function [X] = rrr( A, B, k )
% function [X] = rrr( A, B, k )
%
% Solves the system of equations X*A = B, subject
% to rank(X)=k.
%
% D. Wingate

[QA,RA] = qr( A',0 );
[QB,RB] = qr( B',0 );

[U,S,V] = svds( QB'*QA, k );

X = RB' * U * S * V' * inv(RA');

return;