butools.map.CheckMRAPRepresentation¶

butools.map.CheckMRAPRepresentation()¶

Matlab:	r = CheckMRAPRepresentation(H, prec)
Mathematica:	r = CheckMRAPRepresentation[H, prec]
Python/Numpy:	r = CheckMRAPRepresentation(H, prec)

Checks if the input matrixes define a continuous time MRAP.

All matrices H0...HK must have the same size, the dominant eigenvalue of H0 is negative and real, and the rowsum of H0+H1+...+HK is 0 (up to the numerical precision).

Parameters:	H : list/cell of matrices, length(K) The H0...HK matrices of the MRAP to check
Returns:	r : bool The result of the check

Examples

For Matlab:

>>> x = 0.18;
>>> H0 = [-5., 0.1+x, 0.9, 1.; 1., -8., 0.9, 0.1; 0.9, 0.1, -4., 1.; 1., 2., 3., -9.];
>>> H1 = [0.1-x, 0.7, 0.1, 0.1; 0.1, 1., 1.8, 0.1; 0.1, 0.1, 0.1, 0.7; 0.7, 0.1, 0.1, 0.1];
>>> H2 = [0.1, 0.1, 0.1, 1.7; 1.8, 0.1, 1., 0.1; 0.1, 0.1, 0.7, 0.1; 0.1, 1., 0.1, 0.8];
>>> flag = CheckMRAPRepresentation({H0, H1, H2});
>>> disp(flag);
     1

For Mathematica:

>>> x = 0.18;
>>> H0 = {{-5., 0.1+x, 0.9, 1.},{1., -8., 0.9, 0.1},{0.9, 0.1, -4., 1.},{1., 2., 3., -9.}};
>>> H1 = {{0.1-x, 0.7, 0.1, 0.1},{0.1, 1., 1.8, 0.1},{0.1, 0.1, 0.1, 0.7},{0.7, 0.1, 0.1, 0.1}};
>>> H2 = {{0.1, 0.1, 0.1, 1.7},{1.8, 0.1, 1., 0.1},{0.1, 0.1, 0.7, 0.1},{0.1, 1., 0.1, 0.8}};
>>> flag = CheckMRAPRepresentation[{H0, H1, H2}];
>>> Print[flag];
True

For Python/Numpy:

>>> x = 0.18
>>> H0 = ml.matrix([[-5., 0.1+x, 0.9, 1.],[1., -8., 0.9, 0.1],[0.9, 0.1, -4., 1.],[1., 2., 3., -9.]])
>>> H1 = ml.matrix([[0.1-x, 0.7, 0.1, 0.1],[0.1, 1., 1.8, 0.1],[0.1, 0.1, 0.1, 0.7],[0.7, 0.1, 0.1, 0.1]])
>>> H2 = ml.matrix([[0.1, 0.1, 0.1, 1.7],[1.8, 0.1, 1., 0.1],[0.1, 0.1, 0.7, 0.1],[0.1, 1., 0.1, 0.8]])
>>> flag = CheckMRAPRepresentation([H0, H1, H2])
>>> print(flag)
True