run_markov_chain_ABC module

itrails.run_markov_chain_ABC.compute_matrices_start_end_wrapper(prob_mats, exponential_time, omega_start_masks, omega_end_masks, num_combinations)

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. :type prob_mats: list or np.ndarray. :param prob_mats: List or array of probability matrices where each element is a numpy array. :type prob_mats: list or np.ndarray. :type exponential_time: np.ndarray. :param exponential_time: Numpy array representing the matrix computed by applying the exponential function to the transition matrix multiplied by time. :type exponential_time: np.ndarray. :type omega_start_masks: list or np.ndarray of bool. :param omega_start_masks: List or array of boolean vectors used to mask the rows of the exponential_time matrix for each combination. :type omega_start_masks: list or np.ndarray of bool. :type omega_end_masks: list or np.ndarray of bool. :param omega_end_masks: List or array of boolean vectors used to mask the columns of the exponential_time matrix for each combination. :type omega_end_masks: list or np.ndarray of bool. :type num_combinations: int. :param num_combinations: Total number of combinations (iterations) over which to compute the sliced matrix. :type num_combinations: int. :return: Numpy array containing the resulting matrices computed for each combination. :rtype: np.ndarray.

itrails.run_markov_chain_ABC.compute_matrix_start_end(prob_mat, exponential_time, omega_start_mask, omega_end_mask)

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_ABC.deepest_parallel_inner(deepest_idx, trans_mat_noabs, omega_dict_noabs, deepest_keys_acc_array, deepest_paths_acc_array, deepest_path_lengths_array, acc_prob_mats_noabs)

Parallel wrapper that schedules deepest_worker_inner tasks to compute the matrix for the deepest time interval when multiple coalescents occur in the last time interval; it first serializes the omega dictionary (excluding absorbing states), then constructs a list of tasks from the accumulated keys, paths, and path lengths arrays along with the corresponding probability matrices without absorbing states, executes these tasks in parallel using ncpu.N_CPU_GLOBAL workers, and finally aggregates and flattens the results into arrays of updated keys and computed probability matrices along with the total count of valid tasks processed. :type deepest_idx: int. :param deepest_idx: number of indices in the deepest keys accumulator array. :type deepest_idx: int. :type trans_mat_noabs: numpy array. :param trans_mat_noabs: transition matrix without absorbing states used for deepest time interval computations. :type trans_mat_noabs: numpy array. :type omega_dict_noabs: dict. :param omega_dict_noabs: dictionary mapping omega state keys (without absorbing states) to boolean vectors. :type omega_dict_noabs: dict. :type deepest_keys_acc_array: list or numpy array. :param deepest_keys_acc_array: accumulated array of keys for each deepest subpath combination. :type deepest_keys_acc_array: list or numpy array. :type deepest_paths_acc_array: list or numpy array. :param deepest_paths_acc_array: accumulated array of paths for each deepest subpath combination. :type deepest_paths_acc_array: list or numpy array. :type deepest_path_lengths_array: list or numpy array. :param deepest_path_lengths_array: accumulated array of subpath lengths for each deepest subpath combination. :type deepest_path_lengths_array: list or numpy array. :type acc_prob_mats_noabs: list or numpy array. :param acc_prob_mats_noabs: list or array of probability matrices representing the initial state for deepest subpaths without absorbing states. :type acc_prob_mats_noabs: list or numpy array. :return: tuple containing (flattened_keys, flattened_results, total_valid) where flattened_keys is an array of updated keys, flattened_results is an array of computed probability matrices, and total_valid is the total number of valid tasks processed. :rtype: tuple.

itrails.run_markov_chain_ABC.deepest_worker_inner(idx_i, idx_j, trans_mat_noabs, omega_dict_noabs_serialized, key, paths_array_j, acc_prob_mat_noabs, path_lengths_j)

Ray worker function for every combination of subpaths when multiple coalescents happen in the last time interval (Deepest TI).

Parameters:

• idx_i (int) – Marker of the path index within all possible Deepest TI paths.

• idx_j (int) – Marker of the subpath index within all possible subpaths.

• trans_mat_noabs (Numpy array) – Transition matrix without absorbing states.

• omega_dict_noabs_serialized (Serialized dictionary) – Serialized dictionary of omega indices (key) and vector of booleans where each key has the states (value), lacks absorbing states.

• paths_array_j (Numpy array) – Array of possible transitions within a subpath.

• acc_prob_mat_noabs (Numpy array) – Array of probabilities for each state at the start of the time interval without absorbing states.

• path_lengths_j (Numpy array) – Array of lengths of each subpath.

Returns:

I and J indices, Probability matrix summed over every possible transitions for a subpath, Updated Key.

Return type:

Tuple(int, int, Numpy array, Numpy array)

itrails.run_markov_chain_ABC.run_markov_chain_ABC(trans_mat, times, omega_dict, prob_dict, omega_nonrev_counts, inverted_omega_nonrev_counts, n_int_ABC, species, absorbing_state=(7, 7))

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

Parameters:

• trans_mat (Numpy array) – Transition matrix.

• times (Numpy array) – Array of cut times, last timepoint is infinity.

• 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).

• omega_nonrev_counts (Numba typed dictionary) – Dictionary of omega indices (key) and number of non-reversible transitions (value).

• inverted_omega_nonrev_counts (Numba typed dictionary) – Dictionary of omega indices (key) and number of non-reversible transitions (value), inverted.

• n_int_ABC (int) – Number of intervals for species A, B, and C.

• species (int) – Number of species.

• absorbing_state (tuple, optional) – State where all coalecents have happened, defaults to (7, 7)

Returns:

Updated dictionary of each path (keys) and probabilities for each state at the end of the Markov chain (time equals inf)(values).

Return type:

Numba typed dictionary

itrails.run_markov_chain_ABC.vanloan_parallel_inner(vl_idx, time, trans_mat, omega_dict, vl_keys_acc_array, vl_paths_acc_array, vl_omega_masks_start, vl_omega_masks_end, vl_prob_mats)

Parallel wrapper that schedules vanloan_worker_inner tasks to compute the Van Loan integral for every combination of subpaths when multiple coalescents occur in the same time interval; it first serializes the provided omega dictionary, then builds a list of tasks from the accumulated keys, paths, omega masks, and probability matrices arrays, executes these tasks in parallel using ncpu.N_CPU_GLOBAL workers, and finally aggregates and flattens the results into arrays of updated keys and computed probability matrices along with the total number of valid tasks processed. :type vl_idx: int. :param vl_idx: number of indices in the vanloan keys accumulator array. :type vl_idx: int. :type time: float. :param time: end time of the current time interval used in the Van Loan integral computation. :type time: float. :type trans_mat: numpy array. :param trans_mat: transition matrix used for the Van Loan integral computation. :type trans_mat: numpy array. :type omega_dict: dict. :param omega_dict: dictionary mapping omega state keys to boolean vectors indicating valid states. :type omega_dict: dict. :type vl_keys_acc_array: list or numpy array. :param vl_keys_acc_array: accumulated array of keys for each vanloan subpath combination. :type vl_keys_acc_array: list or numpy array. :type vl_paths_acc_array: list or numpy array. :param vl_paths_acc_array: accumulated array of paths for each vanloan subpath combination. :type vl_paths_acc_array: list or numpy array. :type vl_omega_masks_start: list or numpy array of bool. :param vl_omega_masks_start: list or array of boolean masks applied to the rows of the matrix for each vanloan subpath. :type vl_omega_masks_start: list or numpy array of bool. :type vl_omega_masks_end: list or numpy array of bool. :param vl_omega_masks_end: list or array of boolean masks applied to the columns of the matrix for each vanloan subpath. :type vl_omega_masks_end: list or numpy array of bool. :type vl_prob_mats: list or numpy array. :param vl_prob_mats: list or array of probability matrices representing the initial state for each vanloan subpath. :type vl_prob_mats: list or numpy array. :return: tuple containing (flattened_keys, flattened_results, total_valid) where flattened_keys is an array of updated keys, flattened_results is an array of computed probability matrices, and total_valid is the total number of valid tasks processed. :rtype: tuple.

itrails.run_markov_chain_ABC.vanloan_worker_inner(idx_i, idx_j, trans_mat, omega_dict_serialized, key, time, paths_array_j, omega_start_mask, omega_end_mask, prob_mat)

Ray worker function for every combination of subpaths when multiple coalescents happen in a same time interval (Van Loan).

Parameters:

• idx_i (int) – Marker of the path index within all possible Van Loan paths.

• idx_j (int) – Marker of the subpath index within all possible subpaths.

• trans_mat (Numpy array) – Transition matrix.

• omega_dict_serialized (Serialized dictionary) – Serialized dictionary of omega indices (key) and vector of booleans where each key has the states (value).

• key (Numpy array) – Key that represents the current state.

• time (float) – End time of the interval.

• paths_array_j (Numpy array) – Array of possible transitions within a subpath.

• omega_start_mask (Numpy array) – 2D array to mask the matrix based on initial omega, array of booleans.

• omega_end_mask (Numpy array) – 2D array to mask the matrix based on final omega, array of booleans.

• prob_mat (Numpy array) – Array of probabilities for each state at the start of the time interval.

Returns:

I and J indices, Probability matrix summed over every possible transitions for a subpath, Updated Key.

Return type:

Tuple(int, int, Numpy array, Numpy array)