function [fg,theta]=FE_inner_product(f,g,M)

[fg,theta]=FE_inner_product(f,g,M)

     f :     Nodal variables
     g :     Nodal variables
     M :     The FE mass matrix, this you can find as the field MUA.M

    fg :     FE inner product between the nodal variables f and g
 theta :     The angle between f and g

Examples:

fg=FE_inner_product(f,g,MUA.M)   ;

fNorm=sqrt(FE_inner_product(f,f,MUA.M))   ;

Note: If you just need to calculate the norm of a nodal variable f, you can do so simply as:

fNorm= f'*MUA.M* f

So you don't really need to call this m-File.

nf=numel(f) ; ng=numel(g) ;

[nM,mM]=size(M);

theta=nan;

if nM==nf

    fg=f'*M*g;   % = (M*f)' * g

    if nargout>1
        fNorm=sqrt(f'*M*f) ;
        gNorm=sqrt(g'*M*g) ;
        theta=acos(fg/(fNorm*gNorm)) ;
    else
        theta=nan;
    end

elseif nf==2*nM

    fg=f(1:nM)'*M*g(1:nM)+f(1+nM:nf)'*M*g(1+nM:ng);

    if nargout>1
    fNorm=sqrt(f(1:nM)'*M*f(1:nM)+f(1+nM:nf)'*M*f(1+nM:nf)) ;
    gNorm=sqrt(g(1:nM)'*M*g(1:nM)+g(1+nM:ng)'*M*g(1+nM:ng)) ;
    theta=acos(fg/(fNorm*gNorm)) ;
    else
        theta=nan;
    end

end

end

Published with MATLAB® R2024a