NAG Library Function Document

nag_init_vavilov (g01zuc)

nag_init_vavilov (g01zuc) initializes the array comm_arr for use by nag_prob_vavilov (g01euc) or nag_prob_density_vavilov (g01muc) in the evaluation of the Vavilov functions

ϕ_{V} (λ; κ, β^{2})

and

Φ_{V} (λ; κ, β^{2})

respectively.

Multiple calls to nag_prob_vavilov (g01euc) or nag_prob_density_vavilov (g01muc) can be made following a single call to nag_init_vavilov (g01zuc), provided that rkappa or beta2 do not change, and that either all calls are to nag_prob_vavilov (g01euc) or all calls are to nag_prob_density_vavilov (g01muc). If you wish to call both nag_prob_vavilov (g01euc) and nag_prob_density_vavilov (g01muc), then you will need to initialize both separately.

4 References

Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm. 7 215–224

1: rkappa – doubleInput: On entry: the argument $κ$ of the function.
Constraint: $0.01 \leq rkappa \leq 10.0$ .
2: beta2 – doubleInput: On entry: the argument $β^{2}$ of the function.
Constraint: $0.0 \leq beta2 \leq 1.0$ .
3: mode – IntegerInput: On entry: if $mode = 0$ , then nag_prob_density_vavilov (g01muc) is to be called after the call to nag_init_vavilov (g01zuc). Otherwise, nag_prob_vavilov (g01euc) is to be called.
4: xl – double *Output: On exit: $x_{l}$ , a threshold value below which $ϕ_{V} (λ; κ, β^{2})$ will be set to zero by nag_prob_density_vavilov (g01muc) and $Φ_{V} (λ; κ, β^{2})$ will be set to zero by nag_prob_vavilov (g01euc) if $λ < x_{l}$ .
5: xu – double *Output: On exit: $x_{u}$ , a threshold value above which $ϕ_{V} (λ; κ, β^{2})$ will be set to zero by nag_prob_density_vavilov (g01muc) and $Φ_{V} (λ; κ, β^{2})$ will be set to unity by nag_prob_vavilov (g01euc) if $λ > x_{u}$ .
6: comm_arr[ $322$ ] – doubleCommunication Array: On exit: this argument should be passed unchanged to nag_prob_vavilov (g01euc) or nag_prob_density_vavilov (g01muc).
7: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL: On entry, $beta2 = ⟨value⟩$ .
Constraint: $beta2 \leq 1.0$ .
On entry, $beta2 = ⟨value⟩$ .
Constraint: $beta2 \geq 0.0$ .
On entry, $rkappa = ⟨value⟩$ .
Constraint: $rkappa \leq 10.0$ .
On entry, $rkappa = ⟨value⟩$ .
Constraint: $rkappa \geq 0.01$ .