Computationally hazardous(!), but you could try one of these modifications with e.g. 1e-300 as an approximation for zero and see how far you get... Take care of error propagation.

  $lnpam[$i][$j] = log( $matrix[$i][$j]  || 1e-300);
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  $lnpam[$i][$j] = $matrix[$i][$j]  ? log( $matrix[$i][$j]) : -1000;
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