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@ -34,7 +34,7 @@ except ImportError:
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warnings.warn('fig import only supported on Windows')
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warnings.warn('fig import only supported on Windows')
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__all__ = ['TKDE', 'KDE', 'kde_demo1', 'kde_demo2', 'test_docstrings',
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__all__ = ['TKDE', 'KDE', 'kde_demo1', 'kde_demo2', 'test_docstrings',
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'KRegression', 'KDEgauss']
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'KRegression', 'BKRegression']
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def _assert(cond, msg):
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def _assert(cond, msg):
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@ -439,6 +439,13 @@ class TKDE(_KDE):
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self.L2 = L2
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self.L2 = L2
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super(TKDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc)
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super(TKDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc)
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# @property
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# def dataset(self):
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# return self._dataset
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#
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# @dataset.setter
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# def dataset(self, data):
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def _initialize(self):
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def _initialize(self):
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self._check_xmin()
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self._check_xmin()
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tdataset = self._dat2gaus(self.dataset)
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tdataset = self._dat2gaus(self.dataset)
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@ -761,7 +768,7 @@ class KDE(_KDE):
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def _eval_grid(self, *args, **kwds):
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def _eval_grid(self, *args, **kwds):
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grd = meshgrid(*args) if len(args) > 1 else list(args)
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grd = meshgrid(*args)
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shape0 = grd[0].shape
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shape0 = grd[0].shape
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d = len(grd)
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d = len(grd)
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for i in range(d):
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for i in range(d):
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@ -838,82 +845,7 @@ class KDE(_KDE):
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return self._loop_over_points(self.dataset, points, y, r)
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return self._loop_over_points(self.dataset, points, y, r)
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class KDEgauss(KDE):
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class KRegression(object): # _KDE):
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""" Kernel-Density Estimator base class.
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data : (# of dims, # of data)-array
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datapoints to estimate from
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hs : array-like (optional)
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smooting parameter vector/matrix.
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(default compute from data using kernel.get_smoothing function)
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kernel : kernel function object.
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kernel must have get_smoothing method
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alpha : real scalar (optional)
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sensitivity parameter (default 0 regular KDE)
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A good choice might be alpha = 0.5 ( or 1/D)
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alpha = 0 Regular KDE (hs is constant)
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0 < alpha <= 1 Adaptive KDE (Make hs change)
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xmin, xmax : vectors
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specifying the default argument range for the kde.eval_grid methods.
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For the kde.eval_grid_fast methods the values must cover the range of
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the data.
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(default min(data)-range(data)/4, max(data)-range(data)/4)
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If a single value of xmin or xmax is given, then the boundary is the
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the same for all dimensions.
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inc : scalar integer (default 512)
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defining the default dimension of the output from kde.eval_grid methods
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(For kde.eval_grid_fast: A value below 50 is very fast to compute but
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may give some inaccuracies. Values between 100 and 500 give very
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accurate results)
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Members
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-------
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d : int
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number of dimensions
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n : int
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number of datapoints
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Methods
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-------
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kde.eval_grid_fast(x0, x1,..., xd) : array
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evaluate the estimated pdf on meshgrid(x0, x1,..., xd)
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kde(x0, x1,..., xd) : array
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same as kde.eval_grid_fast(x0, x1,..., xd)
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"""
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def _eval_grid_fast(self, *args, **kwds):
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X = np.vstack(args)
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d, inc = X.shape
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# dx = X[:, 1] - X[:, 0]
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R = X.max(axis=-1) - X.min(axis=-1)
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t_star = (self.hs / R) ** 2
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I = (np.asfarray(np.arange(0, inc)) * pi) ** 2
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In = []
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for i in range(d):
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In.append(I * t_star[i] * 0.5)
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r = kwds.get('r', 0)
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fun = self._moment_fun(r)
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Inc = meshgrid(*In) if d > 1 else In
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kw = np.zeros((inc,) * d)
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for i in range(d):
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kw += exp(-Inc[i]) * fun(Inc[i])
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y = kwds.get('y', 1.0)
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d, n = self.dataset.shape
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# Find the binned kernel weights, c.
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c = gridcount(self.dataset, X, y=y)
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# Perform the convolution.
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at = dctn(c) * kw / n
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z = idctn(at) * (at.size-1) / np.prod(R)
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return z * (z > 0.0)
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__call__ = _KDE.eval_grid_fast
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class KRegression(_KDE):
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""" Kernel-Regression
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""" Kernel-Regression
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@ -1325,17 +1257,17 @@ def kde_demo2():
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x = np.linspace(1.5e-2, 5, 55)
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x = np.linspace(1.5e-2, 5, 55)
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kde = KDE(data)
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kde = KDE(data)
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f = kde(output='plot', title='Ordinary KDE (hs={0:g})'.format(kde.hs))
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f = kde(output='plot', title='Ordinary KDE (hs={0:})'.format(kde.hs))
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plt.figure(0)
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plt.figure(0)
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f.plot()
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f.plot()
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plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
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plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
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# plotnorm((data).^(L2)) # gives a straight line => L2 = 0.5 reasonable
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# plotnorm((data).^(L2)) # gives a straight line => L2 = 0.5 reasonable
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hs = Kernel('gauss').get_smoothing(data**0.5)
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tkde = TKDE(data, L2=0.5)
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tkde = TKDE(data, hs=hs, L2=0.5)
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ft = tkde(x, output='plot',
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ft = tkde(x, output='plot',
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title='Transformation KDE (hs={0:g})'.format(tkde.tkde.hs))
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title='Transformation KDE (hs={0:})'.format(tkde.tkde.hs))
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plt.figure(1)
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plt.figure(1)
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ft.plot()
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ft.plot()
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@ -1507,7 +1439,6 @@ def _logitinv(x):
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def _get_data(n=100, symmetric=False, loc1=1.1, scale1=0.6, scale2=1.0):
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def _get_data(n=100, symmetric=False, loc1=1.1, scale1=0.6, scale2=1.0):
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st = scipy.stats
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st = scipy.stats
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# from sg_filter import SavitzkyGolay
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dist = st.norm
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dist = st.norm
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norm1 = scale2 * (dist.pdf(-loc1, loc=-loc1, scale=scale1) +
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norm1 = scale2 * (dist.pdf(-loc1, loc=-loc1, scale=scale1) +
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@ -1575,8 +1506,8 @@ def kreg_demo3(x, y, fun1, hs=None, fun='hisj', plotlog=False):
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df = np.diff(fiii)
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df = np.diff(fiii)
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eerr = np.abs((yiii - fiii)).std() + 0.5 * (df[:-1] * df[1:] < 0).sum() / n
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eerr = np.abs((yiii - fiii)).std() + 0.5 * (df[:-1] * df[1:] < 0).sum() / n
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err = (fiii - fit).std()
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err = (fiii - fit).std()
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msg = '{} err={1:1.3f},eerr={2:1.3f}, n={:d}, hs={:1.3f}, hs1={:1.3f}, '\
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msg = '{0} err={1:1.3f},eerr={2:1.3f}, n={3:d}, hs={4:}, hs1={5:}, '\
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'hs2={:1.3f}'
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'hs2={6:}'
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title = (msg.format(fun, err, eerr, n, hs, hs1, hs2))
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title = (msg.format(fun, err, eerr, n, hs, hs1, hs2))
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f = kreg(xiii, output='plotobj', title=title, plotflag=1)
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f = kreg(xiii, output='plotobj', title=title, plotflag=1)
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@ -1684,8 +1615,8 @@ def kreg_demo3(x, y, fun1, hs=None, fun='hisj', plotlog=False):
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label='{:d} CI2'.format(int(100 * (1 - alpha))))
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label='{:d} CI2'.format(int(100 * (1 - alpha))))
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plt.plot(xiii, fun1(xiii), 'r', label='True model')
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plt.plot(xiii, fun1(xiii), 'r', label='True model')
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plt.scatter(xi, yi, label='data')
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plt.scatter(xi, yi, label='data')
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print('maxp = {:g}'.format(np.nanmax(f.data)))
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print('maxp = {}'.format(np.nanmax(f.data)))
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print('hs = {:g}'.format(kreg.tkde.tkde.hs))
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print('hs = {}'.format(kreg.tkde.tkde.hs))
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plt.legend()
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plt.legend()
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h = plt.gca()
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h = plt.gca()
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if plotlog:
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if plotlog:
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@ -1875,7 +1806,7 @@ def check_bkregression():
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fig.tile(range(0, k))
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fig.tile(range(0, k))
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plt.ioff()
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plt.ioff()
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plt.show()
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plt.show('hold')
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def _get_regression_smooting(x, y, fun='hste'):
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def _get_regression_smooting(x, y, fun='hste'):
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@ -1999,8 +1930,8 @@ def smoothed_bin_prb(x, y, hs, hopt, alpha=0.05, color='r', label='',
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f.aicc = aicc
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f.aicc = aicc
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f.fun = kreg
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f.fun = kreg
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f.labels.title = ('perr={:1.3f},aicc={:1.3f}, n={:d}, '
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ttl = "perr={0:1.3f}, aicc={1:1.3f}, n={2:d}, hs={3}"
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'hs={:1.3f}'.format(f.prediction_error_avg, aicc, n, hs))
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f.labels.title = ttl.format(f.prediction_error_avg, aicc, n, hs)
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return f
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return f
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@ -2033,114 +1964,17 @@ def regressionbin(x, y, alpha=0.05, color='r', label=''):
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return fbest
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return fbest
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def kde_gauss_demo(n=50):
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"""KDEDEMO Demonstrate the KDEgauss.
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KDEDEMO1 shows the true density (dotted) compared to KDE based on 7
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observations (solid) and their individual kernels (dashed) for 3
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different values of the smoothing parameter, hs.
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"""
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st = scipy.stats
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# x = np.linspace(-4, 4, 101)
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# data = np.random.normal(loc=0, scale=1.0, size=n)
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# data = np.random.exponential(scale=1.0, size=n)
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# n1 = 128
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# I = (np.arange(n1)*pi)**2 *0.01*0.5
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# kw = exp(-I)
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# plt.plot(idctn(kw))
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# return
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dist = st.norm
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# dist = st.expon
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data = dist.rvs(loc=0, scale=1.0, size=n)
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d, _N = np.atleast_2d(data).shape
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if d == 1:
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plot_options = [dict(color='red', label='KDE hste'),
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dict(color='green', label='TKDE hisj'),
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dict(color='black', label='KDEgauss hste')]
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else:
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plot_options = [dict(colors='red'), dict(colors='green'),
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dict(colors='black')]
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plt.figure(1)
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t0 = time.time()
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kde0 = KDE(data, kernel=Kernel('gauss', 'hste'))
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f0 = kde0.eval_grid_fast(output='plot', ylab='Density', r=0)
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t1 = time.time()
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total1 = t1-t0
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f0.plot('.', **plot_options[0])
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if dist.name != 'norm':
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kde1 = TKDE(data, kernel=Kernel('gauss', 'hisj'), L2=.5)
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f1 = kde1.eval_grid_fast(output='plot', ylab='Density', r=0)
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f1.plot(**plot_options[1])
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else:
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kde1 = kde0
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f1 = f0
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t1 = time.time()
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kde2 = KDEgauss(data)
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f2 = kde2(output='plot', ylab='Density', r=0)
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t2 = time.time()
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total2 = t2-t1
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x = f2.args
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f2.plot(**plot_options[2])
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fmax = dist.pdf(x, 0, 1).max()
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if d == 1:
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plt.plot(x, dist.pdf(x, 0, 1), 'k:', label='True pdf')
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plt.axis([x.min(), x.max(), 0, fmax])
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plt.legend()
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plt.show()
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print(fmax / f2.data.max())
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try:
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print('hs0={:s} hs1={:s} hs2={:s}'.format(str(kde0.hs.tolist()),
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str(kde1.tkde.hs.tolist()),
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str(kde2.hs.tolist())))
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except:
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pass
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print('inc0 = {:d}, inc1 = {:d}, inc2 = {:d}'.format(kde0.inc, kde1.inc,
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kde2.inc))
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print(np.trapz(f0.data, f0.args), np.trapz(f2.data, f2.args))
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print(total1, total2)
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def test_kde():
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data = np.array([
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0.75355792, 0.72779194, 0.94149169, 0.07841119, 2.32291887,
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1.10419995, 0.77055114, 0.60288273, 1.36883635, 1.74754326,
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1.09547561, 1.01671133, 0.73211143, 0.61891719, 0.75903487,
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1.8919469, 0.72433808, 1.92973094, 0.44749838, 1.36508452])
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x = np.linspace(0.01, max(data + 1), 10)
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kde = TKDE(data, hs=0.5, L2=0.5)
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_f = kde(x)
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# f = array([1.03982714, 0.45839018, 0.39514782, 0.32860602, 0.26433318,
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# 0.20717946, 0.15907684, 0.1201074 , 0.08941027, 0.06574882])
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_f1 = kde.eval_grid(x)
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# array([ 1.03982714, 0.45839018, 0.39514782, 0.32860602, 0.26433318,
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# 0.20717946, 0.15907684, 0.1201074 , 0.08941027, 0.06574882])
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_f2 = kde.eval_grid_fast(x)
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# array([ 1.06437223, 0.46203314, 0.39593137, 0.32781899, 0.26276433,
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# 0.20532206, 0.15723498, 0.11843998, 0.08797755, 0. ])
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if __name__ == '__main__':
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if __name__ == '__main__':
|
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|
|
if True:
|
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|
if False:
|
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|
|
test_docstrings(__file__)
|
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|
|
test_docstrings(__file__)
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|
else:
|
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|
else:
|
|
|
|
# test_kde()
|
|
|
|
kde_demo2()
|
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|
|
# check_bkregression()
|
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|
|
# check_bkregression()
|
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|
|
# check_regression_bin()
|
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|
|
# check_regression_bin()
|
|
|
|
# check_kreg_demo3()
|
|
|
|
# check_kreg_demo3()
|
|
|
|
# check_kreg_demo4()
|
|
|
|
# check_kreg_demo4()
|
|
|
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|
|
# kde_demo2()
|
|
|
|
|
|
|
|
# kreg_demo1(fast=True)
|
|
|
|
# kreg_demo1(fast=True)
|
|
|
|
kde_gauss_demo(n=50)
|
|
|
|
|
|
|
|
# kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True)
|
|
|
|
# kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True)
|
|
|
|
plt.show('hold')
|
|
|
|
plt.show('hold')
|
|
|
|