butools.ph.MomentsFromME¶

butools.ph.MomentsFromME()¶

Matlab:	moms = MomentsFromME(alpha, A, K, prec)
Mathematica:	moms = MomentsFromME[alpha, A, K, prec]
Python/Numpy:	moms = MomentsFromME(alpha, A, K, prec)

Returns the first K moments of a matrix-exponential distribution.

Parameters:	alpha : vector, shape (1,M) The initial vector of the matrix-exponential distribution. A : matrix, shape (M,M) The matrix parameter of the matrix-exponential distribution. K : int, optional Number of moments to compute. If K=0, 2*M-1 moments are computed. The default value is K=0. prec : double, optional Numerical precision for checking the input. The default value is 1e-14.
Returns:	moms : row vector of doubles The vector of moments.

Examples

For Matlab:

>>> a = [0.2,0.3,0.5];
>>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
>>> moms = MomentsFromME(a, A);
>>> disp(moms);
      0.35385      0.41893       1.1552       4.6998       23.838
>>> moms = MomentsFromME(a, A, 9);
>>> disp(moms);
  Columns 1 through 6
      0.35385      0.41893       1.1552       4.6998       23.838       143.78
  Columns 7 through 9
       1007.8       8064.3        72578

For Mathematica:

>>> a = {0.2,0.3,0.5};
>>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
>>> moms = MomentsFromME[a, A];
>>> Print[moms];
{0.35384615384615387, 0.41893491124260357, 1.1552116522530724, 4.699835439935577, 23.837756165615836}
>>> moms = MomentsFromME[a, A, 9];
>>> Print[moms];
{0.35384615384615387, 0.41893491124260357, 1.1552116522530724, 4.699835439935577, 23.837756165615836, 143.78185836646944, 1007.8194071104502, 8064.272882521486, 72578.13371878522}

For Python/Numpy:

>>> a = ml.matrix([[0.2,0.3,0.5]])
>>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
>>> moms = MomentsFromME(a, A)
>>> print(moms)
[0.35384615384615381, 0.41893491124260357, 1.1552116522530724, 4.6998354399355771, 23.837756165615836]
>>> moms = MomentsFromME(a, A, 9)
>>> print(moms)
[0.35384615384615381, 0.41893491124260357, 1.1552116522530724, 4.6998354399355771, 23.837756165615836, 143.78185836646944, 1007.8194071104502, 8064.2728825214863, 72578.133718785219]