###### Description

asr_varioGram calculates the empirical variogram from regular or irregular one or two dimensional data.

###### Usage

asr_varioGram(x, y, z, composite = TRUE, model = c("empirical"), metric = c("euclidean", "manhattan"), angle = 0, angle.tol = 180, nlag = 20, maxdist = 0.5, xlag = NA, lag.tol = 0.5, grid = TRUE)

###### Arguments

`x` |
Numeric vector of x coordinates, may also be a matrix or data frame with 2 or 3 columns. If `ncol(x)` is 3, the columns are taken to be the x and y coordinates and the response (z), respectively. If `ncol(x)` is 2, the columns are taken to be the x coordinates and the response, respectively. In this case the y coordinates are generated as `rep(1,nrow(x))` . |

`y` |
Numeric vector of y coordinates. |

`z` |
The response vector. |

`composite` |
For data on a regular grid. If `TRUE` , the average of the variograms in quadrants (x,y) and (x,-y) is returned. Otherwise, both variograms are returned and identiﬁed as quadrants 1 and 4. |

`model` |
Can only be “`empirical` ” at present. |

`metric` |
The distance between (x,y) points. Valid measures are “`euclidean` ” or “`manhattan` “. |

`angle` |
A vector of directions. Angles are measured in degrees anticlockwise from the x axis. Default is 0. |

`angle.tol` |
The angle subtended by each direction. That is, an arc`angle+- angle.tol/2` .Default is 180 which gives an omnidirectional variogram. |

`nlag` |
The maximum number of lags; default is 20. |

`maxdist` |
The fraction of the maximum distance to include in the calculation. The default is half the maximum distance in the data. |

`xlag` |
The width of the lags. If missing, `xlag` is set to `maxdist/nlag` . |

`lag.tol` |
The distance tolerance. If missing, `lag.tol` is set to `xlag/2` . |

`grid` |
If `FALSE` , forces polar variograms if (x,y) speciﬁes a regular grid; default is `TRUE` . |

###### Details

For one dimensional data the *y* coordinates need not be supplied and a vector of ones is generated. The function identiﬁes data on a complete regular array and in such cases only computes polar variograms If `grid = FALSE`

. The data is assumed sorted with the *x* coordinates changing the fastest; the data is sorted internally if this is not the case.

###### Value

A data frame including the following components: | |

`x` |
The original x coordinates. |

`y` |
The original y coordinates. |

`gamma` |
The variogram estimate. |

`distance` |
The average distance for pairs in the lag. |

`np` |
The number of pairs in the lag. |

`angle` |
Direction if not a regular grid. |

###### References

Webster W and Oliver MA (2001). *Geostatistics for Environmental Scientists*. John Wiley: West Sussex.