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Small bugfix

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master
per.andreas.brodtkorb 13 years ago
parent 485ecfcd2f
commit a664f15e78
2 changed files with 80 additions and 61 deletions
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132
pywafo/src/wafo/kdetools.py
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@ -16,7 +16,7 @@ from numpy import pi, sqrt, atleast_2d, exp, newaxis #@UnresolvedImport
from scipy import interpolate, linalg, sparse from scipy import interpolate, linalg, sparse
from scipy.special import gamma from scipy.special import gamma
import scipy.optimize as optimize import scipy.optimize as optimize
from wafo.misc import meshgrid from wafo.misc import meshgrid, nextpow2
from wafo.wafodata import WafoData from wafo.wafodata import WafoData
from dctpack import dct, dctn, idctn from dctpack import dct, dctn, idctn
@ -25,7 +25,7 @@ import copy
import numpy as np import numpy as np
import scipy import scipy
import warnings import warnings
import pylab import matplotlib.pyplot as plt
_stats_epan = (1. / 5, 3. / 5, np.inf) _stats_epan = (1. / 5, 3. / 5, np.inf)
_stats_biwe = (1. / 7, 5. / 7, 45. / 2) _stats_biwe = (1. / 7, 5. / 7, 45. / 2)
@ -95,7 +95,7 @@ class KDEgauss(object):
same as kde.eval_grid_fast(x0, x1,..., xd) same as kde.eval_grid_fast(x0, x1,..., xd)
""" """
def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128): def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=512):
self.dataset = atleast_2d(data) self.dataset = atleast_2d(data)
self.hs = hs self.hs = hs
self.kernel = kernel if kernel else Kernel('gauss') self.kernel = kernel if kernel else Kernel('gauss')
@ -315,7 +315,7 @@ class _KDE(object):
same as kde.eval_grid(x0, x1,..., xd) same as kde.eval_grid(x0, x1,..., xd)
""" """
def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128): def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=512):
self.dataset = atleast_2d(data) self.dataset = atleast_2d(data)
self.hs = hs self.hs = hs
self.kernel = kernel if kernel else Kernel('gauss') self.kernel = kernel if kernel else Kernel('gauss')
@ -337,10 +337,10 @@ class _KDE(object):
amin = self.dataset.min(axis= -1) amin = self.dataset.min(axis= -1)
amax = self.dataset.max(axis= -1) amax = self.dataset.max(axis= -1)
iqr = iqrange(self.dataset, axis= -1) iqr = iqrange(self.dataset, axis= -1)
sigma = np.minimum(np.std(self.dataset, axis= -1, ddof=1), iqr / 1.34) self._sigma = np.minimum(np.std(self.dataset, axis= -1, ddof=1), iqr / 1.34)
#xyzrange = amax - amin #xyzrange = amax - amin
#offset = xyzrange / 4.0 #offset = xyzrange / 4.0
offset = 2 * sigma offset = 2 * self._sigma
if self.xmin is None: if self.xmin is None:
self.xmin = amin - offset self.xmin = amin - offset
else: else:
@ -349,6 +349,8 @@ class _KDE(object):
self.xmax = amax + offset self.xmax = amax + offset
else: else:
self.xmax = self.xmax * np.ones((self.d,1)) self.xmax = self.xmax * np.ones((self.d,1))
def eval_grid_fast(self, *args, **kwds): def eval_grid_fast(self, *args, **kwds):
"""Evaluate the estimated pdf on a grid. """Evaluate the estimated pdf on a grid.
@ -492,7 +494,7 @@ class TKDE(_KDE):
If a single value of xmin or xmax is given then the boundary is the is If a single value of xmin or xmax is given then the boundary is the is
the same for all dimensions. the same for all dimensions.
inc : scalar integer inc : scalar integer
defining the default dimension of the output from kde.eval_grid methods (default 128) defining the default dimension of the output from kde.eval_grid methods (default 512)
(For kde.eval_grid_fast: A value below 50 is very fast to compute but (For kde.eval_grid_fast: A value below 50 is very fast to compute but
may give some inaccuracies. Values between 100 and 500 give very may give some inaccuracies. Values between 100 and 500 give very
accurate results) accurate results)
@ -552,7 +554,7 @@ class TKDE(_KDE):
""" """
def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None,
xmax=None, inc=128, L2=None): xmax=None, inc=512, L2=None):
self.L2 = L2 self.L2 = L2
super(TKDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc) super(TKDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc)
@ -567,6 +569,8 @@ class TKDE(_KDE):
xmax = self._dat2gaus(np.reshape(xmax,(-1,1))) xmax = self._dat2gaus(np.reshape(xmax,(-1,1)))
self.tkde = KDE(tdataset, self.hs, self.kernel, self.alpha, xmin, xmax, self.tkde = KDE(tdataset, self.hs, self.kernel, self.alpha, xmin, xmax,
self.inc) self.inc)
if self.inc is None:
self.inc = self.tkde.inc
def _check_xmin(self): def _check_xmin(self):
if self.L2 is not None: if self.L2 is not None:
amin = self.dataset.min(axis= -1) amin = self.dataset.min(axis= -1)
@ -713,7 +717,7 @@ class KDE(_KDE):
If a single value of xmin or xmax is given then the boundary is the is If a single value of xmin or xmax is given then the boundary is the is
the same for all dimensions. the same for all dimensions.
inc : scalar integer inc : scalar integer
defining the default dimension of the output from kde.eval_grid methods (default 128) defining the default dimension of the output from kde.eval_grid methods (default 512)
(For kde.eval_grid_fast: A value below 50 is very fast to compute but (For kde.eval_grid_fast: A value below 50 is very fast to compute but
may give some inaccuracies. Values between 100 and 500 give very may give some inaccuracies. Values between 100 and 500 give very
accurate results) accurate results)
@ -786,7 +790,7 @@ class KDE(_KDE):
t = np.trapz(f, x) t = np.trapz(f, x)
""" """
def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128): def __init__(self, data, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=512):
super(KDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc) super(KDE, self).__init__(data, hs, kernel, alpha, xmin, xmax, inc)
def _initialize(self): def _initialize(self):
@ -799,6 +803,12 @@ class KDE(_KDE):
g = np.exp(np.mean(np.log(f))) g = np.exp(np.mean(np.log(f)))
self._lambda = (f / g) ** (-self.alpha) self._lambda = (f / g) ** (-self.alpha)
if self.inc is None:
unused_tau, tau = self.kernel.effective_support()
xyzrange = 8 * self._sigma
L1 = 10
self.inc = 2 ** nextpow2(max(48,(L1 * xyzrange/ (tau * self.hs) ).max()))
pass
def _compute_smoothing(self): def _compute_smoothing(self):
"""Computes the smoothing matrix """Computes the smoothing matrix
""" """
@ -851,9 +861,16 @@ class KDE(_KDE):
Xn = np.dot(self.inv_hs, np.vstack(Xnc)) Xn = np.dot(self.inv_hs, np.vstack(Xnc))
# Obtain the kernel weights. # Obtain the kernel weights.
kw = self.kernel(Xn) kw = self.kernel(Xn)
norm_fact = (kw.sum()*dx.prod()*self.n)
norm_fact2 = (self._norm_factor * self.kernel.norm_factor(d, self.n)) #plt.plot(kw)
#plt.draw()
#plt.show()
norm_fact0 = (kw.sum()*dx.prod()*self.n)
norm_fact = (self._norm_factor * self.kernel.norm_factor(d, self.n))
if np.abs(norm_fact0-norm_fact)>0.05*norm_fact:
warnings.warn('Numerical inaccuracy due to too low discretization. Increase the discretization (inc=%d)!' % self.inc)
norm_fact = norm_fact0
kw = kw/norm_fact kw = kw/norm_fact
r = kwds.get('r', 0) r = kwds.get('r', 0)
@ -1668,9 +1685,9 @@ class Kernel(object):
else: else:
ai = bi ai = bi
#y = np.asarray([fun(j) for j in x]) #y = np.asarray([fun(j) for j in x])
#pylab.figure(1) #plt.figure(1)
#pylab.plot(x,y) #plt.plot(x,y)
#pylab.show() #plt.show()
# use fzero to solve the equation t=zeta*gamma^[5](t) # use fzero to solve the equation t=zeta*gamma^[5](t)
try: try:
@ -2774,20 +2791,20 @@ def kde_demo1():
hVec = [hs / 2, hs, 2 * hs] hVec = [hs / 2, hs, 2 * hs]
for ix, h in enumerate(hVec): for ix, h in enumerate(hVec):
pylab.figure(ix) plt.figure(ix)
kde = KDE(data, hs=h, kernel=kernel) kde = KDE(data, hs=h, kernel=kernel)
f2 = kde(x, output='plot', title='h_s = %2.2f' % h, ylab='Density') f2 = kde(x, output='plot', title='h_s = %2.2f' % h, ylab='Density')
f2.plot('k-') f2.plot('k-')
pylab.plot(x, st.norm.pdf(x, 0, 1), 'k:') plt.plot(x, st.norm.pdf(x, 0, 1), 'k:')
n = len(data) n = len(data)
pylab.plot(data, np.zeros(data.shape), 'bx') plt.plot(data, np.zeros(data.shape), 'bx')
y = kernel(x0) / (n * h * kernel.norm_factor(d=1, n=n)) y = kernel(x0) / (n * h * kernel.norm_factor(d=1, n=n))
for i in range(n): for i in range(n):
pylab.plot(data[i] + x0 * h, y, 'b--') plt.plot(data[i] + x0 * h, y, 'b--')
pylab.plot([data[i], data[i]], [0, np.max(y)], 'b') plt.plot([data[i], data[i]], [0, np.max(y)], 'b')
pylab.axis([x.min(), x.max(), 0, 0.5]) plt.axis([x.min(), x.max(), 0, 0.5])
def kde_demo2(): def kde_demo2():
'''Demonstrate the difference between transformation- and ordinary-KDE in 1D '''Demonstrate the difference between transformation- and ordinary-KDE in 1D
@ -2802,21 +2819,21 @@ def kde_demo2():
kde = KDE(data) kde = KDE(data)
f = kde(output='plot', title='Ordinary KDE (hs=%g)' % kde.hs) f = kde(output='plot', title='Ordinary KDE (hs=%g)' % kde.hs)
pylab.figure(0) plt.figure(0)
f.plot() f.plot()
pylab.plot(x, st.rayleigh.pdf(x, scale=1), ':') plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
#plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable #plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable
tkde = TKDE(data, L2=0.5) tkde = TKDE(data, L2=0.5)
ft = tkde(x, output='plot', title='Transformation KDE (hs=%g)' % tkde.tkde.hs) ft = tkde(x, output='plot', title='Transformation KDE (hs=%g)' % tkde.tkde.hs)
pylab.figure(1) plt.figure(1)
ft.plot() ft.plot()
pylab.plot(x, st.rayleigh.pdf(x, scale=1), ':') plt.plot(x, st.rayleigh.pdf(x, scale=1), ':')
pylab.figure(0) plt.figure(0)
def kde_demo3(): def kde_demo3():
'''Demonstrate the difference between transformation and ordinary-KDE in 2D '''Demonstrate the difference between transformation and ordinary-KDE in 2D
@ -2831,10 +2848,10 @@ def kde_demo3():
kde = KDE(data) kde = KDE(data)
f = kde(output='plot', title='Ordinary KDE', plotflag=1) f = kde(output='plot', title='Ordinary KDE', plotflag=1)
pylab.figure(0) plt.figure(0)
f.plot() f.plot()
pylab.plot(data[0], data[1], '.') plt.plot(data[0], data[1], '.')
#plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable #plotnorm((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable
@ -2842,12 +2859,12 @@ def kde_demo3():
ft = tkde.eval_grid_fast(output='plot', title='Transformation KDE', plotflag=1) ft = tkde.eval_grid_fast(output='plot', title='Transformation KDE', plotflag=1)
pylab.figure(1) plt.figure(1)
ft.plot() ft.plot()
pylab.plot(data[0],data[1], '.') plt.plot(data[0],data[1], '.')
pylab.figure(0) plt.figure(0)
@ -2873,14 +2890,14 @@ def kde_demo4(N=50):
kde1 = KDE(data, kernel=Kernel('gauss', 'hisj')) kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
f1 = kde1(output='plot', label='Ordinary KDE', plotflag=1) f1 = kde1(output='plot', label='Ordinary KDE', plotflag=1)
pylab.figure(0) plt.figure(0)
f.plot('r', label='hns=%g' % kde.hs) f.plot('r', label='hns=%g' % kde.hs)
#pylab.figure(2) #plt.figure(2)
f1.plot('b', label='hisj=%g' % kde1.hs) f1.plot('b', label='hisj=%g' % kde1.hs)
x = np.linspace(-4,4) x = np.linspace(-4,4)
for loc in [-5,5]: for loc in [-5,5]:
pylab.plot(x + loc, st.norm.pdf(x, 0, scale=1)/2, 'k:', label='True density') plt.plot(x + loc, st.norm.pdf(x, 0, scale=1)/2, 'k:', label='True density')
pylab.legend() plt.legend()
def kde_demo5(N=500): def kde_demo5(N=500):
'''Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior '''Demonstrate that the improved Sheather-Jones plug-in (hisj) is superior
@ -2899,14 +2916,14 @@ def kde_demo5(N=500):
kde1 = KDE(data, kernel=Kernel('gauss', 'hisj')) kde1 = KDE(data, kernel=Kernel('gauss', 'hisj'))
f1 = kde1(output='plot', title='Ordinary KDE (hisj=%g %g)' % tuple(kde1.hs.tolist()), plotflag=1) f1 = kde1(output='plot', title='Ordinary KDE (hisj=%g %g)' % tuple(kde1.hs.tolist()), plotflag=1)
pylab.figure(0) plt.figure(0)
pylab.clf() plt.clf()
f.plot() f.plot()
pylab.plot(data[0], data[1], '.') plt.plot(data[0], data[1], '.')
pylab.figure(1) plt.figure(1)
pylab.clf() plt.clf()
f1.plot() f1.plot()
pylab.plot(data[0], data[1], '.') plt.plot(data[0], data[1], '.')
def kreg_demo1(hs=None, fast=False, fun='hisj'): def kreg_demo1(hs=None, fast=False, fun='hisj'):
''' '''
@ -2945,22 +2962,22 @@ def kreg_demo1(hs=None, fast=False, fun='hisj'):
kreg.__call__ = kreg.eval_grid_fast kreg.__call__ = kreg.eval_grid_fast
f = kreg(output='plot', title='Kernel regression', plotflag=1) f = kreg(output='plot', title='Kernel regression', plotflag=1)
pylab.figure(0) plt.figure(0)
f.plot(label='p=0') f.plot(label='p=0')
kreg.p=1 kreg.p=1
f1 = kreg(output='plot', title='Kernel regression', plotflag=1) f1 = kreg(output='plot', title='Kernel regression', plotflag=1)
f1.plot(label='p=1') f1.plot(label='p=1')
pylab.plot(x,y,'.', x,y0, 'k') plt.plot(x,y,'.', x,y0, 'k')
pylab.legend() plt.legend()
pylab.show() plt.show()
print(kreg.tkde.tkde.inv_hs) print(kreg.tkde.tkde.inv_hs)
print(kreg.tkde.tkde.hs) print(kreg.tkde.tkde.hs)
def kde_gauss_demo(n=50000): def kde_gauss_demo(n=50):
''' '''
KDEDEMO Demonstrate the KDEgauss KDEDEMO Demonstrate the KDEgauss
@ -2976,7 +2993,7 @@ def kde_gauss_demo(n=50000):
# n1 = 128 # n1 = 128
# I = (np.arange(n1)*pi)**2 *0.01*0.5 # I = (np.arange(n1)*pi)**2 *0.01*0.5
# kw = exp(-I) # kw = exp(-I)
# pylab.plot(idctn(kw)) # plt.plot(idctn(kw))
# return # return
dist = st.norm dist = st.norm
dist = st.expon dist = st.expon
@ -2988,12 +3005,12 @@ def kde_gauss_demo(n=50000):
else: else:
plot_options = [dict(colors='red'), dict(colors='green'), dict(colors='black')] plot_options = [dict(colors='red'), dict(colors='green'), dict(colors='black')]
pylab.figure(1) plt.figure(1)
kde0 = KDE(data, kernel=Kernel('gauss', 'hisj')) kde0 = KDE(data, kernel=Kernel('gauss', 'hste'))
f0 = kde0.eval_grid_fast(output='plot', ylab='Density') f0 = kde0.eval_grid_fast(output='plot', ylab='Density')
f0.plot(**plot_options[0]) f0.plot(**plot_options[0])
kde1 = TKDE(data, kernel=Kernel('gauss', 'hisj'), L2=0) kde1 = TKDE(data, kernel=Kernel('gauss', 'hisj'), L2=.5)
f1 = kde1.eval_grid_fast(output='plot', ylab='Density') f1 = kde1.eval_grid_fast(output='plot', ylab='Density')
f1.plot(**plot_options[1]) f1.plot(**plot_options[1])
@ -3004,19 +3021,20 @@ def kde_gauss_demo(n=50000):
fmax = dist.pdf(x, 0, 1).max() fmax = dist.pdf(x, 0, 1).max()
if d==1: if d==1:
pylab.plot(x, dist.pdf(x, 0, 1), 'k:') plt.plot(x, dist.pdf(x, 0, 1), 'k:')
pylab.axis([x.min(), x.max(), 0, fmax]) plt.axis([x.min(), x.max(), 0, fmax])
pylab.show() plt.show()
print(fmax/f2.data.max()) print(fmax/f2.data.max())
format_ = ''.join(('%g, ')*d) format_ = ''.join(('%g, ')*d)
format_ = 'hs0=%s hs2=%s' % (format_,format_) format_ = 'hs0=%s hs1=%s hs2=%s' % (format_, format_, format_)
print(format_ % tuple(kde0.hs.tolist()+kde2.hs.tolist())) print(format_ % tuple(kde0.hs.tolist()+kde1.tkde.hs.tolist()+kde2.hs.tolist()))
print('inc0 = %d, inc1 = %d, inc2 = %d' % (kde0.inc, kde1.inc,kde2.inc))
def test_docstrings(): def test_docstrings():
import doctest import doctest
doctest.testmod() doctest.testmod()
if __name__ == '__main__': if __name__ == '__main__':
plt.ioff()
#test_docstrings() #test_docstrings()
#kde_demo2() #kde_demo2()
#kreg_demo1(fast=True) #kreg_demo1(fast=True)

9
pywafo/src/wafo/test/test_kdetools.py
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@ -172,9 +172,10 @@ def test_KDE2D():
[ 6.78845466e-02, 1.42195839e-01, 1.41676003e-03], [ 6.78845466e-02, 1.42195839e-01, 1.41676003e-03],
[ 1.39466746e-04, 4.26983850e-03, 2.52736185e-05]]) [ 1.39466746e-04, 4.26983850e-03, 2.52736185e-05]])
>>> kde0.eval_grid_fast(x, x) >>> kde0.eval_grid_fast(x, x)
array([[ 0.08670654, 0.12577712, 0.00808478], array([[ 0.04435061, 0.06433531, 0.00413538],
[ 0.1411195 , 0.24160579, 0.01816001], [ 0.07218297, 0.12358196, 0.00928889],
[ 0.0031541 , 0.01553967, 0.00114854]]) [ 0.00161333, 0.00794858, 0.00058748]])
''' '''
def test_smooth_params(): def test_smooth_params():
@ -215,7 +216,7 @@ def test_smooth_params():
>>> gauss.hisj(data) >>> gauss.hisj(data)
array([ 0.29400043, 0.74277133, 0.51251583]) array([ 0.24222479, 0.74277133, 0.15492661])
>>> data = np.array([0.753557920000000, 0.727791940000000, 0.941491690000000, >>> data = np.array([0.753557920000000, 0.727791940000000, 0.941491690000000,
... 0.078411190000000, 2.322918870000000, 1.104199950000000, 0.770551140000000, ... 0.078411190000000, 2.322918870000000, 1.104199950000000, 0.770551140000000,

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