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/*
* Copyright (c) 1996-2001 Lucent Technologies.
* See README file for details.
*/
/*
Functions implementing the adaptive bandwidth selection.
Will make the final call to nbhd() to set smoothing weights
for selected bandwidth, But will **not** make the
final call to locfit().
*/
#include "local.h"
static double hmin;
double acri(lk,t0,t2,pen)
double lk, t0, t2, pen;
{ double y;
/* return(-2*lk/(t0*exp(pen*log(1-t2/t0)))); */
/* return((-2*lk+pen*t2)/t0); */
y = (MAX(-2*lk,t0-t2)+pen*t2)/t0;
return(y);
}
double mmse(lf,des)
lfit *lf;
design *des;
{ int i, ii, j, p, p1;
double sv, sb, *l, dp;
l = des->wd;
wdiag(lf,des,l,(INT)0,(INT)1,(INT)0);
sv = sb = 0;
p = lf->mi[MP];
for (i=0; i<des->n; i++)
{ sv += l[i]*l[i];
ii = des->ind[i];
dp = des->di[ii];
for (j=0; j<lf->mi[MDEG]; j++) dp *= des->di[ii];
sb += fabs(l[i])*dp;
}
p1 = factorial((int)lf->mi[MDEG]+1);
return(sv+sb*sb*lf->dp[DADP]*lf->dp[DADP]/(p1*p1));
}
static double mcp, clo, cup;
/*
Initial bandwidth will be (by default)
k-nearest neighbors for k small, just lage enough to
get defined estimate (unless user provided nonzero DALP
or DFXH components)
*/
INT ainitband(des,lf)
design *des;
lfit *lf;
{ INT lf_status = LF_OK, p, z, cri, noit, redo;
double h, ho, t[6];
p = des->p;
cri = lf->mi[MACRI];
noit = !((cri==AOK) | (cri==ANONE));
z = (INT)(lf->mi[MN]*lf->dp[DALP]);
if ((noit) && (z<p+2)) z = p+2;
redo = 0; ho = -1;
do
{ h = nbhd(lf,des,z,lf->dp[DFXH],redo);
if (z<des->n) z = des->n;
if (h>ho) lf_status = locfit(lf,des,h,noit);
if (cri==ANONE) return(lf_status);
z++;
redo = 1;
} while ((z<=lf->mi[MN]) && ((h==0)||(lf_status!=LF_OK)));
hmin = h;
switch(lf->mi[MACRI])
{ case ACP:
local_df(lf,des,t);
mcp = acri(des->llk,t[0],t[2],lf->dp[DADP]);
return(lf_status);
case AKAT:
local_df(lf,des,t);
clo = des->cf[0]-lf->dp[DADP]*t[5];
cup = des->cf[0]+lf->dp[DADP]*t[5];
return(lf_status);
case AMDI:
mcp = mmse(lf,des);
return(lf_status);
case AOK: return(lf_status);
}
ERROR(("aband1: unknown criterion"));
return(LF_ERR);
}
/*
aband2 increases the initial bandwidth until lack of fit results,
or the fit is close to a global fit. Increase h by 1+0.3/d at
each iteration.
*/
double aband2(des,lf,h0)
design *des;
lfit *lf;
double h0;
{ double t[6], h, h1, nu1, cp, ncp, tlo, tup;
INT d, inc, n, p, done;
d = lf->mi[MDIM]; n = lf->mi[MN]; p = lf->mi[MP];
h1 = h = h0;
done = 0; nu1 = 0.0;
inc = 0; ncp = 0.0;
while ((!done) & (nu1<(n-p)*0.95))
{ h = nbhd(lf,des,0,(1+0.3/d)*h,1);
if (locfit(lf,des,h,1)>0) WARN(("aband2: failed fit"));
local_df(lf,des,t);
nu1 = t[0]-t[2]; /* tr(A) */
switch(lf->mi[MACRI])
{ case AKAT:
tlo = des->cf[0]-lf->dp[DADP]*t[5];
tup = des->cf[0]+lf->dp[DADP]*t[5];
/* printf("h %8.5f tlo %8.5f tup %8.5f\n",h,tlo,tup); */
done = ((tlo>cup) | (tup<clo));
if (!done)
{ clo = MAX(clo,tlo);
cup = MIN(cup,tup);
h1 = h;
}
break;
case ACP:
cp = acri(des->llk,t[0],t[2],lf->dp[DADP]);
/* printf("h %8.5f lk %8.5f t0 %8.5f t2 %8.5f cp %8.5f\n",h,des->llk,t[0],t[2],cp); */
if (cp<mcp) { mcp = cp; h1 = h; }
if (cp>=ncp) inc++; else inc = 0;
ncp = cp;
done = (inc>=10) | ((inc>=3) & ((t[0]-t[2])>=10) & (cp>1.5*mcp));
break;
case AMDI:
cp = mmse(lf,des);
if (cp<mcp) { mcp = cp; h1 = h; }
if (cp>ncp) inc++; else inc = 0;
ncp = cp;
done = (inc>=3);
break;
}
}
return(h1);
}
/*
aband3 does a finer search around best h so far. Try
h*(1-0.2/d), h/(1-0.1/d), h*(1+0.1/d), h*(1+0.2/d)
*/
double aband3(des,lf,h0)
design *des;
lfit *lf;
double h0;
{ double t[6], h, h1, cp, tlo, tup;
INT i, i0, d, n;
d = lf->mi[MDIM]; n = lf->mi[MN];
h1 = h0;
i0 = (lf->mi[MACRI]==AKAT) ? 1 : -2;
if (h0==hmin) i0 = 1;
for (i=i0; i<=2; i++)
{ if (i==0) i++;
h = h0*(1+0.1*i/lf->mi[MDIM]);
h = nbhd(lf,des,0,h,1);
if (locfit(lf,des,h,1)>0) WARN(("aband3: failed fit"));
local_df(lf,des,t);
switch (lf->mi[MACRI])
{ case AKAT:
tlo = des->cf[0]-lf->dp[DADP]*t[5];
tup = des->cf[0]+lf->dp[DADP]*t[5];
if ((tlo>cup) | (tup<clo)) /* done */
i = 2;
else
{ h1 = h;
clo = MAX(clo,tlo);
cup = MIN(cup,tup);
}
break;
case ACP:
cp = acri(des->llk,t[0],t[2],lf->dp[DADP]);
if (cp<mcp) { mcp = cp; h1 = h; }
else
{ if (i>0) i = 2; }
break;
case AMDI:
cp = mmse(lf,des);
if (cp<mcp) { mcp = cp; h1 = h; }
else
{ if (i>0) i = 2; }
}
}
return(h1);
}
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