Description Usage Arguments Details Value References See Also Examples
Implement a deterministic algorithm for multidimensional numerical
integration. Its algorithm uses one of several cubature rules in a
globally adaptive subdivision scheme.
The subdivision algorithm is similar to
suave
's.
1 2 3 4 5 
ndim 
the number of dimensions of the integral. It should be less or equal to 40. 
ncomp 
the number of components of the integrand. It should be less or equal to 10. 
integrand 
the R function which computes the integrand. It is expected to be declared as
where
The value returned by this R function should be a vector of length

... 
optional additional parameters to be passed to

lower 
the lower bounds of the integration region.
Vector of length 
upper 
the upper bounds of the integration region.
Vector of length 
rel.tol 
the requested relative accuracy. Default, 0.001. 
abs.tol 
the requested absolute accuracy. The algorithm stops when either the relative or the absolute accuracies are met. Default, near 0 (the algorithm stops when the relative accuracy is met). 
flags 
flags governing the integration. A list with components:    when  the seed for the Mersenne Twister algorithm, when 
min.eval 
the minimum number of integrand evaluations required. 
max.eval 
the (approximate) maximum number of integrand evaluations allowed. 
key 
chooses the basic integration rule:
For other values, the default rule is taken, which is the degree13 rule in 2 dimensions, the degree11 rule in 3 dimensions, and the degree9 rule otherwise. 
See details in the documentation.
A list of the S3class cuba
with components:
method 
here, “cuhre” 
nregions 
the actual number of subregions needed. 
neval 
the actual number of integrand evaluations needed. 
ifail 
an error flag:

value 
vector of length 
abs.error 
vector of length 
prob 
vector of length 
message 
“OK” or a character string giving the error message. 
call 
The matched call. 
J. Berntsen, T. O. Espelid (1991) An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, 17(4), 437451.
T. Hahn (2005) CUBAa library for multidimensional numerical integration. Computer Physics Communications, 168, 7895.
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Cuhre input parameters:
ndim 3
ncomp 1
rel.tol 0.001
abs.tol 1e12
pseudo.random 0
final 0
verbose 2
min.eval 0
max.eval 50000
key 0
Iteration 1: 127 integrand evaluations so far
[1] 0.66467 + 7.2682e10 chisq 0 (0 df)
Iteration 2: 381 integrand evaluations so far
[1] 0.66467 + 3.33018e11 chisq 0 (1 df)
integral: 0.6646697 (+3.3e11)
nregions: 2; number of evaluations: 381; probability: 0
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