Program Cast_eigen;

Const
     np = 20;

Type
   Rmat = Array [1..np,1..np] of Real;
   Rvec = Array [1..np] of Real;

Procedure Matvec(n:Integer;Var M:Rmat; Var Vold,Vnew:Rvec);

Var i,j:integer;

BEGIN
     FOR i:=1 TO n DO BEGIN
         Vnew[i] := 0.;
         FOR j:= 1 TO n DO
             Vnew[i] := Vnew[i] + M[i,j] * Vold[j];
         END;
END;

Const eps=1.e-5;
VAR a,apom: RMat;
    n,i,j,k: integer;
    l,lmin,lmax:Real;
    v1,v2, vpom: RVec;
    fvst:Text;
    vstnam:String;
Begin
    Writeln('Zadej jmeno vstupniho souboru');
    Readln(vstnam);
    ASSIGN(fvst,vstnam);
    RESET(fvst);
    Readln(fvst,n);
    FOR i:=1 TO n DO BEGIN
        FOR j:=1 TO n DO Read(fvst,a[i,j]); Readln(fvst)
        END;
    FOR i:=1 TO n DO
        FOR j:=1 TO n DO
                   apom[i,j] := a[i,j];
    FOR i:=1 TO n DO Read(fvst,v2[i]); Readln(fvst);
    Writeln(' Stary vektor ');
    FOR i:=1 TO n DO Write(v2[i]); Writeln;
    k:=0;
    Repeat
       k:=k+1;
       Writeln(' Iterace ',k);
       Writeln(' Stary vektor ');
       FOR i:=1 TO n DO Write(v2[i]); Writeln;
       FOR i:=1 TO n DO v1[i]:=v2[i];
       Matvec(n,a,v1,v2);
       Writeln(' Novy vektor ');
       FOR i:=1 TO n DO Write(v2[i]); Writeln;
       lmax := -1.e+30;
       lmin := 1.e+30;
       FOR i:= 1 TO n DO
           if(v1[i] <> 0) OR (v2[i] <> 0) THEN BEGIN
                IF v1[i] <> 0 THEN
                         l := v2[i]/v1[i]
                   ELSE
                         IF v2[i] > 0 THEN
                                  l := 1.e+30
                            else
                                  l := -1.e+30;
                IF l < lmin THEN lmin:= l;
                IF l > lmax THEN lmax:= l;
           END;
       l := 0;
       FOR i:= 1 TO n DO l := l + sqr(v2[i]);
       FOR i:= 1 TO n DO v2[i] := v2[i]/sqrt(l);
       Writeln(' lmin = ',lmin,'   lmax = ',lmax);
       Readln;
       UNTIL (lmax-lmin)/(abs(lmax) + abs(lmin)) < eps;
       Writeln('Vysledek');
       Writeln(' Vlastni cislo ',(lmin+lmax)*0.5);
       Writeln(' Vlastni vektor ');
       FOR i:=1 TO n DO Write(v2[i]); Writeln;
       Readln;
END.