butools.dmap.CheckDMAPRepresentation¶

butools.dmap.CheckDMAPRepresentation()¶

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

Checks if the input matrixes define a discrete time MAP.

Matrices D0 and D1 must have the same size, D0 must be a transient probability matrix, D1 has only non-negative elements, and the rowsum of D0+D1 is 1 (up to the numerical precision).

Parameters:	D0 : matrix, shape (M,M) The D0 matrix of the DMAP to check D1 : matrix, shape (M,M) The D1 matrix of the DMAP 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 = [0, 0.02, 0; 0, 0.17, 0.2; 0.16, 0.17, 0.02];
>>> D1 = [0, 0.88, 0.1, 0; 0.18, 0.07, 0.14, 0.1; 0.13, 0.15, 0.15, 0.04; 0.31, 0.18, 0.12, 0.27];
>>> flag = CheckDMAPRepresentation(D0, D1);
CheckDMAPRepresentation: D0 and D1 have different sizes!
>>> disp(flag);
     0
>>> D0 = [0, 0.02, 0; 0, 0.17, 0.2; 0.16, 0.17, 0.02];
>>> D1 = [0, 0.88, 0.1; 0.18, 0.07, 0.14; 0.13, 0.15, 0.15];
>>> flag = CheckDMAPRepresentation(D0, D1);
CheckDMAPRepresentation: A rowsum of matrix0+matrix1 is not 1 (at precision 1e-12)!
>>> disp(flag);
     0
>>> D0 = [0, 0.02, 0, 0; 0, 0.17, 0.2, 0.14; 0.16, 0.17, 0.02, 0.18; 0, 0, 0, 0.12];
>>> D1 = [0, 0.88, 0.1, 0; 0.18, 0.07, 0.14, 0.1; 0.13, 0.15, 0.15, 0.04; 0.31, 0.18, 0.12, 0.27];
>>> flag = CheckDMAPRepresentation(D0, D1);
>>> disp(flag);
     1

For Mathematica:

>>> D0 = {{0, 0.02, 0},{0, 0.17, 0.2},{0.16, 0.17, 0.02}};
>>> D1 = {{0, 0.88, 0.1, 0},{0.18, 0.07, 0.14, 0.1},{0.13, 0.15, 0.15, 0.04},{0.31, 0.18, 0.12, 0.27}};
>>> flag = CheckDMAPRepresentation[D0, D1];
"CheckDMAPRepresentation: D0 and D1 have different sizes!"
>>> Print[flag];
False
>>> D0 = {{0, 0.02, 0},{0, 0.17, 0.2},{0.16, 0.17, 0.02}};
>>> D1 = {{0, 0.88, 0.1},{0.18, 0.07, 0.14},{0.13, 0.15, 0.15}};
>>> flag = CheckDMAPRepresentation[D0, D1];
"CheckMAPRepresentation: A rowsum of D0+D1 is not 1 (at precision "1.*^-12")!"
>>> Print[flag];
False
>>> D0 = {{0, 0.02, 0, 0},{0, 0.17, 0.2, 0.14},{0.16, 0.17, 0.02, 0.18},{0, 0, 0, 0.12}};
>>> D1 = {{0, 0.88, 0.1, 0},{0.18, 0.07, 0.14, 0.1},{0.13, 0.15, 0.15, 0.04},{0.31, 0.18, 0.12, 0.27}};
>>> flag = CheckDMAPRepresentation[D0, D1];
>>> Print[flag];
True

For Python/Numpy:

>>> D0 = ml.matrix([[0, 0.02, 0],[0, 0.17, 0.2],[0.16, 0.17, 0.02]])
>>> D1 = ml.matrix([[0, 0.88, 0.1, 0],[0.18, 0.07, 0.14, 0.1],[0.13, 0.15, 0.15, 0.04],[0.31, 0.18, 0.12, 0.27]])
>>> flag = CheckDMAPRepresentation(D0, D1)
CheckDMAPRepresentation: D0 and D1 have different sizes!
>>> print(flag)
False
>>> D0 = ml.matrix([[0, 0.02, 0],[0, 0.17, 0.2],[0.16, 0.17, 0.02]])
>>> D1 = ml.matrix([[0, 0.88, 0.1],[0.18, 0.07, 0.14],[0.13, 0.15, 0.15]])
>>> flag = CheckDMAPRepresentation(D0, D1)
CheckDMAPRepresentation: The rowsum of D0+D1 is not 1!
>>> print(flag)
False
>>> D0 = ml.matrix([[0, 0.02, 0, 0],[0, 0.17, 0.2, 0.14],[0.16, 0.17, 0.02, 0.18],[0, 0, 0, 0.12]])
>>> D1 = ml.matrix([[0, 0.88, 0.1, 0],[0.18, 0.07, 0.14, 0.1],[0.13, 0.15, 0.15, 0.04],[0.31, 0.18, 0.12, 0.27]])
>>> flag = CheckDMAPRepresentation(D0, D1)
>>> print(flag)
True