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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 971 of file mpr_numeric.cc.

972  : LiPM_cols(cols), LiPM_rows(rows)
973 {
974  int i;
975 
978 
979  LiPM = (mprfloat **)omAlloc( LiPM_rows * sizeof(mprfloat *) ); // LP matrix
980  for( i= 0; i < LiPM_rows; i++ )
981  {
982  // Mem must be allocated aligned, also for type double!
983  LiPM[i] = (mprfloat *)omAlloc0Aligned( LiPM_cols * sizeof(mprfloat) );
984  }
985 
986  iposv = (int *)omAlloc0( 2*LiPM_rows*sizeof(int) );
987  izrov = (int *)omAlloc0( 2*LiPM_rows*sizeof(int) );
988 
989  m=n=m1=m2=m3=icase=0;
990 
991 #ifdef mprDEBUG_ALL
992  Print("LiPM size: %d, %d\n",LiPM_rows,LiPM_cols);
993 #endif
994 }
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 996 of file mpr_numeric.cc.

997 {
998  // clean up
999  int i;
1000  for( i= 0; i < LiPM_rows; i++ )
1001  {
1002  omFreeSize( (void *) LiPM[i], LiPM_cols * sizeof(mprfloat) );
1003  }
1004  omFreeSize( (void *) LiPM, LiPM_rows * sizeof(mprfloat *) );
1005 
1006  omFreeSize( (void *) iposv, 2*LiPM_rows*sizeof(int) );
1007  omFreeSize( (void *) izrov, 2*LiPM_rows*sizeof(int) );
1008 }
#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 1094 of file mpr_numeric.cc.

1095 {
1096  int i,ip,ir,is,k,kh,kp,m12,nl1,nl2;
1097  int *l1,*l2,*l3;
1098  mprfloat q1, bmax;
1099 
1100  if ( m != (m1+m2+m3) )
1101  {
1102  // error: bad input
1103  error(WarnS("simplex::compute: Bad input constraint counts!");)
1104  icase=-2;
1105  return;
1106  }
1107 
1108  l1= (int *) omAlloc0( (n+1) * sizeof(int) );
1109  l2= (int *) omAlloc0( (m+1) * sizeof(int) );
1110  l3= (int *) omAlloc0( (m+1) * sizeof(int) );
1111 
1112  nl1= n;
1113  for ( k=1; k<=n; k++ ) l1[k]=izrov[k]=k;
1114  nl2=m;
1115  for ( i=1; i<=m; i++ )
1116  {
1117  if ( LiPM[i+1][1] < 0.0 )
1118  {
1119  // error: bad input
1120  error(WarnS("simplex::compute: Bad input tableau!");)
1121  error(Warn("simplex::compute: in input Matrix row %d, column 1, value %f",i+1,LiPM[i+1][1]);)
1122  icase=-2;
1123  // free mem l1,l2,l3;
1124  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1125  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1126  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1127  return;
1128  }
1129  l2[i]= i;
1130  iposv[i]= n+i;
1131  }
1132  for ( i=1; i<=m2; i++) l3[i]= 1;
1133  ir= 0;
1134  if (m2+m3)
1135  {
1136  ir=1;
1137  for ( k=1; k <= (n+1); k++ )
1138  {
1139  q1=0.0;
1140  for ( i=m1+1; i <= m; i++ ) q1+= LiPM[i+1][k];
1141  LiPM[m+2][k]= -q1;
1142  }
1143 
1144  do
1145  {
1146  simp1(LiPM,m+1,l1,nl1,0,&kp,&bmax);
1147  if ( bmax <= SIMPLEX_EPS && LiPM[m+2][1] < -SIMPLEX_EPS )
1148  {
1149  icase= -1; // no solution found
1150  // free mem l1,l2,l3;
1151  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1152  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1153  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1154  return;
1155  }
1156  else if ( bmax <= SIMPLEX_EPS && LiPM[m+2][1] <= SIMPLEX_EPS )
1157  {
1158  m12= m1+m2+1;
1159  if ( m12 <= m )
1160  {
1161  for ( ip= m12; ip <= m; ip++ )
1162  {
1163  if ( iposv[ip] == (ip+n) )
1164  {
1165  simp1(LiPM,ip,l1,nl1,1,&kp,&bmax);
1166  if ( fabs(bmax) >= SIMPLEX_EPS)
1167  goto one;
1168  }
1169  }
1170  }
1171  ir= 0;
1172  --m12;
1173  if ( m1+1 <= m12 )
1174  for ( i=m1+1; i <= m12; i++ )
1175  if ( l3[i-m1] == 1 )
1176  for ( k=1; k <= n+1; k++ )
1177  LiPM[i+1][k] = -(LiPM[i+1][k]);
1178  break;
1179  }
1180  //#if DEBUG
1181  //print_bmat( a, m+2, n+3);
1182  //#endif
1183  simp2(LiPM,n,l2,nl2,&ip,kp,&q1);
1184  if ( ip == 0 )
1185  {
1186  icase = -1; // no solution found
1187  // free mem l1,l2,l3;
1188  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1189  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1190  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1191  return;
1192  }
1193  one: simp3(LiPM,m+1,n,ip,kp);
1194  // #if DEBUG
1195  // print_bmat(a,m+2,n+3);
1196  // #endif
1197  if ( iposv[ip] >= (n+m1+m2+1))
1198  {
1199  for ( k= 1; k <= nl1; k++ )
1200  if ( l1[k] == kp ) break;
1201  --nl1;
1202  for ( is=k; is <= nl1; is++ ) l1[is]= l1[is+1];
1203  ++(LiPM[m+2][kp+1]);
1204  for ( i= 1; i <= m+2; i++ ) LiPM[i][kp+1] = -(LiPM[i][kp+1]);
1205  }
1206  else
1207  {
1208  if ( iposv[ip] >= (n+m1+1) )
1209  {
1210  kh= iposv[ip]-m1-n;
1211  if ( l3[kh] )
1212  {
1213  l3[kh]= 0;
1214  ++(LiPM[m+2][kp+1]);
1215  for ( i=1; i<= m+2; i++ )
1216  LiPM[i][kp+1] = -(LiPM[i][kp+1]);
1217  }
1218  }
1219  }
1220  is= izrov[kp];
1221  izrov[kp]= iposv[ip];
1222  iposv[ip]= is;
1223  } while (ir);
1224  }
1225  /* end of phase 1, have feasible sol, now optimize it */
1226  loop
1227  {
1228  // #if DEBUG
1229  // print_bmat( a, m+1, n+5);
1230  // #endif
1231  simp1(LiPM,0,l1,nl1,0,&kp,&bmax);
1232  if (bmax <= /*SIMPLEX_EPS*/0.0)
1233  {
1234  icase=0; // finite solution found
1235  // free mem l1,l2,l3
1236  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1237  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1238  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1239  return;
1240  }
1241  simp2(LiPM,n,l2,nl2,&ip,kp,&q1);
1242  if (ip == 0)
1243  {
1244  //printf("Unbounded:");
1245  // #if DEBUG
1246  // print_bmat( a, m+1, n+1);
1247  // #endif
1248  icase=1; /* unbounded */
1249  // free mem
1250  omFreeSize( (void *) l3, (m+1) * sizeof(int) );
1251  omFreeSize( (void *) l2, (m+1) * sizeof(int) );
1252  omFreeSize( (void *) l1, (n+1) * sizeof(int) );
1253  return;
1254  }
1255  simp3(LiPM,m,n,ip,kp);
1256  is= izrov[kp];
1257  izrov[kp]= iposv[ip];
1258  iposv[ip]= is;
1259  }/*for ;;*/
1260 }
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:965
#define SIMPLEX_EPS
Definition: mpr_numeric.h:181
#define loop
Definition: structs.h:80

◆ mapFromMatrix()

BOOLEAN simplex::mapFromMatrix ( matrix  m)

Definition at line 1010 of file mpr_numeric.cc.

1011 {
1012  int i,j;
1013 // if ( MATROWS( m ) > LiPM_rows || MATCOLS( m ) > LiPM_cols ) {
1014 // WarnS("");
1015 // return FALSE;
1016 // }
1017 
1018  number coef;
1019  for ( i= 1; i <= MATROWS( mm ); i++ )
1020  {
1021  for ( j= 1; j <= MATCOLS( mm ); j++ )
1022  {
1023  if ( MATELEM(mm,i,j) != NULL )
1024  {
1025  coef= pGetCoeff( MATELEM(mm,i,j) );
1026  if ( coef != NULL && !nIsZero(coef) )
1027  LiPM[i][j]= (double)(*(gmp_float*)coef);
1028  //#ifdef mpr_DEBUG_PROT
1029  //Print("%f ",LiPM[i][j]);
1030  //#endif
1031  }
1032  }
1033  // PrintLn();
1034  }
1035 
1036  return TRUE;
1037 }
#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 1039 of file mpr_numeric.cc.

1040 {
1041  int i,j;
1042 // if ( MATROWS( mm ) < LiPM_rows-3 || MATCOLS( m ) < LiPM_cols-2 ) {
1043 // WarnS("");
1044 // return NULL;
1045 // }
1046 
1047 //Print(" %d x %d\n",MATROWS( mm ),MATCOLS( mm ));
1048 
1049  number coef;
1050  gmp_float * bla;
1051  for ( i= 1; i <= MATROWS( mm ); i++ )
1052  {
1053  for ( j= 1; j <= MATCOLS( mm ); j++ )
1054  {
1055  pDelete( &(MATELEM(mm,i,j)) );
1056  MATELEM(mm,i,j)= NULL;
1057 //Print(" %3.0f ",LiPM[i][j]);
1058  if ( LiPM[i][j] != 0.0 )
1059  {
1060  bla= new gmp_float(LiPM[i][j]);
1061  coef= (number)bla;
1062  MATELEM(mm,i,j)= pOne();
1063  pSetCoeff( MATELEM(mm,i,j), coef );
1064  }
1065  }
1066 //PrintLn();
1067  }
1068 
1069  return mm;
1070 }
#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 1072 of file mpr_numeric.cc.

1073 {
1074  int i;
1075  intvec * iv = new intvec( m );
1076  for ( i= 1; i <= m; i++ )
1077  {
1078  IMATELEM(*iv,i,1)= iposv[i];
1079  }
1080  return iv;
1081 }
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 1262 of file mpr_numeric.cc.

1263 {
1264  int k;
1265  mprfloat test;
1266 
1267  if( nll <= 0)
1268  { /* init'tion: fixed */
1269  *bmax = 0.0;
1270  return;
1271  }
1272  *kp=ll[1];
1273  *bmax=a[mm+1][*kp+1];
1274  for (k=2;k<=nll;k++)
1275  {
1276  if (iabf == 0)
1277  {
1278  test=a[mm+1][ll[k]+1]-(*bmax);
1279  if (test > 0.0)
1280  {
1281  *bmax=a[mm+1][ll[k]+1];
1282  *kp=ll[k];
1283  }
1284  }
1285  else
1286  { /* abs values: have fixed it */
1287  test=fabs(a[mm+1][ll[k]+1])-fabs(*bmax);
1288  if (test > 0.0)
1289  {
1290  *bmax=a[mm+1][ll[k]+1];
1291  *kp=ll[k];
1292  }
1293  }
1294  }
1295 }
CanonicalForm test
Definition: cfModGcd.cc:4098

◆ simp2()

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

Definition at line 1297 of file mpr_numeric.cc.

1298 {
1299  int k,ii,i;
1300  mprfloat qp,q0,q;
1301 
1302  *ip= 0;
1303  for ( i=1; i <= nl2; i++ )
1304  {
1305  if ( a[l2[i]+1][kp+1] < -SIMPLEX_EPS )
1306  {
1307  *q1= -a[l2[i]+1][1] / a[l2[i]+1][kp+1];
1308  *ip= l2[i];
1309  for ( i= i+1; i <= nl2; i++ )
1310  {
1311  ii= l2[i];
1312  if (a[ii+1][kp+1] < -SIMPLEX_EPS)
1313  {
1314  q= -a[ii+1][1] / a[ii+1][kp+1];
1315  if (q - *q1 < -SIMPLEX_EPS)
1316  {
1317  *ip=ii;
1318  *q1=q;
1319  }
1320  else if (q - *q1 < SIMPLEX_EPS)
1321  {
1322  for ( k=1; k<= nn; k++ )
1323  {
1324  qp= -a[*ip+1][k+1]/a[*ip+1][kp+1];
1325  q0= -a[ii+1][k+1]/a[ii+1][kp+1];
1326  if ( q0 != qp ) break;
1327  }
1328  if ( q0 < qp ) *ip= ii;
1329  }
1330  }
1331  }
1332  }
1333  }
1334 }

◆ simp3()

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

Definition at line 1336 of file mpr_numeric.cc.

1337 {
1338  int kk,ii;
1339  mprfloat piv;
1340 
1341  piv= 1.0 / a[ip+1][kp+1];
1342  for ( ii=1; ii <= i1+1; ii++ )
1343  {
1344  if ( ii -1 != ip )
1345  {
1346  a[ii][kp+1] *= piv;
1347  for ( kk=1; kk <= k1+1; kk++ )
1348  if ( kk-1 != kp )
1349  a[ii][kk] -= a[ip+1][kk] * a[ii][kp+1];
1350  }
1351  }
1352  for ( kk=1; kk<= k1+1; kk++ )
1353  if ( kk-1 != kp ) a[ip+1][kk] *= -piv;
1354  a[ip+1][kp+1]= piv;
1355 }

◆ zrovToIV()

intvec * simplex::zrovToIV ( )

Definition at line 1083 of file mpr_numeric.cc.

1084 {
1085  int i;
1086  intvec * iv = new intvec( n );
1087  for ( i= 1; i <= n; i++ )
1088  {
1089  IMATELEM(*iv,i,1)= izrov[i];
1090  }
1091  return iv;
1092 }

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: