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*npoints` matrix containing the density's values scattered on the discretization grid defined by `npoints, equi, eps` (see `discretize`). `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)

```

[Package BMAmevt version 1.0.4 Index]