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#include "precomp.hpp"
#include <climits>
#include <algorithm>
#include <cstdarg>
#define dprintf(x)
#define print_matrix(x)
namespace cv
{
using std::vector;
#ifdef ALEX_DEBUG
static void print_simplex_state(const Mat& c,const Mat& b,double v,const std::vector<int> N,const std::vector<int> B){
printf("\tprint simplex state\n");
printf("v=%g\n",v);
printf("here c goes\n");
print_matrix(c);
printf("non-basic: ");
print(Mat(N));
printf("\n");
printf("here b goes\n");
print_matrix(b);
printf("basic: ");
print(Mat(B));
printf("\n");
}
#else
#define print_simplex_state(c,b,v,N,B)
#endif
/**Due to technical considerations, the format of input b and c is somewhat special:
*both b and c should be one column bigger than corresponding b and c of linear problem and the leftmost column will be used internally
by this procedure - it should not be cleaned before the call to procedure and may contain mess after
it also initializes N and B and does not make any assumptions about their init values
* @return SOLVELP_UNFEASIBLE if problem is unfeasible, 0 if feasible.
*/
static int initialize_simplex(Mat_<double>& c, Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,vector<unsigned int>& indexToRow);
static inline void pivot(Mat_<double>& c,Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,int leaving_index,
int entering_index,vector<unsigned int>& indexToRow);
/**@return SOLVELP_UNBOUNDED means the problem is unbdd, SOLVELP_MULTI means multiple solutions, SOLVELP_SINGLE means one solution.
*/
static int inner_simplex(Mat_<double>& c, Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,vector<unsigned int>& indexToRow);
static void swap_columns(Mat_<double>& A,int col1,int col2);
#define SWAP(type,a,b) {type tmp=(a);(a)=(b);(b)=tmp;}
//return codes:-2 (no_sol - unbdd),-1(no_sol - unfsbl), 0(single_sol), 1(multiple_sol=>least_l2_norm)
int solveLP(const Mat& Func, const Mat& Constr, Mat& z){
dprintf(("call to solveLP\n"));
//sanity check (size, type, no. of channels)
CV_Assert(Func.type()==CV_64FC1 || Func.type()==CV_32FC1);
CV_Assert(Constr.type()==CV_64FC1 || Constr.type()==CV_32FC1);
CV_Assert((Func.rows==1 && (Constr.cols-Func.cols==1))||
(Func.cols==1 && (Constr.cols-Func.rows==1)));
//copy arguments for we will shall modify them
Mat_<double> bigC=Mat_<double>(1,(Func.rows==1?Func.cols:Func.rows)+1),
bigB=Mat_<double>(Constr.rows,Constr.cols+1);
if(Func.rows==1){
Func.convertTo(bigC.colRange(1,bigC.cols),CV_64FC1);
}else{
Mat FuncT=Func.t();
FuncT.convertTo(bigC.colRange(1,bigC.cols),CV_64FC1);
}
Constr.convertTo(bigB.colRange(1,bigB.cols),CV_64FC1);
double v=0;
vector<int> N,B;
vector<unsigned int> indexToRow;
if(initialize_simplex(bigC,bigB,v,N,B,indexToRow)==SOLVELP_UNFEASIBLE){
return SOLVELP_UNFEASIBLE;
}
Mat_<double> c=bigC.colRange(1,bigC.cols),
b=bigB.colRange(1,bigB.cols);
int res=0;
if((res=inner_simplex(c,b,v,N,B,indexToRow))==SOLVELP_UNBOUNDED){
return SOLVELP_UNBOUNDED;
}
//return the optimal solution
z.create(c.cols,1,CV_64FC1);
MatIterator_<double> it=z.begin<double>();
unsigned int nsize = (unsigned int)N.size();
for(int i=1;i<=c.cols;i++,it++){
if(indexToRow[i]<nsize){
*it=0;
}else{
*it=b.at<double>(indexToRow[i]-nsize,b.cols-1);
}
}
return res;
}
static int initialize_simplex(Mat_<double>& c, Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,vector<unsigned int>& indexToRow){
N.resize(c.cols);
N[0]=0;
for (std::vector<int>::iterator it = N.begin()+1 ; it != N.end(); ++it){
*it=it[-1]+1;
}
B.resize(b.rows);
B[0]=(int)N.size();
for (std::vector<int>::iterator it = B.begin()+1 ; it != B.end(); ++it){
*it=it[-1]+1;
}
indexToRow.resize(c.cols+b.rows);
indexToRow[0]=0;
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
*it=it[-1]+1;
}
v=0;
int k=0;
{
double min=DBL_MAX;
for(int i=0;i<b.rows;i++){
if(b(i,b.cols-1)<min){
min=b(i,b.cols-1);
k=i;
}
}
}
if(b(k,b.cols-1)>=0){
N.erase(N.begin());
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
--(*it);
}
return 0;
}
Mat_<double> old_c=c.clone();
c=0;
c(0,0)=-1;
for(int i=0;i<b.rows;i++){
b(i,0)=-1;
}
print_simplex_state(c,b,v,N,B);
dprintf(("\tWE MAKE PIVOT\n"));
pivot(c,b,v,N,B,k,0,indexToRow);
print_simplex_state(c,b,v,N,B);
inner_simplex(c,b,v,N,B,indexToRow);
dprintf(("\tAFTER INNER_SIMPLEX\n"));
print_simplex_state(c,b,v,N,B);
unsigned int nsize = (unsigned int)N.size();
if(indexToRow[0]>=nsize){
int iterator_offset=indexToRow[0]-nsize;
if(b(iterator_offset,b.cols-1)>0){
return SOLVELP_UNFEASIBLE;
}
pivot(c,b,v,N,B,iterator_offset,0,indexToRow);
}
vector<int>::iterator iterator;
{
int iterator_offset=indexToRow[0];
iterator=N.begin()+iterator_offset;
std::iter_swap(iterator,N.begin());
SWAP(int,indexToRow[*iterator],indexToRow[0]);
swap_columns(c,iterator_offset,0);
swap_columns(b,iterator_offset,0);
}
dprintf(("after swaps\n"));
print_simplex_state(c,b,v,N,B);
//start from 1, because we ignore x_0
c=0;
v=0;
for(int I=1;I<old_c.cols;I++){
if(indexToRow[I]<nsize){
dprintf(("I=%d from nonbasic\n",I));
int iterator_offset=indexToRow[I];
c(0,iterator_offset)+=old_c(0,I);
print_matrix(c);
}else{
dprintf(("I=%d from basic\n",I));
int iterator_offset=indexToRow[I]-nsize;
c-=old_c(0,I)*b.row(iterator_offset).colRange(0,b.cols-1);
v+=old_c(0,I)*b(iterator_offset,b.cols-1);
print_matrix(c);
}
}
dprintf(("after restore\n"));
print_simplex_state(c,b,v,N,B);
N.erase(N.begin());
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
--(*it);
}
return 0;
}
static int inner_simplex(Mat_<double>& c, Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,vector<unsigned int>& indexToRow){
int count=0;
for(;;){
dprintf(("iteration #%d\n",count));
count++;
static MatIterator_<double> pos_ptr;
int e=-1,pos_ctr=0,min_var=INT_MAX;
bool all_nonzero=true;
for(pos_ptr=c.begin();pos_ptr!=c.end();pos_ptr++,pos_ctr++){
if(*pos_ptr==0){
all_nonzero=false;
}
if(*pos_ptr>0){
if(N[pos_ctr]<min_var){
e=pos_ctr;
min_var=N[pos_ctr];
}
}
}
if(e==-1){
dprintf(("hello from e==-1\n"));
print_matrix(c);
if(all_nonzero==true){
return SOLVELP_SINGLE;
}else{
return SOLVELP_MULTI;
}
}
int l=-1;
min_var=INT_MAX;
double min=DBL_MAX;
int row_it=0;
MatIterator_<double> min_row_ptr=b.begin();
for(MatIterator_<double> it=b.begin();it!=b.end();it+=b.cols,row_it++){
double myite=0;
//check constraints, select the tightest one, reinforcing Bland's rule
if((myite=it[e])>0){
double val=it[b.cols-1]/myite;
if(val<min || (val==min && B[row_it]<min_var)){
min_var=B[row_it];
min_row_ptr=it;
min=val;
l=row_it;
}
}
}
if(l==-1){
return SOLVELP_UNBOUNDED;
}
dprintf(("the tightest constraint is in row %d with %g\n",l,min));
pivot(c,b,v,N,B,l,e,indexToRow);
dprintf(("objective, v=%g\n",v));
print_matrix(c);
dprintf(("constraints\n"));
print_matrix(b);
dprintf(("non-basic: "));
print_matrix(Mat(N));
dprintf(("basic: "));
print_matrix(Mat(B));
}
}
static inline void pivot(Mat_<double>& c,Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,
int leaving_index,int entering_index,vector<unsigned int>& indexToRow){
double Coef=b(leaving_index,entering_index);
for(int i=0;i<b.cols;i++){
if(i==entering_index){
b(leaving_index,i)=1/Coef;
}else{
b(leaving_index,i)/=Coef;
}
}
for(int i=0;i<b.rows;i++){
if(i!=leaving_index){
double coef=b(i,entering_index);
for(int j=0;j<b.cols;j++){
if(j==entering_index){
b(i,j)=-coef*b(leaving_index,j);
}else{
b(i,j)-=(coef*b(leaving_index,j));
}
}
}
}
//objective function
Coef=c(0,entering_index);
for(int i=0;i<(b.cols-1);i++){
if(i==entering_index){
c(0,i)=-Coef*b(leaving_index,i);
}else{
c(0,i)-=Coef*b(leaving_index,i);
}
}
dprintf(("v was %g\n",v));
v+=Coef*b(leaving_index,b.cols-1);
SWAP(int,N[entering_index],B[leaving_index]);
SWAP(int,indexToRow[N[entering_index]],indexToRow[B[leaving_index]]);
}
static inline void swap_columns(Mat_<double>& A,int col1,int col2){
for(int i=0;i<A.rows;i++){
double tmp=A(i,col1);
A(i,col1)=A(i,col2);
A(i,col2)=tmp;
}
}
}