Table 1. Number of PDB entries in which at least one of the physical conditions on TLS matrices is broken.

The statistics are shown for the matrices in the PDB (25904 entries with TLS matrices from a total number of 106761 entries as of March 2015) with the default condition tr(S) = 0 (upper line) and with the optimal choice of the diagonal S elements whenever possible as described in 3 and 4 (bottom line). The conditions are, from left to right: matrices T and L are positive semidefinite (T 0 and L 0); an absence of libration around one of the axes requires the corresponding elements of the S matrix to be equal to 0 (s = 0 and w = 0); matrix T is positive semidefinite after the contribution owing to the displacement of libration axes is removed (T _C 0); elements of the S matrix are limited by the corresponding elements of the T and L matrices according to the Cauchy conditions (S TL); the residual V matrix is positive semidefinite (V 0). The column (V 0) includes all conditions from 4.3 and 4.4. When one of the conditions was broken further conditions were not checked.

			Conditions broken
Mode	Total No. of PDB entries	Total No. of TLS	T 0 and L 0	s = 0 and w = 0	T C 0	S TL	V 0	Total No. of TLS broken	Total No. of TLS OK	Total No. of PDB entries broken
t S = 0	25904	203261	71362	3104	52254	n/a	10492	137212	66049	22707
Best t S	25904	203261	71362	3104	52255	133	3776	130630	72631	22201