structmatrix soverrelaxation(structmatrix *A, structmatrix *b){
const unsigned int MAXITER=100;
const double TOL=1e-6;
double *xp=calloc(A->nrows,sizeof(double));//init guess 0s
double *x= calloc(A->nrows,sizeof(double));//
structmatrix XP=creatematrix(xp
,A->nrows,1//solns in col vector
,endt(MATDOUBLE),rowmjr);
structmatrix X=creatematrix(x
,A->nrows,1//solns in col vector
,endt(MATDOUBLE),rowmjr);
fpidx idxA= getidxingfunc( A);
fpidx idxb= getidxingfunc( b);
fpidx idxX= getidxingfunc(&X);
fpidx idxXP=getidxingfunc(&XP);
#define Xv(ri,ci) *(double*) idxX( &ri,&ci,&X)
#define XPv(ri,ci) *(double*) idxXP(&ri,&ci,&XP)
#define Av(ri,ci) *(double*) idxA( &ri,&ci, A)
#define bv(ri,ci) *(double*) idxb( &ri,&ci, b)
unsigned int zero=0;
double omega=.5;//b/w 0 and 2
unsigned int k=0;
while(k<MAXITER){
unsigned ri;
for(ri=0;ri<A->nrows;ri++){
double newsumsoln=0;unsigned int sumi=0;
for(sumi=0;(sumi<(ri));sumi++)//tricky iter
{newsumsoln=newsumsoln-Av(ri,sumi)*Xv(sumi,zero);}
double oldsumsoln=0;
for(sumi=ri+1;(sumi<A->nrows);sumi++)
{oldsumsoln=oldsumsoln-Av(ri,sumi)*XPv(sumi,zero);}
Xv(ri,zero)=(1/Av(ri,ri))*(newsumsoln+oldsumsoln+bv(ri,zero))*omega
+(1-omega)*XPv(ri,zero);
}
double normofdiff=0;
for(ri=0;ri<X.nrows;ri++){
normofdiff+=pow((Xv(ri,zero)-XPv(ri,zero)),2);}
normofdiff=pow(normofdiff,.5);
if(normofdiff<TOL){printf("converged in %d iterations\n",k+1);return X;}
for(ri=0;ri<X.nrows;ri++){XPv(ri,zero)=Xv(ri,zero);}
k++; }
free(XP.data);
return X;
#undef Xv
#undef XPv
#undef Av
#undef bv
}
int main() {
double a,b;
int cases,i,j,id;
scanf("%d",&cases);
while(cases--) {
for(i=0;i<26;i++) scanf("%lf",&pr[i]);
scanf("%s %s",p,q);
pl=strlen(p); ql=strlen(q);
findstates();
creatematrix();
expmatrix();
for(a=b=i=0;i<=pl;i++) for(j=0;j<=ql;j++) if((id=statestoid[i][j])>-1) {
if(i==pl) id=statestoid[i][j],a+=m[0][id];
if(j==ql) id=statestoid[i][j],b+=m[0][id];
}
printf("%.14f\n",a/(a+b));
}
return 0;
}
structmatrix backsolve(structmatrix *echform){
structmatrix solnm=creatematrix(malloc(sizeof(double)*echform->nrows)
,echform->nrows,1//solns in col vector
,endt(MATDOUBLE),rowmjr);
unsigned int zero=0,lci=echform->ncols-1;
fpidx idxe=getidxingfunc(echform);//(r,c,mat)
fpidx idxm=getidxingfunc(&solnm);
#define ave(ri,ci) *(double*) idxe(&ri,&ci,echform)
#define avs(ri,ci) *(double*) idxm(&ri,&ci,&solnm)
unsigned int ri;
for(ri=echform->nrows-1;ri<-1;ri--){
double rowsum=0;unsigned int ci=0;
for(ci=ri+1;ci<echform->nrows;ci++){
;rowsum=rowsum+(ave(ri,ci))*(avs(ci,zero));}
avs(ri,zero)=(ave(ri,lci)-rowsum)/ave(ri,ri);
}
return solnm;
#undef ave
#undef avs
}
//todo put convergence into one function
structmatrix conjugategradient(structmatrix *A,structmatrix *b){
const unsigned int MAXITER=100;
const MATDOUBLE TOL=1e-6;
MATDOUBLE *xp=calloc(A->nrows,sizeof(MATDOUBLE));//init guess 0s
MATDOUBLE *x= malloc(A->nrows*sizeof(MATDOUBLE));//
structmatrix XP=creatematrix(xp
,A->nrows,1//solns in col vector
,endt(MATDOUBLE),rowmjr);
structmatrix X=creatematrix(x
,A->nrows,1//solns in col vector
,endt(MATDOUBLE),rowmjr);
structmatrix rP=copymatrix(b); //previous error
structmatrix pP=copymatrix(b); //CG vec
structmatrix r=creatematrix(malloc(sizeof(MATDOUBLE)*rP.nrows)
,rP.nrows,1
,endt(MATDOUBLE),rowmjr);
structmatrix p=creatematrix(malloc(sizeof(MATDOUBLE)*pP.nrows)
,pP.nrows,1
,endt(MATDOUBLE),rowmjr);
fpidx idxA= getidxingfunc( A);
fpidx idxb= getidxingfunc( b);
fpidx idxX= getidxingfunc(&X);
fpidx idxXP=getidxingfunc(&XP);
fpidx idxrP=getidxingfunc(&rP);
fpidx idxpP=getidxingfunc(&pP);
fpidx idxr =getidxingfunc(&r );
fpidx idxp =getidxingfunc(&p );
#define Xv(ri,ci) *(double*) idxX( &ri,&ci,&X)
#define XPv(ri,ci) *(double*) idxXP(&ri,&ci,&XP)
#define Av(ri,ci) *(double*) idxA( &ri,&ci, A)
#define bv(ri,ci) *(double*) idxb( &ri,&ci, b)
#define rPv(ri,ci) *(double*) idxrP( &ri,&ci, &rP)
#define pPv(ri,ci) *(double*) idxb( &ri,&ci, &pP)
#define rv(ri,ci) *(double*) idxA( &ri,&ci, &r)
#define pv(ri,ci) *(double*) idxb( &ri,&ci, &p)
//result definition
#define ApPv(ri,ci) *(double*) idxApP(&ri,&ci,&ApP)
unsigned int zero=0;
unsigned int k=0;
while(k<MAXITER){
double alpha, beta;//scalars to compute in each interatin
structmatrix rPT=(vecT(&rP)),pPT=vecT(&pP);
structmatrix rPTrP=matrixmatrixmuldbl(&rPT,&rP);//1x1
structmatrix ApP=matrixmatrixmuldbl(A,&pP);// vec nrows
fpidx idxApP =getidxingfunc(&ApP);
double alphan=*(double*) rPTrP.data;
double alphad=*(double*) (matrixmatrixmuldbl(&pPT,&ApP)).data;
alpha=alphan/alphad;//alpha new
unsigned int ri;
for(ri=0;ri<XP.nrows;ri++){
Xv(ri,zero)=XPv(ri,zero)+alpha*pPv(ri,zero); //new x approx soln
rv(ri,zero)=rPv(ri,zero)-alpha*ApPv(ri,zero);//new r error
}
structmatrix rT=vecT(&r);
structmatrix rTr=matrixmatrixmuldbl(&rT,&r);
beta=(*(double*) rTr.data)/(*(double*) rPTrP.data); //scalar/scalar
for(ri=0;ri<p.nrows;ri++){
pv(ri,zero)=rv(ri,zero)+beta*pPv(ri,zero);
}
double normofr=0;
for(ri=0;ri<X.nrows;ri++){normofr+=pow(rv(ri,zero),2);}
normofr=pow(normofr,.5);
if(normofr<TOL){printf("converged\n in %d iterations\n",k+1);return X;}
//previous=current
for(ri=0;ri<X.nrows;ri++){
XPv(ri,zero)=Xv(ri,zero);
pPv(ri,zero)=pv(ri,zero);
rPv(ri,zero)=rv(ri,zero);
}
/* todo does not work if i add these free statements
does the memory get freed with each loop? i thought it would not!*/
/*
free(rPT.data);
free(rPTrP.data);
free(ApP.data);
free(rT.data);
free(rTr.data);
*/
k++;}
free(XP.data);
free(rP.data);
free(pP.data);
free(r.data);
free(p.data);
return X;
#undef Xv
#undef XPv
#undef Av
#undef bv
#undef rPv
#undef pPv
#undef rv
#undef pv
#undef ApPv
}
