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Per.Andreas.Brodtkorb 13 years ago
parent 25b47ebc04
commit 4c2b92f276
1 changed files with 80 additions and 51 deletions
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pywafo/src/wafo/kdetools.py
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@ -3077,7 +3077,7 @@ def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3, maxiter
errp = 0.1;
# Relaxation factor RF: to speedup convergence
RF = 1 + 0.75 if weight else 1.0
RF = 1 + 0.75 if weight is None else 1.0
norm = linalg.norm
# Main iterative process
@ -3476,7 +3476,7 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
from sg_filter import SavitzkyGolay
dist = st.norm
scale1 = 0.3
loc1= 0
loc1= 1
norm1 = dist.pdf(-loc1, loc=-loc1, scale=scale1) + dist.pdf(-loc1, loc=loc1, scale=scale1)
fun1 = lambda x : (dist.pdf(x, loc=-loc1, scale=scale1) + dist.pdf(x, loc=loc1, scale=scale1))/norm1
@ -3489,16 +3489,23 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
alpha=0.05
z0 = -_invnorm(alpha/2)
kernel = Kernel('gauss',fun=fun)
hopt = kernel.get_smoothing(x)
if hs is None:
hs = hopt
if symmetric:
xi = np.hstack((x.ravel(),-x.ravel()))
yi = np.hstack((y, y))
i = np.argsort(xi)
x = xi[i]
y = yi[i]
hisj = Kernel('gauss', fun='hisj').get_smoothing(x)
hste = Kernel('gauss', fun='hste').get_smoothing(x)
#kernel = Kernel('gauss',fun=fun)
hopt = (hste+hisj)/2 #kernel.get_smoothing(x)
if hs is None:
hs = hopt
forward = _logit
reverse = _logitinv
#forward = np.log
#reverse = np.exp
xmin, xmax = x.min(), x.max()
ni = 2*int((xmax-xmin)/hopt)+1
@ -3507,10 +3514,13 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
xi = np.linspace(xmin-hopt,xmax+hopt, ni)
xiii = np.linspace(xmin-hopt,xmax+hopt, 4*ni+1)
kreg = KRegression(x, y, hs=hs*0.5)
from wafo.interpolate import stineman_interp
fact = stineman_interp([x.size], [0, 2000], [0.25, 1.0], yp=[0.75/2000,0.75/2000]).clip(min=0.25,max=1.3)
print("fact=%g" % (fact))
kreg = KRegression(x, y, hs=hs*fact, p=0)
fi = kreg(xi)
f = kreg(xiii,output='plotobj', title='Kernel regression n=%d, %s=%g' % (n,fun,hs), plotflag=1)
f = kreg(xiii,output='plotobj', title='Kernel regression n=%d, hste=%g, hisj=%g' % (n,hste,hisj), plotflag=1)
c = gridcount(x, xi)
c0 = gridcount(x[y==True],xi)
@ -3518,45 +3528,38 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
yi = np.where(c==0, 0, c0/c)
#yi[yi==0] = 1.0/(c[c!=0].min()+4)#
#yi[yi==1] = 1-1.0/(c[c!=0].min()+4) #
yi[yi==0] = fi[yi==0] #yi[yi>0].min()/sqrt(n)
#yi[yi==0] = fi[yi==0]
#yi[yi==0] = np.exp(stineman_interp(xi[yi==0], xi[yi>0],np.log(yi[yi>0])))
#yi[yi==0] = fun1(xi[yi==0])
yi[yi==0] = yi[yi>0].min()/sqrt(n)
yi[yi==1] =1-(1-yi[yi<1].max())/sqrt(n)
logity =_logit(yi)
logity =forward(yi)
# plt.plot(xi, np.log(yi/(1-yi)), xi,logity,'.')
# plt.show()
# return
logity[logity==-40]=np.nan
slogity = smoothn(logity, robust=True)
slogity2 = SavitzkyGolay(n=2, degree=2).smooth(logity)
sa1 = sqrt(evar(logity))
sa = (slogity-logity).std()
print('estd = %g %g' % (sa,sa1))
plo3 = _logitinv(slogity-z0*sa)
pup3 = _logitinv(slogity+z0*sa)
syi = _logitinv(slogity)
syi2 = _logitinv(slogity2)
ymin = np.log(yi[yi>0].min())-1
logyi = np.log(yi).clip(min=ymin)
#plt.scatter(xi,logyi)
#return
# ymin = np.log(yi[yi>0].min())-1
# logyi = np.log(yi).clip(min=ymin)
# plt.scatter(xi,logyi)
# plt.show()
# return
#print(logyi)
gkreg = KRegression(xi, logity, hs=hs*0.4, xmin=xmin-2*hopt,xmax=xmax+2*hopt)
gkreg = KRegression(xi, logity, hs=hs*fact, xmin=xmin-hopt,xmax=xmax+hopt)
fg = gkreg.eval_grid(xi,output='plotobj', title='Kernel regression', plotflag=1)
sa = (fg.data-logity).std()
sa2 = iqrange(fg.data-logity) / 1.349
print('sa=%g %g' % (sa, sa2))
#print('sa=%g %g' % (sa, sa2))
sa = min(sa,sa2)
plt.figure(1)
plt.plot(xi, slogity-logity,'r.')
#plt.plot(xi, logity-,'b.')
plt.plot(xi, fg.data-logity, 'b.')
# plt.figure(1)
# plt.plot(xi, slogity-logity,'r.')
# #plt.plot(xi, logity-,'b.')
# plt.plot(xi, fg.data-logity, 'b.')
# plt.show()
# return
@ -3568,13 +3571,15 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
#ci = ckreg.eval_grid_fast(xi)*n*dx
ciii = ckreg.eval_grid_fast(xiii)*dx*n*(1+symmetric)
pi = _logitinv(fg.data)
pi = reverse(fg.data)
sa1 = np.sqrt(1./(ciii*pi*(1-pi)))
plo3 = _logitinv(fg.data-z0*sa)
pup3 = _logitinv(fg.data+z0*sa)
plo3 = reverse(fg.data-z0*sa)
pup3 = reverse(fg.data+z0*sa)
fg.data = pi
pi = f.data
#pi = f.data
@ -3584,36 +3589,56 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
b = 2*(1+z0**2/(ciii+1e-16))
plo2 = ((a-sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1)
pup2 = ((a+sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1)
pup = (pi + z0*np.sqrt(pi*(1-pi)/ciii)).clip(min=0,max=1)
plo = (pi - z0*np.sqrt(pi*(1-pi)/ciii)).clip(min=0,max=1)
den = 1+(z0**2./ciii);
xc=(pi+(z0**2)/(2*ciii))/den;
halfwidth=(z0*sqrt((pi*(1-pi)/ciii)+(z0**2/(4*(ciii**2)))))/den
plo = xc-halfwidth # wilson score
pup = xc+halfwidth # wilson score
# Jeffreys intervall a=b=0.5
#st.beta.isf(alpha/2, x+a, n-x+b)
ab = 0.05
pi1 = pi #fun1(xiii)
pup2 = np.where(pi==1, 1, st.beta.isf(alpha/2, ciii*pi1+ab, ciii*(1-pi1)+ab))
plo2 = np.where(pi==0, 0, st.beta.isf(1-alpha/2, ciii*pi1+ab, ciii*(1-pi1)+ab))
#pup = (pi + z0*np.sqrt(pi*(1-pi)/ciii)).clip(min=0,max=1)
#plo = (pi - z0*np.sqrt(pi*(1-pi)/ciii)).clip(min=0,max=1)
# Wilson score
den = 1+(z0**2./ciii);
xc=(pi1+(z0**2)/(2*ciii))/den;
halfwidth=(z0*sqrt((pi1*(1-pi1)/ciii)+(z0**2/(4*(ciii**2)))))/den
plo = (xc-halfwidth).clip(min=0) # wilson score
pup = (xc+halfwidth).clip(max=1.0) # wilson score
logity[logity==-40] = np.nan
#saz = (logity-forward(stineman_interp(xi, xiii, plo)))/z0
# slogity = smoothn(logity, robust=False) #, weight=1./saz)
# slogity2 = SavitzkyGolay(n=2, degree=2).smooth(logity)
# sa1 = sqrt(evar(logity))
# sa = (slogity-logity).std()
# #print('estd = %g %g' % (sa,sa1))
#
#
# plo3 = reverse(slogity-z0*sa)
# pup3 = reverse(slogity+z0*sa)
# syi = reverse(slogity)
# syi2 = reverse(slogity2)
#print(fg.data)
#fg.data = np.exp(fg.data)
plt.figure(2)
#plt.figure(2)
fg.plot(label='KReg grid')
f.plot(label='KRegression')
labtxt = '%d CI' % (int(100*(1-alpha)))
plt.plot(xi, syi, 'k',xi, syi2,'k--', label='smoothn')
#plt.plot(xi, syi, 'k',xi, syi2,'k--', label='smoothn')
plt.fill_between(xiii, pup, plo, alpha=0.20,color='r', linestyle='--', label=labtxt)
#plt.fill_between(xiii, pup2, plo2,alpha = 0.20, color='b', linestyle=':',label='%d CI2' % (int(100*(1-alpha))))
plt.fill_between(xiii, pup2, plo2,alpha = 0.20, color='b', linestyle=':',label='%d CI2' % (int(100*(1-alpha))))
#plt.plot(xiii, 0.5*np.cos(xiii)+.5, 'r', label='True model')
plt.plot(xiii, fun1(xiii), 'r', label='True model')
plt.scatter(xi,yi, label='data')
print(np.nanmax(f.data))
print(kreg.tkde.tkde.hs)
print('maxp = %g' % (np.nanmax(f.data)))
print('hs = %g' %( kreg.tkde.tkde.hs))
plt.legend()
h = plt.gca()
if plotlog:
plt.setp(h,yscale='log')
plt.show()
#plt.show()
def kde_gauss_demo(n=50):
'''
@ -3679,6 +3704,10 @@ if __name__ == '__main__':
#kde_demo2()
#kreg_demo1(fast=True)
#kde_gauss_demo()
kreg_demo2(n=180,symmetric=True,fun='hste', plotlog=False)
#kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True)
for i, n in enumerate([10,100,1000,2000,4000]):
plt.figure(i)
kreg_demo2(n=n,symmetric=True,fun='hste', plotlog=False)
plt.show()
#test_smoothn_2d()
#test_smoothn_cardioid()
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