CDF *G(Bernouilli_CDF)(int n, double *weight)
{ int i;
double sum;
double *tab;
Cdf *bin;
bin = new_cdf((n+1)*sizeof(double),"Bernouilli_CDF");
bin->kind = BERNOUILLI;
bin->low = 0;
bin->spn = n;
tab = bin->tab;
sum = 0.;
for (i = 0; i < n; i++)
{ tab[i] = sum;
sum += weight[i];
}
for (i = 1; i < n; i++)
tab[i] /= sum;
tab[n] = 1.;
#ifdef DEBUG
printf(" CDF:\n");
for (i = 0; i <= n; i++)
printf(" %4d: %10.9f\n",i,tab[i]);
#endif
return ((CDF *) bin);
}
CDF *G(FairCoin_CDF)(int n)
{ Cdf *bin;
bin = new_cdf(sizeof(double),"FairCoin_CDF");
bin->kind = FAIRCOIN;
bin->parm3 = n;
bin->spn = 0;
return ((CDF *) bin);
}
CDF *G(Exponential_CDF)(double a)
{ Cdf *bin;
bin = new_cdf(sizeof(double),"Exponential_CDF");
bin->kind = EXPONENTIAL;
bin->parm1 = a;
bin->spn = 0;
return ((CDF *) bin);
}
CDF *G(Geometric_CDF)(double p)
{ Cdf *bin;
bin = new_cdf(sizeof(double),"Geometric_CDF");
bin->kind = GEOMETRIC;
bin->parm1 = p;
bin->spn = 0;
return ((CDF *) bin);
}
static inline Cdf *copy_cdf(Cdf *cdf)
{ Cdf *copy = new_cdf(cdf_tsize(cdf),"Copy_CDF");
void *_tab = copy->tab;
*copy = *cdf;
copy->tab = _tab;
if (cdf->tab != NULL)
memcpy(copy->tab,cdf->tab,cdf_tsize(cdf));
return (copy);
}
CDF *G(Uniform_CDF)(double low, double hgh)
{ Cdf *bin;
bin = new_cdf(sizeof(double),"Uniform_CDF");
bin->kind = UNIFORM;
bin->parm1 = low;
bin->parm2 = hgh - low;
bin->spn = 0;
return ((CDF *) bin);
}
CDF *G(Normal_CDF)(double mean, double stdev)
{ Cdf *bin;
bin = new_cdf(sizeof(double),"Normal_CDF");
bin->kind = NORMAL;
bin->parm1 = mean;
bin->parm2 = stdev;
bin->spn = 1;
if (unorm_defined == 0)
{ unorm_defined = 1;
init_unorm();
}
return ((CDF *) bin);
}
static inline Cdf *read_cdf(FILE *input)
{ char name[3];
fread(name,3,1,input);
if (strncmp(name,"CDF",3) != 0)
return (NULL);
Cdf *obj = new_cdf(0,"Read_CDF");
fread(obj,sizeof(Cdf),1,input);
obj->tab = NULL;
if (cdf_tsize(obj) != 0)
{ allocate_cdf_tab(obj,cdf_tsize(obj),"Read_CDF");
fread(obj->tab,cdf_tsize(obj),1,input);
}
return (obj);
}
int main() {
std::cout << "____________________________________" << std::endl
<< " Testing transformations from cdf to pdf and inversely" <<std::endl;
int zval[5] = {1,2,3,4,5};
double prob[5] = {0.2, 0.3, 0.6, 0.8, 1};
typedef Non_param_pdf<int> Pdf;
typedef Categ_non_param_cdf<int> Cdf;
Cdf categ_cdf( 5, prob);
Pdf pdf(zval, zval+5);
cdf_to_pdf(pdf, categ_cdf);
for(int i=0; i<=4; i++)
std::cout << pdf.prob(i) << " " ;
std::cout << std::endl;
Cdf back(5);
pdf_to_cdf(back,pdf);
for(int i=0; i<=4; i++)
std::cout << back.prob(i) << " " ;
std::cout << std::endl;
cdf_to_pdf(pdf, back);
for(int i=0; i<=4; i++)
std::cout << pdf.prob(i) << " " ;
std::cout << std::endl;
Pdf new_pdf(categ_cdf);
for(int i=0; i<=4; i++)
std::cout << new_pdf.prob(i) << " " ;
std::cout << std::endl;
std::cout << std::endl
<< "____________________________________" << std::endl
<< " Testing transformations from cdf to pdf and inversely "<<std::endl;
Gaussian_cdf normal(0,1);
std::vector<double> range(1000);
for(std::vector<double>::iterator it=range.begin(); it!=range.end(); it++)
*it = drand48()*100;
std::ofstream out1( "uniform.dbg" );
std::copy( range.begin(), range.end(),
std::ostream_iterator<double>( out1, "\n" ) );
cdf_transform(range.begin(), range.end(), normal);
std::ofstream out2( "nscore.dbg" );
std::copy( range.begin(), range.end(),
std::ostream_iterator<double>( out2, "\n" ) );
std::cout << std::endl
<< "____________________________________" << std::endl
<< " Testing cdf correction "<<std::endl;
double order_relation[5] = {0.2, 0.3, -0.2, 0.1, 1.2};
Cdf bad_cdf(5, order_relation);
std::cout << "Is bad cdf ok? " << is_valid_cdf(bad_cdf) << std::endl;
make_cdf_valid(bad_cdf);
std::cout << "Corrected cdf: " << std::endl;
for(int i=0; i<bad_cdf.size(); i++)
std::cout << bad_cdf.prob(i) << " " ;
std::cout << std::endl;
std::cout << std::endl
<< "____________________________________" << std::endl
<< " Testing cdf construction "<<std::endl;
double val_range[9] = {1,1,1,4,7,12,31,55,60};
double z_values[7] = {1,4,7,12,31,55,60};
Non_param_cdf<> new_cdf( z_values, z_values+7);
build_cdf( val_range, val_range+9,
new_cdf.z_begin(), new_cdf.z_end(), new_cdf.p_begin() );
Non_param_cdf<>::z_iterator z_it = new_cdf.z_begin();
for( ; z_it != new_cdf.z_end(); z_it++ ) {
std::cout << "P( " << *z_it << " ) = " << new_cdf.prob( *z_it ) << std::endl;
}
std::cout << std::endl;
build_cdf( val_range, val_range+9, new_cdf, true );
z_it = new_cdf.z_begin();
for( ; z_it != new_cdf.z_end(); z_it++ ) {
std::cout << "P( " << *z_it << " ) = " << new_cdf.prob( *z_it ) << std::endl;
}
}
CDF *G(Poisson_CDF)(double a)
{ double *tab;
double pek, nxt, sum;
double nap;
int i, k, c;
int low, hgh, spn;
Cdf *pois;
nap = exp(1.);
c = i = k = a;
pek = 1.;
while (i > 0 || c > 0)
if (pek < a && c > 0)
{ pek *= a;
c -= 1;
}
else
{ pek /= (nap*i);
i -= 1;
}
#ifdef DEBUG
printf("Poisson(%g):\n",a);
printf(" Peak at %d : %g\n",k,pek);
#endif
/* Compute length of non-zero tails on either side of peak */
nxt = pek;
for (i = k-1; i >= 0; i--)
{ nxt *= (i+1.)/a;
if (nxt < 1e-50) break;
}
low = i;
nxt = pek;
for (i = k+1; 1; i++)
{ nxt *= a/i;
if (nxt < 1e-50) break;
}
hgh = i-1;
spn = hgh - low;
#ifdef DEBUG
printf(" Span is [%d,%d] of length %d\n",low,hgh,spn+1);
#endif
/* Allocate Poisson data structure */
pois = new_cdf((spn+1)*sizeof(double),"Poisson_CDF");
pois->kind = POISSON;
pois->low = low;
pois->spn = spn;
tab = pois->tab;
/* Compute tails again, this time storing them */
tab[k-low] = pek;
nxt = pek;
for (i = k-1; i > low; i--)
tab[i-low] = nxt *= (i+1.)/a;
nxt = pek;
for (i = k+1; i <= hgh; i++)
tab[i-low] = nxt *= a/i;
#ifdef DEBUG
if (low >= 0)
{ sum = (low+1)/a;
printf(" Low tail truncated < %g (r = %g)\n",tab[1]/(1.-sum),sum);
}
sum = a/(hgh+1.);
printf(" Hgh tail truncated < %g (r = %g)\n",tab[spn]/(1.-sum),sum);
printf(" PDF:\n");
for (i = 1; i <= spn; i++)
printf(" %4d: %10.9f\n",low+i,tab[i]);
#endif
/* Compute cdf and normalize sum */
sum = 0.;
for (i = 0; i < spn; i++)
{ tab[i] = sum;
sum += tab[i+1];
}
for (i = 1; i < spn; i++)
tab[i] /= sum;
tab[spn] = 1.;
#ifdef DEBUG
printf(" CDF:\n");
for (i = 0; i <= spn; i++)
printf(" %4d: %10.9f\n",low+i,tab[i]);
#endif
return ((CDF *) pois);
}
CDF *G(Binomial_CDF)(int n, double p)
{ double *tab;
double pek, nxt, sum;
double pm1, var;
int i, k, c;
int low, hgh, spn;
Cdf *bin;
/* Compute p-value at k = pn */
pm1 = 1.-p;
var = p*pm1;
k = p*n;
if (p <= .5)
{ pek = 1.;
c = i = k-1;
while (i >= 2*k-n || c >= 0)
{ if (pek < n && c >= 0)
{ pek *= (n-c) / (c+1.);
c -= 1;
}
else if (i >= 0)
{ pek *= var;
i -= 1;
}
else
{ pek *= pm1;
i -= 1;
}
}
}
else
{ if (k < n) k += 1;
pek = 1.;
c = i = n-k-1;
while (i >= n-2*k || c >= 0)
{ if (pek < n && c >= 0)
{ pek *= (n-c) / (c+1.);
c -= 1;
}
else if (i >= 0)
{ pek *= var;
i -= 1;
}
else
{ pek *= p;
i -= 1;
}
}
}
#ifdef DEBUG
printf("Binomial(%d,%d):\n",n,p);
printf(" Peak at %d : %g\n",k,pek);
#endif
/* Compute length of non-zero tails on either side of peak */
nxt = pek;
for (i = k-1; i >= 0; i--)
{ nxt *= ((i+1)*pm1)/((n-i)*p);
if (nxt < 1e-50) break;
}
low = i;
nxt = pek;
for (i = k+1; i <= n; i++)
{ nxt *= (((n-i)+1)*p)/(i*pm1);
if (nxt < 1e-50) break;
}
hgh = i-1;
spn = hgh - low;
#ifdef DEBUG
printf(" Span is [%d,%d] of length %d\n",low,hgh,spn+1);
#endif
/* Allocate binomial data structure */
bin = new_cdf((spn+1)*sizeof(double),"Binomial_CDF");
bin->kind = BINOMIAL;
bin->low = low;
bin->spn = spn;
tab = bin->tab;
/* Compute tails again, this time storing them */
tab[k-low] += pek;
nxt = pek;
for (i = k-1; i > low; i--)
tab[i-low] = nxt *= ((i+1)*pm1)/((n-i)*p);
nxt = pek;
for (i = k+1; i <= hgh; i++)
tab[i-low] = nxt *= (((n-i)+1)*p)/(i*pm1);
#ifdef DEBUG
if (low >= 0)
{ sum = ((low+1)*pm1)/((n-low)*p);
printf(" Low tail truncated < %g (r = %g)\n",tab[1]/(1.-sum),sum);
}
if (hgh < n)
{ sum = ((n-hgh)*p)/((hgh+1)*pm1);
printf(" Hgh tail truncated < %g (r = %g)\n",tab[spn]/(1.-sum),sum);
}
printf(" PDF:\n");
for (i = 1; i <= spn; i++)
printf(" %4d: %10.9f\n",low+i,tab[i]);
#endif
/* Compute cdf and normalize sum */
sum = 0.;
for (i = 0; i < spn; i++)
{ tab[i] = sum;
sum += tab[i+1];
}
for (i = 1; i < spn; i++)
tab[i] /= sum;
tab[spn] = 1.;
#ifdef DEBUG
printf(" CDF:\n");
for (i = 0; i <= spn; i++)
printf(" %4d: %10.9f\n",low+i,tab[i]);
#endif
return ((CDF *) bin);
}
