Moved code from sg_filter.py to demo_sg.py

wafo/demo_sg.py

@@ -1,13 +1,18 @@
-import matplotlib.pyplot as plt
 import numpy as np
-from wafo.sg_filter import SavitzkyGolay, smoothn  # calc_coeff, smooth
+from scipy.sparse.linalg import expm
+from scipy.signal import medfilt
+from wafo.plotbackend import plotbackend as plt
+from wafo.sg_filter import (SavitzkyGolay, smoothn, Kalman, HodrickPrescott,
+                            HampelFilter)
 
 
-def example_reconstruct_noisy_chirp():
+def demo_savitzky_on_noisy_chirp():
     """
     Example
     -------
-    >>> example_reconstruct_noisy_chirp()
+    >>> demo_savitzky_on_noisy_chirp()
+
+    >>> plt.close()
     """
     plt.figure(figsize=(7, 12))
 
@@ -47,8 +52,437 @@ def example_reconstruct_noisy_chirp():
     plt.title('smoothed derivative of signal')
 
 
+def demo_kalman_voltimeter():
+    """
+    Example
+    -------
+    >>> demo_kalman_voltimeter()
+
+    >>> plt.close()
+    """
+    V0 = 12
+    h = np.atleast_2d(1)  # voltimeter measure the voltage itself
+    q = 1e-9  # variance of process noise as the car operates
+    r = 0.05 ** 2  # variance of measurement error
+    b = 0  # no system input
+    u = 0  # no system input
+    filt = Kalman(R=r, A=1, Q=q, H=h, B=b)
+
+    # Generate random voltages and watch the filter operate.
+    n = 50
+    truth = np.random.randn(n) * np.sqrt(q) + V0
+    z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
+    x = np.zeros(n)
+
+    for i, zi in enumerate(z):
+        x[i] = filt(zi, u)  # perform a Kalman filter iteration
+
+    _hz = plt.plot(z, 'r.', label='observations')
+    # a-posteriori state estimates:
+    _hx = plt.plot(x, 'b-', label='Kalman output')
+    _ht = plt.plot(truth, 'g-', label='true voltage')
+    plt.legend()
+    plt.title('Automobile Voltimeter Example')
+
+
+def lti_disc(F, L=None, Q=None, dt=1):
+    """LTI_DISC  Discretize LTI ODE with Gaussian Noise.
+
+    Syntax:
+     [A,Q] = lti_disc(F,L,Qc,dt)
+
+    In:
+     F  - NxN Feedback matrix
+     L  - NxL Noise effect matrix        (optional, default identity)
+     Qc - LxL Diagonal Spectral Density  (optional, default zeros)
+     dt - Time Step                      (optional, default 1)
+
+    Out:
+     A - Transition matrix
+     Q - Discrete Process Covariance
+
+    Description:
+     Discretize LTI ODE with Gaussian Noise. The original
+     ODE model is in form
+
+       dx/dt = F x + L w,  w ~ N(0,Qc)
+
+     Result of discretization is the model
+
+       x[k] = A x[k-1] + q, q ~ N(0,Q)
+
+     Which can be used for integrating the model
+     exactly over time steps, which are multiples
+     of dt.
+
+    """
+    n = np.shape(F)[0]
+    if L is None:
+        L = np.eye(n)
+
+    if Q is None:
+        Q = np.zeros((n, n))
+    # Closed form integration of transition matrix
+    A = expm(F * dt)
+
+    # Closed form integration of covariance
+    # by matrix fraction decomposition
+
+    Phi = np.vstack((np.hstack((F, np.dot(np.dot(L, Q), L.T))),
+                     np.hstack((np.zeros((n, n)), -F.T))))
+    AB = np.dot(expm(Phi * dt), np.vstack((np.zeros((n, n)), np.eye(n))))
+    # Q = AB[:n, :] / AB[n:(2 * n), :]
+    Q = np.linalg.solve(AB[n:(2 * n), :].T, AB[:n, :].T)
+    return A, Q
+
+
+def demo_kalman_sine():
+    """Kalman Filter demonstration with sine signal.
+
+    Example
+    -------
+    >>> demo_kalman_sine()
+
+    >>> plt.close()
+    """
+    sd = 0.5
+    dt = 0.1
+    w = 1
+    T = np.arange(0, 30 + dt / 2, dt)
+    n = len(T)
+    X = 3*np.sin(w * T)
+    Y = X + sd * np.random.randn(n)
+
+    ''' Initialize KF to values
+       x = 0
+       dx/dt = 0
+     with great uncertainty in derivative
+    '''
+    M = np.zeros((2, 1))
+    P = np.diag([0.1, 2])
+    R = sd ** 2
+    H = np.atleast_2d([1, 0])
+    q = 0.1
+    F = np.atleast_2d([[0, 1],
+                       [0, 0]])
+    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
+
+    # Track and animate
+    m = M.shape[0]
+    _MM = np.zeros((m, n))
+    _PP = np.zeros((m, m, n))
+    '''In this demonstration we estimate a stationary sine signal from noisy
+    measurements by using the classical Kalman filter.'
+    '''
+    filt = Kalman(R=R, x=M, P=P, A=A, Q=Q, H=H, B=0)
+
+    # Generate random voltages and watch the filter operate.
+    # n = 50
+    # truth = np.random.randn(n) * np.sqrt(q) + V0
+    # z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
+    truth = X
+    z = Y
+    x = np.zeros((n, m))
+
+    for i, zi in enumerate(z):
+        x[i] = np.ravel(filt(zi, u=0))
+
+    _hz = plt.plot(z, 'r.', label='observations')
+    # a-posteriori state estimates:
+    _hx = plt.plot(x[:, 0], 'b-', label='Kalman output')
+    _ht = plt.plot(truth, 'g-', label='true voltage')
+    plt.legend()
+    plt.title('Automobile Voltimeter Example')
+    plt.show('hold')
+
+#     for k in range(m):
+#         [M,P] = kf_predict(M,P,A,Q);
+#         [M,P] = kf_update(M,P,Y(k),H,R);
+#
+#         MM(:,k) = M;
+#         PP(:,:,k) = P;
+#
+#       %
+#       % Animate
+#       %
+#       if rem(k,10)==1
+#         plot(T,X,'b--',...
+#              T,Y,'ro',...
+#              T(k),M(1),'k*',...
+#              T(1:k),MM(1,1:k),'k-');
+#         legend('Real signal','Measurements','Latest estimate',
+#                'Filtered estimate')
+#         title('Estimating a noisy sine signal with Kalman filter.');
+#         drawnow;
+#
+#         pause;
+#       end
+#     end
+#
+#     clc;
+#     disp('In this demonstration we estimate a stationary sine signal '
+#        'from noisy measurements by using the classical Kalman filter.');
+#     disp(' ');
+#     disp('The filtering results are now displayed sequantially for 10 time '
+#            'step at a time.');
+#     disp(' ');
+#     disp('<push any key to see the filtered and smoothed results together>')
+#     pause;
+#     %
+#     % Apply Kalman smoother
+#     %
+#     SM = rts_smooth(MM,PP,A,Q);
+#     plot(T,X,'b--',...
+#          T,MM(1,:),'k-',...
+#          T,SM(1,:),'r-');
+#     legend('Real signal','Filtered estimate','Smoothed estimate')
+#     title('Filtered and smoothed estimate of the original signal');
+#
+#     clc;
+#     disp('The filtered and smoothed estimates of the signal are now '
+#        'displayed.')
+#     disp(' ');
+#     disp('RMS errors:');
+#     %
+#     % Errors
+#     %
+#     fprintf('KF = %.3f\nRTS = %.3f\n',...
+#             sqrt(mean((MM(1,:)-X(1,:)).^2)),...
+#             sqrt(mean((SM(1,:)-X(1,:)).^2)));
+
+
+def demo_hampel():
+    """
+    Example
+    -------
+    >>> demo_hampel()
+
+    >>> plt.close()
+    """
+    randint = np.random.randint
+    Y = 5000 + np.random.randn(1000)
+    outliers = randint(0, 1000, size=(10,))
+    Y[outliers] = Y[outliers] + randint(1000, size=(10,))
+    YY, res = HampelFilter(dx=3, t=3, fulloutput=True)(Y)
+    YY1, res1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=True)(Y)
+    YY2, res2 = HampelFilter(dx=3, t=0, fulloutput=True)(Y)  # median
+    plt.figure(1)
+    plot_hampel(Y, YY, res)
+    plt.title('Standard HampelFilter')
+    plt.figure(2)
+    plot_hampel(Y, YY1, res1)
+    plt.title('Adaptive HampelFilter')
+    plt.figure(3)
+    plot_hampel(Y, YY2, res2)
+    plt.title('Median filter')
+
+
+def plot_hampel(Y, YY, res):
+    X = np.arange(len(YY))
+    plt.plot(X, Y, 'b.')  # Original Data
+    plt.plot(X, YY, 'r')  # Hampel Filtered Data
+    plt.plot(X, res['Y0'], 'b--')  # Nominal Data
+    plt.plot(X, res['LB'], 'r--')  # Lower Bounds on Hampel Filter
+    plt.plot(X, res['UB'], 'r--')  # Upper Bounds on Hampel Filter
+    i = res['outliers']
+    plt.plot(X[i], Y[i], 'ks')  # Identified Outliers
+
+
+def demo_tide_filter():
+    """
+    Example
+    -------
+    >>> demo_tide_filter()
+
+    >>> plt.close()
+    """
+    # import statsmodels.api as sa
+    import wafo.spectrum.models as sm
+    sd = 10
+    Sj = sm.Jonswap(Hm0=4.*sd)
+    S = Sj.tospecdata()
+
+    q = (0.1 * sd) ** 2   # variance of process noise s the car operates
+    r = (100 * sd) ** 2  # variance of measurement error
+    b = 0  # no system input
+    u = 0  # no system input
+
+    from scipy.signal import butter, filtfilt, lfilter_zi  # lfilter,
+    freq_tide = 1. / (12 * 60 * 60)
+    freq_wave = 1. / 10
+    freq_filt = freq_wave / 10
+    dt = 1.
+    freq = 1. / dt
+    fn = (freq / 2)
+
+    P = 10 * np.diag([1, 0.01])
+    R = r
+    H = np.atleast_2d([1, 0])
+
+    F = np.atleast_2d([[0, 1],
+                       [0, 0]])
+    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
+
+    t = np.arange(0, 60 * 12, 1. / freq)
+    w = 2 * np.pi * freq  # 1 Hz
+    tide = 100 * np.sin(freq_tide * w * t + 2 * np.pi / 4) + 100
+    y = tide + S.sim(len(t), dt=1. / freq)[:, 1].ravel()
+#     lowess = sa.nonparametric.lowess
+#     y2 = lowess(y, t, frac=0.5)[:,1]
+
+    filt = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
+    filt2 = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
+    # y = tide + 0.5 * np.sin(freq_wave * w * t)
+    # Butterworth filter
+    b, a = butter(9, (freq_filt / fn), btype='low')
+    # y2 = [lowess(y[max(i-60,0):i + 1], t[max(i-60,0):i + 1], frac=.3)[-1,1]
+    #    for i in range(len(y))]
+    # y2 = [lfilter(b, a, y[:i + 1])[i] for i in range(len(y))]
+    # y3 = filtfilt(b, a, y[:16]).tolist() + [filtfilt(b, a, y[:i + 1])[i]
+    #    for i in range(16, len(y))]
+    # y0 = medfilt(y, 41)
+    _zi = lfilter_zi(b, a)
+    # y2 = lfilter(b, a, y)#, zi=y[0]*zi)  # standard filter
+    y3 = filtfilt(b, a, y)  # filter with phase shift correction
+    y4 = []
+    y5 = []
+    for _i, j in enumerate(y):
+        tmp = np.ravel(filt(j, u=u))
+        tmp = np.ravel(filt2(tmp[0], u=u))
+#         if i==0:
+#             print(filt.x)
+#             print(filt2.x)
+        y4.append(tmp[0])
+        y5.append(tmp[1])
+    _y0 = medfilt(y4, 41)
+    print(filt.P)
+    # plot
+
+    plt.plot(t, y, 'r.-', linewidth=2, label='raw data')
+    # plt.plot(t, y2, 'b.-', linewidth=2, label='lowess @ %g Hz' % freq_filt)
+    # plt.plot(t, y2, 'b.-', linewidth=2, label='filter @ %g Hz' % freq_filt)
+    plt.plot(t, y3, 'g.-', linewidth=2, label='filtfilt @ %g Hz' % freq_filt)
+    plt.plot(t, y4, 'k.-', linewidth=2, label='kalman')
+    # plt.plot(t, y5, 'k.', linewidth=2, label='kalman2')
+    plt.plot(t, tide, 'y-', linewidth=2, label='True tide')
+    plt.legend(frameon=False, fontsize=14)
+    plt.xlabel("Time [s]")
+    plt.ylabel("Amplitude")
+
+
+def demo_savitzky_on_exponential():
+    """
+    Example
+    -------
+    >>> demo_savitzky_on_exponential()
+
+    >>> plt.close()
+    """
+    t = np.linspace(-4, 4, 500)
+    y = np.exp(-t ** 2) + np.random.normal(0, 0.05, np.shape(t))
+    n = 11
+    ysg = SavitzkyGolay(n, degree=1, diff_order=0)(y)
+    plt.plot(t, y, t, ysg, '--')
+
+
+def demo_smoothn_on_1d_cos():
+    """
+    Example
+    -------
+    >>> demo_smoothn_on_1d_cos()
+
+    >>> plt.close()
+    """
+    x = np.linspace(0, 100, 2 ** 8)
+    y = np.cos(x / 10) + (x / 50) ** 2 + np.random.randn(np.size(x)) / 10
+    y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6])
+    z = smoothn(y)  # Regular smoothing
+    zr = smoothn(y, robust=True)  # Robust smoothing
+    _h0 = plt.subplot(121),
+    _h = plt.plot(x, y, 'r.', x, z, 'k', linewidth=2)
+    plt.title('Regular smoothing')
+    plt.subplot(122)
+    plt.plot(x, y, 'r.', x, zr, 'k', linewidth=2)
+    plt.title('Robust smoothing')
+
+
+def demo_smoothn_on_2d_exp_sin():
+    """
+    Example
+    -------
+    >>> demo_smoothn_on_2d_exp_sin()
+
+    >>> plt.close()
+    """
+    xp = np.arange(0, 1, 0.02)  # np.r_[0:1:0.02]
+    [x, y] = np.meshgrid(xp, xp)
+    f = np.exp(x + y) + np.sin((x - 2 * y) * 3)
+    fn = f + np.random.randn(*f.shape) * 0.5
+    _fs, s = smoothn(fn, fulloutput=True)
+    fs2 = smoothn(fn, s=2 * s)
+    _h = plt.subplot(131),
+    _h = plt.contourf(xp, xp, fn)
+    _h = plt.subplot(132),
+    _h = plt.contourf(xp, xp, fs2)
+    _h = plt.subplot(133),
+    _h = plt.contourf(xp, xp, f)
+
+
+def _cardioid(n=1000):
+    t = np.linspace(0, 2 * np.pi, n)
+    x0 = 2 * np.cos(t) * (1 - np.cos(t))
+    y0 = 2 * np.sin(t) * (1 - np.cos(t))
+    x = x0 + np.random.randn(x0.size) * 0.1
+    y = y0 + np.random.randn(y0.size) * 0.1
+    return x, y, x0, y0
+
+
+def demo_smoothn_on_cardioid():
+    """
+    Example
+    -------
+    >>> demo_smoothn_cardoid()
+
+    >>> plt.close()
+    """
+    x, y, x0, y0 = _cardioid()
+    z = smoothn(x + 1j * y, robust=False)
+    plt.plot(x0, y0, 'y',
+             x, y, 'r.',
+             np.real(z), np.imag(z), 'k', linewidth=2)
+
+
+def demo_hodrick_on_cardioid():
+    """
+    Example
+    -------
+    >>> demo_hodrick_on_cardioid()
+
+    >>> plt.close()
+    """
+    x, y, x0, y0 = _cardioid()
+
+    smooth = HodrickPrescott(w=20000)
+    # smooth = HampelFilter(adaptive=50)
+    xs, ys = smooth(x), smooth(y)
+    plt.plot(x0, y0, 'y',
+             x, y, 'r.',
+             xs, ys, 'k', linewidth=2)
+
 if __name__ == '__main__':
     from wafo.testing import test_docstrings
     test_docstrings(__file__)
-    # example_reconstruct_noisy_chirp()
+    # demo_savitzky_on_noisy_chirp()
     # plt.show('hold')  # show plot
+    # demo_kalman_sine()
+    # demo_tide_filter()
+    # demo_hampel()
+    # demo_kalman_voltimeter()
+    # demo_savitzky_on_exponential()
+#     plt.figure(1)
+#     demo_hodrick_on_cardioid()
+#     plt.figure(2)
+#     # demo_smoothn_on_1d_cos()
+#     demo_smoothn_on_cardioid()
+#     plt.show('hold')
+

wafo/gaussian.py

@@ -9,17 +9,17 @@ import warnings
 import numpy as np
 
 try:
-    from . import mvn  # @UnresolvedImport
+    from wafo import mvn  # @UnresolvedImport
 except ImportError:
     warnings.warn('mvn not found. Check its compilation.')
     mvn = None
 try:
-    from . import mvnprdmod  # @UnresolvedImport
+    from wafo import mvnprdmod  # @UnresolvedImport
 except ImportError:
     warnings.warn('mvnprdmod not found. Check its compilation.')
     mvnprdmod = None
 try:
-    from . import rindmod  # @UnresolvedImport
+    from wafo import rindmod  # @UnresolvedImport
 except ImportError:
     warnings.warn('rindmod not found. Check its compilation.')
     rindmod = None
@@ -27,7 +27,7 @@ except ImportError:
 
 __all__ = ['Rind', 'rindmod', 'mvnprdmod', 'mvn', 'cdflomax', 'prbnormtndpc',
            'prbnormndpc', 'prbnormnd', 'cdfnorm2d', 'prbnorm2d', 'cdfnorm',
-           'invnorm', 'test_docstring']
+           'invnorm']
 
 
 class Rind(object):
@@ -1028,12 +1028,9 @@ def bvd(lo, up, r):
     return cdfnorm2d(-lo, -up, r)
 
 
-def test_docstrings():
-    import doctest
-    doctest.testmod()
-
 if __name__ == '__main__':
-    test_docstrings()
+    from wafo.testing import test_docstrings
+    test_docstrings(__file__)
 # if __name__ == '__main__':
 #    if False: #True: #
 #        test_rind()

wafo/sg_filter.py

@@ -1,21 +1,23 @@
 from __future__ import absolute_import, division
 import numpy as np
-# from math import pow
+from numpy import (pi, linalg, concatenate, sqrt)
-# from numpy import zeros,dot
-from numpy import (pi, convolve, linalg, concatenate, sqrt)
 from scipy.sparse import spdiags
-from scipy.sparse.linalg import spsolve, expm
+from scipy.sparse.linalg import spsolve
-from scipy.signal import medfilt
-from .dctpack import dctn, idctn
-from .plotbackend import plotbackend as plt
 import scipy.optimize as optimize
 from scipy.signal import _savitzky_golay
 from scipy.ndimage import convolve1d
 from scipy.ndimage.morphology import distance_transform_edt
 import warnings
+from wafo.dctpack import dctn, idctn
 
 
-__all__ = ['SavitzkyGolay', 'Kalman', 'HodrickPrescott', 'smoothn']
+__all__ = ['SavitzkyGolay', 'Kalman', 'HodrickPrescott', 'smoothn',
+           'HampelFilter', 'SmoothNd']
+
+
+def _assert(cond, msg):
+    if not cond:
+        raise ValueError(msg)
 
 
 class SavitzkyGolay(object):
@@ -162,43 +164,6 @@ class SavitzkyGolay(object):
             y = convolve1d(x, coeffs, axis=axis, mode=mode, cval=self.cval)
         return y
 
-    def _smooth(self, signal, pad=True):
-        """
-        Returns smoothed signal (or it's n-th derivative).
-
-        Parameters
-        ----------
-        y : array_like, shape (N,)
-            the values of the time history of the signal.
-        pad : bool
-           pad first and last values to lessen the end effects.
-
-        Returns
-        -------
-        ys : ndarray, shape (N)
-            the smoothed signal (or it's n-th derivative).
-        """
-        coeff = self._coeff
-        n = np.size(coeff - 1) // 2
-        y = np.squeeze(signal)
-        if n == 0:
-            return y
-        if pad:
-            first_vals = y[0] - np.abs(y[n:0:-1] - y[0])
-            last_vals = y[-1] + np.abs(y[-2:-n - 2:-1] - y[-1])
-            y = concatenate((first_vals, y, last_vals))
-            n *= 2
-        d = y.ndim
-        if d > 1:
-            y1 = y.reshape(y.shape[0], -1)
-            res = []
-            for i in range(y1.shape[1]):
-                res.append(convolve(y1[:, i], coeff)[n:-n])
-            res = np.asarray(res).T
-        else:
-            res = convolve(y, coeff)[n:-n]
-        return res
-
 
 def evar(y):
     """Noise variance estimation. Assuming that the deterministic function Y
@@ -236,7 +201,7 @@ def evar(y):
 
     3D function
     >>> yp = np.linspace(-2,2,50)
-    >>> [x,y,z] = np.meshgrid(yp,yp,yp, sparse=True)
+    >>> [x,y,z] = np.meshgrid(yp, yp, yp, sparse=True)
     >>> f = x*np.exp(-x**2-y**2-z**2)
     >>> var0 = 0.5  # noise variance
     >>> fn = f + np.sqrt(var0)*np.random.randn(*f.shape)
@@ -417,8 +382,7 @@ class _Filter(object):
         (Inf/NaN values = missing data).
         """
         weights = weight * is_finite
-        if (weights < 0).any():
+        _assert(np.all(0 <= weights), 'Weights must all be >=0')
-            raise ValueError('Weights must all be >=0')
         return weights / weights.max()
 
     @staticmethod
@@ -523,6 +487,66 @@ class _Filter(object):
         return z, s, converged
 
 
+class SmoothNd(object):
+    def __init__(self, s=None, weight=None, robust=False, z0=None, tolz=1e-3,
+                 maxiter=100, fulloutput=False):
+        self.s = s
+        self.weight = weight
+        self.robust = robust
+        self.z0 = z0
+        self.tolz = tolz
+        self.maxiter = maxiter
+        self.fulloutput = fulloutput
+
+    @property
+    def weightstr(self):
+        if isinstance(self._weight, str):
+            return self._weight.lower()
+        return 'bisquare'
+
+    @property
+    def weight(self):
+        if self._weight is None or isinstance(self._weight, str):
+            return 1.0
+        return self._weight
+
+    @weight.setter
+    def weight(self, weight):
+        self._weight = weight
+
+    def _init_filter(self, y):
+        return _Filter(y, self.z0, self.weightstr, self.weight, self.s,
+                       self.robust, self.maxiter, self.tolz)
+
+    @property
+    def num_steps(self):
+        return 3 if self.robust else 1
+
+    def __call__(self, data):
+
+        y = np.atleast_1d(data)
+        if y.size < 2:
+            return data
+
+        _filter = self._init_filter(y)
+        z = _filter.z0
+        s = _filter.s
+        converged = False
+        for _i in range(self.num_steps):
+            z, s, converged = _filter(z, s)
+
+        if not converged:
+            msg = '''Maximum number of iterations (%d) has been exceeded.
+            Increase MaxIter option or decrease TolZ value.''' % (self.maxiter)
+            warnings.warn(msg)
+
+        _filter.check_smooth_parameter(s)
+
+        if self.fulloutput:
+            return z, s
+        return z
+
+
 def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3,
             maxiter=100, fulloutput=False):
     '''
@@ -656,115 +680,6 @@ def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3,
     return SmoothNd(s, weight, robust, z0, tolz, maxiter, fulloutput)(data)
 
 
-class SmoothNd(object):
-    def __init__(self, s=None, weight=None, robust=False, z0=None, tolz=1e-3,
-                 maxiter=100, fulloutput=False):
-        self.s = s
-        self.weight = weight
-        self.robust = robust
-        self.z0 = z0
-        self.tolz = tolz
-        self.maxiter = maxiter
-        self.fulloutput = fulloutput
-
-    @property
-    def weightstr(self):
-        if isinstance(self._weight, str):
-            return self._weight.lower()
-        return 'bisquare'
-
-    @property
-    def weight(self):
-        if self._weight is None or isinstance(self._weight, str):
-            return 1.0
-        return self._weight
-
-    @weight.setter
-    def weight(self, weight):
-        self._weight = weight
-
-    def _init_filter(self, y):
-        return _Filter(y, self.z0, self.weightstr, self.weight, self.s,
-                       self.robust, self.maxiter, self.tolz)
-
-    @property
-    def num_steps(self):
-        return 3 if self.robust else 1
-
-    def __call__(self, data):
-
-        y = np.atleast_1d(data)
-        if y.size < 2:
-            return data
-
-        _filter = self._init_filter(y)
-        z = _filter.z0
-        s = _filter.s
-        converged = False
-        for _i in range(self.num_steps):
-            z, s, converged = _filter(z, s)
-
-        if not converged:
-            msg = '''Maximum number of iterations (%d) has been exceeded.
-            Increase MaxIter option or decrease TolZ value.''' % (self.maxiter)
-            warnings.warn(msg)
-
-        _filter.check_smooth_parameter(s)
-
-        if self.fulloutput:
-            return z, s
-        return z
-
-
-def test_smoothn_1d():
-    x = np.linspace(0, 100, 2 ** 8)
-    y = np.cos(x / 10) + (x / 50) ** 2 + np.random.randn(x.size) / 10
-    y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6])
-    z = smoothn(y)  # Regular smoothing
-    zr = smoothn(y, robust=True)  # Robust smoothing
-    _h0 = plt.subplot(121),
-    _h = plt.plot(x, y, 'r.', x, z, 'k', linewidth=2)
-    plt.title('Regular smoothing')
-    plt.subplot(122)
-    plt.plot(x, y, 'r.', x, zr, 'k', linewidth=2)
-    plt.title('Robust smoothing')
-    plt.show('hold')
-
-
-def test_smoothn_2d():
-
-    # import mayavi.mlab as plt
-    xp = np.r_[0:1:0.02]
-    [x, y] = np.meshgrid(xp, xp)
-    f = np.exp(x + y) + np.sin((x - 2 * y) * 3)
-    fn = f + np.random.randn(*f.shape) * 0.5
-    _fs, s = smoothn(fn, fulloutput=True)
-    fs2 = smoothn(fn, s=2 * s)
-    _h = plt.subplot(131),
-    _h = plt.contourf(xp, xp, fn)
-    _h = plt.subplot(132),
-    _h = plt.contourf(xp, xp, fs2)
-    _h = plt.subplot(133),
-    _h = plt.contourf(xp, xp, f)
-    plt.show('hold')
-
-
-def test_smoothn_cardioid():
-    t = np.linspace(0, 2 * pi, 1000)
-    cos = np.cos
-    sin = np.sin
-    randn = np.random.randn
-    x0 = 2 * cos(t) * (1 - cos(t))
-    x = x0 + randn(t.size) * 0.1
-    y0 = 2 * sin(t) * (1 - cos(t))
-    y = y0 + randn(t.size) * 0.1
-    z = smoothn(x + 1j * y, robust=False)
-    plt.plot(x0, y0, 'y',
-             x, y, 'r.',
-             z.real, z.imag, 'k', linewidth=2)
-    plt.show('hold')
-
-
 class HodrickPrescott(object):
 
     '''Smooth data with a Hodrick-Prescott filter.
@@ -1066,192 +981,6 @@ class Kalman(object):
         return self._filter(z, u)
 
 
-def test_kalman():
-    V0 = 12
-    h = np.atleast_2d(1)  # voltimeter measure the voltage itself
-    q = 1e-9  # variance of process noise as the car operates
-    r = 0.05 ** 2  # variance of measurement error
-    b = 0  # no system input
-    u = 0  # no system input
-    filt = Kalman(R=r, A=1, Q=q, H=h, B=b)
-
-    # Generate random voltages and watch the filter operate.
-    n = 50
-    truth = np.random.randn(n) * np.sqrt(q) + V0
-    z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
-    x = np.zeros(n)
-
-    for i, zi in enumerate(z):
-        x[i] = filt(zi, u)  # perform a Kalman filter iteration
-
-    _hz = plt.plot(z, 'r.', label='observations')
-    # a-posteriori state estimates:
-    _hx = plt.plot(x, 'b-', label='Kalman output')
-    _ht = plt.plot(truth, 'g-', label='true voltage')
-    plt.legend()
-    plt.title('Automobile Voltimeter Example')
-    plt.show('hold')
-
-
-def lti_disc(F, L=None, Q=None, dt=1):
-    """LTI_DISC  Discretize LTI ODE with Gaussian Noise.
-
-    Syntax:
-     [A,Q] = lti_disc(F,L,Qc,dt)
-
-    In:
-     F  - NxN Feedback matrix
-     L  - NxL Noise effect matrix        (optional, default identity)
-     Qc - LxL Diagonal Spectral Density  (optional, default zeros)
-     dt - Time Step                      (optional, default 1)
-
-    Out:
-     A - Transition matrix
-     Q - Discrete Process Covariance
-
-    Description:
-     Discretize LTI ODE with Gaussian Noise. The original
-     ODE model is in form
-
-       dx/dt = F x + L w,  w ~ N(0,Qc)
-
-     Result of discretization is the model
-
-       x[k] = A x[k-1] + q, q ~ N(0,Q)
-
-     Which can be used for integrating the model
-     exactly over time steps, which are multiples
-     of dt.
-
-    """
-    n = np.shape(F)[0]
-    if L is None:
-        L = np.eye(n)
-
-    if Q is None:
-        Q = np.zeros((n, n))
-    # Closed form integration of transition matrix
-    A = expm(F * dt)
-
-    # Closed form integration of covariance
-    # by matrix fraction decomposition
-
-    Phi = np.vstack((np.hstack((F, np.dot(np.dot(L, Q), L.T))),
-                     np.hstack((np.zeros((n, n)), -F.T))))
-    AB = np.dot(expm(Phi * dt), np.vstack((np.zeros((n, n)), np.eye(n))))
-    # Q = AB[:n, :] / AB[n:(2 * n), :]
-    Q = np.linalg.solve(AB[n:(2 * n), :].T, AB[:n, :].T)
-    return A, Q
-
-
-def test_kalman_sine():
-    """Kalman Filter demonstration with sine signal."""
-    sd = 0.5
-    dt = 0.1
-    w = 1
-    T = np.arange(0, 30 + dt / 2, dt)
-    n = len(T)
-    X = 3*np.sin(w * T)
-    Y = X + sd * np.random.randn(n)
-
-    ''' Initialize KF to values
-       x = 0
-       dx/dt = 0
-     with great uncertainty in derivative
-    '''
-    M = np.zeros((2, 1))
-    P = np.diag([0.1, 2])
-    R = sd ** 2
-    H = np.atleast_2d([1, 0])
-    q = 0.1
-    F = np.atleast_2d([[0, 1],
-                       [0, 0]])
-    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
-
-    # Track and animate
-    m = M.shape[0]
-    _MM = np.zeros((m, n))
-    _PP = np.zeros((m, m, n))
-    '''In this demonstration we estimate a stationary sine signal from noisy
-    measurements by using the classical Kalman filter.'
-    '''
-    filt = Kalman(R=R, x=M, P=P, A=A, Q=Q, H=H, B=0)
-
-    # Generate random voltages and watch the filter operate.
-    # n = 50
-    # truth = np.random.randn(n) * np.sqrt(q) + V0
-    # z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
-    truth = X
-    z = Y
-    x = np.zeros((n, m))
-
-    for i, zi in enumerate(z):
-        x[i] = np.ravel(filt(zi, u=0))
-
-    _hz = plt.plot(z, 'r.', label='observations')
-    # a-posteriori state estimates:
-    _hx = plt.plot(x[:, 0], 'b-', label='Kalman output')
-    _ht = plt.plot(truth, 'g-', label='true voltage')
-    plt.legend()
-    plt.title('Automobile Voltimeter Example')
-    plt.show('hold')
-
-#     for k in range(m):
-#         [M,P] = kf_predict(M,P,A,Q);
-#         [M,P] = kf_update(M,P,Y(k),H,R);
-#
-#         MM(:,k) = M;
-#         PP(:,:,k) = P;
-#
-#       %
-#       % Animate
-#       %
-#       if rem(k,10)==1
-#         plot(T,X,'b--',...
-#              T,Y,'ro',...
-#              T(k),M(1),'k*',...
-#              T(1:k),MM(1,1:k),'k-');
-#         legend('Real signal','Measurements','Latest estimate',
-#                'Filtered estimate')
-#         title('Estimating a noisy sine signal with Kalman filter.');
-#         drawnow;
-#
-#         pause;
-#       end
-#     end
-#
-#     clc;
-#     disp('In this demonstration we estimate a stationary sine signal '
-#        'from noisy measurements by using the classical Kalman filter.');
-#     disp(' ');
-#     disp('The filtering results are now displayed sequantially for 10 time '
-#            'step at a time.');
-#     disp(' ');
-#     disp('<push any key to see the filtered and smoothed results together>')
-#     pause;
-#     %
-#     % Apply Kalman smoother
-#     %
-#     SM = rts_smooth(MM,PP,A,Q);
-#     plot(T,X,'b--',...
-#          T,MM(1,:),'k-',...
-#          T,SM(1,:),'r-');
-#     legend('Real signal','Filtered estimate','Smoothed estimate')
-#     title('Filtered and smoothed estimate of the original signal');
-#
-#     clc;
-#     disp('The filtered and smoothed estimates of the signal are now '
-#        'displayed.')
-#     disp(' ');
-#     disp('RMS errors:');
-#     %
-#     % Errors
-#     %
-#     fprintf('KF = %.3f\nRTS = %.3f\n',...
-#             sqrt(mean((MM(1,:)-X(1,:)).^2)),...
-#             sqrt(mean((SM(1,:)-X(1,:)).^2)));
-
-
 class HampelFilter(object):
     """Hampel Filter.
 
@@ -1322,10 +1051,8 @@ class HampelFilter(object):
 
     @staticmethod
     def _check(dx):
-        if not np.isscalar(dx):
+        _assert(np.isscalar(dx), 'DX must be a scalar.')
-            raise ValueError('DX must be a scalar.')
+        _assert(0 < dx, 'DX must be larger than zero.')
-        if dx < 0:
-            raise ValueError('DX must be larger than zero.')
 
     @staticmethod
     def localwindow(X, Y, DX, i):
@@ -1421,154 +1148,6 @@ class HampelFilter(object):
         return YY
 
 
-def demo_hampel():
-    randint = np.random.randint
-    Y = 5000 + np.random.randn(1000)
-    outliers = randint(0, 1000, size=(10,))
-    Y[outliers] = Y[outliers] + randint(1000, size=(10,))
-    YY, res = HampelFilter(dx=3, t=3, fulloutput=True)(Y)
-    YY1, res1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=True)(Y)
-    YY2, res2 = HampelFilter(dx=3, t=0, fulloutput=True)(Y)  # median
-    plt.figure(1)
-    plot_hampel(Y, YY, res)
-    plt.title('Standard HampelFilter')
-    plt.figure(2)
-    plot_hampel(Y, YY1, res1)
-    plt.title('Adaptive HampelFilter')
-    plt.figure(3)
-    plot_hampel(Y, YY2, res2)
-    plt.title('Median filter')
-    plt.show('hold')
-
-
-def plot_hampel(Y, YY, res):
-    X = np.arange(len(YY))
-    plt.plot(X, Y, 'b.')  # Original Data
-    plt.plot(X, YY, 'r')  # Hampel Filtered Data
-    plt.plot(X, res['Y0'], 'b--')  # Nominal Data
-    plt.plot(X, res['LB'], 'r--')  # Lower Bounds on Hampel Filter
-    plt.plot(X, res['UB'], 'r--')  # Upper Bounds on Hampel Filter
-    i = res['outliers']
-    plt.plot(X[i], Y[i], 'ks')  # Identified Outliers
-    # plt.show('hold')
-
-
-def test_tide_filter():
-    # import statsmodels.api as sa
-    import wafo.spectrum.models as sm
-    sd = 10
-    Sj = sm.Jonswap(Hm0=4.*sd)
-    S = Sj.tospecdata()
-
-    q = (0.1 * sd) ** 2   # variance of process noise s the car operates
-    r = (100 * sd) ** 2  # variance of measurement error
-    b = 0  # no system input
-    u = 0  # no system input
-
-    from scipy.signal import butter, filtfilt, lfilter_zi  # lfilter,
-    freq_tide = 1. / (12 * 60 * 60)
-    freq_wave = 1. / 10
-    freq_filt = freq_wave / 10
-    dt = 1.
-    freq = 1. / dt
-    fn = (freq / 2)
-
-    P = 10 * np.diag([1, 0.01])
-    R = r
-    H = np.atleast_2d([1, 0])
-
-    F = np.atleast_2d([[0, 1],
-                       [0, 0]])
-    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
-
-    t = np.arange(0, 60 * 12, 1. / freq)
-    w = 2 * np.pi * freq  # 1 Hz
-    tide = 100 * np.sin(freq_tide * w * t + 2 * np.pi / 4) + 100
-    y = tide + S.sim(len(t), dt=1. / freq)[:, 1].ravel()
-#     lowess = sa.nonparametric.lowess
-#     y2 = lowess(y, t, frac=0.5)[:,1]
-
-    filt = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
-    filt2 = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
-    # y = tide + 0.5 * np.sin(freq_wave * w * t)
-    # Butterworth filter
-    b, a = butter(9, (freq_filt / fn), btype='low')
-    # y2 = [lowess(y[max(i-60,0):i + 1], t[max(i-60,0):i + 1], frac=.3)[-1,1]
-    #    for i in range(len(y))]
-    # y2 = [lfilter(b, a, y[:i + 1])[i] for i in range(len(y))]
-    # y3 = filtfilt(b, a, y[:16]).tolist() + [filtfilt(b, a, y[:i + 1])[i]
-    #    for i in range(16, len(y))]
-    # y0 = medfilt(y, 41)
-    _zi = lfilter_zi(b, a)
-    # y2 = lfilter(b, a, y)#, zi=y[0]*zi)  # standard filter
-    y3 = filtfilt(b, a, y)  # filter with phase shift correction
-    y4 = []
-    y5 = []
-    for _i, j in enumerate(y):
-        tmp = filt(j, u=u).ravel()
-        tmp = filt2(tmp[0], u=u).ravel()
-#         if i==0:
-#             print(filt.x)
-#             print(filt2.x)
-        y4.append(tmp[0])
-        y5.append(tmp[1])
-    _y0 = medfilt(y4, 41)
-    print(filt.P)
-    # plot
-
-    plt.plot(t, y, 'r.-', linewidth=2, label='raw data')
-    # plt.plot(t, y2, 'b.-', linewidth=2, label='lowess @ %g Hz' % freq_filt)
-    # plt.plot(t, y2, 'b.-', linewidth=2, label='filter @ %g Hz' % freq_filt)
-    plt.plot(t, y3, 'g.-', linewidth=2, label='filtfilt @ %g Hz' % freq_filt)
-    plt.plot(t, y4, 'k.-', linewidth=2, label='kalman')
-    # plt.plot(t, y5, 'k.', linewidth=2, label='kalman2')
-    plt.plot(t, tide, 'y-', linewidth=2, label='True tide')
-    plt.legend(frameon=False, fontsize=14)
-    plt.xlabel("Time [s]")
-    plt.ylabel("Amplitude")
-    plt.show('hold')
-
-
-def test_smooth():
-    t = np.linspace(-4, 4, 500)
-    y = np.exp(-t ** 2) + np.random.normal(0, 0.05, t.shape)
-    n = 11
-    ysg = SavitzkyGolay(n, degree=1, diff_order=0)(y)
-
-    plt.plot(t, y, t, ysg, '--')
-    plt.show('hold')
-
-
-def test_hodrick_cardioid():
-    t = np.linspace(0, 2 * np.pi, 1000)
-    cos = np.cos
-    sin = np.sin
-    randn = np.random.randn
-    x0 = 2 * cos(t) * (1 - cos(t))
-    x = x0 + randn(t.size) * 0.1
-    y0 = 2 * sin(t) * (1 - cos(t))
-    y = y0 + randn(t.size) * 0.1
-    smooth = HodrickPrescott(w=20000)
-    # smooth = HampelFilter(adaptive=50)
-    z = smooth(x) + 1j * smooth(y)
-    plt.plot(x0, y0, 'y',
-             x, y, 'r.',
-             z.real, z.imag, 'k', linewidth=2)
-    plt.show('hold')
-
-
-def test_docstrings():
-    import doctest
-    print('Testing docstrings in %s' % __file__)
-    doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
-
 if __name__ == '__main__':
-    test_docstrings()
+    from wafo.testing import test_docstrings
-    # test_kalman_sine()
+    test_docstrings(__file__)
-    # test_tide_filter()
-    # demo_hampel()
-    # test_kalman()
-    # test_smooth()
-    # test_hodrick_cardioid()
-    # test_smoothn_1d()
-    # test_smoothn_cardioid()