butools.dmap.CheckDRAPRepresentation¶

butools.dmap.CheckDRAPRepresentation()¶

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

Checks if the input matrixes define a discrete time RAP.

Matrices H0 and H1 must have the same size, the dominant eigenvalue of H0 is real and less than 1, and the rowsum of H0+H1 is 1 (up to the numerical precision).

Parameters:	H0 : matrix, shape (M,M) The H0 matrix of the DRAP to check H1 : matrix, shape (M,M) The H1 matrix of the DRAP to check prec : double, optional Numerical precision, the default value is 1e-14
Returns:	r : bool The result of the check

Examples

For Matlab:

>>> H0 = [0, 0, 0.13; 0, 0.6, 0.18; 0.31, 0.26, 0.02; 0.2, 0, 0];
>>> H1 = [0, 1., -0.13; 0, 0.18, 0.04; 0.03, 0.09, 0.29; 0, 0.8, 0];
>>> flag = CheckDRAPRepresentation(H0, H1);
CheckDRAPRepresentation: D0 and D1 have different sizes!
>>> disp(flag);
     0
>>> H0 = [0.2, 0, 0.13; 0, 0.6, 0.18; 0.31, 0.26, 0.02];
>>> H1 = [0, 1., -0.13; 0, 0.18, 0.04; 0.03, 0.09, 0.29];
>>> flag = CheckDRAPRepresentation(H0, H1);
CheckDRAPRepresentation: A rowsum of D0+D1 is not 1 (at precision 1e-12)!
>>> disp(flag);
     0
>>> H0 = [-1., 0, 0; 0, -2., 2.; 0, 3., -3.];
>>> H1 = [0, 0, 1.; 0, -1., 1.; 1., 0, -1.];
>>> flag = CheckDRAPRepresentation(H0, H1);
CheckDRAPRepresentation: A rowsum of D0+D1 is not 1 (at precision 1e-12)!
>>> disp(flag);
     0
>>> H0 = [0, 0, 15.; 0, 0.6, 0.18; 0.31, 0.26, 0.02];
>>> H1 = [0, 1., -15.; 0, 0.18, 0.04; 0.03, 0.09, 0.29];
>>> flag = CheckDRAPRepresentation(H0, H1);
CheckDRAPRepresentation: The dominant eigenvalue of D0 is greater than 1!
>>> disp(flag);
     0
>>> H0 = [0, 0.5, 0.1; 0, -1.4, 3.1; 0.67, 0, 0.4];
>>> H1 = [0, 0.4, 0; 0, -0.2, -0.5; 0.3, -0.7, 0.33];
>>> flag = CheckDRAPRepresentation(H0, H1);
CheckDRAPRepresentation: The dominant eigenvalue of the D0 is complex!
>>> disp(flag);
     0
>>> H0 = [0, 0, 0.13; 0, 0.6, 0.18; 0.31, 0.26, 0.02];
>>> H1 = [0, 1., -0.13; 0, 0.18, 0.04; 0.03, 0.09, 0.29];
>>> flag = CheckDRAPRepresentation(H0, H1);
>>> disp(flag);
     1

For Mathematica:

>>> H0 = {{0, 0, 0.13},{0, 0.6, 0.18},{0.31, 0.26, 0.02},{0.2, 0, 0}};
>>> H1 = {{0, 1., -0.13},{0, 0.18, 0.04},{0.03, 0.09, 0.29},{0, 0.8, 0}};
>>> flag = CheckDRAPRepresentation[H0, H1];
"CheckDRAPRepresentation: D0 is not a quadratic matrix!"
>>> Print[flag];
False
>>> H0 = {{0.2, 0, 0.13},{0, 0.6, 0.18},{0.31, 0.26, 0.02}};
>>> H1 = {{0, 1., -0.13},{0, 0.18, 0.04},{0.03, 0.09, 0.29}};
>>> flag = CheckDRAPRepresentation[H0, H1];
"CheckDRAPRepresentation: A rowsum of D0+D1 is not 1! (precision:"1.*^-12")"
>>> Print[flag];
False
>>> H0 = {{-1., 0, 0},{0, -2., 2.},{0, 3., -3.}};
>>> H1 = {{0, 0, 1.},{0, -1., 1.},{1., 0, -1.}};
>>> flag = CheckDRAPRepresentation[H0, H1];
"CheckDRAPRepresentation: A rowsum of D0+D1 is not 1! (precision:"1.*^-12")"
>>> Print[flag];
False
>>> H0 = {{0, 0, 15.},{0, 0.6, 0.18},{0.31, 0.26, 0.02}};
>>> H1 = {{0, 1., -15.},{0, 0.18, 0.04},{0.03, 0.09, 0.29}};
>>> flag = CheckDRAPRepresentation[H0, H1];
"CheckDRAPRepresentation: The dominant eigenvalue of D0 is greater than 1!"
>>> Print[flag];
False
>>> H0 = {{0, 0.5, 0.1},{0, -1.4, 3.1},{0.67, 0, 0.4}};
>>> H1 = {{0, 0.4, 0},{0, -0.2, -0.5},{0.3, -0.7, 0.33}};
>>> flag = CheckDRAPRepresentation[H0, H1];
"CheckDRAPRepresentation: The dominant eigenvalue of D0 is complex!"
>>> Print[flag];
False
>>> H0 = {{0, 0, 0.13},{0, 0.6, 0.18},{0.31, 0.26, 0.02}};
>>> H1 = {{0, 1., -0.13},{0, 0.18, 0.04},{0.03, 0.09, 0.29}};
>>> flag = CheckDRAPRepresentation[H0, H1];
>>> Print[flag];
True

For Python/Numpy:

>>> H0 = ml.matrix([[0, 0, 0.13],[0, 0.6, 0.18],[0.31, 0.26, 0.02],[0.2, 0, 0]])
>>> H1 = ml.matrix([[0, 1., -0.13],[0, 0.18, 0.04],[0.03, 0.09, 0.29],[0, 0.8, 0]])
>>> flag = CheckDRAPRepresentation(H0, H1)
CheckDRAPRepresentation: D0 is not a quadratic matrix!
>>> print(flag)
False
>>> H0 = ml.matrix([[0.2, 0, 0.13],[0, 0.6, 0.18],[0.31, 0.26, 0.02]])
>>> H1 = ml.matrix([[0, 1., -0.13],[0, 0.18, 0.04],[0.03, 0.09, 0.29]])
>>> flag = CheckDRAPRepresentation(H0, H1)
CheckDRAPRepresentation: A rowsum of D0+D1 is not 1!
>>> print(flag)
False
>>> H0 = ml.matrix([[-1., 0, 0],[0, -2., 2.],[0, 3., -3.]])
>>> H1 = ml.matrix([[0, 0, 1.],[0, -1., 1.],[1., 0, -1.]])
>>> flag = CheckDRAPRepresentation(H0, H1)
CheckDRAPRepresentation: A rowsum of D0+D1 is not 1!
>>> print(flag)
False
>>> H0 = ml.matrix([[0, 0, 15.],[0, 0.6, 0.18],[0.31, 0.26, 0.02]])
>>> H1 = ml.matrix([[0, 1., -15.],[0, 0.18, 0.04],[0.03, 0.09, 0.29]])
>>> flag = CheckDRAPRepresentation(H0, H1)
CheckDRAPRepresentation: The largest eigenvalue of matrix D0 is greater than 1!
>>> print(flag)
False
>>> H0 = ml.matrix([[0, 0.5, 0.1],[0, -1.4, 3.1],[0.67, 0, 0.4]])
>>> H1 = ml.matrix([[0, 0.4, 0],[0, -0.2, -0.5],[0.3, -0.7, 0.33]])
>>> flag = CheckDRAPRepresentation(H0, H1)
CheckDRAPRepresentation: The largest eigenvalue of matrix D0 is complex!
>>> print(flag)
False
>>> H0 = ml.matrix([[0, 0, 0.13],[0, 0.6, 0.18],[0.31, 0.26, 0.02]])
>>> H1 = ml.matrix([[0, 1., -0.13],[0, 0.18, 0.04],[0.03, 0.09, 0.29]])
>>> flag = CheckDRAPRepresentation(H0, H1)
>>> print(flag)
True