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#include "Global.h"
#include "Rat.h"
#undef TEST_Wbase
#undef USE_Old_Wbase
#define NO_COORD_IMPROVEMENT /* switch off weight permutation */
typedef struct {Long x[AMBI_Dmax][AMBI_Dmax]; int n, N;} CWLatticeBasis;
void Make_CWS_Points(CWS *_C, PolyPointList *_P);
void CWS_to_PermCWS(CWS *Cin, CWS *C, int *pi);
/* ========== I/O functions: ========== */
int IsNextDigit(){
char c; c=fgetc(inFILE); ungetc(c,inFILE);
if(c=='0') return -1; if((c<'0') || ('9'<c)) return 0; else return 1;
}
void Print_PPL(PolyPointList *_P, const char *comment){
int i,j;
if(_P->np>20){
fprintf(outFILE,"%d %d %s\n",_P->np,_P->n,comment);
for(i=0;i<_P->np;i++) {
for(j=0;j<_P->n;j++) fprintf(outFILE,"%d ",(int) _P->x[i][j]);
fprintf(outFILE,"\n");}}
else {
fprintf(outFILE,"%d %d %s\n",_P->n,_P->np,comment);
for(i=0;i<_P->n;i++) {
for(j=0;j<_P->np;j++) fprintf(outFILE," %4d",(int) _P->x[j][i]);
fprintf(outFILE,"\n");}}
}
void Print_VL(PolyPointList *_P, VertexNumList *_V, const char *comment){
int i,j;
if(_V->nv>20){
fprintf(outFILE,"%d %d %s\n",_V->nv,_P->n,comment);
for(i=0;i<_V->nv;i++) {
for(j=0;j<_P->n;j++) fprintf(outFILE,"%d ",(int) _P->x[_V->v[i]][j]);
fprintf(outFILE,"\n");}}
else {
fprintf(outFILE,"%d %d %s\n",_P->n,_V->nv,comment);
for(i=0;i<_P->n;i++) {
for(j=0;j<_V->nv;j++) fprintf(outFILE," %4d",(int) _P->x[_V->v[j]][i]);
fprintf(outFILE,"\n");}}
}
void Print_EL(EqList *_E, int *n, int suppress_c, const char *comment){
int i,j;
fprintf(outFILE,"%d %d %s\n",_E->ne,*n,comment);
for(i=0;i<_E->ne;i++) {
for(j=0;j<*n;j++) fprintf(outFILE," %3d",(int) _E->e[i].a[j]);
if (!suppress_c) fprintf(outFILE," %5d",(int) _E->e[i].c);
fprintf(outFILE,"\n");}
}
void Print_Matrix(Long Matrix[][VERT_Nmax], int n_lines, int n_columns,
const char *comment){
int i,j;
fprintf(outFILE,"%d %d %s\n",n_lines, n_columns, comment);
for(i=0;i<n_lines;i++) {
for(j=0;j<n_columns;j++) fprintf(outFILE," %3d",(int) Matrix[i][j]);
fprintf(outFILE,"\n");}
}
int auxString2Int(char *c,int *n)
{ int j=0; *n=0; while(('0'<=c[j])&&(c[j]<='9')) *n = 10*(*n)+c[j++]-'0';
if(j) while(c[j]==' ') j++; return j;
}
void CWSZerror(char *c)
{ printf("Format error %s in Read_CWS_Zinfo\n",c);exit(0);
}
void Print_CWS_Zinfo(CWS *CW)
{ int i,j; if(CW->nw) for(i=0;i<CW->nz;i++)
{ fprintf(outFILE,"/Z%d: ",CW->m[i]);
for(j=0;j<CW->N;j++) fprintf(outFILE,"%d ",CW->z[i][j]);
}
}
int Read_CWS_Zinfo(FILE *inFILE,CWS *CW) /* return !EOF */
{ int *nz=&CW->nz; int i=0,n; char c[999],b=' '; *nz=0;
for(n=0;n<999;n++)
{ c[n]=fgetc(inFILE); if(feof(inFILE)) return 0; if(c[n]=='\n') break;
} if(n==999) {puts("Out of space in Read_CWS_Zinfo");exit(0);}
while(c[i]==b)i++; if((c[i]=='=')&&(c[i+1]=='d'))i+=2; while(c[i]==b)i++;
/* printf("Read_CWS_Zinfo n=%d -> ",n);
{int I; for(I=0;I<n;I++)printf("%c",c[I]);puts("");} */
while(i<n)
{ int j, k, s; if((c[i]!='/')||(c[i+1]!='Z')) return 1;
i+=2; assert(*nz<POLY_Dmax);
if((j=auxString2Int(&c[i],&CW->m[*nz])))
{ if(c[i+j]!=':') CWSZerror(":"); else {i+=j+1; while(c[i]==b)i++;}
for(k=0;k<CW->N;k++)
{ if((j=auxString2Int(&c[i],&CW->z[*nz][k])))
{if((j)) i+=j; else CWSZerror("missing");} /* ????? */
} s=0;
for(k=0;k<CW->N;k++) s+=CW->z[*nz][k];
/* if(s % CW->m[*nz]) CWSZerror("det!=1"); */
(CW->nz)++;
} else CWSZerror("Order");
} return 1;
}
int Read_CWS_PP(CWS *_CW, PolyPointList *_P)
{ int i, j, FilterFlag=(inFILE==NULL);
int IN[AMBI_Dmax*(AMBI_Dmax+1)], S;
static int InputOK;
_CW->nw=_CW->N=_CW->nz=0;
if(FilterFlag) inFILE=stdin;
else if(inFILE==stdin) {
printf("Degrees and weights `d1 w11 w12 ... d2 w21 w22 ...'\n or `#");
printf("lines #colums' (= `PolyDim #Points' or `#Points PolyDim'):\n");}
for(i=0;i<AMBI_Dmax*(AMBI_Dmax+1);i++)
{ char c;
while(' '==(c=fgetc(inFILE ))); ungetc(c,inFILE); /* read blanks */
if(IsNextDigit()) fscanf(inFILE,"%d",&IN[i]); else break;
}
if(i==0) { if(!InputOK){puts("-h gives you help\n"); exit(0);}
else return 0; } InputOK++;
if(i==1) { puts("Error in INPUT: need at least 2 numbers!"); exit(0);}
if(i==2) /* READ PolyPointList */
{ int tr=0; while('\n'!=fgetc(inFILE)); /* read to end of line */
if(IN[0]>IN[1]) {tr=IN[0];IN[0]=IN[1];IN[1]=tr;} tr=!tr;
if(IN[0]>POLY_Dmax) {puts("increase POLY_Dmax!"); exit(0);}
if(IN[1]>POINT_Nmax) {puts("increase POINT_Nmax!"); exit(0);}
if((inFILE==stdin)&&!FilterFlag)
printf("Type the %d coordinates as %s=%d lines with %s=%d colums:\n",
IN[0]*IN[1], tr ? "dim" : "#pts", tr ? IN[0] : IN[1],
tr ? "#pts" : "dim", tr ? IN[1] : IN[0]);
_P->n=IN[0]; _P->np=IN[1];
/* allow all numbers in one string (distributed over lines) or
* matrix blocks with trailing comments */
if(tr) for(i=0;i<IN[0];i++) for(j=0;j<IN[1];j++)
{ int X; fscanf(inFILE,"%d",&X); _P->x[j][i]=X; }
else for(i=0;i<IN[1];i++) for(j=0;j<IN[0];j++)
{ int X; fscanf(inFILE,"%d",&X); _P->x[i][j]=X; }
/* Finish_Poly_Points(_P); */
while(fgetc(inFILE )-'\n') if(feof(inFILE)) return 0;/* read to EOL */
if(FilterFlag) inFILE=NULL; return 1;
} assert(i!=3);
S=IN[i-1]; for(j=0;j<i-1;j++) if(S<IN[j]) break;
if(j==i-1) /* Single Weights with: "w1 ... d" */
{ _CW->nw=1; _CW->d[0]=S; _CW->N=i-1;
assert(_CW->N <= POLY_Dmax+1); /* Increase POLY_Dmax */
for(j=0;j<_CW->N;j++) {_CW->W[0][j]=IN[j]; assert(IN[j]>0);}
goto MAP;
}
S=_CW->d[_CW->nw]=IN[0]; /* ASSIGN WEIGHTS */
for(j=1; j<i; j++)
{ if(S<IN[j])
{ if(S) { puts("Error in INPUT: degree vs. weights!"); exit(0);}
else
{ S=_CW->d[++(_CW->nw)]=IN[j];
if(1==_CW->nw)
{ if(i%(1+_CW->N)) {puts("INPUT error: numbers?"); exit(0);}
} if(j%(1+_CW->N)) {puts("INPUT error: degrees?"); exit(0);}
}
}
else
{ _CW->W[_CW->nw][j - 1 - (1 + _CW->N)*_CW->nw] = IN[j]; S-=IN[j];
if(0==_CW->nw) if(++(_CW->N)>AMBI_Dmax)
{ puts("Increase AMBI_Dmax!"); exit(0);
}
}
}
++(_CW->nw);
if(_CW->N-_CW->nw > POLY_Dmax){
printf("Please increase POLY_Dmax to at least %d\n", _CW->N-_CW->nw);
exit(0);} /* increase POLY_Dmax */
MAP: for(i=0;i<_CW->nw;i++) /* check consistency of CWS */
{ Long sum=_CW->d[i], *w=_CW->W[i];
for(j=0;j<_CW->N;j++) { assert(w[j]>=0); sum-=w[j]; }
if(sum){ printf("Use poly.x -w for (single) WeightSystems with ");
printf("d!=\\sum(w)\n(only Read_Weight makes the correct ");
puts("PolyPointList in that case"); exit(0);}
}
_CW->nz=0;
if(!Read_CWS_Zinfo(inFILE,_CW)) /* read Z to EOL */
{ if(!InputOK) puts("-h gives you help\n"); return 0;}
Make_CWS_Points(_CW, _P); /* now make POLY */
if(FilterFlag) inFILE=NULL; return 1;
}
void Print_CWH(CWS *_W, BaHo *_BH){
int i, j;
for(i=0;i<_W->nw;i++) {
fprintf(outFILE,"%d ",(int) _W->d[i]);
for(j=0;j<_W->N;j++) fprintf(outFILE,"%d ",(int) _W->W[i][j]);
if(i+1<_W->nw) fprintf(outFILE," "); }
Print_CWS_Zinfo(_W);
if(_BH->np) {
fprintf(outFILE,"M:%d %d N:%d %d",_BH->mp,_BH->mv,_BH->np,_BH->nv);
if (_BH->n == 3) fprintf(outFILE," Pic:%d Cor:%d",_BH->pic, _BH->cor);
if (_BH->n > 3) {
fprintf(outFILE," H:%d",_BH->h1[1]);
for(i=2;i<_BH->n-1;i++) fprintf(outFILE,",%d",_BH->h1[i]);
if(_BH->n==4) fprintf(outFILE," [%d]",2*(_BH->h1[1]-_BH->h1[2]));
if(_BH->n==5)
fprintf(outFILE," [%d]",48+6*(_BH->h1[1]-_BH->h1[2]+_BH->h1[3]));}}
else if(_BH->mp)
fprintf(outFILE,"M:%d %d F:%d",_BH->mp,_BH->mv,_BH->nv);
else fprintf(outFILE,"V:%d F:%d",_BH->mv,_BH->nv);
fprintf(outFILE,"\n");
}
/* ========== END of I/O functions ========== */
/* ========== Solve W-Eq. -> triangular LatticeBasis
*
* B[0]:= (-n1, n0, 0, ...) / GCD(n0,n1);
* B[i]:= (0,...,0,g/G,0,...)- (ni/G) * ExtGCD.K(n0,...,n(i-1),0,...);
* with g=GCD(n0,...,n[i-1]); G=GCD(g,ni);
*
* CWS by iteration: NextWeight=W[]*B; NewB=Basis(NextW); B[i+1]=B[i]*NewB;
* */
void PrintBasis(CWLatticeBasis *_B)
{ int i,j; puts("Basis:");
for(i=0;i<_B->n;i++)
{ for(j=0;j<_B->N;j++) fprintf(outFILE,"%6d ",(int) _B->x[i][j]);
puts("");
} puts("End of Basis - -");
}
void Orig_Solve_Next_WEq(Long *NW, CWLatticeBasis *_B)
{ int i, j, P=0, p[AMBI_Dmax]; Long W[AMBI_Dmax], G; _B->n=_B->N-1;
for(i=0;i<_B->N;i++)
{ for(j=0;j<_B->n;j++) _B->x[j][i]=0; /* init B.x=0 */
if(NW[i]) {p[P]=i; W[P++]=NW[i];} /* non-zero weights */
}
if(P<2) puts("need two non-zero weights in >>Solve_Next_WEq<<");
for(i=0;i<p[0];i++) _B->x[i][i]=1; while((++i)<p[1]) _B->x[i-1][i]=1;
G=Fgcd(W[0],W[1]); if(W[0]/G<0) G=-G;
_B->x[i-1][p[0]]=-W[1]/G; _B->x[i-1][p[1]]=W[0]/G;
j=2; while(++i<_B->N)
{ if(NW[i])
{ int k; Long *X=_B->x[i-1], K[AMBI_Dmax], g=REgcd(W, &j, K);
G=Fgcd(g,NW[i]); if(g/G<0) G=-G; X[i]= g/G; g=W[j]/G;
for(k=0;k<j;k++) X[p[k]]=-K[k]*g; j++;
}
else _B->x[i-1][i]=1;
}
}
void Solve_Next_WEq(Long *NW, CWLatticeBasis *_B)
{ Long W[AMBI_Dmax], *X[AMBI_Dmax], GLZ[AMBI_Dmax][AMBI_Dmax];
int i, j, P=0, p[AMBI_Dmax]; _B->n=_B->N-1;
#ifdef TEST_Wbase
Orig_Solve_Next_WEq(NW,_B); PrintBasis(_B);
#endif
for(i=0;i<_B->N;i++)
{ for(j=0;j<_B->n;j++) _B->x[j][i]=0; /* init B.x=0 */
if(NW[i]) {p[P]=i; X[P]=GLZ[P]; W[P++]=NW[i];} /* non-zero weights */
} if(P>1) W_to_GLZ(W,&P,X); /* P>1, compute GLZ */
else {/* printf("P=%d W[0]=%d for W_to_GLZ\n",P,W[0]);exit(0);*/assert(P);
for(i=0;i<p[0];i++)_B->x[i][i]=1; while((++i)<_B->N)_B->x[i-1][i]=1;
return; }
for(i=1;i<P;i++) if(X[i][i]<0) for(j=0;j<=i;j++) X[i][j] *= -1;
for(i=0;i<p[0];i++) _B->x[i][i]=1; while((++i)<p[1]) _B->x[i-1][i]=1;
_B->x[i-1][p[0]]=X[1][0]; _B->x[i-1][p[1]]=X[1][1]; j=2;
while(++i<_B->N)
{ if(NW[i])
{ int k; Long *B=_B->x[i-1]; for(k=0;k<=j;k++) B[p[k]]=X[j][k]; j++;
}
else _B->x[i-1][i]=1;
}
#ifdef TEST_Wbase
/* for(i=0;i<_B->N;i++)printf("%d ",NW[i]);puts("=NW");for(i=0;i<P;i++)
{for(j=0;j<P;j++)printf("%4d ",GLZ[i][j]);puts("=GL");} */
printf("New version: "); PrintBasis(_B);
#endif
#ifdef USE_Old_Wbase
Orig_Solve_Next_WEq(NW,_B);
#endif
}
void Make_CWS_Basis(CWS *_C, CWLatticeBasis *_B){
int i,j,k,l; Long W[AMBI_Dmax]; CWLatticeBasis NB, AuxB;
AuxB.N=_B->N=_C->N;
Solve_Next_WEq(_C->W[0],_B);
for(i=1;i<_C->nw;i++){
for(j=0;j<_B->n;j++){
W[j]=0;
for(k=0;k<_B->N;k++) W[j]+=_C->W[i][k]*_B->x[j][k]; }
NB.N=_B->n;
Solve_Next_WEq(W,&NB);
AuxB.n=NB.n;
for(j=0;j<AuxB.N;j++) for(k=0;k<AuxB.n;k++) {
AuxB.x[k][j]=0;
for(l=0;l<NB.N;l++) AuxB.x[k][j] += NB.x[k][l] * _B->x[l][j]; }
*_B=AuxB; }
/* init coordinate hyperplanes */
_C->B.ne=_B->N; /* == transposed of Basis */
for(i=0;i<_B->N;i++) {
for(j=0;j<_B->n;j++) _C->B.e[i].a[j]=_B->x[j][i];
_C->B.e[i].c=1;}
}
void Poly_To_Ambi(CWLatticeBasis *_B, Long *x, Long *X)
{ int i, j;
for(i=0;i<_B->N;i++)
{ X[i]=1; for(j=0;j<_B->n;j++) X[i] += _B->x[j][i] * x[j];
}
}
/* B.x[i][A] is lower triangular: zero for i<p and Amin[p] <= A <Amin[p+1]
* X^A=x^p B_p^A+1, hence for A \in [ Amin[p],Amin[p+1] ) and all k:
* x^iB_i^A \in [0,d_k/w_k^A] - 1 - \sum_{l<i} x^l B_l^A
* */
void QuotZ_2_SublatG(Long Z[][VERT_Nmax],int *zm,Long *M,int *d,
Long G[][POLY_Dmax]); /* normalize and diagonalize Z */
void CWS_2_SublatZ(CWS *C,CWLatticeBasis *B, /* in */
int *m, Long *M, Long G[POLY_Dmax][POLY_Dmax]) /* out */
{ int i,j,k,d=C->N-C->nw; Long Z[POLY_Dmax][VERT_Nmax]; *m=C->nz;
for(i=0;i<C->nz;i++){ M[i]=C->m[i]; for(j=0;j<d;j++)
{ Z[i][j]=0; for(k=0;k<C->N;k++) Z[i][j]+=C->z[i][k]*B->x[j][k];}
} /* PrintBasis(B); */ QuotZ_2_SublatG(Z,m,M,&d,G);
}
void Reduce_PPL_2_Sublat(PolyPointList *P,int *nm,Long *M,Long G[][POLY_Dmax])
{ int i,j,n=0,N; for(N=0;N<P->np;N++)
{ Long X[POLY_Dmax]; for(i=0;i<P->n;i++)
{ X[i]=0; for(j=0;j<P->n;j++) X[i]+=G[i][j]*P->x[N][j];
} for(i=0;i<*nm;i++) if(X[i]%M[i]) break; if(i<*nm) continue;
for(i=0;i<*nm;i++) P->x[n][i]=X[i]/M[i];
for(i=*nm;i<P->n;i++) P->x[n][i]=X[i]; n++;
} P->np=n; /* Print_PPL(P,"");printf("nm=%d\n",*nm); */
}
Long PD_Floor(Long N,Long D) /* assuming PosDenom D>0: F <= N/D < F+1 */
{ Long F=N/D; return (F*D>N) ? F-1 : F;
}
void Make_CWS_Points(CWS *Cin, PolyPointList *_P)
{ int i, j, Amin[POLY_Dmax+1]; Long *x=_P->x[_P->np=0], xmin[POLY_Dmax],
xmax[POLY_Dmax], Xmax[AMBI_Dmax], xaux[POLY_Dmax], L, R; CWS *_C=Cin;
CWLatticeBasis B; Long G[POLY_Dmax][POLY_Dmax],M[POLY_Dmax];int m=Cin->nz;
#ifndef NO_COORD_IMPROVEMENT /* ==== Perm Coord Improvement ==== */
int pi[AMBI_Dmax]; CWS Caux; _C=&Caux; CWS_to_PermCWS(Cin,_C, pi);
#endif /* = End of Perm Coord Improvement = */
Make_CWS_Basis(_C, &B); /* make `triangular' Basis */
#ifndef NO_COORD_IMPROVEMENT /* ==== Perm Coord Improvement ==== */
assert(_C->N==_C->B.ne);
for(i=0;i<Cin->N;i++) Cin->B.e[i]=_C->B.e[pi[i]]; Cin->B.ne=_C->N;
#endif /* = End of Perm Coord Improvement = */
i=_P->n=B.n; Amin[0]=0; Amin[B.n]=j=B.N; /* inversion structure */
while(--i) {while(!B.x[i-1][--j]); Amin[i]=++j;}
for(i=0;i<B.N;i++) /* compute Xmax */
{ Xmax[i]=0; for(j=0;j<_C->nw;j++) if(_C->W[j][i])
{ L=_C->d[j]/_C->W[j][i];
if(Xmax[i]) {if(L<Xmax[i]) Xmax[i]=L;}
else Xmax[i]=L;
}
}
j=B.n-1; i=Amin[j+1]-1; R=B.x[j][i]; /* compute xmin[j] and xmax[j] */
xmin[j]=-PD_Floor(1,R); xmax[j]=PD_Floor(Xmax[i]-1,R); /* since R > 0 */
/** /printf("R=%2d: %2d <= x[%d=&%d] <= %2d\n",R,xmin[j],j,i,xmax[j]);/ **/
while((i--)>Amin[j]) /* if(R=B.x[B.n-1][i]): R!=0 => new limits */
{ Long Low=-1, Upp=Low+Xmax[i]; R=B.x[B.n-1][i];
if(R>0) {if(xmax[j]>(L=PD_Floor(Upp,R))) xmax[j]=L;
if(xmin[j]<(L=-PD_Floor(-Low,R))) xmin[j]=L;}
else {if(xmax[j]>(L=PD_Floor(-Low,-R))) xmax[j]=L;
if(xmin[j]<(L=-PD_Floor(Upp,-R))) xmin[j]=L;}
/** /printf("R=%2d: %2d <= x[%d=&%d] <= %2d\n",R,xmin[j],j,i,xmax[j]);/ **/
} /* this completes the limits for x[B.n-1] */
x[j]=xmin[j]; while(j<B.n)
{ int k; if(x[j]>xmax[j]) {if(B.n==(++j)) break; else x[j]++;}
else /* compute limits[j-1] and initialize x[j-1] */
{ Long Low=-1, Upp=Xmax[i=Amin[j--]-1]; int RangeFlag=0;
for(k=j+1;k<B.n;k++) Low-=x[k]*B.x[k][i]; /* compute offset */
Upp+=Low; R=B.x[j][i];
xmin[j]=-PD_Floor(-Low,R); xmax[j]=PD_Floor(Upp,R);
/** /printf("R=%2d: %2d <= x[%d=&%d] <= %2d\n",R,xmin[j],j,i,xmax[j]);/ **/
while((i--)>Amin[j]) if((R=B.x[j][i])) /* R!=0 => new limits */
{ Low=-1; Upp=Xmax[i];
for(k=j+1;k<B.n;k++) Low-=x[k]*B.x[k][i];
Upp+=Low; R=B.x[j][i];
if(R>0) {if(xmax[j]>(L=PD_Floor(Upp,R))) xmax[j]=L;
if(xmin[j]<(L=-PD_Floor(-Low,R))) xmin[j]=L;}
else {if(xmax[j]>(L=PD_Floor(-Low,-R))) xmax[j]=L;
if(xmin[j]<(L=-PD_Floor(Upp,-R))) xmin[j]=L;}
/** /printf("R=%2d: %2d <= x[%d=&%d] <= %2d\n",R,xmin[j],j,i,xmax[j]);/ **/
} /* completes limits for x[] except */
else /* when R=0 and X out of Range: */
{ Long X=1; for(k=j+1;k<B.n;k++) X+=x[k]*B.x[k][i];
if((X<0)||(X>Xmax[i])) RangeFlag=1;
}
if(RangeFlag) ++x[++j]; else x[j]=xmin[j];
if(j==0)
{ while(x[0]<=xmax[0])
{ Long *y;
if((++_P->np) < POINT_Nmax)
{ y=(_P->x[_P->np]); for(k=0;k<B.n;k++) y[k]=x[k];
}
else if(_P->np == POINT_Nmax)
{ y=xaux; for(k=0;k<B.n;k++) y[k]=x[k];
}
else {puts("Increase POINT_Nmax");exit(0);}
x=y; ++x[0];
}
x[j=1]++;
}
}
} if(m)CWS_2_SublatZ(_C,&B,&m,M,G);if(m)Reduce_PPL_2_Sublat(_P,&m,M,G);
}
/* ========== Coordinate improvement via CWS-Permutations ========== */
typedef struct {Long s, g, *N, **G; int *p;} Tri_GLZ_MPaux;
Long Tri_GLZ_Norm(int *d, Long **S) /* sum-norm = default */
{ Long norm=0; int i,j; for(i=0;i<*d;i++)for(j=0;j<*d;j++)
#ifdef MAX_NORM /* max(|*|) */
{ Long x=S[i][j]; if(x<0) x=-x; if(x>norm) norm=x; } return norm;
#else /* sum(|*|) */
{ Long x=S[i][j]; norm += (x>0) ? x : -x ; } return norm;
#endif
}
void Tri_GLZ_Basis_Perm(int *d,int *pi, /* int *pinv, */ Tri_GLZ_MPaux * AP)
{ Long g, norm, N[AMBI_Dmax], M[AMBI_Dmax][AMBI_Dmax], *S[AMBI_Dmax];
int i, j; /* if(pi[0]>pi[1]) return; *//* eliminate equiv. permut. */
for(i=0;i<*d;i++) { N[i]=AP->N[pi[i]]; S[i]=M[i];}
g=W_to_GLZ(N,d,S); norm=Tri_GLZ_Norm(d,S);
if(AP->s) assert(g==AP->g); else AP->g=g;
#ifdef TEST_MIN_GLZ
{ Long err=0, max=0, tsum=0, pos; for(i=0;i<*d;i++)
{ for(j=0;j<*d;j++) {pos=S[i][j]; if(pos<0)pos=-pos; tsum+=pos;
if(max<pos)max=pos;} if(err==0) {
for(j=0;j<*d;j++) err+=N[j]*S[i][j]; if(i==0)err-=g;}
} assert((norm==tsum)||(norm==max));
printf("max=%lld, sum=%lld\n",(long long) max, (long long) tsum);
if(err) { for(i=0;i<*d;i++) printf("%d",pi[i]);
printf(" g=%d norm=%d",(int)g,(int)norm); puts("");
for(i=0;i<*d;i++){printf("S[%d]=",i);for(j=0;j<*d;j++)printf(" %5d",
S[i][j]);if(!i)printf(" g=%d norm=%d",(int)g,(int)norm);puts("");}}
}
#endif
if((0 == AP->s) || (norm < AP->s)) /* init or improve AP->G */
{ for(i=0;i<*d;i++)for(j=0;j<*d;j++)AP->G[i][pi[j]]=S[i][j]; AP->s=norm;
for(i=0;i<*d;i++) AP->p[i]=pi[i];
}
}
#ifndef NO_COORD_IMPROVEMENT
/* improved by permutation pi=pinv^-1 */
Long Wperm_to_GLZ(Long *W, int *d, Long **G, int *P)
{ Tri_GLZ_MPaux AS; int i, j, pi[AMBI_Dmax], pinv[AMBI_Dmax];
AS.s=0; AS.N=W; AS.G=G; AS.p=P;
Map_Permut(d,pi, /* pinv,*/ (Tri_GLZ_Basis_Perm),(void *) &AS);
for(i=0;i<*d;i++)for(j=0;j<*d;j++)G[i][j]=AS.G[i][j];
#ifdef TEST_MIN_GLZ
for(i=0;i<*d;i++){printf(" G[%d]=",i);for(j=0;j<*d;j++)printf(" %5d",
G[i][j]);if(!i)printf(" g=%d norm=%d",(int)AS.g,(int)AS.s);puts("");}
#endif
return AS.g;
}
void CWS_to_PermCWS(CWS *Cin, CWS *C, int *pi)
{ int i, j, N=C->N=Cin->N, n=C->nw=Cin->nw, l=0, A[AMBI_Dmax];
Long *X, *G[AMBI_Dmax], M[AMBI_Dmax][AMBI_Dmax], W[AMBI_Dmax];
for(j=1;j<n;j++) if(Cin->d[j]>Cin->d[l]) l=j; X=Cin->W[l];
j=0; for(i=0;i<N;i++) if(X[i]) {A[j]=i; W[j]=labs(X[i]); G[j]=M[j]; j++;}
Wperm_to_GLZ(W,&j,G,pi); for(i=0;i<j;i++) pi[i]=A[pi[i]];
for(i=0;i<N;i++) if(X[i]==0) pi[j++]=i;
C->d[0]=Cin->d[l]; for(i=0;i<N;i++) C->W[0][i]=Cin->W[l][pi[i]];
for(j=1;j<n;j++) {int L=j-(j<=l); C->d[j]=Cin->d[L];
for(i=0;i<N;i++) C->W[j][i]=Cin->W[L][pi[i]];}
C->nz=Cin->nz; for(j=0;j<C->nz;j++){C->m[j]=Cin->m[j];
for(i=0;i<N;i++) C->z[j][i]=Cin->z[j][pi[i]];}
}
#endif
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