positivizeMatrix[X_] := Module[{res},

   res = X;

   auxsystDP = Eigensystem[X];

   duDP = DiagonalMatrix[auxsystDP[[1]]];

   powerDP = 20;

   While[Not[PositiveDefiniteMatrixQ[res]],

    wDP =
     ReplacePart[
      duDP, {i_, i_} /;
        duDP[[i, i]] <= 0 :> $MachineEpsilon*2^(-powerDP)];
    (*Adding the smallest nugget possible.*)

    res =
     Transpose[auxsystDP[[2]]].wDP.Inverse[Transpose[auxsystDP[[2]]]];
    (*this matrix is still not symmetric, only PD*)

    powerDP--;
    ];

   Print[PositiveDefiniteMatrixQ[res]];

   res = 0.5*(res + Transpose[res]);

   Print[PositiveDefiniteMatrixQ[res]];
   ];