pyemma.msm.analysis.is_rate_matrix

pyemma.msm.analysis.is_rate_matrix(K, tol=1e-12)

Check if the given matrix is a rate matrix.

Parameters:

• K ((M, M) ndarray or scipy.sparse matrix) – Matrix to check
• tol (float (optional)) – Floating point tolerance to check with

Returns:

is_rate_matrix – True, if K is a valid rate matrix, False otherwise

Return type:

bool

Notes

A valid rate matrix \(K=(k_{ij})\) has non-positive off diagonal elements, \(k_{ij} \leq 0\), for \(i \neq j\), and elements of each row sum up to zero, \(\sum_{j} k_{ij}=0\).

Examples

>>> from pyemma.msm.analysis import is_rate_matrix

>>> A = np.array([[0.5, -0.5, -0.2], [-0.3, 0.6, -0.3], [-0.2, 0.2, 0.0]])
>>> is_rate_matrix(A)
False

>>> K = np.array([[0.3, -0.2, -0.1], [-0.5, 0.5, 0.0], [-0.1, -0.1, 0.2]])
>>> is_rate_matrix(K)
True