updated Kalman and HampelFilter

wafo/sg_filter.py

@@ -572,7 +572,7 @@ def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3,
 
 def gcv(p, aow, Lambda, DCTy, y, Wtot, IsFinite, nof, noe):
     # Search the smoothing parameter s that minimizes the GCV score
-    s = 10 ** p
+    s = 10.0 ** p
     Gamma = 1.0 / (1 + s * Lambda ** 2)
     # RSS = Residual sum-of-squares
     if aow > 0.9:  # aow = 1 means that all of the data are equally weighted
@@ -589,7 +589,6 @@ def gcv(p, aow, Lambda, DCTy, y, Wtot, IsFinite, nof, noe):
     return GCVscore
 
 
-# Robust weights
 def RobustWeights(r, I, h, wstr):
     # weights for robust smoothing.
     MAD = np.median(abs(r[I] - np.median(r[I])))  # median absolute deviation
@@ -882,7 +881,7 @@ class Kalman(object):
         self.x = x  # Initial state estimate.
         self.P = P  # Initial covariance estimate.
         self.A = A  # State transition matrix.
-        self.B = B   # Control matrix.
+        self.B = B  # Control matrix.
         self.Q = Q  # Estimated error in process.
         self.H = H  # Observation matrix.
         self.reset()
@@ -890,38 +889,55 @@ class Kalman(object):
     def reset(self):
         self._filter = self._filter_first
 
-    def _filter_first(self, z, u):
+    def _set_A(self, n):
-
-        self._filter = self._filter_main
-
-        auto_init = self.x is None
-        if auto_init:
-            n = np.size(z)
-        else:
-            n = np.size(self.x)
         if self.A is None:
             self.A = np.eye(n)
         self.A = np.atleast_2d(self.A)
+
+    def _set_Q(self, n):
         if self.Q is None:
             self.Q = np.zeros((n, n))
         self.Q = np.atleast_2d(self.Q)
+
+    def _set_H(self, n):
         if self.H is None:
             self.H = np.eye(n)
         self.H = np.atleast_2d(self.H)
+
+    def _set_P(self, HI):
+        if self.P is None:
+            self.P = np.dot(np.dot(HI, self.R), HI.T)
+        self.P = np.atleast_2d(self.P)
+
+    def _init_first(self, n):
+        self._set_A(n)
+        self._set_Q(n)
+        self._set_H(n)
         try:
             HI = np.linalg.inv(self.H)
         except:
             HI = np.eye(n)
-        if self.P is None:
+        self._set_P(HI)
-            self.P = np.dot(np.dot(HI, self.R), HI.T)
+        return HI
 
-        self.P = np.atleast_2d(self.P)
+    def _first_state(self, z):
-        if auto_init:
+        n = np.size(z)
-            # initialize state estimate from first observation
+        HI = self._init_first(n)
-            self.x = np.dot(HI, z)
+        # initialize state estimate from first observation
+        x = np.dot(HI, z)
+        return x
+
+    def _filter_first(self, z, u):
+
+        self._filter = self._filter_main
+
+        if self.x is None:
+            self.x = self._first_state(z)
             return self.x
-        else:
+
-            return self._filter_main(z, u)
+        n = np.size(self.x)
+        self._init_first(n)
+        return self._filter_main(z, u)
 
     def _predict_state(self, x, u):
         return np.dot(self.A, x) + np.dot(self.B, u)
@@ -1043,12 +1059,12 @@ def lti_disc(F, L=None, Q=None, dt=1):
 
 def test_kalman_sine():
     """Kalman Filter demonstration with sine signal."""
-    sd = 1.
+    sd = 0.5
     dt = 0.1
     w = 1
     T = np.arange(0, 30 + dt / 2, dt)
     n = len(T)
-    X = np.sin(w * T)
+    X = 3*np.sin(w * T)
     Y = X + sd * np.random.randn(n)
 
     ''' Initialize KF to values
@@ -1091,7 +1107,7 @@ def test_kalman_sine():
     _ht = plt.plot(truth, 'g-', label='true voltage')
     plt.legend()
     plt.title('Automobile Voltimeter Example')
-    plt.show()
+    plt.show('hold')
 
 #     for k in range(m):
 #         [M,P] = kf_predict(M,P,A,Q);
@@ -1274,6 +1290,22 @@ class HampelFilter(object):
         ADX = dx * np.ones(Y.shape)
         return Y0, S0, ADX
 
+    def _fixed(self, Y, X, dx):
+        localwindow = self.localwindow
+        Y0, S0, ADX = self._init(Y, dx)
+        for i in range(len(Y)):
+            Y0[i], S0[i] = localwindow(X, Y, dx, i)
+        return Y0, S0, ADX
+
+    def _filter(self, Y, X, dx):
+        if len(X) <= 1:
+            Y0, S0, ADX = self._init(Y, dx)
+        elif self.adaptive is None:
+            Y0, S0, ADX = self._fixed(Y, X, dx)
+        else:
+            Y0, S0, ADX = self._adaptive(Y, X, dx)  # 'adaptive'
+        return Y0, S0, ADX
+
     def __call__(self, y, x=None):
         Y = np.atleast_1d(y).ravel()
         if x is None:
@@ -1283,21 +1315,14 @@ class HampelFilter(object):
         dx = 3 * np.median(np.diff(X)) if self.dx is None else self.dx
         self._check(dx)
 
-        if len(X) > 1:
+        Y0, S0, ADX = self._filter(Y, X, dx)
-            if self.adaptive is None:
-                localwindow = self.localwindow
-                Y0, S0, ADX = self._init(Y, dx)
-                for i in range(len(Y)):
-                    Y0[i], S0[i] = localwindow(X, Y, dx, i)
-            else:  # 'adaptive'
-                Y0, S0, ADX = self._adaptive(Y, X, dx)
         YY = Y.copy()
         T = self.t
         # Prepare Output
         self.UB = Y0 + T * S0
         self.LB = Y0 - T * S0
         outliers = np.abs(Y - Y0) > T * S0  # possible outliers
-        YY[outliers] = Y0[outliers]
+        np.putmask(YY, outliers, Y0)  # YY[outliers] = Y0[outliers]
         self.outliers = outliers
         self.num_outliers = outliers.sum()
         self.ADX = ADX
@@ -1308,7 +1333,7 @@ class HampelFilter(object):
         return YY
 
 
-def test_hampel():
+def demo_hampel():
     randint = np.random.randint
     Y = 5000 + np.random.randn(1000)
     outliers = randint(0, 1000, size=(10,))
@@ -1450,12 +1475,12 @@ def test_docstrings():
     doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
 
 if __name__ == '__main__':
-    test_docstrings()
+    # test_docstrings()
-    # test_kalman_sine()
+    test_kalman_sine()
     # test_tide_filter()
-    # test_hampel()
+    # demo_hampel()
     # test_kalman()
     # test_smooth()
     # test_hodrick_cardioid()
-    test_smoothn_1d()
+    # test_smoothn_1d()
     # test_smoothn_cardioid()