butools.dmap.DMAP2FromMoments¶

butools.dmap.DMAP2FromMoments()¶

Matlab:	[D0, D1] = DMAP2FromMoments(moms, corr1)
Mathematica:	{D0, D1} = DMAP2FromMoments[moms, corr1]
Python/Numpy:	D0, D1 = DMAP2FromMoments(moms, corr1)

Returns a discrete MAP(2) which has the same 3 marginal moments and lag-1 autocorrelation as given.

Parameters:	moms : vector, length(3) First three marginal moments of the inter-arrival times corr1 : double The lag-1 autocorrelation of the inter-arrival times
Returns:	D0 : matrix, shape (2,2) The D0 matrix of the discrete MAP(2) D1 : matrix, shape (2,2) The D1 matrix of the discrete MAP(2)

Notes

Raises an exception if the moments are not feasible with a DMAP(2). This procedure calls butools.dmap.DRAPFromMoments followed by butools.dmap.CanonicalFromDMAP2.

Examples

For Matlab:

>>> D0 = [0.2, 0.7; 0.6, 0.1];
>>> D1 = [0.09, 0.01; 0.2, 0.1];
>>> moms = MarginalMomentsFromDMAP(D0, D1, 3);
>>> disp(moms);
       5.1536       46.587       626.45
>>> corr = LagCorrelationsFromDMAP(D0, D1, 1);
>>> disp(corr);
  -0.00080286
>>> [D0, D1] = DMAP2FromMoments(moms, corr);
>>> disp(D0);
          0.3         0.65
      0.61538            0
>>> disp(D1);
         0.05            0
      0.24462         0.14
>>> rmoms = MarginalMomentsFromDMAP(D0, D1, 3);
>>> disp(rmoms);
       5.1536       46.587       626.45
>>> rcorr = LagCorrelationsFromDMAP(D0, D1, 1);
>>> disp(rcorr);
  -0.00080286

For Mathematica:

>>> D0 = {{0.2, 0.7},{0.6, 0.1}};
>>> D1 = {{0.09, 0.01},{0.2, 0.1}};
>>> moms = MarginalMomentsFromDMAP[D0, D1, 3];
>>> Print[moms];
{5.15358361774744, 46.58703071672353, 626.4505119453922}
>>> corr = LagCorrelationsFromDMAP[D0, D1, 1][[1]];
>>> Print[corr];
-0.0008028615465149905
>>> {D0, D1} = DMAP2FromMoments[moms, corr];
>>> Print[D0];
{{0.29999999999984595, 0.6500000000001445},
 {0.6153846153846679, 0}}
>>> Print[D1];
{{0.050000000000009585, 0},
 {0.24461538461532123, 0.14000000000001087}}
>>> rmoms = MarginalMomentsFromDMAP[D0, D1, 3];
>>> Print[rmoms];
{5.153583617747385, 46.58703071672293, 626.4505119453836}
>>> rcorr = LagCorrelationsFromDMAP[D0, D1, 1][[1]];
>>> Print[rcorr];
-0.0008028615465146371

For Python/Numpy:

>>> D0 = ml.matrix([[0.2, 0.7],[0.6, 0.1]])
>>> D1 = ml.matrix([[0.09, 0.01],[0.2, 0.1]])
>>> moms = MarginalMomentsFromDMAP(D0, D1, 3)
>>> print(moms)
[5.1535836177474383, 46.587030716723511, 626.4505119453919]
>>> corr = LagCorrelationsFromDMAP(D0, D1, 1)[0]
>>> print(corr)
-0.000802861546515
>>> D0, D1 = DMAP2FromMoments(moms, corr)
>>> print(D0)
[[ 0.3      0.65   ]
 [ 0.61538  0.     ]]
>>> print(D1)
[[ 0.05     0.     ]
 [ 0.24462  0.14   ]]
>>> rmoms = MarginalMomentsFromDMAP(D0, D1, 3)
>>> print(rmoms)
[5.1535836177474366, 46.587030716723469, 626.45051194539042]
>>> rcorr = LagCorrelationsFromDMAP(D0, D1, 1)[0]
>>> print(rcorr)
-0.000802861546514