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glemke.c
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/**
* \file glemke.c
*
* LCP solver with GNU Multi Precision arithmetic
*
* Author: Bernhard von Stengel [email protected] 14 July 2000
*/
/* GSoC12: Tobenna Peter, Igwe */
#define GLEMKE
#include <stdio.h>
#include <stdlib.h>
/* free() */
#include <string.h>
/* strcpy */
#include "alloc.h"
#include "col.h"
#include "lemke.h"
#include "gmp.h"
#include "gmpwrap.h"
#include "equilibrium.h"
long record_digits; /* not in the gmp package */
/* used for tableau: */
#define Z(i) (i)
#define W(i) (i+n)
/* VARS = 0..2n = Z(0) .. Z(n) W(1) .. W(n) */
/* ROWCOL = 0..2n, 0 .. n-1: tabl rows (basic vars) */
/* n .. 2n: tabl cols 0..n (cobasic) */
#define RHS (n+1) /* q-column of tableau */
#define TABCOL(v) (bascobas[v]-n)
/* v in VARS, v cobasic: TABCOL(v) is v's tableau col */
/* v basic: TABCOL(v) < 0, TABCOL(v)+n is v's row */
/* LCP input */
Rat **lcpM;
Rat *rhsq;
Rat *vecd;
int lcpdim = 0; /* set in setlcp */
static int n; /* LCP dimension as used here */
/* LCP result */
Rat *solz;
int pivotcount;
/* tableau: */
static gmpt **A; /**< tableau */
static int *bascobas; /**< VARS -> ROWCOL */
static int *whichvar; /**< ROWCOL -> VARS, inverse of bascobas */
/** scale factors for variables z.
* scfa[Z(0)] for d, scfa[RHS] for q
* scfa[Z(1..n)] for cols of M
* result variables to be multiplied with these
*/
static gmpt *scfa;
static gmpt det; /**< determinant */
static int *lextested, *lexcomparisons;/**< statistics for lexminvar */
static int *leavecand;
/* should be local to lexminvar but defined globally for economy */
/* GSoC12: Tobenna Peter, Igwe */
/* User input */
int nrows; /* The number of rows in the payoff matrix */
int ncols; /* The number of columns in the payoff matrix */
int k; /* The missing label */
int k2;
Rat** payoffA; /* The payoff matrix A */
Rat** payoffB; /* The payoff matrix B */
gmpt** invAB; /**< Represents the inverse of AB */
node* neg; /* The negative indexed equilibria */
node* pos; /* The positive indexed equilibria */
/*------------------ error message ----------------*/
/**
* Prints out an error message and exits.
*
* \param info The error message
*/
void errexit (char *info)
{
fflush(stdout);
fprintf(stderr, "Error: %s\n", info);
fprintf(stderr, "Lemke terminated unsuccessfully.\n");
exit(1);
}
/* declares */
int assertbasic (int v, const char *info);
/*------------------ memory allocation -------------------------*/
/**
* Allocates memory for the LCP given its dimensions.
* If the LCP has been previously allocated, it frees the memory and
* reallocates it. If the dimension given for the LCP is < 0 or
* > MAXLCPDIM then it exits with an error.
*
* \param newn The dimension of the LCP.
*/
void setlcp (int newn)
{
if (newn < 1 || newn > MAXLCPDIM)
{
fprintf(stderr, "Problem dimension n= %d not allowed. ", newn);
fprintf(stderr, "Minimum n is 1, maximum %d.\n", MAXLCPDIM);
exit(1);
}
if (lcpdim > 0) /* free previously used space */
{
FREE2(lcpM, lcpdim);
free(rhsq);
free(vecd);
free(solz);
G2CLEAR(A, lcpdim, lcpdim + 2);
FREE2(A, lcpdim);
GCLEAR(scfa, lcpdim + 2);
free(scfa);
free(bascobas);
free(whichvar);
free(leavecand);
gclear(det);
G2CLEAR(invAB, lcpdim, lcpdim);
FREE2(invAB, lcpdim);
}
n = lcpdim = newn;
/* LCP input/output data */
T2ALLOC (lcpM, n, n, Rat);
rhsq = TALLOC(n, Rat);
vecd = TALLOC(n, Rat);
solz = TALLOC(n, Rat);
/* tableau */
T2ALLOC (A, n, n+2, gmpt);
G2INIT (A, n, n+2);
scfa = TALLOC (n+2, gmpt);
GINIT (scfa, n+2);
ginit(det);
bascobas = TALLOC(2*n+1, int);
whichvar = TALLOC(2*n+1, int);
lextested = TALLOC(n+1, int);
lexcomparisons = TALLOC(n+1, int);
leavecand = TALLOC(n, int);
/* should be local to lexminvar but allocated here for economy */
/* initialize all LCP entries to zero */
{
int i,j;
Rat nix = ratfromi(0);
for (i=0; i<n; i++)
{
for (j=0; j<n; j++)
lcpM [i] [j] = nix;
vecd [i] = rhsq [i] = nix;
}
}
T2ALLOC(invAB, n, n, gmpt);
G2INIT(invAB, n, n);
} /* end of setlcp(newn) */
/**
* Checks that the values for q and d are valid.
* Asserts that d >= 0 and not q >= 0 (o/w trivial sol)
* and that q[i] < 0 implies d[i] > 0
*/
void isqdok (void)
{
int i;
int isqpos = 1;
for (i=0; i<n; i++)
{
if (gnegative(vecd[i].num))
{
char str[MAXSTR];
rattoa(vecd[i], str);
fprintf(stderr, "Covering vector d[%d] = %s negative\n",
i+1, str);
errexit("Cannot start Lemke.");
}
else if (gnegative(rhsq[i].num))
{
isqpos = 0;
if (gzero(vecd[i].num))
{
char str[MAXSTR];
rattoa(rhsq[i], str);
fprintf(stderr, "Covering vector d[%d] = 0 ", i+1);
fprintf(stderr, "where q[%d] = %s is negative.\n",
i+1, str);
errexit("Cannot start Lemke.");
}
}
} /* end of for(i=...) */
if (isqpos)
{
printf("No need to start Lemke since q>=0. ");
printf("Trivial solution z=0.\n");
exit(0);
}
} /* end of isqdok() */
/* ------------------- tableau setup ------------------ */
/**
* Initialise tableau variables.
* Z(0)...Z(n) nonbasic, W(1)...W(n) basic
*/
void inittablvars (void)
{
int i;
for (i=0; i<=n; i++)
{
bascobas[Z(i)] = n+i;
whichvar[n+i] = Z(i);
}
for (i=1; i<=n; i++)
{
bascobas[W(i)] = i-1;
whichvar[i-1] = W(i);
}
} /* end of inittablvars() */
/**
* Fill tableau from M, q, d
*/
void filltableau (void)
{
int i,j;
gmpt den, num;
gmpt tmp, tmp2;
ginit(tmp); ginit(tmp2);
ginit(den); ginit(num);
for (j=0; j<=n+1; j++)
{
/* compute lcm scfa[j] of denominators for col j of A */
gitomp(1, scfa[j]);
for (i=0; i<n; i++)
{
/*den = (j==0) ? vecd[i].den :
(j==RHS) ? rhsq[i].den : lcpM[i][j-1].den ;*/
if(j == 0)
{
gset(den, vecd[i].den);
}
else if(j == RHS)
{
gset(den, rhsq[i].den);
}
else
{
gset(den, lcpM[i][j-1].den);
}
gset(tmp, den);
glcm(scfa[j], tmp);
if (j == 0)
record_digits = mpz_sizeinbase( scfa[j], 10)/4 ;
}
/* fill in col j of A */
for (i=0; i<n; i++)
{
/*den = (j==0) ? vecd[i].den :
(j==RHS) ? rhsq[i].den : lcpM[i][j-1].den ;*/
if(j == 0)
{
gset(den, vecd[i].den);
}
else if(j == RHS)
{
gset(den, rhsq[i].den);
}
else
{
gset(den, lcpM[i][j-1].den);
}
/*num = (j==0) ? vecd[i].num :
(j==RHS) ? rhsq[i].num : lcpM[i][j-1].num ;*/
if(j == 0)
{
gset(num, vecd[i].num);
}
else if(j == RHS)
{
gset(num, rhsq[i].num);
}
else
{
gset(num, lcpM[i][j-1].num);
}
/* cols 0..n of A contain LHS cobasic cols of Ax = b */
/* where the system is here -Iw + dz_0 + Mz = -q */
/* cols of q will be negated after first min ratio test */
/* A[i][j] = num * (scfa[j] / den), fraction is integral */
/*gitomp (den, tmp);*/
gset(tmp, den);
gexactdivint(scfa[j], tmp, tmp2);
/*gitomp (num, tmp);*/
gset(tmp, num);
gmulint(tmp2, tmp, A[i][j]);
}
} /* end of for(j=...) */
inittablvars();
gitomp (-1, det);
gclear(tmp); gclear(tmp2);
gclear(num); gclear(den);
} /* end of filltableau() */
/* ---------------- output routines ------------------- */
/**
* Prints the LCP to the standard output
*/
void outlcp (void)
{
int i,j ;
Rat a;
char s[LCPSTRL];
printf("LCP dimension: %d\n", n);
colset(n + 2);
for (j=0; j<n; j++)
colpr("");
colpr("d");
colpr("q");
colnl();
for (i=0; i<n; i++)
{
for (j=0; j<n; j++)
{
a = lcpM [i] [j];
if (gzero(a.num))
colpr(".");
else
{
rattoa(a, s);
colpr(s);
}
}
rattoa( vecd [i], s);
colpr(s);
rattoa( rhsq [i], s);
colpr(s);
}
colout();
}
/**
* Create a string s representing v in VARS, e.g. "w2"
*
* \param v Variable to be converted
* \param s String to be created
* \returns length of string s
*/
int vartoa(int v, char s[])
{
if (v > n)
return sprintf(s, "w%d", v-n);
else
return sprintf(s, "z%d", v);
}
/**
* Output the current tableau, column-adjusted
*/
void outtabl (void)
{
int i, j;
char s[INFOSTRINGLENGTH];
char smp [MAXGMPCHARS]; /* string to print mp into */
gmptoa (det, smp);
printf("Determinant: %s\n", smp);
colset(n+3);
colleft(0);
colpr("var"); /* headers describing variables */
for (j=0; j<=n+1; j++)
{
if (j==RHS)
colpr("RHS");
else
{
vartoa(whichvar[j+n], s);
colpr(s);
}
}
colpr("scfa"); /* scale factors */
for (j=0; j<=n+1; j++)
{
if (j==RHS)
gmptoa(scfa[RHS], smp);
else if (whichvar[j+n] > n) /* col j is some W */
sprintf(smp, "1");
else /* col j is some Z: scfa */
gmptoa( scfa[whichvar[j+n]], smp);
colpr(smp);
}
colnl();
for (i=0; i<n; i++) /* print row i */
{
vartoa(whichvar[i], s);
colpr(s);
for (j=0; j<=n+1; j++)
{
gmptoa( A[i][j], smp);
if (strcmp(smp, "0")==0)
colpr(".");
else
colpr(smp);
}
}
colout();
printf("-----------------end of tableau-----------------\n");
} /* end of outtabl() */
/**
* Output the current basic solution
*/
void outsol (void)
{
char s[INFOSTRINGLENGTH];
char smp [2*MAXGMPCHARS+2]; /* string to print mp into */
/* string to print 2 mp's into */
int i, row, pos;
gmpt num, den;
ginit(num); ginit(den);
colset(n+2); /* column printing to see complementarity of w and z */
colpr("basis=");
for (i=0; i<=n; i++)
{
if (bascobas[Z(i)]<n)
/* Z(i) is a basic variable */
vartoa(Z(i), s);
else if (i>0 && bascobas[W(i)]<n)
/* Z(i) is a basic variable */
vartoa(W(i), s);
else
strcpy (s, " ");
colpr(s);
}
colpr("z=");
for (i=0; i<=2*n; i++)
{
if ( (row = bascobas[i]) < n) /* i is a basic variable */
{
if (i<=n) /* printing Z(i) */
/* value of Z(i): scfa[Z(i)]*rhs[row] / (scfa[RHS]*det) */
gmulint(scfa[Z(i)], A[row][RHS], num);
else /* printing W(i-n) */
/* value of W(i-n) is rhs[row] / (scfa[RHS]*det) */
gset(num, A[row][RHS]);
gmulint(det, scfa[RHS], den);
greduce(num, den);
gmptoa(num, smp);
pos = strlen(smp);
if ( !gone(den)) /* add the denominator */
{
sprintf(&smp[pos], "/");
gmptoa(den, &smp[pos+1]);
}
colpr(smp);
}
else /* i is nonbasic */
colpr("0");
if (i==n) /* new line since printing slack vars w next */
{
colpr("w=");
colpr(""); /* for complementarity in place of W(0) */
}
} /* end of for (i=...) */
colout();
printf("\n Number of pivots: %d\n", pivotcount);
gclear(num); gclear(den);
} /* end of outsol */
/**
* Current basic solution turned into solz [0..n-1].
* Note that Z(1)..Z(n) become indices 0..n-1.
*
* \returns 0
*/
Bool notokcopysol (void)
{
Bool notok = 0;
int i, row;
gmpt num, den;
ginit(num); ginit(den);
for (i=1; i<=n; i++)
if ( (row = bascobas[i]) < n) /* i is a basic variable */
{
/* value of Z(i): scfa[Z(i)]*rhs[row] / (scfa[RHS]*det) */
gmulint(scfa[Z(i)], A[row][RHS], num);
gmulint(det, scfa[RHS], den);
greduce(num, den);
/*
if ( gmptoi(num, &(solz[i-1].num), 1) )
{
printf("(Numerator of z%d overflown)\n", i);
notok = 1;
}
if ( gmptoi(den, &(solz[i-1].den), 1) )
{
printf("(Denominator of z%d overflown)\n", i);
notok = 1;
}*/
gset(solz[i-1].num, num);
gset(solz[i-1].den, den);
}
else /* i is nonbasic */
solz[i-1] = ratfromi(0);
gclear(num); gclear(den);
return notok;
} /* end of copysol */
/* --------------- test output and exception routines ---------------- */
/**
* Assert that v in VARS is a basic variable.
* If v is not basic, then the program terminates with an error message
*
* \param v The variable to be asserted
* \param info Part of the error message.
*/
int assertbasic (int v, const char *info)
{
char s[INFOSTRINGLENGTH];
if (bascobas[v] >= n)
{
vartoa(v, s);
fprintf(stderr, "%s: Cobasic variable %s should be basic.\n", info, s);
/*errexit("");*/
return -1;
}
return 0;
}
/**
* Assert that v in VARS is a cobasic variable.
* If v is not cobasic, the program terminates with an error message
*
* \param v The variable to be asserted
* \param info Part of the error message
*/
int assertcobasic (int v, char *info)
{
char s[INFOSTRINGLENGTH];
if (TABCOL(v) < 0)
{
/*
vartoa(v, s);
fprintf(stderr, "%s: Basic variable %s should be cobasic.\n", info, s);
errexit("");*/
return -1;
}
return 1;
}
/**
* Document the current pivot.
* Asserts leave is basic and enter is cobasic, and
* print the current pivot
*
* \param leave The leaving variable
* \param enter The entering variable
*/
int docupivot (int leave, int enter, Flagsrunlemke flags)
{
char s[INFOSTRINGLENGTH];
if (assertbasic(leave, "docupivot") < 0)
return -1;
if (assertcobasic(enter, "docupivot") < 0)
return -1;
if(flags.boutpiv)
{
vartoa(leave, s);
printf("leaving: %-4s ", s);
vartoa(enter, s);
printf("entering: %s\n", s);
}
return 0;
} /* end of docupivot */
/**
* Outputs an error message and exits when a ray termination
* occurs while trying to pivot in the entering variable.
*
* \param enter The entering variable.
*/
void raytermination (int enter)
{
char s[INFOSTRINGLENGTH];
vartoa(enter, s);
fprintf(stderr, "Ray termination when trying to enter %s\n", s);
outtabl();
printf("Current basis, not an LCP solution:\n");
outsol();
errexit("");
}
/**
* Tests the tableau variables. If the tableau variables are wrong,
* output error and continue.
*/
void testtablvars(void)
{
int i, j;
for (i=0; i<=2*n; i++) /* check if somewhere tableauvars wrong */
if (bascobas[whichvar[i]]!=i || whichvar[bascobas[i]]!=i)
/* found an inconsistency, print everything */
{
printf("Inconsistent tableau variables:\n");
for (j=0; j<=2*n; j++)
{
printf("var j:%3d bascobas:%3d whichvar:%3d ",
j, bascobas[j], whichvar[j]);
printf(" b[w[j]]==j: %1d w[b[j]]==j: %1d\n",
bascobas[whichvar[j]]==j, whichvar[bascobas[j]]==j);
}
break;
}
}
/* --------------- pivoting and related routines -------------- */
/**
* Complement of v in VARS. Error if v==Z(0).
* This is W(i) for Z(i) and vice versa, i=1...n.
*
* \param v The variable
* \returns The complement of v. Z(i) if v is W(i) and vice versa.
*/
int complement (int v)
{
if (v==Z(0))
errexit("Attempt to find complement of z0.");
return (v > n) ? Z(v-n) : W(v) ;
} /* end of complement (v) */
/**
* Initialize statistics for minimum ratio test
*/
void initstatistics(void)
{
int i;
for (i=0; i<=n; i++)
lextested[i] = lexcomparisons[i] = 0;
}
/**
* Output statistics of minimum ratio test
*/
void outstatistics(void)
{
int i;
char s[LCPSTRL];
colset(n+2);
colleft(0);
colpr("lex-column");
for (i=0; i<=n; i++)
colipr(i);
colnl();
colpr("times tested");
for (i=0; i<=n; i++)
colipr(lextested[i]);
colpr("% times tested");
if (lextested[0] > 0)
{
colpr("100");
for (i=1; i<=n; i++)
{
sprintf(s, "%2.0f",
(double) lextested[i] * 100.0 / (double) lextested[0]);
colpr(s);
}
}
else
colnl();
colpr("avg comparisons");
for (i=0; i<=n; i++)
if (lextested[i] > 0)
{
sprintf(s, "%1.1f",
(double) lexcomparisons[i] / (double) lextested[i]);
colpr(s);
}
else
colpr("-");
colout();
}
/**
* Returns the leaving variable in VARS. This is given by lexmin row,
* when enter in VARS is entering variable
* only positive entries of entering column tested
* boolean *z0leave indicates back that z0 can leave the
* basis, but the lex-minratio test is performed fully,
* so the returned value might not be the index of z0.
*
* \param enter The entering variable
* \param z0leave Stores a boolean value stating if z0 can leave.
* \returns The leaving variable
*/
int lexminvar (int enter, int *z0leave)
{
int col, i, j, testcol;
int numcand;
gmpt tmp1, tmp2;
ginit(tmp1); ginit(tmp2);
assertcobasic(enter, "Lexminvar");
col = TABCOL(enter);
numcand = 0;
/* leavecand [0..numcand-1] = candidates (rows) for leaving var */
/* start with leavecand = { i | A[i][col] > 0 } */
for (i=0; i<n; i++)
if (gpositive (A[i][col]))
leavecand[numcand++] = i;
if (numcand==0)
return -1;
/*raytermination(enter);*/
if (numcand==1)
{
lextested[0] += 1 ;
lexcomparisons[0] += 1 ;
*z0leave = (leavecand[0] == bascobas[Z(0)]);
}
for (j = 0; numcand > 1; j++)
/* as long as there is more than one leaving candidate perform
* a minimum ratio test for the columns of j in RHS, W(1),... W(n)
* in the tableau. That test has an easy known result if
* the test column is basic or equal to the entering variable.
*/
{
if (j>n) /* impossible, perturbed RHS should have full rank */
errexit("lex-minratio test failed");
lextested[j] += 1 ;
lexcomparisons[j] += numcand ;
testcol = (j==0) ? RHS : TABCOL(W(j)) ;
if (testcol != col) /* otherwise nothing will change */
{
if (testcol >= 0)
/* not a basic testcolumn: perform minimum ratio tests */
{
int sgn;
int newnum = 0;
/* leavecand[0..newnum] contains the new candidates */
for (i=1; i < numcand; i++)
/* investigate remaining candidates */
{
gmulint(A[leavecand[0]][testcol], A[leavecand[i]][col], tmp1);
gmulint(A[leavecand[i]][testcol], A[leavecand[0]][col], tmp2);
gsub (tmp1, tmp1, tmp2) ;
sgn = gsgn(tmp1) ;
/* sign of A[l_0,t] / A[l_0,col] - A[l_i,t] / A[l_i,col] */
/* note only positive entries of entering column considered */
if (sgn==0) /* new ratio is the same as before */
leavecand[++newnum] = leavecand[i];
else if (sgn==1) /* new smaller ratio detected */
leavecand[newnum=0] = leavecand[i];
}
numcand = newnum+1;
}
else
/* testcol < 0: W(j) basic, Eliminate its row from leavecand */
/* since testcol is the jth unit column */
for (i=0; i < numcand; i++)
if (leavecand[i] == bascobas[W(j)])
{
leavecand[i] = leavecand[--numcand];
/* shuffling of leavecand allowed */
break;
}
} /* end of if(testcol != col) */
} /* end of for ( ... numcand > 1 ... ) */
gclear(tmp1); gclear(tmp2);
*z0leave = (leavecand[0] == bascobas[Z(0)]);
return whichvar[leavecand[0]];
} /* end of lexminvar (col, *z0leave); */
/**
* Returns the leaving variable in VARS as entered by user.
* When enter in VARS is entering variable
* only nonzero entries of entering column admitted
* boolean *z0leave indicates back that z0 has been
* entered as leaving variable, and then
* the returned value is the index of z0.
*
* \param enter The entering variable
* \param z0leave Stores a boolean value stating if z0 can leave.
* \returns The leaving variable
*/
int interactivevar (int enter, int *z0leave)
{
char s[INFOSTRINGLENGTH], instring[2];
int inp, col, var;
int breject = 1;
assertcobasic(enter, "interactivevar");
col = TABCOL(enter);
vartoa(enter, s);
printf(" Entering variable (column): %s\n", s);
while (breject)
{
printf(" Leaving row (basic variable z.. or w..), ");
printf("or 't' for tableau:\n");
strcpy(instring, "?");
if (scanf("%1s", instring)==EOF)
{
printf ("Input terminated too early with EOF\n");
exit(1);
}
if ( instring[0] == 't')
{
printf("\n");
outtabl();
vartoa(enter, s);
printf(" Entering variable (column): %s\n", s);
continue;
}
scanf("%d", &inp);
printf(" You typed %s%d\n", instring, inp);
if ( (inp < 0) || (inp > n))
{
printf("Variable index %d outside 0..n=%d\n",
inp, n);
continue;
}
if ( instring[0] == 'w')
{
if (inp == 0)
{
printf("Variable w0 not allowed\n");
continue;
}
var = inp + n;
}
else if ( instring[0] == 'z')
var = inp;
else
{
printf("Variable not starting with z or w\n");
continue;
}
/* var == variable in VARS giving what has been input */
if ( bascobas[var] >= n)
{
vartoa (var, s);
printf("Variable %s not basic\n", s);
continue;
}
if ( gzero( A [bascobas[var]] [col] ) )
{
vartoa (var, s);
printf("Row %s has zero pivot element, not allowed\n", s);
continue;
}
breject = 0; /* now everything ok */
} /* end of while (breject) for input */
*z0leave = (var == Z(0));
return var;
} /* end of interactivevar (col, *z0leave); */
/**
* Negates tableau column col
* \param col The column of the tableau to be negated.
*/
void negcol(int col)
{
int i;
for (i=0; i<n; i++)
gchangesign(A[i][col]);
}
/**
* Negate tableau row. Used in pivot().
* \param row The row of the tableau to be negated.
*/
void negrow(int row)
{
int j;
for (j=0; j<=n+1; j++)
if (!gzero(A[row][j]))
gchangesign(A[row][j]);
}
/**
* Pivots the tableau given the entering and leaving variable.
* leave, enter in VARS defining row, col of A
* pivot tableau on the element A[row][col] which must be nonzero
* afterwards tableau normalized with positive determinant
* and updated tableau variables
*
* \param leave The leaving variable
* \param enter The entering variable
*/
void pivot (int leave, int enter)
{
int row, col, i, j;
Bool nonzero, negpiv;
gmpt pivelt, tmp1, tmp2;
ginit(pivelt); ginit(tmp1); ginit(tmp2);
row = bascobas[leave];
col = TABCOL(enter);
gset (pivelt, A[row][col]); /* pivelt anyhow later new determinant */
negpiv = gnegative (pivelt);
if (negpiv)
gchangesign(pivelt);
for (i=0; i<n; i++)
if (i != row) /* A[row][..] remains unchanged */
{
nonzero = !gzero(A[i][col]);
for (j=0; j<=n+1; j++) /* assume here RHS==n+1 */
if (j != col)
/* A[i,j] =
(A[i,j] A[row,col] - A[i,col] A[row,j])/ det */
{
gmulint (A[i][j], pivelt, tmp1);
if (nonzero)
{
gmulint(A[i][col], A[row][j], tmp2);
if (negpiv)
gadd(tmp1, tmp1, tmp2);
else
gsub(tmp1, tmp1, tmp2);
}
gexactdivint (tmp1, det, A[i][j]);
}
/* row i has been dealt with, update A[i][col] safely */
if (nonzero && !negpiv)
gchangesign (A[i][col]);
} /* end of for (i=...) */
gset(A[row][col], det);
if (negpiv)
negrow(row);
gset(det, pivelt); /* by construction always positive */
/* update tableau variables */
bascobas[leave] = col+n; whichvar[col+n] = leave;
bascobas[enter] = row; whichvar[row] = enter;
gclear(pivelt); gclear(tmp1); gclear(tmp2);
} /* end of pivot (leave, enter) */
/**
* Returns the best response of a given strategy.
*
* \param l A players strategy such that 1 <= l <= m+n
* \returns The opponents best response strategy
*/
/* GSoC12: Tobenna Peter, Igwe */
int bestResponse(int l)
{
/* m is the best response */
int m = 0;
if(l > nrows) /* if l is p2's strategy*/
{
/* m < l <= m+n */
l -= (nrows + 1);
int i;
/* The best response to l is the row with min value for the lth column
* because payoffA is -A.
*/
for(i = 1; i < nrows; ++i)
{
if(ratgreat(payoffA[m][l], payoffA[i][l]))
m = i;
if(ratiseq(payoffA[m][l], payoffA[i][l])) /* Due to lexmin ratio */
m = i;
}
/* Converts m to p1's strategy */
m += 1;
}
else /* if l is p1's strategy */
{
/* 1 <= l <= m */