butools.map.CheckMAPRepresentation¶

butools.map.CheckMAPRepresentation()¶

Matlab:	r = CheckMAPRepresentation(D0, D1, prec)
Mathematica:	r = CheckMAPRepresentation[D0, D1, prec]
Python/Numpy:	r = CheckMAPRepresentation(D0, D1, prec)

Checks if the input matrixes define a continuous time MAP.

Matrices D0 and D1 must have the same size, D0 must be a transient generator matrix, D1 has only non-negative elements, and the rowsum of D0+D1 is 0 (up to the numerical precision).

Parameters:	D0 : matrix, shape (M,M) The D0 matrix of the MAP to check D1 : matrix, shape (M,M) The D1 matrix of the MAP to check prec : double, optional Numerical precision, the default value is 1e-14
Returns:	r : bool The result of the check

Examples

For Matlab:

>>> D0 = [-1., 0, 1.; 0, -2., 0; 1., 0, -3.];
>>> D1 = [-1., 0, 1., 0; 0, -2., 0, 1.; 1., 0, -3., 0; 1., 2., 2., 1.];
>>> flag = CheckMAPRepresentation(D0, D1);
CheckMAPRepresentation: D0 and D1 have different sizes!
>>> disp(flag);
     0
>>> D0 = [-1., 0, 1.; 0, -2., 0; 1., 0, -3.];
>>> D1 = [1., 0, 1.; 0, 2., 0; 1., 0, 3.];
>>> flag = CheckMAPRepresentation(D0, D1);
CheckMAPRepresentation: The rowsum of D0+D1 is not 0 (precision: 1e-12)!
>>> disp(flag);
     0
>>> D0 = [-3., 0, 1.; 0, -2., 0; 1., 0, -5.];
>>> D1 = [1., 0, 1.; 0, 2., 0; 1., 0, 3.];
>>> flag = CheckMAPRepresentation(D0, D1);
>>> disp(flag);
     1

For Mathematica:

>>> D0 = {{-1., 0, 1.},{0, -2., 0},{1., 0, -3.}};
>>> D1 = {{-1., 0, 1., 0},{0, -2., 0, 1.},{1., 0, -3., 0},{1., 2., 2., 1.}};
>>> flag = CheckMAPRepresentation[D0, D1];
"CheckMAPRepresentation: D0 and D1 have different sizes!"
>>> Print[flag];
False
>>> D0 = {{-1., 0, 1.},{0, -2., 0},{1., 0, -3.}};
>>> D1 = {{1., 0, 1.},{0, 2., 0},{1., 0, 3.}};
>>> flag = CheckMAPRepresentation[D0, D1];
"CheckMAPRepresentation: A rowsum of D0+D1 is not 0 (at precision "1.*^-12")!"
>>> Print[flag];
False
>>> D0 = {{-3., 0, 1.},{0, -2., 0},{1., 0, -5.}};
>>> D1 = {{1., 0, 1.},{0, 2., 0},{1., 0, 3.}};
>>> flag = CheckMAPRepresentation[D0, D1];
>>> Print[flag];
True

For Python/Numpy:

>>> D0 = ml.matrix([[-1., 0, 1.],[0, -2., 0],[1., 0, -3.]])
>>> D1 = ml.matrix([[-1., 0, 1., 0],[0, -2., 0, 1.],[1., 0, -3., 0],[1., 2., 2., 1.]])
>>> flag = CheckMAPRepresentation(D0, D1)
CheckMAPRepresentation: D0 and D1 have different sizes!
>>> print(flag)
False
>>> D0 = ml.matrix([[-1., 0, 1.],[0, -2., 0],[1., 0, -3.]])
>>> D1 = ml.matrix([[1., 0, 1.],[0, 2., 0],[1., 0, 3.]])
>>> flag = CheckMAPRepresentation(D0, D1)
CheckMAPRepresentation: The rowsum of D0+D1 is not 0!
>>> print(flag)
False
>>> D0 = ml.matrix([[-3., 0, 1.],[0, -2., 0],[1., 0, -5.]])
>>> D1 = ml.matrix([[1., 0, 1.],[0, 2., 0],[1., 0, 3.]])
>>> flag = CheckMAPRepresentation(D0, D1)
>>> print(flag)
True