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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _augmenting_row_reduction(self):
 """ Augmenting row reduction step from LAPJV algorithm """

        unassigned = np.where(self._x == -1)[0]
        for i in unassigned:
            for _ in range(self.c.size):
                # Time in this loop can be proportional to 1/epsilon
                # This step is not strictly necessary, so cutoff early
                # to avoid near-infinite loops

                # find smallest 2 values and indices
                temp = self.c[i] - self._v
                j1 = np.argmin(temp)
                u1 = temp[j1]
                temp[j1] = np.inf
                j2 = np.argmin(temp)
                u2 = temp[j2]

                if u1 < u2:
                    self._v[j1] -= u2 - u1
                elif self._y[j1] != -1:
                    j1 = j2
                k = self._y[j1]
                if k != -1:
                    self._x[k] = -1
                    self._x[i] = j1
                    self._y[j1] = i
                    i = k
                if k == -1 or abs(u1 - u2) < self.epsilon:
                    break