My Project
Public Member Functions | Data Fields | Private Member Functions | Private Attributes
simplex Class Reference

Linear Programming / Linear Optimization using Simplex - Algorithm. More...

#include <mpr_numeric.h>

Public Member Functions

 simplex (int rows, int cols)
 #rows should be >= m+2, #cols >= n+1 More...
 
 ~simplex ()
 
BOOLEAN mapFromMatrix (matrix m)
 
matrix mapToMatrix (matrix m)
 
intvecposvToIV ()
 
intveczrovToIV ()
 
void compute ()
 

Data Fields

int m
 
int n
 
int m1
 
int m2
 
int m3
 
int icase
 
int * izrov
 
int * iposv
 
mprfloat ** LiPM
 

Private Member Functions

 simplex (const simplex &)
 
void simp1 (mprfloat **a, int mm, int ll[], int nll, int iabf, int *kp, mprfloat *bmax)
 
void simp2 (mprfloat **a, int n, int l2[], int nl2, int *ip, int kp, mprfloat *q1)
 
void simp3 (mprfloat **a, int i1, int k1, int ip, int kp)
 

Private Attributes

int LiPM_cols
 
int LiPM_rows
 

Detailed Description

Linear Programming / Linear Optimization using Simplex - Algorithm.

On output, the tableau LiPM is indexed by two arrays of integers. ipsov[j] contains, for j=1..m, the number i whose original variable is now represented by row j+1 of LiPM. (left-handed vars in solution) (first row is the one with the objective function) izrov[j] contains, for j=1..n, the number i whose original variable x_i is now a right-handed variable, rep. by column j+1 of LiPM. These vars are all zero in the solution. The meaning of n<i<n+m1+m2 is the same as above.

Definition at line 194 of file mpr_numeric.h.

Constructor & Destructor Documentation

◆ simplex() [1/2]

simplex::simplex ( int  rows,
int  cols 
)

#rows should be >= m+2, #cols >= n+1

Definition at line 972 of file mpr_numeric.cc.

973  : LiPM_cols(cols), LiPM_rows(rows)
974 {
975  int i;
976 
979 
980  LiPM = (mprfloat **)omAlloc( LiPM_rows * sizeof(mprfloat *) ); // LP matrix
981  for( i= 0; i < LiPM_rows; i++ )
982  {
983  // Mem must be allocated aligned, also for type double!
984  LiPM[i] = (mprfloat *)omAlloc0Aligned( LiPM_cols * sizeof(mprfloat) );
985  }
986 
987  iposv = (int *)omAlloc0( 2*LiPM_rows*sizeof(int) );
988  izrov = (int *)omAlloc0( 2*LiPM_rows*sizeof(int) );
989 
990  m=n=m1=m2=m3=icase=0;
991 
992 #ifdef mprDEBUG_ALL
993  Print("LiPM size: %d, %d\n",LiPM_rows,LiPM_cols);
994 #endif
995 }
int i
Definition: cfEzgcd.cc:132
mprfloat ** LiPM
Definition: mpr_numeric.h:205
int * iposv
Definition: mpr_numeric.h:203
int LiPM_rows
Definition: mpr_numeric.h:225
int * izrov
Definition: mpr_numeric.h:203
int icase
Definition: mpr_numeric.h:201
int LiPM_cols
Definition: mpr_numeric.h:225
#define Print
Definition: emacs.cc:80
double mprfloat
Definition: mpr_global.h:17
#define omAlloc0Aligned
Definition: omAllocDecl.h:274
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omAlloc0(size)
Definition: omAllocDecl.h:211

◆ ~simplex()

simplex::~simplex ( )

Definition at line 997 of file mpr_numeric.cc.

998 {
999  // clean up
1000  int i;
1001  for( i= 0; i < LiPM_rows; i++ )
1002  {
1003  omFreeSize( (void *) LiPM[i], LiPM_cols * sizeof(mprfloat) );
1004  }
1005  omFreeSize( (void *) LiPM, LiPM_rows * sizeof(mprfloat *) );
1006 
1007  omFreeSize( (void *) iposv, 2*LiPM_rows*sizeof(int) );
1008  omFreeSize( (void *) izrov, 2*LiPM_rows*sizeof(int) );
1009 }
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260

◆ simplex() [2/2]

simplex::simplex ( const simplex )
private

Member Function Documentation

◆ compute()

void simplex::compute ( )

Definition at line 1095 of file mpr_numeric.cc.

1096 {
1097  int i,ip,ir,is,k,kh,kp,m12,nl1,nl2;
1098  int *l1,*l2,*l3;
1099  mprfloat q1, bmax;
1100 
1101  if ( m != (m1+m2+m3) )
1102  {
1103  // error: bad input
1104  error(WarnS("simplex::compute: Bad input constraint counts!");)
1105  icase=-2;
1106  return;
1107  }
1108 
1109  l1= (int *) omAlloc0( (n+1) * sizeof(int) );
1110  l2= (int *) omAlloc0( (m+1) * sizeof(int) );
1111  l3= (int *) omAlloc0( (m+1) * sizeof(int) );
1112 
1113  nl1= n;
1114  for ( k=1; k<=n; k++ ) l1[k]=izrov[k]=k;
1115  nl2=m;
1116  for ( i=1; i<=m; i++ )
1117  {
1118  if ( LiPM[i+1][1] < 0.0 )
1119  {
1120  // error: bad input
1121  error(WarnS("simplex::compute: Bad input tableau!");)
1122  error(Warn("simplex::compute: in input Matrix row %d, column 1, value %f",i+1,LiPM[i+1][1]);)
1123  icase=-2;
1124  // free mem l1,l2,l3;
1125  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1126  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1127  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1128  return;
1129  }
1130  l2[i]= i;
1131  iposv[i]= n+i;
1132  }
1133  for ( i=1; i<=m2; i++) l3[i]= 1;
1134  ir= 0;
1135  if (m2+m3)
1136  {
1137  ir=1;
1138  for ( k=1; k <= (n+1); k++ )
1139  {
1140  q1=0.0;
1141  for ( i=m1+1; i <= m; i++ ) q1+= LiPM[i+1][k];
1142  LiPM[m+2][k]= -q1;
1143  }
1144 
1145  do
1146  {
1147  simp1(LiPM,m+1,l1,nl1,0,&kp,&bmax);
1148  if ( bmax <= SIMPLEX_EPS && LiPM[m+2][1] < -SIMPLEX_EPS )
1149  {
1150  icase= -1; // no solution found
1151  // free mem l1,l2,l3;
1152  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1153  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1154  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1155  return;
1156  }
1157  else if ( bmax <= SIMPLEX_EPS && LiPM[m+2][1] <= SIMPLEX_EPS )
1158  {
1159  m12= m1+m2+1;
1160  if ( m12 <= m )
1161  {
1162  for ( ip= m12; ip <= m; ip++ )
1163  {
1164  if ( iposv[ip] == (ip+n) )
1165  {
1166  simp1(LiPM,ip,l1,nl1,1,&kp,&bmax);
1167  if ( fabs(bmax) >= SIMPLEX_EPS)
1168  goto one;
1169  }
1170  }
1171  }
1172  ir= 0;
1173  --m12;
1174  if ( m1+1 <= m12 )
1175  for ( i=m1+1; i <= m12; i++ )
1176  if ( l3[i-m1] == 1 )
1177  for ( k=1; k <= n+1; k++ )
1178  LiPM[i+1][k] = -(LiPM[i+1][k]);
1179  break;
1180  }
1181  //#if DEBUG
1182  //print_bmat( a, m+2, n+3);
1183  //#endif
1184  simp2(LiPM,n,l2,nl2,&ip,kp,&q1);
1185  if ( ip == 0 )
1186  {
1187  icase = -1; // no solution found
1188  // free mem l1,l2,l3;
1189  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1190  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1191  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1192  return;
1193  }
1194  one: simp3(LiPM,m+1,n,ip,kp);
1195  // #if DEBUG
1196  // print_bmat(a,m+2,n+3);
1197  // #endif
1198  if ( iposv[ip] >= (n+m1+m2+1))
1199  {
1200  for ( k= 1; k <= nl1; k++ )
1201  if ( l1[k] == kp ) break;
1202  --nl1;
1203  for ( is=k; is <= nl1; is++ ) l1[is]= l1[is+1];
1204  ++(LiPM[m+2][kp+1]);
1205  for ( i= 1; i <= m+2; i++ ) LiPM[i][kp+1] = -(LiPM[i][kp+1]);
1206  }
1207  else
1208  {
1209  if ( iposv[ip] >= (n+m1+1) )
1210  {
1211  kh= iposv[ip]-m1-n;
1212  if ( l3[kh] )
1213  {
1214  l3[kh]= 0;
1215  ++(LiPM[m+2][kp+1]);
1216  for ( i=1; i<= m+2; i++ )
1217  LiPM[i][kp+1] = -(LiPM[i][kp+1]);
1218  }
1219  }
1220  }
1221  is= izrov[kp];
1222  izrov[kp]= iposv[ip];
1223  iposv[ip]= is;
1224  } while (ir);
1225  }
1226  /* end of phase 1, have feasible sol, now optimize it */
1227  loop
1228  {
1229  // #if DEBUG
1230  // print_bmat( a, m+1, n+5);
1231  // #endif
1232  simp1(LiPM,0,l1,nl1,0,&kp,&bmax);
1233  if (bmax <= /*SIMPLEX_EPS*/0.0)
1234  {
1235  icase=0; // finite solution found
1236  // free mem l1,l2,l3
1237  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1238  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1239  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1240  return;
1241  }
1242  simp2(LiPM,n,l2,nl2,&ip,kp,&q1);
1243  if (ip == 0)
1244  {
1245  //printf("Unbounded:");
1246  // #if DEBUG
1247  // print_bmat( a, m+1, n+1);
1248  // #endif
1249  icase=1; /* unbounded */
1250  // free mem
1251  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1252  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1253  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1254  return;
1255  }
1256  simp3(LiPM,m,n,ip,kp);
1257  is= izrov[kp];
1258  izrov[kp]= iposv[ip];
1259  iposv[ip]= is;
1260  }/*for ;;*/
1261 }
int k
Definition: cfEzgcd.cc:99
void simp2(mprfloat **a, int n, int l2[], int nl2, int *ip, int kp, mprfloat *q1)
void simp3(mprfloat **a, int i1, int k1, int ip, int kp)
void simp1(mprfloat **a, int mm, int ll[], int nll, int iabf, int *kp, mprfloat *bmax)
#define Warn
Definition: emacs.cc:77
#define WarnS
Definition: emacs.cc:78
#define error(a)
Definition: mpr_numeric.cc:966
#define SIMPLEX_EPS
Definition: mpr_numeric.h:181
#define loop
Definition: structs.h:75

◆ mapFromMatrix()

BOOLEAN simplex::mapFromMatrix ( matrix  m)

Definition at line 1011 of file mpr_numeric.cc.

1012 {
1013  int i,j;
1014 // if ( MATROWS( m ) > LiPM_rows || MATCOLS( m ) > LiPM_cols ) {
1015 // WarnS("");
1016 // return FALSE;
1017 // }
1018 
1019  number coef;
1020  for ( i= 1; i <= MATROWS( mm ); i++ )
1021  {
1022  for ( j= 1; j <= MATCOLS( mm ); j++ )
1023  {
1024  if ( MATELEM(mm,i,j) != NULL )
1025  {
1026  coef= pGetCoeff( MATELEM(mm,i,j) );
1027  if ( coef != NULL && !nIsZero(coef) )
1028  LiPM[i][j]= (double)(*(gmp_float*)coef);
1029  //#ifdef mpr_DEBUG_PROT
1030  //Print("%f ",LiPM[i][j]);
1031  //#endif
1032  }
1033  }
1034  // PrintLn();
1035  }
1036 
1037  return TRUE;
1038 }
#define TRUE
Definition: auxiliary.h:100
int j
Definition: facHensel.cc:110
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define MATROWS(i)
Definition: matpol.h:26
#define MATCOLS(i)
Definition: matpol.h:27
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
#define nIsZero(n)
Definition: numbers.h:19
#define NULL
Definition: omList.c:12

◆ mapToMatrix()

matrix simplex::mapToMatrix ( matrix  m)

Definition at line 1040 of file mpr_numeric.cc.

1041 {
1042  int i,j;
1043 // if ( MATROWS( mm ) < LiPM_rows-3 || MATCOLS( m ) < LiPM_cols-2 ) {
1044 // WarnS("");
1045 // return NULL;
1046 // }
1047 
1048 //Print(" %d x %d\n",MATROWS( mm ),MATCOLS( mm ));
1049 
1050  number coef;
1051  gmp_float * bla;
1052  for ( i= 1; i <= MATROWS( mm ); i++ )
1053  {
1054  for ( j= 1; j <= MATCOLS( mm ); j++ )
1055  {
1056  pDelete( &(MATELEM(mm,i,j)) );
1057  MATELEM(mm,i,j)= NULL;
1058 //Print(" %3.0f ",LiPM[i][j]);
1059  if ( LiPM[i][j] != 0.0 )
1060  {
1061  bla= new gmp_float(LiPM[i][j]);
1062  coef= (number)bla;
1063  MATELEM(mm,i,j)= pOne();
1064  pSetCoeff( MATELEM(mm,i,j), coef );
1065  }
1066  }
1067 //PrintLn();
1068  }
1069 
1070  return mm;
1071 }
#define pDelete(p_ptr)
Definition: polys.h:186
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
#define pOne()
Definition: polys.h:315

◆ posvToIV()

intvec * simplex::posvToIV ( )

Definition at line 1073 of file mpr_numeric.cc.

1074 {
1075  int i;
1076  intvec * iv = new intvec( m );
1077  for ( i= 1; i <= m; i++ )
1078  {
1079  IMATELEM(*iv,i,1)= iposv[i];
1080  }
1081  return iv;
1082 }
Definition: intvec.h:23
#define IMATELEM(M, I, J)
Definition: intvec.h:85

◆ simp1()

void simplex::simp1 ( mprfloat **  a,
int  mm,
int  ll[],
int  nll,
int  iabf,
int *  kp,
mprfloat bmax 
)
private

Definition at line 1263 of file mpr_numeric.cc.

1264 {
1265  int k;
1266  mprfloat test;
1267 
1268  if( nll <= 0)
1269  { /* init'tion: fixed */
1270  *bmax = 0.0;
1271  return;
1272  }
1273  *kp=ll[1];
1274  *bmax=a[mm+1][*kp+1];
1275  for (k=2;k<=nll;k++)
1276  {
1277  if (iabf == 0)
1278  {
1279  test=a[mm+1][ll[k]+1]-(*bmax);
1280  if (test > 0.0)
1281  {
1282  *bmax=a[mm+1][ll[k]+1];
1283  *kp=ll[k];
1284  }
1285  }
1286  else
1287  { /* abs values: have fixed it */
1288  test=fabs(a[mm+1][ll[k]+1])-fabs(*bmax);
1289  if (test > 0.0)
1290  {
1291  *bmax=a[mm+1][ll[k]+1];
1292  *kp=ll[k];
1293  }
1294  }
1295  }
1296 }
CanonicalForm test
Definition: cfModGcd.cc:4096

◆ simp2()

void simplex::simp2 ( mprfloat **  a,
int  n,
int  l2[],
int  nl2,
int *  ip,
int  kp,
mprfloat q1 
)
private

Definition at line 1298 of file mpr_numeric.cc.

1299 {
1300  int k,ii,i;
1301  mprfloat qp,q0,q;
1302 
1303  *ip= 0;
1304  for ( i=1; i <= nl2; i++ )
1305  {
1306  if ( a[l2[i]+1][kp+1] < -SIMPLEX_EPS )
1307  {
1308  *q1= -a[l2[i]+1][1] / a[l2[i]+1][kp+1];
1309  *ip= l2[i];
1310  for ( i= i+1; i <= nl2; i++ )
1311  {
1312  ii= l2[i];
1313  if (a[ii+1][kp+1] < -SIMPLEX_EPS)
1314  {
1315  q= -a[ii+1][1] / a[ii+1][kp+1];
1316  if (q - *q1 < -SIMPLEX_EPS)
1317  {
1318  *ip=ii;
1319  *q1=q;
1320  }
1321  else if (q - *q1 < SIMPLEX_EPS)
1322  {
1323  for ( k=1; k<= nn; k++ )
1324  {
1325  qp= -a[*ip+1][k+1]/a[*ip+1][kp+1];
1326  q0= -a[ii+1][k+1]/a[ii+1][kp+1];
1327  if ( q0 != qp ) break;
1328  }
1329  if ( q0 < qp ) *ip= ii;
1330  }
1331  }
1332  }
1333  }
1334  }
1335 }

◆ simp3()

void simplex::simp3 ( mprfloat **  a,
int  i1,
int  k1,
int  ip,
int  kp 
)
private

Definition at line 1337 of file mpr_numeric.cc.

1338 {
1339  int kk,ii;
1340  mprfloat piv;
1341 
1342  piv= 1.0 / a[ip+1][kp+1];
1343  for ( ii=1; ii <= i1+1; ii++ )
1344  {
1345  if ( ii -1 != ip )
1346  {
1347  a[ii][kp+1] *= piv;
1348  for ( kk=1; kk <= k1+1; kk++ )
1349  if ( kk-1 != kp )
1350  a[ii][kk] -= a[ip+1][kk] * a[ii][kp+1];
1351  }
1352  }
1353  for ( kk=1; kk<= k1+1; kk++ )
1354  if ( kk-1 != kp ) a[ip+1][kk] *= -piv;
1355  a[ip+1][kp+1]= piv;
1356 }

◆ zrovToIV()

intvec * simplex::zrovToIV ( )

Definition at line 1084 of file mpr_numeric.cc.

1085 {
1086  int i;
1087  intvec * iv = new intvec( n );
1088  for ( i= 1; i <= n; i++ )
1089  {
1090  IMATELEM(*iv,i,1)= izrov[i];
1091  }
1092  return iv;
1093 }

Field Documentation

◆ icase

int simplex::icase

Definition at line 201 of file mpr_numeric.h.

◆ iposv

int * simplex::iposv

Definition at line 203 of file mpr_numeric.h.

◆ izrov

int* simplex::izrov

Definition at line 203 of file mpr_numeric.h.

◆ LiPM

mprfloat** simplex::LiPM

Definition at line 205 of file mpr_numeric.h.

◆ LiPM_cols

int simplex::LiPM_cols
private

Definition at line 225 of file mpr_numeric.h.

◆ LiPM_rows

int simplex::LiPM_rows
private

Definition at line 225 of file mpr_numeric.h.

◆ m

int simplex::m

Definition at line 198 of file mpr_numeric.h.

◆ m1

int simplex::m1

Definition at line 200 of file mpr_numeric.h.

◆ m2

int simplex::m2

Definition at line 200 of file mpr_numeric.h.

◆ m3

int simplex::m3

Definition at line 200 of file mpr_numeric.h.

◆ n

int simplex::n

Definition at line 199 of file mpr_numeric.h.


The documentation for this class was generated from the following files: