cubintegrate {cubature} | R Documentation |

## Unified Cubature Integration Interface

### Description

Integrate a function within specified limits using method
specified. Further arguments specific to method as well as other
arguments to f may be passed. For defaults used in each method, see
help on the method or `default_args()`

.

### Usage

```
cubintegrate(
f,
lower,
upper,
fDim = 1,
method = c("hcubature", "pcubature", "cuhre", "divonne", "suave", "vegas"),
relTol = 1e-05,
absTol = 1e-12,
maxEval = 10^6,
nVec = 1L,
...
)
```

### Arguments

`f` |
The function (integrand) to be integrated. Can be
vectorized version, but the additional arguments |

`lower` |
The lower limit of integration, a vector for hypercubes. |

`upper` |
The upper limit of integration, a vector for hypercubes. |

`fDim` |
The number of components of f, default 1, bears no relation to the dimension of the hypercube over which integration is performed. |

`method` |
the method to use should be one of "hcubature", "pcubature", "cuhre", "divonne", "suave" or "vegas". |

`relTol` |
The maximum tolerance, default 1e-5. |

`absTol` |
the absolute tolerance, default 1e-12. |

`maxEval` |
The maximum number of function evaluations needed, default 10^6. Note that the actual number of function evaluations performed is only approximately guaranteed not to exceed this number. |

`nVec` |
the number of vectorization points for Cuba C library, default 1, but can be set to an integer > 1 for vectorization, for example, 1024. The function f above needs to handle the vector of points appropriately; see vignette examples. Unlike Cuba, the cubature C library manages the number of points on its own and can vary between calls. Therefore, any value for nVec greater than one implies vectorization for a cubature method. |

`...` |
All other arguments which may include integration method specific parameters and those for f. Unrecognized parameters for integration method are presumed to be intended for f and so processed. |

### Value

The returned value is a list of items:

- integral
the value of the integral

- error
the estimated absolute error

- neval
the number of times the function was evaluated

- returnCode
the actual integer return code of the C routine; a non-zero value usually indicates problems; further interpretation depends on method

- nregions
forcCuba routines, the actual number of subregions needed

- prob
the

`\chi^2`

-probability (not the`\chi^2`

-value itself!) that`error`

is not a reliable estimate of the true integration error.

### See Also

`default_args()`

, `hcubature()`

,
`pcubature()`

, `cuhre()`

,
`vegas()`

, `suave()`

, `divonne()`

### Examples

```
I.1d <- function(x) {
sin(4*x) *
x * ((x * ( x * (x*x-4) + 1) - 1))
}
I.1d_v <- function(x) {
matrix(apply(x, 2, function(z)
sin(4 * z) *
z * ((z * ( z * (z * z - 4) + 1) - 1))),
ncol = ncol(x))
}
cubintegrate(f = I.1d, lower = -2, upper = 2, method = "pcubature")
cubintegrate(f = I.1d, lower = -2, upper = 2, method = "cuhre", flags=list(verbose = 2))
cubintegrate(f = I.1d_v, lower = -2, upper = 2, method = "hcubature", nVec = 2L)
cubintegrate(f = I.1d_v, lower = -2, upper = 2, method = "cuhre", nVec = 128L)
```

*cubature*version 2.1.1 Index]