3.7. kda.svd

3.7.1. SVD and Matrix Solvers

The svd module contains code to calculate steady-state probabilities using matrix and singular value decomposition methods.

svd_solver(K, tol=1e-12)

Calculates the steady-state probabilities for an N-state model using singular value decomposition.

Parameters:

• K (ndarray) – Adjacency matrix for the kinetic diagram where each element kij is the edge weight (i.e. transition rate constant). For example, for a 2-state model with k12=3 and k21=4, K=[[0, 3], [4, 0]].

• tol (float, optional) – Tolerance used for singular value determination. Values are considered singular if they are less than the input tolerance. Default is 1e-12.

Returns:

state_probs – Array of state probabilities for N states of the form [p1, p2, p3, ..., pN].

Return type:

NumPy array

matrix_solver(K)

Calculates the steady-state probabilities for an N-state model using a standard matrix solver.

Parameters:

K (ndarray) – Adjacency matrix for the kinetic diagram where each element kij is the edge weight (i.e. transition rate constant). For example, for a 2-state model with k12=3 and k21=4, K=[[0, 3], [4, 0]].

Returns:

state_probs – Array of state probabilities for N states of the form [p1, p2, p3, ..., pN].

Return type:

ndarray

Functions

matrix_solver(K)	Calculates the steady-state probabilities for an N-state model using a standard matrix solver.
svd_solver(K[, tol])	Calculates the steady-state probabilities for an N-state model using singular value decomposition.