```// Copyright (C) 2011  Davis E. King (davis@dlib.net)
#ifndef DLIB_BUILD_SEPARABLE_PoLY_FILTERS_Hh_
#define DLIB_BUILD_SEPARABLE_PoLY_FILTERS_Hh_

#include "../matrix.h"
#include "surf.h"
#include "../uintn.h"
#include <vector>

namespace dlib
{

// ----------------------------------------------------------------------------------------

typedef std::pair<matrix<double,0,1>, matrix<double,0,1> > separable_filter_type;
typedef std::pair<matrix<int32,0,1>, matrix<int32,0,1> > separable_int32_filter_type;

// ----------------------------------------------------------------------------------------

inline std::vector<std::vector<separable_filter_type> > build_separable_poly_filters (
const long order,
const long window_size
)
/*!
requires
- 1 <= order <= 6
- window_size >= 3 && window_size is odd
ensures
- the "first" element is the row_filter, the second is the col_filter.
- Some filters are not totally separable and that's why they are grouped
into vectors of vectors.  The groups are all the parts of a partially
separable filter.
!*/
{
long num_filters = 6;
switch (order)
{
case 1: num_filters = 3; break;
case 2: num_filters = 6; break;
case 3: num_filters = 10; break;
case 4: num_filters = 15; break;
case 5: num_filters = 21; break;
case 6: num_filters = 28; break;
}

matrix<double> X(window_size*window_size,num_filters);
matrix<double,0,1> G(window_size*window_size,1);
const double sigma = window_size/4.0;

long cnt = 0;
for (double x = -window_size/2; x <= window_size/2; ++x)
{
for (double y = -window_size/2; y <= window_size/2; ++y)
{
X(cnt, 0) = 1;
X(cnt, 1) = x;
X(cnt, 2) = y;

if (X.nc() > 5)
{
X(cnt, 3) = x*x;
X(cnt, 4) = x*y;
X(cnt, 5) = y*y;
}
if (X.nc() > 9)
{
X(cnt, 6) = x*x*x;
X(cnt, 7) = y*x*x;
X(cnt, 8) = y*y*x;
X(cnt, 9) = y*y*y;
}
if (X.nc() > 14)
{
X(cnt, 10) = x*x*x*x;
X(cnt, 11) = y*x*x*x;
X(cnt, 12) = y*y*x*x;
X(cnt, 13) = y*y*y*x;
X(cnt, 14) = y*y*y*y;
}
if (X.nc() > 20)
{
X(cnt, 15) = x*x*x*x*x;
X(cnt, 16) = y*x*x*x*x;
X(cnt, 17) = y*y*x*x*x;
X(cnt, 18) = y*y*y*x*x;
X(cnt, 19) = y*y*y*y*x;
X(cnt, 20) = y*y*y*y*y;
}
if (X.nc() > 27)
{
X(cnt, 21) = x*x*x*x*x*x;
X(cnt, 22) = y*x*x*x*x*x;
X(cnt, 23) = y*y*x*x*x*x;
X(cnt, 24) = y*y*y*x*x*x;
X(cnt, 25) = y*y*y*y*x*x;
X(cnt, 26) = y*y*y*y*y*x;
X(cnt, 27) = y*y*y*y*y*y;
}

G(cnt) = std::sqrt(gaussian(x,y,sigma));
++cnt;
}
}

X = diagm(G)*X;

const matrix<double> S = inv(trans(X)*X)*trans(X)*diagm(G);

matrix<double,0,1> row_filter, col_filter;

matrix<double> u,v, temp;
matrix<double,0,1> w;

std::vector<std::vector<separable_filter_type> > results(num_filters);

for (long r = 0; r < S.nr(); ++r)
{
temp = reshape(rowm(S,r), window_size, window_size);
svd3(temp,u,w,v);
const double thresh = max(w)*1e-8;
for (long i = 0; i < w.size(); ++i)
{
if (w(i) > thresh)
{
col_filter = std::sqrt(w(i))*colm(u,i);
row_filter = std::sqrt(w(i))*colm(v,i);
results[r].push_back(std::make_pair(row_filter, col_filter));
}
}
}

return results;
}

// ----------------------------------------------------------------------------------------

inline std::vector<std::vector<separable_int32_filter_type> > build_separable_int32_poly_filters (
const long order,
const long window_size,
const double max_range = 300.0
)
/*!
requires
- 1 <= order <= 6
- window_size >= 3 && window_size is odd
- max_range > 1
ensures
- the "first" element is the row_filter, the second is the col_filter.
!*/
{
const std::vector<std::vector<separable_filter_type> >& filters = build_separable_poly_filters(order, window_size);
std::vector<std::vector<separable_int32_filter_type> > int_filters(filters.size());

for (unsigned long i = 0; i < filters.size(); ++i)
{

double max_val = 0;
for (unsigned long j = 0; j < filters[i].size(); ++j)
{
const separable_filter_type& filt = filters[i][j];
max_val = std::max(max_val, max(abs(filt.first)));
max_val = std::max(max_val, max(abs(filt.second)));
}
if (max_val == 0)
max_val = 1;

int_filters[i].resize(filters[i].size());
for (unsigned long j = 0; j < filters[i].size(); ++j)
{
const separable_filter_type& filt = filters[i][j];
int_filters[i][j].first  = matrix_cast<int32>(round(filt.first*max_range/max_val));
int_filters[i][j].second = matrix_cast<int32>(round(filt.second*max_range/max_val));
}
}

return int_filters;
}

}

// ----------------------------------------------------------------------------------------

#endif // DLIB_BUILD_SEPARABLE_PoLY_FILTERS_Hh_

```