butools.ph.PdfFromME¶

butools.ph.PdfFromME()¶

Matlab:	pdf = PdfFromME(alpha, A, x, prec)
Mathematica:	pdf = PdfFromME[alpha, A, x, prec]
Python/Numpy:	pdf = PdfFromME(alpha, A, x, prec)

Returns the probability density function 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. x : vector of doubles The density function will be computed at these points prec : double, optional Numerical precision to check if the input ME distribution is valid. The default value is 1e-14.
Returns:	pdf : column vector of doubles The values of the density function at the corresponding “x” values

Examples

For Matlab:

>>> a = [0.2,0.3,0.5];
>>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
>>> x = (0.0:0.01:5.0);
>>> pdf = PdfFromME(a, A, x);
>>> plot(x, pdf)

For Mathematica:

>>> a = {0.2,0.3,0.5};
>>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
>>> x = Range[0.0,5.0,0.01];
>>> pdf = PdfFromME[a, A, x];
>>> ListLinePlot[{Transpose[{x, pdf}]}]

For Python/Numpy:

>>> a = ml.matrix([[0.2,0.3,0.5]])
>>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
>>> x = np.arange(0.0,5.01,0.01)
>>> pdf = PdfFromME(a, A, x)
>>> plt.plot(x, pdf)