In some cases when an input contributes fully to the corresponding
output, other inputs may also contribute to the same output. This is the
case, for example, for the default 5.1 to stereo downmix matrix without
normalization.

Do not skip an output if the corresponding input contributes to other output
channels.

If the matrix reduction ends up with no mixing matrix needed, we need to still
reset the mix function accordingly and log the info to the user.

This will print the new matrix if it is set after initialization.