dlib C++ Library - sparse_vector.h

// Copyright (C) 2009 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_SVm_SPARSE_VECTOR
#define DLIB_SVm_SPARSE_VECTOR
#include "sparse_vector_abstract.h"
#include <cmath>
#include <limits>
#include "../algs.h"
#include <vector>
#include <map>
#include "../graph_utils/edge_list_graphs.h"
#include "../matrix.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
 template <typename T, typename U>
 typename T::value_type::second_type distance_squared (
 const T& a,
 const U& b
 )
 {
 typedef typename T::value_type::second_type scalar_type;
 typedef typename U::value_type::second_type scalar_typeU;
 // Both T and U must contain the same kinds of elements
 COMPILE_TIME_ASSERT((is_same_type<scalar_type, scalar_typeU>::value));
 typename T::const_iterator ai = a.begin();
 typename U::const_iterator bi = b.begin();
 scalar_type sum = 0, temp = 0;
 while (ai != a.end() && bi != b.end())
 {
 if (ai->first == bi->first)
 {
 temp = ai->second - bi->second;
 ++ai;
 ++bi;
 }
 else if (ai->first < bi->first)
 {
 temp = ai->second;
 ++ai;
 }
 else 
 {
 temp = bi->second;
 ++bi;
 }
 sum += temp*temp;
 }
 while (ai != a.end())
 {
 sum += ai->second*ai->second;
 ++ai;
 }
 while (bi != b.end())
 {
 sum += bi->second*bi->second;
 ++bi;
 }
 return sum;
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename U, typename V, typename W>
 typename T::value_type::second_type distance_squared (
 const V& a_scale,
 const T& a,
 const W& b_scale,
 const U& b
 )
 {
 typedef typename T::value_type::second_type scalar_type;
 typedef typename U::value_type::second_type scalar_typeU;
 // Both T and U must contain the same kinds of elements
 COMPILE_TIME_ASSERT((is_same_type<scalar_type, scalar_typeU>::value));
 typename T::const_iterator ai = a.begin();
 typename U::const_iterator bi = b.begin();
 scalar_type sum = 0, temp = 0;
 while (ai != a.end() && bi != b.end())
 {
 if (ai->first == bi->first)
 {
 temp = a_scale*ai->second - b_scale*bi->second;
 ++ai;
 ++bi;
 }
 else if (ai->first < bi->first)
 {
 temp = a_scale*ai->second;
 ++ai;
 }
 else 
 {
 temp = b_scale*bi->second;
 ++bi;
 }
 sum += temp*temp;
 }
 while (ai != a.end())
 {
 sum += a_scale*a_scale*ai->second*ai->second;
 ++ai;
 }
 while (bi != b.end())
 {
 sum += b_scale*b_scale*bi->second*bi->second;
 ++bi;
 }
 return sum;
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename U>
 typename T::value_type::second_type distance (
 const T& a,
 const U& b
 )
 {
 return std::sqrt(distance_squared(a,b));
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename U, typename V, typename W>
 typename T::value_type::second_type distance (
 const V& a_scale,
 const T& a,
 const W& b_scale,
 const U& b
 )
 {
 return std::sqrt(distance_squared(a_scale,a,b_scale,b));
 }
// ------------------------------------------------------------------------------------
 // ------------------------------------------------------------------------------------
 template <typename T, typename EXP>
 typename enable_if<is_matrix<T> >::type assign (
 T& dest,
 const matrix_exp<EXP>& src
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(src),
 "\t void assign(dest,src)"
 << "\n\t the src matrix must be a row or column vector"
 );
 dest = src;
 }
 template <typename T, typename EXP>
 typename disable_if<is_matrix<T> >::type assign (
 T& dest,
 const matrix_exp<EXP>& src
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(src),
 "\t void assign(dest,src)"
 << "\n\t the src matrix must be a row or column vector"
 );
 dest.clear();
 typedef typename T::value_type item_type;
 for (long i = 0; i < src.size(); ++i)
 {
 dest.insert(dest.end(),item_type(i, src(i)));
 }
 }
 template <typename T, typename U>
 typename disable_if_c<is_matrix<T>::value || is_matrix<U>::value>::type assign (
 T& dest, // sparse
 const U& src // sparse
 )
 {
 dest.assign(src.begin(), src.end());
 }
 template <typename T, typename U, typename Comp, typename Alloc, typename S>
 typename disable_if<is_matrix<S> >::type assign (
 std::map<T,U,Comp,Alloc>& dest, // sparse
 const S& src // sparse
 )
 {
 dest.clear();
 dest.insert(src.begin(), src.end());
 }
// ------------------------------------------------------------------------------------
 // ------------------------------------------------------------------------------------
 template <typename T>
 struct has_unsigned_keys
 {
 static const bool value = is_unsigned_type<typename T::value_type::first_type>::value;
 };
// ------------------------------------------------------------------------------------
 namespace impl
 {
 template <typename T, typename U>
 typename T::value_type::second_type general_dot (
 const T& a,
 const U& b
 )
 {
 typedef typename T::value_type::second_type scalar_type;
 typename T::const_iterator ai = a.begin();
 typename U::const_iterator bi = b.begin();
 scalar_type sum = 0;
 while (ai != a.end() && bi != b.end())
 {
 if (ai->first == bi->first)
 {
 sum += ai->second * bi->second;
 ++ai;
 ++bi;
 }
 else if (ai->first < bi->first)
 {
 ++ai;
 }
 else 
 {
 ++bi;
 }
 }
 return sum;
 }
 template <typename T, typename U>
 inline typename T::value_type::second_type dot (
 const T& a,
 const U& b
 )
 {
 return general_dot(a,b);
 }
 template <typename T, typename U, typename alloc>
 U dot (
 const std::vector<std::pair<T,U>,alloc>& a,
 const std::vector<std::pair<T,U>,alloc>& b
 )
 {
 // You are getting this error because you are attempting to use sparse sample vectors 
 // but you aren't using an unsigned integer as your key type in the sparse vectors.
 COMPILE_TIME_ASSERT(is_unsigned_type<T>::value);
 if (a.size() == 0 || b.size() == 0)
 return 0;
 // if a is really a dense vector but just represented in a sparse container
 if (a.back().first == a.size()-1)
 {
 double sum = 0;
 for (unsigned long i = 0; i < b.size(); ++i)
 {
 if (b[i].first >= a.size())
 break;
 sum += a[b[i].first].second * b[i].second;
 }
 return sum;
 }
 // if b is really a dense vector but just represented in a sparse container
 else if (b.back().first == b.size()-1)
 {
 double sum = 0;
 for (unsigned long i = 0; i < a.size(); ++i)
 {
 if (a[i].first >= b.size())
 break;
 sum += b[a[i].first].second * a[i].second;
 }
 return sum;
 }
 else
 {
 return general_dot(a,b);
 }
 }
 }
 template <typename T>
 inline typename T::value_type::second_type dot (
 const T& a,
 const T& b
 )
 {
 return impl::dot(a,b);
 }
 template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
 inline T4 dot (
 const std::vector<T1,T2>& a,
 const std::map<T3,T4,T5,T6>& b
 )
 {
 return impl::dot(a,b);
 }
 template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
 inline T4 dot (
 const std::map<T3,T4,T5,T6>& a,
 const std::vector<T1,T2>& b
 )
 {
 return impl::dot(a,b);
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename EXP>
 typename T::value_type::second_type dot (
 const T& a,
 const matrix_exp<EXP>& b
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(b),
 "\t scalar_type dot(sparse_vector a, dense_vector b)"
 << "\n\t 'b' must be a vector to be used in a dot product." 
 );
 typedef typename T::value_type::second_type scalar_type;
 typedef typename T::value_type::first_type first_type;
 scalar_type sum = 0;
 for (typename T::const_iterator ai = a.begin(); 
 (ai != a.end()) && (ai->first < static_cast<first_type>(b.size())); 
 ++ai)
 {
 sum += ai->second * b(ai->first);
 }
 return sum;
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename EXP>
 typename T::value_type::second_type dot (
 const matrix_exp<EXP>& b,
 const T& a
 )
 {
 return dot(a,b);
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename T::value_type::second_type length_squared (
 const T& a
 )
 {
 typedef typename T::value_type::second_type scalar_type;
 typename T::const_iterator i;
 scalar_type sum = 0;
 for (i = a.begin(); i != a.end(); ++i)
 {
 sum += i->second * i->second;
 }
 return sum;
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename T::value_type::second_type length (
 const T& a
 )
 {
 return std::sqrt(length_squared(a));
 }
// ------------------------------------------------------------------------------------
 template <typename T, typename U>
 typename disable_if<is_matrix<T>,void>::type scale_by (
 T& a,
 const U& value
 )
 {
 for (typename T::iterator i = a.begin(); i != a.end(); ++i)
 {
 i->second *= value;
 }
 }
 template <typename T, typename U>
 typename enable_if<is_matrix<T>,void>::type scale_by (
 T& a,
 const U& value
 )
 {
 a *= value;
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename disable_if<is_matrix<T>,T>::type add (
 const T& a,
 const T& b
 )
 {
 T temp;
 typename T::const_iterator i = a.begin();
 typename T::const_iterator j = b.begin();
 while (i != a.end() && j != b.end())
 {
 if (i->first == j->first)
 {
 temp.insert(temp.end(), std::make_pair(i->first, i->second + j->second));
 ++i;
 ++j;
 }
 else if (i->first < j->first)
 {
 temp.insert(temp.end(), *i);
 ++i;
 }
 else
 {
 temp.insert(temp.end(), *j);
 ++j;
 }
 }
 while (i != a.end())
 {
 temp.insert(temp.end(), *i);
 ++i;
 }
 while (j != b.end())
 {
 temp.insert(temp.end(), *j);
 ++j;
 }
 return temp;
 }
 template <typename T, typename U>
 typename enable_if_c<is_matrix<T>::value && is_matrix<U>::value, matrix_add_exp<T,U> >::type add (
 const T& a,
 const U& b
 )
 {
 return matrix_add_exp<T,U>(a.ref(),b.ref());
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename disable_if<is_matrix<T>,T>::type subtract (
 const T& a,
 const T& b
 )
 {
 T temp;
 typename T::const_iterator i = a.begin();
 typename T::const_iterator j = b.begin();
 while (i != a.end() && j != b.end())
 {
 if (i->first == j->first)
 {
 temp.insert(temp.end(), std::make_pair(i->first, i->second - j->second));
 ++i;
 ++j;
 }
 else if (i->first < j->first)
 {
 temp.insert(temp.end(), *i);
 ++i;
 }
 else
 {
 temp.insert(temp.end(), std::make_pair(j->first, -j->second));
 ++j;
 }
 }
 while (i != a.end())
 {
 temp.insert(temp.end(), *i);
 ++i;
 }
 while (j != b.end())
 {
 temp.insert(temp.end(), std::make_pair(j->first, -j->second));
 ++j;
 }
 return temp;
 }
 template <typename T, typename U>
 typename enable_if_c<is_matrix<T>::value && is_matrix<U>::value, matrix_subtract_exp<T,U> >::type subtract (
 const T& a,
 const U& b
 )
 {
 return matrix_subtract_exp<T,U>(a.ref(),b.ref());
 }
// ------------------------------------------------------------------------------------
// ------------------------------------------------------------------------------------
 namespace impl
 {
 template <typename T>
 typename enable_if<is_matrix<typename T::type>,unsigned long>::type max_index_plus_one (
 const T& samples
 ) 
 {
 if (samples.size() > 0)
 return samples(0).size();
 else
 return 0;
 }
 template <typename T>
 typename enable_if<is_built_in_scalar_type<typename T::type>,unsigned long>::type max_index_plus_one (
 const T& sample
 ) 
 {
 return sample.size();
 }
 // This !is_built_in_scalar_type<typename T::type>::value is here to avoid an inexplicable bug in Vistual Studio 2005
 template <typename T>
 typename enable_if_c<(!is_built_in_scalar_type<typename T::type>::value) && (is_pair<typename T::type::value_type>::value) ,unsigned long>::type 
 max_index_plus_one (
 const T& samples
 ) 
 {
 typedef typename T::type sample_type;
 // You are getting this error because you are attempting to use sparse sample vectors 
 // but you aren't using an unsigned integer as your key type in the sparse vectors.
 COMPILE_TIME_ASSERT(has_unsigned_keys<sample_type>::value);
 // these should be sparse samples so look over all them to find the max index.
 unsigned long max_dim = 0;
 for (long i = 0; i < samples.size(); ++i)
 {
 if (samples(i).size() > 0)
 max_dim = std::max<unsigned long>(max_dim, (--samples(i).end())->first + 1);
 }
 return max_dim;
 }
 }
 template <typename T>
 typename enable_if<is_pair<typename T::value_type>,unsigned long>::type max_index_plus_one (
 const T& sample
 ) 
 {
 if (sample.size() > 0)
 return (--sample.end())->first + 1;
 return 0;
 }
 template <typename T>
 typename disable_if_c<is_pair<typename T::value_type>::value ||
 is_same_type<typename T::value_type,sample_pair>::value ||
 is_same_type<typename T::value_type,ordered_sample_pair>::value , unsigned long>::type 
 max_index_plus_one (
 const T& samples
 ) 
 {
 return impl::max_index_plus_one(mat(samples));
 }
// ------------------------------------------------------------------------------------
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
 inline void add_to (
 matrix<T,NR,NC,MM,L>& dest,
 const matrix_exp<EXP>& src 
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void add_to(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (long r = 0; r < src.size(); ++r)
 dest(r) += src(r);
 }
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
 inline typename disable_if<is_matrix<EXP> >::type add_to (
 matrix<T,NR,NC,MM,L>& dest,
 const EXP& src
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void add_to(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
 dest(i->first) += i->second;
 }
// ------------------------------------------------------------------------------------
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
 inline void add_to (
 matrix<T,NR,NC,MM,L>& dest,
 const matrix_exp<EXP>& src,
 const U& C
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void add_to(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (long r = 0; r < src.size(); ++r)
 dest(r) += C*src(r);
 }
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
 inline typename disable_if<is_matrix<EXP> >::type add_to (
 matrix<T,NR,NC,MM,L>& dest,
 const EXP& src,
 const U& C
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void add_to(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
 dest(i->first) += C*i->second;
 }
// ------------------------------------------------------------------------------------
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
 inline void subtract_from (
 matrix<T,NR,NC,MM,L>& dest,
 const matrix_exp<EXP>& src 
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void subtract_from(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (long r = 0; r < src.size(); ++r)
 dest(r) -= src(r);
 }
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
 inline typename disable_if<is_matrix<EXP> >::type subtract_from (
 matrix<T,NR,NC,MM,L>& dest,
 const EXP& src
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void subtract_from(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
 dest(i->first) -= i->second;
 }
// ------------------------------------------------------------------------------------
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
 inline void subtract_from (
 matrix<T,NR,NC,MM,L>& dest,
 const matrix_exp<EXP>& src,
 const U& C
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void subtract_from(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (long r = 0; r < src.size(); ++r)
 dest(r) -= C*src(r);
 }
 template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
 inline typename disable_if<is_matrix<EXP> >::type subtract_from (
 matrix<T,NR,NC,MM,L>& dest,
 const EXP& src,
 const U& C
 ) 
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
 "\t void subtract_from(dest,src)"
 << "\n\t dest must be a vector large enough to hold the src vector."
 << "\n\t is_vector(dest): " << is_vector(dest)
 << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
 << "\n\t dest.size(): " << dest.size() 
 );
 for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
 dest(i->first) -= C*i->second;
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename T::value_type::second_type min (
 const T& a
 )
 {
 typedef typename T::value_type::second_type type;
 type temp = 0;
 for (typename T::const_iterator i = a.begin(); i != a.end(); ++i)
 {
 if (temp > i->second)
 temp = i->second;
 }
 return temp;
 }
// ------------------------------------------------------------------------------------
 template <typename T>
 typename T::value_type::second_type max (
 const T& a
 )
 {
 typedef typename T::value_type::second_type type;
 type temp = 0;
 for (typename T::const_iterator i = a.begin(); i != a.end(); ++i)
 {
 if (temp < i->second)
 temp = i->second;
 }
 return temp;
 }
// ----------------------------------------------------------------------------------------
 namespace impl
 {
 template <typename sparse_vector_type>
 inline matrix<typename sparse_vector_type::value_type::second_type,0,1> sparse_to_dense (
 const sparse_vector_type& vect,
 unsigned long num_dimensions 
 )
 {
 // You must use unsigned integral key types in your sparse vectors
 typedef typename sparse_vector_type::value_type::first_type idx_type;
 typedef typename sparse_vector_type::value_type::second_type value_type;
 COMPILE_TIME_ASSERT(is_unsigned_type<idx_type>::value);
 matrix<value_type,0,1> result;
 if (vect.size() == 0)
 return result;
 result.set_size(num_dimensions);
 result = 0;
 for (typename sparse_vector_type::const_iterator j = vect.begin(); j != vect.end(); ++j)
 {
 if ((long)(j->first) < result.size())
 {
 result(j->first) += j->second;
 }
 }
 return result;
 }
 }
// ----------------------------------------------------------------------------------------
 template <typename idx_type, typename value_type, typename alloc>
 matrix<value_type,0,1> sparse_to_dense (
 const std::vector<std::pair<idx_type,value_type>,alloc>& vect,
 unsigned long num_dimensions 
 )
 {
 return impl::sparse_to_dense(vect,num_dimensions);
 }
// ----------------------------------------------------------------------------------------
 template <typename idx_type, typename value_type, typename alloc>
 matrix<value_type,0,1> sparse_to_dense (
 const std::vector<std::pair<idx_type,value_type>,alloc>& vect
 )
 {
 return impl::sparse_to_dense(vect, max_index_plus_one(vect));
 }
// ----------------------------------------------------------------------------------------
 template <typename T1, typename T2, typename T3, typename T4>
 matrix<T2,0,1> sparse_to_dense (
 const std::map<T1,T2,T3,T4>& vect,
 unsigned long num_dimensions 
 )
 {
 return impl::sparse_to_dense(vect,num_dimensions);
 }
// ----------------------------------------------------------------------------------------
 template <typename T1, typename T2, typename T3, typename T4>
 matrix<T2,0,1> sparse_to_dense (
 const std::map<T1,T2,T3,T4>& vect
 )
 {
 return impl::sparse_to_dense(vect, max_index_plus_one(vect));
 }
// ----------------------------------------------------------------------------------------
 template <typename T>
 typename enable_if<is_matrix<T>,T&>::type sparse_to_dense(
 T& item
 ) { return item; }
 
 template <typename EXP>
 matrix<typename EXP::type,0,1> sparse_to_dense(
 const matrix_exp<EXP>& item,
 unsigned long num
 ) 
 { 
 typedef typename EXP::type type;
 if (item.size() == (long)num)
 return item; 
 else if (item.size() < (long)num)
 return join_cols(item, zeros_matrix<type>((long)num-item.size(),1));
 else
 return colm(item,0,(long)num);
 }
 
// ----------------------------------------------------------------------------------------
 template <typename sample_type, typename alloc>
 std::vector<matrix<typename sample_type::value_type::second_type,0,1> > sparse_to_dense (
 const std::vector<sample_type, alloc>& samples,
 unsigned long num_dimensions
 )
 {
 typedef typename sample_type::value_type pair_type;
 typedef typename pair_type::second_type value_type;
 std::vector< matrix<value_type,0,1> > result;
 // now turn all the samples into dense samples
 result.resize(samples.size());
 for (unsigned long i = 0; i < samples.size(); ++i)
 {
 result[i] = sparse_to_dense(samples[i],num_dimensions);
 }
 return result;
 }
// ----------------------------------------------------------------------------------------
 template <typename sample_type, typename alloc>
 std::vector<matrix<typename sample_type::value_type::second_type,0,1> > sparse_to_dense (
 const std::vector<sample_type, alloc>& samples
 )
 {
 return sparse_to_dense(samples, max_index_plus_one(samples));
 }
// ----------------------------------------------------------------------------------------
 template <
 typename T
 >
 T make_sparse_vector (
 const T& v
 )
 {
 // You must use unsigned integral key types in your sparse vectors
 typedef typename T::value_type::first_type idx_type;
 typedef typename T::value_type::second_type value_type;
 COMPILE_TIME_ASSERT(is_unsigned_type<idx_type>::value);
 std::map<idx_type,value_type> temp;
 for (typename T::const_iterator i = v.begin(); i != v.end(); ++i)
 {
 temp[i->first] += i->second;
 }
 return T(temp.begin(), temp.end());
 }
// ----------------------------------------------------------------------------------------
 template <
 typename T
 >
 void make_sparse_vector_inplace(
 T& vect
 )
 {
 vect = make_sparse_vector(vect);
 }
// ----------------------------------------------------------------------------------------
 template <
 typename T,
 typename U,
 typename alloc
 >
 void make_sparse_vector_inplace (
 std::vector<std::pair<T,U>,alloc>& vect
 )
 {
 if (vect.size() > 0)
 {
 std::sort(vect.begin(), vect.end());
 // merge duplicates
 for (unsigned long i = 1; i < vect.size(); ++i)
 {
 // if we found a duplicate
 if (vect[i-1].first == vect[i].first)
 {
 // now start collapsing and merging the vector
 unsigned long j = i-1;
 for (unsigned long k = i; k < vect.size(); ++k)
 {
 if (vect[j].first == vect[k].first)
 {
 vect[j].second += vect[k].second;
 }
 else
 {
 ++j;
 vect[j] = vect[k];
 }
 }
 // we removed elements when we merged so we need to adjust the size.
 vect.resize(j+1);
 return;
 }
 }
 }
 }
// ----------------------------------------------------------------------------------------
 template <typename EXP, typename T, long NR, long NC, typename MM, typename L>
 void sparse_matrix_vector_multiply (
 const std::vector<sample_pair>& edges,
 const matrix_exp<EXP>& v,
 matrix<T,NR,NC,MM,L>& result
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(max_index_plus_one(edges) <= (unsigned long)v.size() &&
 is_col_vector(v),
 "\t void sparse_matrix_vector_multiply()"
 << "\n\t Invalid inputs were given to this function"
 << "\n\t max_index_plus_one(edges): " << max_index_plus_one(edges)
 << "\n\t v.size(): " << v.size() 
 << "\n\t is_col_vector(v): " << is_col_vector(v) 
 );
 result.set_size(v.nr(),v.nc());
 result = 0;
 for (unsigned long k = 0; k < edges.size(); ++k)
 {
 const long i = edges[k].index1();
 const long j = edges[k].index2();
 const double d = edges[k].distance();
 result(i) += v(j)*d;
 if (i != j)
 result(j) += v(i)*d;
 }
 }
// ----------------------------------------------------------------------------------------
 template <typename EXP>
 matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
 const std::vector<sample_pair>& edges,
 const matrix_exp<EXP>& v
 )
 {
 matrix<typename EXP::type,0,1> result;
 sparse_matrix_vector_multiply(edges,v,result);
 return result;
 }
// ----------------------------------------------------------------------------------------
 template <typename EXP, typename T, long NR, long NC, typename MM, typename L>
 void sparse_matrix_vector_multiply (
 const std::vector<ordered_sample_pair>& edges,
 const matrix_exp<EXP>& v,
 matrix<T,NR,NC,MM,L>& result
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(max_index_plus_one(edges) <= (unsigned long)v.size() &&
 is_col_vector(v),
 "\t void sparse_matrix_vector_multiply()"
 << "\n\t Invalid inputs were given to this function"
 << "\n\t max_index_plus_one(edges): " << max_index_plus_one(edges)
 << "\n\t v.size(): " << v.size() 
 << "\n\t is_col_vector(v): " << is_col_vector(v) 
 );
 result.set_size(v.nr(),v.nc());
 result = 0;
 for (unsigned long k = 0; k < edges.size(); ++k)
 {
 const long i = edges[k].index1();
 const long j = edges[k].index2();
 const double d = edges[k].distance();
 result(i) += v(j)*d;
 }
 }
// ----------------------------------------------------------------------------------------
 template <typename EXP>
 matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
 const std::vector<ordered_sample_pair>& edges,
 const matrix_exp<EXP>& v
 )
 {
 matrix<typename EXP::type,0,1> result;
 sparse_matrix_vector_multiply(edges,v,result);
 return result;
 }
// ----------------------------------------------------------------------------------------
 template <
 typename EXP, 
 typename sparse_vector_type,
 typename T,
 long NR,
 long NC,
 typename MM,
 typename L
 >
 void sparse_matrix_vector_multiply (
 const matrix_exp<EXP>& m,
 const sparse_vector_type& v,
 matrix<T,NR,NC,MM,L>& result
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(max_index_plus_one(v) <= (unsigned long)m.nc(),
 "\t void sparse_matrix_vector_multiply()"
 << "\n\t Invalid inputs were given to this function"
 << "\n\t max_index_plus_one(v): " << max_index_plus_one(v)
 << "\n\t m.size(): " << m.size() 
 );
 result.set_size(m.nr(),1);
 result = 0;
 for (typename sparse_vector_type::const_iterator i = v.begin(); i != v.end(); ++i)
 {
 for (long r = 0; r < result.nr(); ++r)
 {
 result(r) += m(r, i->first)*i->second;
 }
 }
 }
// ----------------------------------------------------------------------------------------
 template <
 typename EXP, 
 typename sparse_vector_type
 >
 matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
 const matrix_exp<EXP>& m,
 const sparse_vector_type& v
 )
 {
 matrix<typename EXP::type,0,1> result;
 sparse_matrix_vector_multiply(m,v,result);
 return result;
 }
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_SVm_SPARSE_VECTOR