void
reducearray ( lrs_mp_vector p, long n )
/* find largest gcd of p[0]..p[n-1] and divide through */
{
lrs_mp divisor;
lrs_mp Temp;
long i = 0L;
while ( ( i < n ) && zero ( p[i] ) )
i++;
if ( i == n )
return;
copy ( divisor, p[i] );
storesign ( divisor, POS );
i++;
while ( i < n ) {
if ( !zero ( p[i] ) ) {
copy ( Temp, p[i] );
storesign ( Temp, POS );
gcd ( divisor, Temp );
}
i++;
}
/* reduce by divisor */
for ( i = 0; i < n; i++ )
if ( !zero ( p[i] ) )
reduceint ( p[i], divisor );
} /* end of reducearray */
void
reduce ( lrs_mp Na, lrs_mp Da ) { /* reduces Na Da by gcd(Na,Da) */
lrs_mp Nb, Db, Nc, Dc;
copy ( Nb, Na );
copy ( Db, Da );
storesign ( Nb, POS );
storesign ( Db, POS );
copy ( Nc, Na );
copy ( Dc, Da );
gcd ( Nb, Db ); /* Nb is the gcd(Na,Da) */
exactdivint ( Nc, Nb, Na );
exactdivint ( Dc, Nb, Da );
}
void
atomp ( char s[], lrs_mp a ) { /*convert string to lrs_mp integer */
lrs_mp mpone;
long diff, ten, i, sig;
itomp ( 1L, mpone );
ten = 10L;
for ( i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++ );
/*skip white space */
sig = POS;
if ( s[i] == '+' || s[i] == '-' ) /* sign */
sig = ( s[i++] == '+' ) ? POS : NEG;
itomp ( 0L, a );
while ( s[i] >= '0' && s[i] <= '9' ) {
diff = s[i] - '0';
linint ( a, ten, mpone, diff );
i++;
}
storesign ( a, sig );
if ( s[i] ) {
fprintf ( stderr, "\nIllegal character in number: '%s'\n", s + i );
exit ( 1 );
}
} /* end of atomp */
void
mulint ( lrs_mp a, lrs_mp b, lrs_mp c ) /* multiply two integers a*b --> c */
/***Handbook of Algorithms and Data Structures, p239 ***/
{
long nlength, i, j, la, lb;
/*** b and c may coincide ***/
la = length ( a );
lb = length ( b );
nlength = la + lb - 2;
if ( nlength > lrs_digits )
digits_overflow();
for ( i = 0; i < la - 2; i++ )
c[lb + i] = 0;
for ( i = lb - 1; i > 0; i-- ) {
for ( j = 2; j < la; j++ )
if ( ( c[i + j - 1] += b[i] * a[j] ) >
MAXD - ( BASE - 1 ) * ( BASE - 1 ) - MAXD / BASE ) {
c[i + j - 1] -= ( MAXD / BASE ) * BASE;
c[i + j] += MAXD / BASE;
}
c[i] = b[i] * a[1];
}
storelength ( c, nlength );
storesign ( c, sign ( a ) == sign ( b ) ? POS : NEG );
normalize ( c );
}
void
normalize ( lrs_mp a ) {
long cy, i, la;
la = length ( a );
start:
cy = 0;
for ( i = 1; i < la; i++ ) {
cy = ( a[i] += cy ) / BASE;
a[i] -= cy * BASE;
if ( a[i] < 0 ) {
a[i] += BASE;
cy--;
}
}
while ( cy > 0 ) {
a[i++] = cy % BASE;
cy /= BASE;
}
if ( cy < 0 ) {
a[la - 1] += cy * BASE;
for ( i = 1; i < la; i++ )
a[i] = ( -a[i] );
storesign ( a, sign ( a ) == POS ? NEG : POS );
goto start;
}
while ( a[i - 1] == 0 && i > 2 )
i--;
if ( i > lrs_record_digits ) {
if ( ( lrs_record_digits = i ) > lrs_digits )
digits_overflow();
};
storelength ( a, i );
if ( i == 2 && a[1] == 0 )
storesign ( a, POS );
} /* end of normalize */
void
itomp (long in, lrs_mp a)
/* convert integer i to multiple precision with base BASE */
{
long i;
a[0] = 2; /* initialize to zero */
for (i = 1; i < lrs_digits; i++)
a[i] = 0;
if (in < 0)
{
storesign (a, NEG);
in = in * (-1);
}
i = 0;
while (in != 0)
{
i++;
a[i] = in - BASE * (in / BASE);
in = in / BASE;
storelength (a, i + 1);
}
} /* end of itomp */
void
divint ( lrs_mp a, lrs_mp b, lrs_mp c ) { /* c=a/b, a contains remainder on return */
long cy, la, lb, lc, d1, s, t, sig;
long i, j, qh;
/* figure out and save sign, do everything with positive numbers */
sig = sign ( a ) * sign ( b );
la = length ( a );
lb = length ( b );
lc = la - lb + 2;
if ( la < lb ) {
storelength ( c, TWO );
storesign ( c, POS );
c[1] = 0;
normalize ( c );
return;
}
for ( i = 1; i < lc; i++ )
c[i] = 0;
storelength ( c, lc );
storesign ( c, ( sign ( a ) == sign ( b ) ) ? POS : NEG );
/******************************/
/* division by a single word: */
/* do it directly */
/******************************/
if ( lb == 2 ) {
cy = 0;
t = b[1];
for ( i = la - 1; i > 0; i-- ) {
cy = cy * BASE + a[i];
a[i] = 0;
cy -= ( c[i] = cy / t ) * t;
}
a[1] = cy;
storesign ( a, ( cy == 0 ) ? POS : sign ( a ) );
storelength ( a, TWO );
/* set sign of c to sig (**mod**) */
storesign ( c, sig );
normalize ( c );
return;
} else {
/* mp's are actually DIGITS+1 in length, so if length of a or b = */
/* DIGITS, there will still be room after normalization. */
/****************************************************/
/* Step D1 - normalize numbers so b > floor(BASE/2) */
d1 = BASE / ( b[lb - 1] + 1 );
if ( d1 > 1 ) {
cy = 0;
for ( i = 1; i < la; i++ ) {
cy = ( a[i] = a[i] * d1 + cy ) / BASE;
a[i] %= BASE;
}
a[i] = cy;
cy = 0;
for ( i = 1; i < lb; i++ ) {
cy = ( b[i] = b[i] * d1 + cy ) / BASE;
b[i] %= BASE;
}
b[i] = cy;
} else {
a[la] = 0; /* if la or lb = DIGITS this won't work */
b[lb] = 0;
}
/*********************************************/
/* Steps D2 & D7 - start and end of the loop */
for ( j = 0; j <= la - lb; j++ ) {
/*************************************/
/* Step D3 - determine trial divisor */
if ( a[la - j] == b[lb - 1] )
qh = BASE - 1;
else {
s = ( a[la - j] * BASE + a[la - j - 1] );
qh = s / b[lb - 1];
while ( qh * b[lb - 2] > ( s - qh * b[lb - 1] ) * BASE + a[la - j - 2] )
qh--;
}
/*******************************************************/
/* Step D4 - divide through using qh as quotient digit */
cy = 0;
for ( i = 1; i <= lb; i++ ) {
s = qh * b[i] + cy;
a[la - j - lb + i] -= s % BASE;
cy = s / BASE;
if ( a[la - j - lb + i] < 0 ) {
a[la - j - lb + i] += BASE;
cy++;
}
}
/*****************************************************/
/* Step D6 - adjust previous step if qh is 1 too big */
if ( cy ) {
qh--;
cy = 0;
for ( i = 1; i <= lb; i++ ) { /* add a back in */
a[la - j - lb + i] += b[i] + cy;
cy = a[la - j - lb + i] / BASE;
a[la - j - lb + i] %= BASE;
}
}
/***********************************************************************/
/* Step D5 - write final value of qh. Saves calculating array indices */
/* to do it here instead of before D6 */
c[la - lb - j + 1] = qh;
}
/**********************************************************************/
/* Step D8 - unnormalize a and b to get correct remainder and divisor */
for ( i = lc; c[i - 1] == 0 && i > 2; i-- ); /* strip excess 0's from quotient */
storelength ( c, i );
if ( i == 2 && c[1] == 0 )
storesign ( c, POS );
cy = 0;
for ( i = lb - 1; i >= 1; i-- ) {
cy = ( a[i] += cy * BASE ) % d1;
a[i] /= d1;
}
for ( i = la; a[i - 1] == 0 && i > 2; i-- ); /* strip excess 0's from quotient */
storelength ( a, i );
if ( i == 2 && a[1] == 0 )
storesign ( a, POS );
if ( cy )
fprintf ( lrs_ofp, "divide error" );
for ( i = lb - 1; i >= 1; i-- ) {
cy = ( b[i] += cy * BASE ) % d1;
b[i] /= d1;
}
}
}
long
lrs_getfirstbasis2 (lrs_dic ** D_p, lrs_dat * Q, lrs_dic * P2orig, lrs_mp_matrix * Lin, long no_output)
/* gets first basis, FALSE if none */
/* P may get changed if lin. space Lin found */
/* no_output is TRUE supresses output headers */
{
long i, j, k;
/* assign local variables to structures */
lrs_mp_matrix A;
long *B, *C, *Row, *Col;
long *inequality;
long *linearity;
long hull = Q->hull;
long m, d, lastdv, nlinearity, nredundcol;
static long ocount=0;
m = D->m;
d = D->d;
lastdv = Q->lastdv;
nredundcol = 0L; /* will be set after getabasis */
nlinearity = Q->nlinearity; /* may be reset if new linearity read */
linearity = Q->linearity;
A = D->A;
B = D->B;
C = D->C;
Row = D->Row;
Col = D->Col;
inequality = Q->inequality;
/* default is to look for starting cobasis using linearies first, then */
/* filling in from last rows of input as necessary */
/* linearity array is assumed sorted here */
/* note if restart/given start inequality indices already in place */
/* from nlinearity..d-1 */
for (i = 0; i < nlinearity; i++) /* put linearities first in the order */
inequality[i] = linearity[i];
k = 0; /* index for linearity array */
if (Q->givenstart)
k = d;
else
k = nlinearity;
for (i = m; i >= 1; i--)
{
j = 0;
while (j < k && inequality[j] != i)
j++; /* see if i is in inequality */
if (j == k)
inequality[k++] = i;
}
if (Q->debug)
{
fprintf (lrs_ofp, "\n*Starting cobasis uses input row order");
for (i = 0; i < m; i++)
fprintf (lrs_ofp, " %ld", inequality[i]);
}
if (!Q->maximize && !Q->minimize)
for (j = 0; j <= d; j++)
itomp (ZERO, A[0][j]);
/* Now we pivot to standard form, and then find a primal feasible basis */
/* Note these steps MUST be done, even if restarting, in order to get */
/* the same index/inequality correspondance we had for the original prob. */
/* The inequality array is used to give the insertion order */
/* and is defaulted to the last d rows when givenstart=FALSE */
if (!getabasis2 (D, Q,P2orig, inequality))
return FALSE;
if(Q->debug)
{
fprintf(lrs_ofp,"\nafter getabasis2");
printA(D, Q);
}
nredundcol = Q->nredundcol;
lastdv = Q->lastdv;
d = D->d;
/********************************************************************/
/* now we start printing the output file unless no output requested */
/********************************************************************/
if (!no_output || Q->debug)
{
fprintf (lrs_ofp, "\nV-representation");
/* Print linearity space */
/* Don't print linearity if first column zero in hull computation */
k = 0;
if (nredundcol > k)
{
fprintf (lrs_ofp, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */
for (i = 1; i <= nredundcol - k; i++)
fprintf (lrs_ofp, " %ld", i);
} /* end print of linearity space */
fprintf (lrs_ofp, "\nbegin");
fprintf (lrs_ofp, "\n***** %ld rational", Q->n);
} /* end of if !no_output ....... */
/* Reset up the inequality array to remember which index is which input inequality */
/* inequality[B[i]-lastdv] is row number of the inequality with index B[i] */
/* inequality[C[i]-lastdv] is row number of the inequality with index C[i] */
for (i = 1; i <= m; i++)
inequality[i] = i;
if (nlinearity > 0) /* some cobasic indices will be removed */
{
for (i = 0; i < nlinearity; i++) /* remove input linearity indices */
inequality[linearity[i]] = 0;
k = 1; /* counter for linearities */
for (i = 1; i <= m - nlinearity; i++)
{
while (k <= m && inequality[k] == 0)
k++; /* skip zeroes in corr. to linearity */
inequality[i] = inequality[k++];
}
} /* end if linearity */
if (Q->debug)
{
fprintf (lrs_ofp, "\ninequality array initialization:");
for (i = 1; i <= m - nlinearity; i++)
fprintf (lrs_ofp, " %ld", inequality[i]);
}
if (nredundcol > 0)
{
*Lin = lrs_alloc_mp_matrix (nredundcol, Q->n);
for (i = 0; i < nredundcol; i++)
{
if (!(Q->homogeneous && Q->hull && i == 0)) /* skip redund col 1 for homog. hull */
{
lrs_getray (D, Q, Col[0], D->C[0] + i - hull, (*Lin)[i]); /* adjust index for deletions */
}
if (!removecobasicindex (D, Q, 0L))
return FALSE;
}
} /* end if nredundcol > 0 */
if (Q->verbose)
{
fprintf (lrs_ofp, "\nNumber of pivots for starting dictionary: %ld",Q->count[3]);
ocount=Q->count[3];
}
/* Do dual pivots to get primal feasibility */
if (!primalfeasible (D, Q))
{
if ( Q->verbose )
{
fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]);
fprintf (lrs_ofp, " - No feasible solution");
ocount=Q->count[3];
}
return FALSE;
}
if (Q->verbose)
{
fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]);
ocount=Q->count[3];
}
/* Now solve LP if objective function was given */
if (Q->maximize || Q->minimize)
{
Q->unbounded = !lrs_solvelp (D, Q, Q->maximize);
/* check to see if objective is dual degenerate */
j = 1;
while (j <= d && !zero (A[0][j]))
j++;
if (j <= d)
Q->dualdeg = TRUE;
}
else
/* re-initialize cost row to -det */
{
for (j = 1; j <= d; j++)
{
copy (A[0][j], D->det);
storesign (A[0][j], NEG);
}
itomp (ZERO, A[0][0]); /* zero optimum objective value */
}
/* reindex basis to 0..m if necessary */
/* we use the fact that cobases are sorted by index value */
if (Q->debug)
printA (D, Q);
while (C[0] <= m)
{
i = C[0];
j = inequality[B[i] - lastdv];
inequality[B[i] - lastdv] = inequality[C[0] - lastdv];
inequality[C[0] - lastdv] = j;
C[0] = B[i];
B[i] = i;
reorder1 (C, Col, ZERO, d);
}
if (Q->debug)
{
fprintf (lrs_ofp, "\n*Inequality numbers for indices %ld .. %ld : ", lastdv + 1, m + d);
for (i = 1; i <= m - nlinearity; i++)
fprintf (lrs_ofp, " %ld ", inequality[i]);
printA (D, Q);
}
if (Q->restart)
{
if (Q->debug)
fprintf (lrs_ofp, "\nPivoting to restart co-basis");
if (!restartpivots (D, Q))
return FALSE;
D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */
if (Q->debug)
printA (D, Q);
}
/* Check to see if necessary to resize */
if (Q->inputd > D->d)
*D_p = resize (D, Q);
return TRUE;
}
