leave_prob

mdtools.dtrj.leave_prob(*args, **kwargs)[source]

Calculate the probability that a compound leaves its state after a lag time \(\Delta t\) given that it has entered the state at time \(t_0\).

Take a discrete trajectory and calculate the probability that a compound leaves its state at time \(t_0 + \Delta t\) given that it has entered the state at time \(t_0\).

Parameters:: args, kwargs – This function takes the same parameters as mdtools.dtrj.n_leaves_vs_time(). See there for more information.
Returns:: prob (numpy.ndarray) – Array of shape (f,) containing for all possible lag times \(\Delta t\) the probability that a compound leaves its state at time \(t_0 + \Delta t\) given that they have entered the state at time \(t_0\).

See also

mdtools.dtrj.leave_prob_discrete(): Calculate the probability that a compound leaves its state after a lag time \(\Delta t\) given that it has entered the state at time \(t_0\) resolved with respect to the states in a second discrete trajectory
mdtools.dtrj.n_leaves_vs_time(): Calculate the number of compounds that leave their state after a lag time \(\Delta t\) given that they have entered the state at time \(t_0\)
mdtools.dtrj.remain_prob(): Calculate the probability that a compound is still (or again) in the same state as at time \(t_0\) after a lag time \(\Delta t\)
mdtools.dtrj.back_jump_prob(): Calculate the back-jump probability averaged over all states

Notes

This function simply calls mdtools.dtrj.n_leaves_vs_time(), calculates n_leaves / n_risk and checks that the result lies within the interval \([0, 1]\).

Important

A leaving probability of zero means that no state leaving could be observed at the given lag time. However, this does not necessarily mean that there definitely are no state leavings at this lag time, because if the lag time coincides with a censoring time, we simply do not know what happens.

Examples

>>> # No detectable leave, two censored lifetimes.
>>> dtrj = np.array([2, 2, 5, 5, 5, 5, 5])
>>> mdt.dtrj.leave_prob(dtrj)
array([ 0.,  0.,  0.,  0.,  0.,  0., nan])
>>> # One detectable leave, two censored lifetimes.
>>> dtrj = np.array([2, 2, 3, 3, 3, 2, 2])
>>> mdt.dtrj.leave_prob(dtrj)
array([ 0.,  0.,  0.,  1., nan, nan, nan])
>>> # Two detectable leaves, two censored lifetimes.
>>> dtrj = np.array([1, 3, 3, 3, 1, 2, 2])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.  , 0.25, 0.  , 1.  ,  nan,  nan,  nan])
>>> dtrj = np.array([1, 3, 3, 3, 2, 2, 1])
>>> mdt.dtrj.leave_prob(dtrj)
array([0. , 0. , 0.5, 1. , nan, nan, nan])
>>> dtrj = np.array([3, 3, 3, 1, 2, 2, 1])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.  , 0.25, 0.5 , 0.  ,  nan,  nan,  nan])

>>> dtrj = np.array([[2, 2, 5, 5, 5, 5, 5],
...                  [2, 2, 3, 3, 3, 2, 2],
...                  [1, 3, 3, 3, 1, 2, 2],
...                  [1, 3, 3, 3, 2, 2, 1],
...                  [3, 3, 3, 1, 2, 2, 1]])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.        , 0.11764706, 0.18181818, 0.6       , 0.        ,
       0.        ,        nan])
>>> dtrj = np.array([[1, 2, 2, 3, 3, 3],
...                  [2, 2, 3, 3, 3, 1],
...                  [3, 3, 3, 1, 2, 2],
...                  [1, 3, 3, 3, 2, 2]])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.        , 0.08333333, 0.125     , 0.5       ,        nan,
              nan])

Discarding negative states:

>>> dtrj = np.array([[1, 2, 2, 3, 3, 3],
...                  [2, 2, 3, 3, 3, 1],
...                  [3, 3, 3, 1, 2, 2],
...                  [1, 3, 3, 3, 2, 2],
...                  [1, 4, 4, 4, 4, 1]])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.        , 0.06666667, 0.11111111, 0.4       , 1.        ,
              nan])
>>> mdt.dtrj.leave_prob(dtrj, discard_neg_start=True)
array([0.        , 0.06666667, 0.11111111, 0.4       , 1.        ,
              nan])
>>> mdt.dtrj.leave_prob(dtrj, discard_all_neg=True)
array([0.        , 0.06666667, 0.11111111, 0.4       , 1.        ,
              nan])
>>> dtrj = np.array([[ 1, -2, -2,  3,  3,  3],
...                  [-2, -2,  3,  3,  3,  1],
...                  [ 3,  3,  3,  1, -2, -2],
...                  [ 1,  3,  3,  3, -2, -2],
...                  [ 1,  4,  4,  4,  4, -1]])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.        , 0.06666667, 0.11111111, 0.4       , 1.        ,
              nan])
>>> mdt.dtrj.leave_prob(dtrj, discard_neg_start=True)
array([0. , 0.1, 0. , 0.4, 1. , nan])
>>> mdt.dtrj.leave_prob(dtrj, discard_all_neg=True)
array([0. , 0. , 0. , 0.2, 0. , nan])
>>> dtrj = np.array([[ 1, -2, -2,  3,  3,  3],
...                  [-2, -2,  3,  3,  3,  1],
...                  [ 3,  3,  3,  1, -2, -2],
...                  [ 1,  3,  3,  3, -2, -2],
...                  [ 1,  4,  4,  4,  4, -1],
...                  [ 6,  6,  6,  6,  6,  6],
...                  [-6, -6, -6, -6, -6, -6]])
>>> mdt.dtrj.leave_prob(dtrj)
array([0.        , 0.05882353, 0.09090909, 0.28571429, 0.33333333,
       0.        ])
>>> mdt.dtrj.leave_prob(dtrj, discard_neg_start=True)
array([0.        , 0.09090909, 0.        , 0.33333333, 0.5       ,
       0.        ])
>>> mdt.dtrj.leave_prob(dtrj, discard_all_neg=True)
array([0.        , 0.        , 0.        , 0.16666667, 0.        ,
       0.        ])