run_markov_chain_AB module

itrails.run_markov_chain_AB.compute_matrices_end_wrapper(prob_mats, exponential_time, omega_end_masks, num_combinations)[source]

Parallel wrapper that computes the sliced matrix result for each combination by invoking compute_matrix_end on each set of inputs; for every index from 0 to num_combinations-1, it multiplies the corresponding probability matrix (from prob_mats) with the result of slicing the exponential_time matrix using the corresponding omega_end_mask, and aggregates all results into a single numpy array; the computations are performed in parallel using joblib.Parallel with ncpu.N_CPU_GLOBAL workers.

Parameters:

  • prob_mats (list or np.ndarray.) – List or array of probability matrices where each element is a numpy array.

  • exponential_time (np.ndarray.) – Numpy array representing the matrix computed by applying the exponential function to the transition matrix multiplied by time.

  • omega_end_masks (list or np.ndarray of bool.) – List or array of boolean vectors used to mask the columns of the exponential_time matrix for each combination.

  • num_combinations (int.) – Total number of combinations (iterations) over which to compute the sliced matrix.

Returns:

Numpy array containing the resulting matrices computed for each combination.

Return type:

np.ndarray.

itrails.run_markov_chain_AB.compute_matrices_start_end_wrapper(prob_mats, exponential_time, omega_start_masks, omega_end_masks, num_combinations)[source]

Parallel wrapper that computes the sliced matrix result for each combination by invoking compute_matrix_start_end on each set of inputs; for every index from 0 to num_combinations-1, it multiplies the corresponding probability matrix (from prob_mats) with the result of slicing the exponential_time matrix using the corresponding omega_start_mask and omega_end_mask, and aggregates all results into a single numpy array; the computations are performed in parallel using joblib.Parallel with ncpu.N_CPU_GLOBAL workers.

Parameters:

  • prob_mats (list or np.ndarray.) – List or array of probability matrices where each element is a numpy array.

  • exponential_time (np.ndarray.) – Numpy array representing the matrix computed by applying the exponential function to the transition matrix multiplied by time.

  • omega_start_masks (list or np.ndarray of bool.) – List or array of boolean vectors used to mask the rows of the exponential_time matrix for each combination.

  • omega_end_masks (list or np.ndarray of bool.) – List or array of boolean vectors used to mask the columns of the exponential_time matrix for each combination.

  • num_combinations (int.) – Total number of combinations (iterations) over which to compute the sliced matrix.

Returns:

Numpy array containing the resulting matrices computed for each combination.

Return type:

np.ndarray.

itrails.run_markov_chain_AB.compute_matrix_end(prob_mat, exponential_time, omega_end_mask)[source]

Helper function that computes the first matrix multiplication, then slices the matrix to get the columns corresponding to the end state.

Parameters:

  • prob_mat (Numpy array) – Matrix of probabilities

  • exponential_time (Numpy array) – Exponential matrix of transition matrix multiplied by time.

  • omega_end_mask (Numpy array of booleans.) – Vector of booleans that masks the columns of the matrix.

Returns:

Sliced matrix

Return type:

Numpy array

itrails.run_markov_chain_AB.compute_matrix_start_end(prob_mat, exponential_time, omega_start_mask, omega_end_mask)[source]

Helper function that computes all matrix multiplications but the first, then slices the matrix to get the rows corresponding to the starting state and columns corresponding to the end state.

Parameters:

  • prob_mat (Numpy array) – Matrix of probabilities

  • exponential_time (Numpy array) – Exponential matrix of transition matrix multiplied by time.

  • omega_start_mask (Numpy array of booleans.) – Vector of booleans that masks the rows of the matrix.

  • omega_end_mask (Numpy array of booleans.) – Vector of booleans that masks the columns of the matrix.

Returns:

Sliced matrix

Return type:

Numpy array

itrails.run_markov_chain_AB.run_markov_chain_AB(trans_mat, times, omega_dict, prob_dict, n_int_AB)[source]

Function that runs the Discrete Time Markov chain for species A and B.

Parameters:

  • trans_mat (Numpy array) – Transition matrix.

  • times (Numpy array) – Array of cut times.

  • omega_dict (Numba typed dictionary) – Dictionary of omega indices (key) and vector of booleans where each key has the states (value).

  • prob_dict (Numba typed dictionary) – Dictionary of each path (keys) and probabilities for each state at the start of the first time interval (values).

  • n_int_AB (int) – Number of intervals for species A and B.

Returns:

Updated dictionary of each path (keys) and probabilities for each state at the end of the last time interval (values).

Return type:

Numba typed dictionary