/**
* Computes the density function <SPAN CLASS="MATH"><I>f</I> (<I>x</I>)</SPAN>, with <SPAN
* CLASS="MATH"><I>λ</I><SUB>i</SUB> =</SPAN> <TT>lambda[<SPAN CLASS="MATH"><I>i</I> -
* 1</SPAN>]</TT>, <SPAN CLASS="MATH"><I>i</I> = 1,…, <I>k</I></SPAN>.
*
* @param lambda rates of the hypoexponential distribution
* @param x value at which the density is evaluated
* @return density at <SPAN CLASS="MATH"><I>x</I></SPAN>
*/
public static double density(double[] lambda, double x) {
testLambda(lambda);
if (x < 0) return 0;
DoubleMatrix2D Ax = buildMatrix(lambda, x);
DoubleMatrix2D M = DMatrix.expBidiagonal(Ax);
int k = lambda.length;
return lambda[k - 1] * M.getQuick(0, k - 1);
}
// Builds the bidiagonal matrix A out of the lambda
private static DoubleMatrix2D buildMatrix(double[] lambda, double x) {
int k = lambda.length;
DoubleFactory2D F2 = DoubleFactory2D.dense;
DoubleMatrix2D A = F2.make(k, k);
for (int j = 0; j < k - 1; j++) {
A.setQuick(j, j, -lambda[j] * x);
A.setQuick(j, j + 1, lambda[j] * x);
}
A.setQuick(k - 1, k - 1, -lambda[k - 1] * x);
return A;
}
/**
* Computes the complementary distribution <SPAN CLASS="MATH">bar(F)(<I>x</I>)</SPAN>, with <SPAN
* CLASS="MATH"><I>λ</I><SUB>i</SUB> =</SPAN> <TT>lambda[<SPAN CLASS="MATH"><I>i</I> -
* 1</SPAN>]</TT>, <SPAN CLASS="MATH"><I>i</I> = 1,…, <I>k</I></SPAN>.
*
* @param lambda rates of the hypoexponential distribution
* @param x value at which the complementary distribution is evaluated
* @return complementary distribution at <SPAN CLASS="MATH"><I>x</I></SPAN>
*/
public static double barF(double[] lambda, double x) {
testLambda(lambda);
if (x <= 0.0) return 1.0;
if (x >= Double.MAX_VALUE) return 0.0;
DoubleMatrix2D M = buildMatrix(lambda, x);
M = DMatrix.expBidiagonal(M);
// prob is first row of final matrix
int k = lambda.length;
double sum = 0;
for (int j = 0; j < k; j++) sum += M.getQuick(0, j);
return sum;
}
