butools.mc.CheckGenerator¶

butools.mc.CheckGenerator()¶

Matlab:	r = CheckGenerator(Q, transient, prec)
Mathematica:	r = CheckGenerator[Q, transient, prec]
Python/Numpy:	r = CheckGenerator(Q, transient, prec)

Checks if the matrix is a valid generator matrix: the matrix is a square matrix, the matrix has positive or zero off-diagonal elements, the diagonal of the matrix is negative, the rowsum of the matrix is 0.

If the “transient” parameter is set to false, it checks if the real part of the maximum absolute eigenvalue is less than zero and the rowsum is equal or less than 0.

Parameters:	Q : matrix, shape (M,M) The generator to check. transient : bool, optional If true, the procedure checks if Q is a transient generator, otherwise it checks if it is a valid generator. The default value is false. prec : double, optional Entries with absolute value less than prec are considered to be zeros. The default value is 1e-14.
Returns:	r : bool The result of the check.

Examples

For Matlab:

>>> Q = [-0.9, 0.2, 0.4; 0, 0.9, 0.9; 0, 0.6, -0.6];
>>> flag = CheckGenerator(Q, true);
CheckGenerator: The diagonal of the generator is not negative (precision: 1e-12)!
>>> disp(flag);
     0
>>> Q = [-0.9, 0.5, 0.4; 0.9, -0.9, 0; 0.3, 0.3, -0.6];
>>> flag = CheckGenerator(Q, true);
>>> disp(flag);
     1
>>> Q = [-0.9, 0.2, 0.4; 0.9, -0.9, 0; 0.3, 0.3, -0.6];
>>> flag = CheckGenerator(Q, true);
>>> disp(flag);
     1
>>> Q = [-0.9, 0.5, 0.4; 0.9, -1.1, 0; 0.3, 0.3, -0.6];
>>> flag = CheckGenerator(Q);
CheckGenerator: The rowsum of the generator is not 0 (precision: 1e-12)!
>>> disp(flag);
     0
>>> Q = [-0.9, 0.5, 0.4; 0.9, -0.9, 0; 0.3, 0.3, -0.6];
>>> flag = CheckGenerator(Q);
>>> disp(flag);
     1

For Mathematica:

>>> Q = {{-0.9, 0.2, 0.4},{0, 0.9, 0.9},{0, 0.6, -0.6}};
>>> flag = CheckGenerator[Q, True];
"CheckGenerator: The diagonal of the generator is not negative (at precision "1.*^-12")!"
>>> Print[flag];
False
>>> Q = {{-0.9, 0.5, 0.4},{0.9, -0.9, 0},{0.3, 0.3, -0.6}};
>>> flag = CheckGenerator[Q, True];
>>> Print[flag];
True
>>> Q = {{-0.9, 0.2, 0.4},{0.9, -0.9, 0},{0.3, 0.3, -0.6}};
>>> flag = CheckGenerator[Q, True];
>>> Print[flag];
True
>>> Q = {{-0.9, 0.5, 0.4},{0.9, -1.1, 0},{0.3, 0.3, -0.6}};
>>> flag = CheckGenerator[Q];
"CheckGenerator: A rowsum of the generator is not 0 (precision:"1.*^-12")!!"
>>> Print[flag];
False
>>> Q = {{-0.9, 0.5, 0.4},{0.9, -0.9, 0},{0.3, 0.3, -0.6}};
>>> flag = CheckGenerator[Q];
>>> Print[flag];
True

For Python/Numpy:

>>> Q = ml.matrix([[-0.9, 0.2, 0.4],[0, 0.9, 0.9],[0, 0.6, -0.6]])
>>> flag = CheckGenerator(Q, True)
CheckGenerator: The diagonal of the generator is not negative (precision: 1e-12)!
>>> print(flag)
False
>>> Q = ml.matrix([[-0.9, 0.5, 0.4],[0.9, -0.9, 0],[0.3, 0.3, -0.6]])
>>> flag = CheckGenerator(Q, True)
>>> print(flag)
True
>>> Q = ml.matrix([[-0.9, 0.2, 0.4],[0.9, -0.9, 0],[0.3, 0.3, -0.6]])
>>> flag = CheckGenerator(Q, True)
>>> print(flag)
True
>>> Q = ml.matrix([[-0.9, 0.5, 0.4],[0.9, -1.1, 0],[0.3, 0.3, -0.6]])
>>> flag = CheckGenerator(Q)
CheckGenerator: The rowsum of the generator is not 0 (precision: 1e-12)!
>>> print(flag)
False
>>> Q = ml.matrix([[-0.9, 0.5, 0.4],[0.9, -0.9, 0],[0.3, 0.3, -0.6]])
>>> flag = CheckGenerator(Q)
>>> print(flag)
True