%---------------------;
% Question 3(b)-(c)   ;
%---------------------;
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','w');
fprintf(fidc,'Answers to question 8(b)\n\n');
status=fclose(fidc);

D=[1 1 1 1 0 0 0 0 0 0;
   1 1 1 1 1 0 0 0 0 0;
   1 1 1 1 1 1 0 0 0 0;
   1 1 1 1 1 1 1 0 0 0;
   0 1 1 1 1 1 1 1 0 0;
   0 0 1 1 1 1 1 1 1 0;
   0 0 0 1 1 1 1 1 1 1;
   0 0 0 0 1 1 1 1 1 1;
   0 0 0 0 0 1 1 1 1 1;
   0 0 0 0 0 0 1 1 1 1];
lambda_D=eig(D);
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'Eigenvalues of D are: %4.4f\n\n',lambda_D);
status=fclose(fidc);
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'Answers to question 8(c)\n\n');
status=fclose(fidc);
count=0;
for n=1:1000
   u=normrnd(0,1,10,1);
   k=u'*D*u;
   if k<0
      count=count+1;
   end   
end
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'k is negative %4.0f times\n\n',count);
status=fclose(fidc);
%---------------------;
% Question 3(d)-(e)   ;
%---------------------;
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'Answers to question 8(d)\n\n');
status=fclose(fidc);

C=(1/4)*[4 3 2 1 0 0 0 0 0 0;
         3 4 3 2 1 0 0 0 0 0;
         2 3 4 3 2 1 0 0 0 0;
         1 2 3 4 3 2 1 0 0 0;
         0 1 2 3 4 3 2 1 0 0;
         0 0 1 2 3 4 3 2 1 0;
         0 0 0 1 2 3 4 3 2 1;
         0 0 0 0 1 2 3 4 3 2;
         0 0 0 0 0 1 2 3 4 3;
         0 0 0 0 0 0 1 2 3 4];
lambda_C=eig(C);
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'Eigenvalues of C are: %4.4f\n\n',lambda_C);
status=fclose(fidc);
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'Answers to question 8(e)\n\n');
status=fclose(fidc);
count=0;
for n=1:1000
   u=normrnd(0,1,10,1);
   k=u'*C*u;
   if k<0
      count=count+1;
   end   
end
fidc=fopen('c:\arh\courses\ecg790\2005\pracprb\prac_3_prog.out','a');
fprintf(fidc,'k is negative %4.0f times\n\n',count);
status=fclose(fidc);