Constructor Detail

Method Detail

• dtmc_makestochastic

   final static Matrix dtmc_makestochastic(Matrix P)

  Normalizes a matrix to be a valid stochastic matrix. Rescales rows to sum to 1. Rows with zero sum get 1 at diagonal.

  Parameters:

  P - Input matrix

  Returns:

  Valid stochastic transition matrix

• dtmc_isfeasible

   final static Integer dtmc_isfeasible(Matrix P)

  Checks feasibility of a stochastic matrix. Verifies if row sums are close to 1 and elements are non-negative.

  Parameters:

  P - Matrix to check

  Returns:

  Precision level (1-15) if feasible, or 0 if not feasible

• dtmc_solve

   final static DoubleArray dtmc_solve(Matrix P)

  Computes the equilibrium distribution of a discrete-time Markov chain.

  Parameters:

  P - Stochastic transition matrix

  Returns:

  Equilibrium distribution vector

• dtmc_rand

   final static Matrix dtmc_rand(Integer n)

  Generates a random stochastic transition matrix.

  Parameters:

  n - Size of the matrix (n x n)

  Returns:

  Random stochastic transition matrix

• dtmc_simulate

   final static IntArray dtmc_simulate(Matrix P, DoubleArray pi0, Integer nSteps)

  Simulates a trajectory of a discrete-time Markov chain.

  Parameters:

  P - Stochastic transition matrix

  pi0 - Initial probability distribution vector

  nSteps - Number of steps to simulate

  Returns:

  Vector of state indices visited in the simulation (0-based)

• dtmc_stochcomp

   final static Matrix dtmc_stochcomp(Matrix P, IntArray I)

  Computes the stochastic complement of a DTMC partition.

  Parameters:

  P - Stochastic transition matrix

  I - Indices of states to retain (0-based)

  Returns:

  Stochastic complement matrix for the subset I

• dtmc_timereverse

   final static Matrix dtmc_timereverse(Matrix P)

  Computes the time-reversed transition matrix of a DTMC.

  Parameters:

  P - Stochastic transition matrix of the original process

  Returns:

  Stochastic transition matrix of the time-reversed process

• dtmc_uniformization

   final static Pair<DoubleArray, Integer> dtmc_uniformization(DoubleArray pi0, Matrix P, Double t, Double tol, Integer maxiter)

  Computes transient probabilities for a DTMC using uniformization.

  Parameters:

  pi0 - Initial probability distribution vector

  P - Transition probability matrix

  t - Time point for transient analysis (default: 1e4)

  tol - Error tolerance (default: 1e-12)

  maxiter - Maximum iterations (default: 100)

  Returns:

  Pair of (probability distribution at time t, number of iterations)