piecewise matrix multiplication with vector

Hi,

I am trying to minimize a function s = b - Yr in a vectorized form. Y is a projection matrix and r the coordinates. I would like to multiply the first two rows of Y with the first vector in r and then the two second ones in y with the second one in r. Now this works:

b = zeros(2,1);
Y = [1 2 3 ; 0 0 1 ]
r = [0 0 1]';
s =

      -3
      -1

Now how could I extend this? Like this:

Y = [1 2 3 ; 0 0 1 ; 4 5 6 ; 0 0 1]
r = [0 0 1 ; 0 0 1]';

Such that I have the same form answer as in b variable? like b = zeros(2,90);

The variable Y i make like this:

angles = -88:2:90
for i= 1:size(angles,2)  
if i== 1
    Y = [cos(angles(1,i)) 0 sin(angles(1,i)); 0 1 0];
else
    Y = vertcat(Y,[cos(angles(1,i)) 0 sin(angles(1,i)); 0 1 0]);
end
end

And in the minimization I try to find the z coordinate in r variable: r = [0 0 x]

Many thanks for any help!

Answer 1

[dpb]

Sometimes it's just easiest to write a loop...

j=0;
for i=1:2:length(Y)
  j=j+1;;
  p(:,j)=Y(i:i+1,:)*r(:,j);
end
s=b-p;  % objective function

With some thought this could be written w/ accumarray or the like but the above is straightforward and easy to debug. If it turns out the loop is a bottleneck verified by profiler, then I'd worry about it.

[mb]

thanks dpb! this will not be in the cost function so this will be perfect!