The function "ordqz" can be called with a logical select vector to order the the corresponding eigenvalues up front, in the example below it moves the 1st, 4th and 5th eigenvalue to the left.

>> select = [1 0 0 1 1 0];
>> [ar, br, qr, zr] = ordqz (aa, bb, q, z, select)

In Matlab, it is possible to order the eigenvalues in clusters. For instance, in the example below, it moves the 1st, 4th and 5th eigenvalue to the left followed by the 6th eigenvalue and then the remaining ones.

>> cluster = [1 3 3 1 1 2];
>> [ar, br, qr, zr] = ordqz (aa, bb, q, z, cluster)

It seems possible to achieve this by calling ordqz several times using appropriate logical select vectors, but this assumes that unaffected eigenvalues are not moved during the call. However, this is not documented, so it cannot be relied upon.

>> [ar, br, qr, zr] = ordqz (aa, bb, q, z, [1 0 0 1 1 0])
>> [arr, brr, qrr, zrr] = ordqz (ar, br, qr, zr, [1 1 1 0 0 1])

Using the proposed cluster feature, would make it possible to group eigenvalues in a flexible way.