butools.mc.CheckProbMatrix¶

butools.mc.CheckProbMatrix()¶

Matlab:	r = CheckProbMatrix(P, transient, prec)
Mathematica:	r = CheckProbMatrix[P, transient, prec]
Python/Numpy:	r = CheckProbMatrix(P, transient, prec)

Checks if the matrix is a valid probability matrix: the matrix is a square matrix, the matrix has positive or zero off-diagonal elements, the rowsum of the matrix is 1.

If “transient” is true, it checks if the matrix is a valid transient probability matrix: the matrix is a square matrix, the matrix has positive or zero off-diagonal elements, the rowsum of the matrix is less than or equal to 1, the maximum absolute eigenvalue is less than 1.

Parameters:	P : matrix, shape (M,M) The matrix to check. transient : bool, optional If true, the procedure checks if P is a transient probability matrix, otherwise it checks if it is a valid probability matrix. 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 = [0.1, 0.5, 0.4; 0.9, 0.1, 0; 0.3, -0.1, 0.4];
>>> flag = CheckProbMatrix(Q);
CheckProbMatrix: the matrix has negative element (precision: 1e-12)!
>>> disp(flag);
     0
>>> Q = [0.1, 0.5, 0.4; 0.9, 0.1, 0; 0.3, 0.1, 0.4];
>>> flag = CheckProbMatrix(Q);
CheckProbMatrix: The rowsum of the matrix is not 1 (precision: 1e-12)!
>>> disp(flag);
     0
>>> Q = [0.1, 0.5, 0.4; 0.9, 0.1, 0; 0.3, 0.3, 0.4];
>>> flag = CheckProbMatrix(Q);
>>> disp(flag);
     1
>>> Q = [0.1, 0.5, 0.4; 0.9, 0.1, 0; 0.3, 0.3, 0.4];
>>> flag = CheckProbMatrix(Q, true);
CheckProbMatrix: The real part of the largest eigenvalue of the transient matrix is not less than 1 (precision: 1e-12)!
>>> disp(flag);
     0
>>> Q = [0.1, 0.5, 0.4; 0.9, 0.1, 0; 0.3, 0.1, 0.4];
>>> flag = CheckProbMatrix(Q, true);
>>> disp(flag);
     1

For Mathematica:

>>> Q = {{0.1, 0.5, 0.4},{0.9, 0.1, 0},{0.3, -0.1, 0.4}};
>>> flag = CheckProbMatrix[Q];
"CheckProbMatrix: the matrix has negative element (at precision "1.*^-12")!"
>>> Print[flag];
False
>>> Q = {{0.1, 0.5, 0.4},{0.9, 0.1, 0},{0.3, 0.1, 0.4}};
>>> flag = CheckProbMatrix[Q];
"CheckProbMatrix: A rowsum of the matrix is not 1 (precision:"1.*^-12")!!"
>>> Print[flag];
False
>>> Q = {{0.1, 0.5, 0.4},{0.9, 0.1, 0},{0.3, 0.3, 0.4}};
>>> flag = CheckProbMatrix[Q];
>>> Print[flag];
True
>>> Q = {{0.1, 0.5, 0.4},{0.9, 0.1, 0},{0.3, 0.3, 0.4}};
>>> flag = CheckProbMatrix[Q, True];
"CheckProbMatrix: The real part of the largest eigenvalue of the transient matrix is not less than 1!"
>>> Print[flag];
False
>>> Q = {{0.1, 0.5, 0.4},{0.9, 0.1, 0},{0.3, 0.1, 0.4}};
>>> flag = CheckProbMatrix[Q, True];
>>> Print[flag];
True

For Python/Numpy:

>>> Q = ml.matrix([[0.1, 0.5, 0.4],[0.9, 0.1, 0],[0.3, -0.1, 0.4]])
>>> flag = CheckProbMatrix(Q)
CheckProbMatrix: the matrix has negative element (precision: 1e-12)!
>>> print(flag)
False
>>> Q = ml.matrix([[0.1, 0.5, 0.4],[0.9, 0.1, 0],[0.3, 0.1, 0.4]])
>>> flag = CheckProbMatrix(Q)
CheckProbMatrix: The rowsum of the matrix is not 1 (precision: 1e-12)!
>>> print(flag)
False
>>> Q = ml.matrix([[0.1, 0.5, 0.4],[0.9, 0.1, 0],[0.3, 0.3, 0.4]])
>>> flag = CheckProbMatrix(Q)
>>> print(flag)
True
>>> Q = ml.matrix([[0.1, 0.5, 0.4],[0.9, 0.1, 0],[0.3, 0.3, 0.4]])
>>> flag = CheckProbMatrix(Q, True)
CheckProbMatrix: The real part of the largest eigenvalue of the transient matrix is not less than 1 (precision: 1e-12)!
>>> print(flag)
False
>>> Q = ml.matrix([[0.1, 0.5, 0.4],[0.9, 0.1, 0],[0.3, 0.1, 0.4]])
>>> flag = CheckProbMatrix(Q, True)
>>> print(flag)
True