function [P,w,U]=vtb4_1(M,K,dispar)

%VTB4_1 Natural frequencies and eigenvectors for an undamped
%system.
% [P,w,U]=VTB4_1(M,K) will return the natural frequencies (w),
% eigenvectors (P), and mode shapes (U) for an undamped system.  
% The inputs are the mass matrix M and the stiffness matrix K.  
% [P,w,U]=VTB4_1(M,K,1) will also print the output of the function
% to the screen.



if nargin==2

  dispar=0;

end



%Calculates evectors and evalues

[P,lam]=eig(M^(-.5)*K*M^(-.5));



[w,k]=sort(sqrt(diag(lam)));

P=P(:,k);



%Makes sure the first entry of every column is positive

for i=1:length(M)

  if P(1,i)<0

     P(:,i)=-P(:,i);

  end

end



U=M^(-.5)*P;



if dispar==1

  clc

  disp('The natural frequencies are')

  disp(' ')

  for i=1:length(M)

    disp(['omega',num2str(i),' = ',num2str(w(i)),' rad/s'])

  end

  disp(' ')

  disp('The eigenvectors of the system are')

  P

  disp(' ')

  disp('The mode shapes of the system are')

  U

end