rect.integrate {BMAmevt} | R Documentation |

## Density integration on the two-dimensional simplex

### Description

The integral is approximated by a rectangular method, using the values stored in matrix `density`

.

### Usage

```
rect.integrate(density, npoints, eps)
```

### Arguments

`density` |
A |

`npoints` |
The number of grid nodes on the squared grid containing the desired triangle. |

`eps` |
Positive number: minimum distance from any node inside the simplex to the simplex boundary |

### Details

Integration is made with respect to the Lebesgue measure on the projection of the simplex onto the plane `(x,y): x > 0, y > 0, x+y < 1`

.
It is assumed that `density`

has been constructed on a
grid obtained *via* function `discretize`

,
with argument `equi`

set to `FALSE`

and `npoints`

and `eps`

equal to those passed to `rect.integrate`

.

### Value

The value of the estimated integral of `density`

.

### Examples

```
wrapper <- function(x, y, my.fun,...)
{
sapply(seq_along(x), FUN = function(i) my.fun(x[i], y[i],...))
}
grid <- discretize(npoints=40,eps=1e-3,equi=FALSE)
Density <- outer(grid$X,grid$Y,FUN=wrapper,
my.fun=function(x,y){10*((x/2)^2+y^2)})
rect.integrate(Density,npoints=40,eps=1e-3)
```

*BMAmevt*version 1.0.5 Index]