y=t_true_data),
+             go.Scatter(y=t_real_data), go.Scatter(y=t_d_data)], filename="t.html")
+
+class AdjointFFTResponse(LinearOperator):
+    def __init__(self, FFT, R, default_spaces=None):
+        super(AdjointFFTResponse, self).__init__(default_spaces)
         self._domain = FFT.target
-        self._target = Instrument.target
-        self.function = function
-        self.derivative = derivative
-        self.I = Instrument
+        self._target = R.target
+        self.R = R
         self.FFT = FFT
 
-
     def _times(self, x, spaces=None):
-        return self.I(self.function(self.FFT.adjoint_times(x)))
+        return self.R(self.FFT.adjoint_times(x))
 
     def _adjoint_times(self, x, spaces=None):
-        return self.FFT(self.function(self.I.adjoint_times(x)))
-
-    def derived_times(self, x, position):
-        position_derivative = self.derivative(self.FFT.adjoint_times(position))
-        return self.I(position_derivative * self.FFT.adjoint_times(x))
-
-    def derived_adjoint_times(self, x, position):
-        position_derivative = self.derivative(self.FFT.adjoint_times(position))
-        return self.FFT(position_derivative * self.I.adjoint_times(x))
-
+        return self.FFT(self.R.adjoint_times(x))
     @property
     def domain(self):
         return self._domain
@@ -47,16 +47,6 @@ class NonlinearResponse(LinearOperator):
     def unitary(self):
         return False
 
-def plot_parameters(m,t,t_true, t_real):
-    m = fft.adjoint_times(m)
-    m_data = m.val.get_full_data().real
-    t_data = t.val.get_full_data().real
-    t_true_data = t_true.val.get_full_data().real
-    t_real_data = t_real.val.get_full_data().real
-    pl.plot([go.Heatmap(z=m_data)], filename='map.html')
-    pl.plot([go.Scatter(y=t_data), go.Scatter(y=t_true_data),
-             go.Scatter(y=t_real_data)], filename="t.html")
-
 if __name__ == "__main__":
 
     distribution_strategy = 'not'
@@ -70,11 +60,11 @@ if __name__ == "__main__":
     h_space = fft.target[0]
 
     # Setting up power space
-    p_space = PowerSpace(h_space, logarithmic = True,
-                         distribution_strategy=distribution_strategy)
+    p_space = PowerSpace(h_space, logarithmic=False,
+                         distribution_strategy=distribution_strategy, nbin=128)
 
     # Choosing the prior correlation structure and defining correlation operator
-    pow_spec = (lambda k: (.05 / (k + 1) ** 3))
+    pow_spec = (lambda k: (.05 / (k + 1) ** 2))
     S = create_power_operator(h_space, power_spectrum=pow_spec,
                               distribution_strategy=distribution_strategy)
 
@@ -89,43 +79,11 @@ if __name__ == "__main__":
     Instrument = DiagonalOperator(s_space, diagonal=1.)
 #    Instrument._diagonal.val[200:400, 200:400] = 0
 
-    #   Choosing nonlinearity
-
-    # log-normal model:
-
-    function = exp
-    derivative = exp
-
-    # tan-normal model
-
-    # def function(x):
-    #     return 0.5 * tanh(x) + 0.5
-    # def derivative(x):
-    #     return 0.5*(1 - tanh(x)**2)
-
-    # no nonlinearity, Wiener Filter
-
-    # def function(x):
-    #     return x
-    # def derivative(x):
-    #     return 1
-
-    # small quadratic pertubarion
-
-    # def function(x):
-    #     return 0.5*x**2 + x
-    # def derivative(x):
-    #     return x + 1
-
-    # def function(x):
-    #     return 0.9*x**4 +0.2*x**2 + x
-    # def derivative(x):
-    #     return 0.9*4*x**3 + 0.4*x +1
-    #
 
     #Adding a harmonic transformation to the instrument
-    R = NonlinearResponse(fft, Instrument, function, derivative)
-    noise = .01
+    R = AdjointFFTResponse(fft, Instrument)
+
+    noise = 1.
     N = DiagonalOperator(s_space, diagonal=noise, bare=True)
     n = Field.from_random(domain=s_space,
                           random_type='normal',
@@ -134,66 +92,64 @@ if __name__ == "__main__":
 
     # Creating the mock data
     d = R(sh) + n
-    realized_power = log(sh.power_analyze(logarithmic=p_space.config["logarithmic"])**2)
+
+    realized_power = log(sh.power_analyze(logarithmic=p_space.config["logarithmic"],
+                                          nbin=p_space.config["nbin"])**2)
+    data_power  = log(fft(d).power_analyze(logarithmic=p_space.config["logarithmic"],
+                                          nbin=p_space.config["nbin"])**2)
     d_data = d.val.get_full_data().real
     if rank == 0:
         pl.plot([go.Heatmap(z=d_data)], filename='data.html')
 
-    # Choosing the minimization strategy
+    #  minimization strategy
 
     def convergence_measure(a_energy, iteration): # returns current energy
         x = a_energy.value
         print (x, iteration)
 
-    # minimizer1 = SteepestDescent(convergence_tolerance=0,
-    #                            iteration_limit=50,
-    #                            callback=convergence_measure)
 
     minimizer1 = RelaxedNewton(convergence_tolerance=0,
                               convergence_level=1,
-                              iteration_limit=5,
+                              iteration_limit=2,
                               callback=convergence_measure)
-    # minimizer2 = RelaxedNewton(convergence_tolerance=0,
-    #                           convergence_level=1,
-    #                           iteration_limit=2,
-    #                           callback=convergence_measure)
-    #
-    # minimizer1 = VL_BFGS(convergence_tolerance=0,
-    #                    iteration_limit=5,
-    #                    callback=convergence_measure,
-    #                    max_history_length=3)
-
-
+    minimizer2 = VL_BFGS(convergence_tolerance=0,
+                       iteration_limit=50,
+                       callback=convergence_measure,
+                       max_history_length=3)
 
     # Setting starting position
     flat_power = Field(p_space,val=10e-8)
     m0 = flat_power.power_synthesize(real_signal=True)
 
     t0 = Field(p_space, val=log(1./(1+p_space.kindex)**2))
-    # t0 = Field(p_space,val=-8)
-    # t0 = log(sp.copy()**2)
+    #t0 = data_power
     S0 = create_power_operator(h_space, power_spectrum=exp(t0),
                                distribution_strategy=distribution_strategy)
 
 
-
     for i in range(100):
         S0 = create_power_operator(h_space, power_spectrum=exp(t0),
                               distribution_strategy=distribution_strategy)
 
         # Initializing the  nonlinear Wiener Filter energy
-        map_energy = NonlinearWienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S0)
+        map_energy = WienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S0)
         # Minimization with chosen minimizer
-        (map_energy, convergence) = minimizer1(map_energy)
+        map_energy = map_energy.analytic_solution()
+
         # Updating parameters for correlation structure reconstruction
         m0 = map_energy.position
         D0 = map_energy.curvature
         # Initializing the power energy with updated parameters
         power_energy = CriticalPowerEnergy(position=t0, m=m0, D=D0, sigma=10., samples=3)
-        (power_energy, convergence) = minimizer1(power_energy)
+        if i > 0:
+            (power_energy, convergence) = minimizer1(power_energy)
+        else:
+            (power_energy, convergence) = minimizer2(power_energy)
         # Setting new power spectrum
         t0 = power_energy.position
-        plot_parameters(m0,t0,log(sp**2),realized_power)
+        t0.val[-1] = t0.val[-2]
+        # Plotting current estimate
+        plot_parameters(m0,t0,log(sp**2),realized_power, data_power)
 
     # Transforming fields to position space for plotting
 
@@ -223,10 +179,3 @@ if __name__ == "__main__":
     m_data = m.val.get_full_data().real
     if rank == 0:
         pl.plot([go.Heatmap(z=m_data)], filename='map.html')
-
-    f_m_data = function(m).val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=f_m_data)], filename='f_map.html')
-    f_ss_data = function(ss).val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=f_ss_data)], filename='f_ss.html')

demos/laplace_testing.py

+from nifty import *
+
+import numpy as np
+from nifty import Field,\
+                  EndomorphicOperator,\
+                  PowerSpace
+import plotly.offline as pl
+import plotly.graph_objs as go
+
+import numpy as np
+from nifty import Field, \
+    EndomorphicOperator, \
+    PowerSpace
+
+
+class TestEnergy(Energy):
+    def __init__(self, position, Op):
+        super(TestEnergy, self).__init__(position)
+        self.Op = Op
+
+    def at(self, position):
+        return self.__class__(position=position, Op=self.Op)
+
+    @property
+    def value(self):
+        return 0.5 * self.position.dot(self.Op(self.position))
+
+    @property
+    def gradient(self):
+        return self.Op(self.position)
+
+    @property
+    def curvature(self):
+        curv = CurvOp(self.Op)
+        return curv
+
+class CurvOp(InvertibleOperatorMixin, EndomorphicOperator):
+    def __init__(self, Op,inverter=None, preconditioner=None):
+        self.Op = Op
+        self._domain = Op.domain
+        super(CurvOp, self).__init__(inverter=inverter,
+                                                     preconditioner=preconditioner)
+
+    def _times(self, x, spaces):
+        return self.Op(x)
+
+if __name__ == "__main__":
+
+    distribution_strategy = 'not'
+
+    # Set up position space
+    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
+    p_space = PowerSpace(h_space, logarithmic=False,
+                         distribution_strategy=distribution_strategy, nbin=16)
+
+    # Choosing the prior correlation structure and defining correlation operator
+    pow_spec = (lambda k: (.05 / (k + 1) ** 2))
+    # t = Field(p_space, val=pow_spec)
+    t= Field.from_random("normal", domain=p_space)
+    lap = LogLaplaceOperator(p_space)
+    T = SmoothnessOperator(p_space,sigma=1.)
+    test_energy = TestEnergy(t,T)
+
+    def convergence_measure(a_energy, iteration): # returns current energy
+        x = a_energy.value
+        print (x, iteration)
+    minimizer1 = VL_BFGS(convergence_tolerance=0,
+                       iteration_limit=1000,
+                       callback=convergence_measure,
+                       max_history_length=3)
+
+
+    def explicify(op, domain):
+        space = domain
+        d = space.dim
+        res = np.zeros((d, d))
+        for i in range(d):
+            x = np.zeros(d)
+            x[i] = 1.
+            f = Field(space, val=x)
+            res[:, i] = op(f).val
+        return res
+    A = explicify(lap.times, p_space)
+    B = explicify(lap.adjoint_times, p_space)
+    test_energy,convergence = minimizer1(test_energy)
+    data = test_energy.position.val.get_full_data()
+    pl.plot([go.Scatter(x=log(p_space.kindex)[1:], y=data[1:])], filename="t.html")
+    tt = Field.from_random("normal", domain=t.domain)
+    print "adjointness"
+    print t.dot(lap(tt))
+    print tt.dot(lap.adjoint_times(t))
+    print "log kindex"
+    aa = Field(p_space, val=p_space.kindex.copy())
+    aa.val[0] = 1
+
+    print lap(log(aa)).val
+    print "######################"
+    print test_energy.position.val
\ No newline at end of file

demos/nonlinear_wiener_filter.py

-
-from nifty import *
-
-import plotly.offline as pl
-import plotly.graph_objs as go
-
-from mpi4py import MPI
-comm = MPI.COMM_WORLD
-rank = comm.rank
-
-np.random.seed(42)
-
-class NonlinearResponse(LinearOperator):
-    def __init__(self, FFT, Instrument, function, derivative, default_spaces=None):
-        super(NonlinearResponse, self).__init__(default_spaces)
-        self._domain = FFT.target
-        self._target = Instrument.target
-        self.function = function
-        self.derivative = derivative
-        self.I = Instrument
-        self.FFT = FFT
-
-
-    def _times(self, x, spaces=None):
-        return self.I(self.function(self.FFT.adjoint_times(x)))
-
-    def _adjoint_times(self, x, spaces=None):
-        return self.FFT(self.function(self.I.adjoint_times(x)))
-
-    def derived_times(self, x, position):
-        position_derivative = self.derivative(self.FFT.adjoint_times(position))
-        return self.I(position_derivative * self.FFT.adjoint_times(x))
-
-    def derived_adjoint_times(self, x, position):
-        position_derivative = self.derivative(self.FFT.adjoint_times(position))
-        return self.FFT(position_derivative * self.I.adjoint_times(x))
-
-    @property
-    def domain(self):
-        return self._domain
-
-    @property
-    def target(self):
-        return self._target
-
-    @property
-    def unitary(self):
-        return False
-
-
-
-if __name__ == "__main__":
-
-    distribution_strategy = 'not'
-
-    # Set up position space
-    s_space = RGSpace([100,100])
-    # s_space = HPSpace(32)
-
-    # Define harmonic transformation and associated harmonic space
-    fft = FFTOperator(s_space)
-    h_space = fft.target[0]
-
-    # Setting up power space
-    p_space = PowerSpace(h_space, distribution_strategy=distribution_strategy)
-
-    # Choosing the prior correlation structure and defining correlation operator
-    pow_spec = (lambda k: (1. / (k + 1) ** 3))
-    S = create_power_operator(h_space, power_spectrum=pow_spec,
-                              distribution_strategy=distribution_strategy)
-
-    # Drawing a sample sh from the prior distribution in harmonic space
-    sp = Field(p_space, val=lambda z: pow_spec(z)**(1./2),
-               distribution_strategy=distribution_strategy)
-    sh = sp.power_synthesize(real_signal=True)
-
-
-    # Choosing the measurement instrument
-#    Instrument = SmoothingOperator(s_space, sigma=0.01)
-    Instrument = DiagonalOperator(s_space, diagonal=1.)
-#    Instrument._diagonal.val[200:400, 200:400] = 0
-
-    #   Choosing nonlinearity
-    #
-    # function = exp
-    # derivative = exp
-    def function(x):
-        return 0.5 * tanh(x) + 0.5
-    def derivative(x):
-        return 0.5*(1. - tanh(x)**2)
-    # def function(x):
-    #     return 20*x
-    # def derivative(x):
-    #     return 20.
-
-    # def function(x):
-    #     return 0.1*0.5*x**2 + x
-    # def derivative(x):
-    #     return 0.1*x + 1
-
-    # def function(x):
-    #     return 0.9*x**4 +0.2*x**2 + x
-    # def derivative(x):
-    #     return 0.9*4*x**3 + 0.4*x +1
-    #
-
-    #Adding a harmonic transformation to the instrument
-
-    noise = 10.
-    N = DiagonalOperator(s_space, diagonal=noise, bare=True)
-    n = Field.from_random(domain=s_space,
-                          random_type='normal',
-                          std=sqrt(noise),
-                          mean=0)
-    R = NonlinearResponse(fft, Instrument, function, derivative)
-    # Creating the mock data
-    d = R(sh) + n
-
-    # Choosing the minimization strategy
-
-    def convergence_measure(energy, iteration): # returns current energy
-        x = energy.value
-        print (x, iteration)
-
-#    minimizer = SteepestDescent(convergence_tolerance=0,
-#                                iteration_limit=50,
-#                                callback=convergence_measure)
-#
-    minimizer = RelaxedNewton(convergence_tolerance=0,
-                              convergence_level=1,
-                              iteration_limit=3,
-                              callback=convergence_measure)
-
-    # minimizer = VL_BFGS(convergence_tolerance=0,
-    #                    iteration_limit=50,
-    #                    callback=convergence_measure,
-    #                    max_history_length=3)
-    #
-
-
-    # Setting starting position
-    flat_power = Field(p_space,val=10e-8)
-    m0 = flat_power.power_synthesize(real_signal=True)
-
-    # Initializing the Wiener Filter energy
-    energy = NonlinearWienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S)
-
-    # Solving the problem with chosen minimization strategy
-    (energy, convergence) = minimizer(energy)
-
-    # Transforming fields to position space for plotting
-
-    ss = fft.adjoint_times(sh)
-    m = fft.adjoint_times(energy.position)
-
-
-    # Plotting
-
-    d_data = d.val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=d_data)], filename='data.html')
-
-
-    ss_data = ss.val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=ss_data)], filename='ss.html')
-
-    sh_data = sh.val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=sh_data)], filename='sh.html')
-
-
-    m_data = m.val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=m_data)], filename='map.html')
-
-    f_m_data = function(m).val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=f_m_data)], filename='f_map.html')
-    f_ss_data = function(ss).val.get_full_data().real
-    if rank == 0:
-        pl.plot([go.Heatmap(z=f_ss_data)], filename='f_ss.html')

demos/train_example.py

@@ -54,12 +54,36 @@ def plot_parameters(m,t, t_real):
     pl.plot([go.Scatter(y=m_data)], filename='map.html')
     pl.plot([go.Scatter(y=t_data),
              go.Scatter(y=t_real_data)], filename="t.html")
+class AdjointFFTResponse(LinearOperator):
+    def __init__(self, FFT, R, default_spaces=None):
+        super(AdjointFFTResponse, self).__init__(default_spaces)
+        self._domain = FFT.target
+        self._target = R.target
+        self.R = R
+        self.FFT = FFT
+
+    def _times(self, x, spaces=None):
+        return self.R(self.FFT.adjoint_times(x))
+
+    def _adjoint_times(self, x, spaces=None):
+        return self.FFT(self.R.adjoint_times(x))
+    @property
+    def domain(self):
+        return self._domain
+
+    @property
+    def target(self):
+        return self._target
+
+    @property
+    def unitary(self):
+        return False
 
 if __name__ == "__main__":
 
     distribution_strategy = 'not'
     full_data = np.genfromtxt("train_data.csv", delimiter = ',')
-    d = full_data.T[2]
+    d = full_data.T[3]
     d[0] = 0.
     d -= d.mean()
     d[0] = 0.
@@ -80,42 +104,9 @@ if __name__ == "__main__":
     Instrument = DiagonalOperator(s_space, diagonal=1.)
 #    Instrument._diagonal.val[200:400, 200:400] = 0
 
-    #   Choosing nonlinearity
-
-    # log-normal model:
-
-    # function = exp
-    # derivative = exp
-
-    # tan-normal model
-
-    # def function(x):
-    #     return 0.5 * tanh(x) + 0.5
-    # def derivative(x):
-    #     return 0.5*(1 - tanh(x)**2)
-
-    # no nonlinearity, Wiener Filter
-
-    def function(x):
-        return x
-    def derivative(x):
-        return 1
-
-    # small quadratic pertubarion
-
-    # def function(x):
-    #     return 0.5*x**2 + x
-    # def derivative(x):
-    #     return x + 1
-
-    # def function(x):
-    #     return 0.9*x**4 +0.2*x**2 + x
-    # def derivative(x):
-    #     return 0.9*4*x**3 + 0.4*x +1
-    #
 
     #Adding a harmonic transformation to the instrument
-    R = NonlinearResponse(fft, Instrument, function, derivative)
+    R = AdjointFFTResponse(fft, Instrument)
     noise = .1
     N = DiagonalOperator(s_space, diagonal=noise, bare=True)
 
@@ -139,13 +130,13 @@ if __name__ == "__main__":
                               callback=convergence_measure)
     minimizer2 = RelaxedNewton(convergence_tolerance=0,
                               convergence_level=1,
-                              iteration_limit=10,
+                              iteration_limit=30,
                               callback=convergence_measure)
 
-    # minimizer1 = VL_BFGS(convergence_tolerance=0,
-    #                    iteration_limit=5,
-    #                    callback=convergence_measure,
-    #                    max_history_length=3)
+    minimizer1 = VL_BFGS(convergence_tolerance=0,
+                       iteration_limit=30,
+                       callback=convergence_measure,
+                       max_history_length=3)
 
 
 
@@ -159,25 +150,31 @@ if __name__ == "__main__":
     S0 = create_power_operator(h_space, power_spectrum=exp(t0),
                                distribution_strategy=distribution_strategy)
 
-
-    data_power = fft(d).power_analyze()
+    data_power  = log(fft(d).power_analyze(logarithmic=p_space.config["logarithmic"],
+                                          nbin=p_space.config["nbin"])**2)
     for i in range(100):
         S0 = create_power_operator(h_space, power_spectrum=exp(t0),