Extends the class NortaInitDisc and implements the algorithm NI3. More...
Public Member Functions | |
| NI3 (double rX, DiscreteDistributionInt dist1, DiscreteDistributionInt dist2, double tr, double tolerance) | |
| Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2, the parameter for the truncation tr (see the constructor of class NortaInitDisc ), and the specific parameter \(\epsilon=\) tolerance for the algorithm NI3, as defined above. | |
| double | computeCorr () |
| Computes and returns the correlation \(\rho_Z\) using algorithm NI3. | |
| Public Member Functions inherited from umontreal.ssj.probdistmulti.norta.NortaInitDisc | |
| NortaInitDisc (double rX, DiscreteDistributionInt dist1, DiscreteDistributionInt dist2, double tr) | |
| Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2 and the parameter for the truncation tr. | |
| void | computeParams () |
| Computes the following inputs of each marginal distribution: | |
| double | integ (double r) |
| Computes the function. | |
| double | deriv (double r) |
| Computes the derivative of \(g_r\), given by. | |
Detailed Description
Extends the class NortaInitDisc and implements the algorithm NI3.
It uses the function \(g_r\) and its derivative \(g’_r\), so it calls the methods integ and deriv, given in ( gr_M ) and ( grp_M ) and uses an adapted version of the Newton-Raphson algorithm. At any iteration, if the solution falls outside the search interval, the algorithm uses bisection and halves the interval length to guarantee convergence. The initial solution is taken as \(\rho_0=2 \sin(\pi r_X /6)\), and then at each iteration \(k\), \(f_r(\rho_k)\) and
\(f_r^’(\rho_k)\) are calculated and a solution is computed by the recurrence formula:
\[ \rho_{k+1}=\rho_k-\frac{f_r(\rho_k)}{f_r^’(\rho_k)}. \]
The algorithm stops at iteration \(k\) if \(|\rho_{k-1}-\rho_k|\leq\epsilon\). The function \(f_r\) is the one given in ( fr ).
Constructor & Destructor Documentation
◆ NI3()
| umontreal.ssj.probdistmulti.norta.NI3.NI3 | ( | double | rX, |
| DiscreteDistributionInt | dist1, | ||
| DiscreteDistributionInt | dist2, | ||
| double | tr, | ||
| double | tolerance ) |
Constructor with the target rank correlation rX, the two discrete marginals dist1 and dist2, the parameter for the truncation tr (see the constructor of class NortaInitDisc ), and the specific parameter \(\epsilon=\) tolerance for the algorithm NI3, as defined above.
Member Function Documentation
◆ computeCorr()
| double umontreal.ssj.probdistmulti.norta.NI3.computeCorr | ( | ) |
Computes and returns the correlation \(\rho_Z\) using algorithm NI3.
f, df, dx correspond to f(rho_k), f'(rho_k) and f(rho_k)/f'(rho_k), respectively, in the paper (paragraph "Method NI3"of section 3).
Reimplemented from umontreal.ssj.probdistmulti.norta.NortaInitDisc.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/probdistmulti/norta/NI3.java
