Randomly thins a spatial point pattern (M.A. Mugglestone, S.A. Harding, B.Y.Y. Lee, P.J. Diggle & B.S. Rowlingson).

### Option

`PRINT` = string token |
What to print (`summary` ); default `summ` |
---|

### Parameters

`OLDY` = variates |
Vertical coordinates of each spatial point pattern; no default – this parameter must be set |
---|---|

`OLDX` = variates |
Horizontal coordinates of each spatial point pattern; no default – this parameter must be set |

`NPOINTS` = scalars |
How many points to return from each pattern; no default – this parameter must be set |

`NEWY` = variates |
Variates to receive the vertical coordinates of the randomly thinned patterns |

`NEWX` = variates |
Variates to receive the horizontal coordinates of the randomly thinned patterns |

`SEED` = scalars |
Seeds for the random numbers used to select the thinned points; default 0 |

`THINNED` = variates |
Variate whose values indicate whether the coordinates of each spatial point pattern are included (1) or excluded (0) from the thinned pattern |

### Description

This procedure randomly thins a spatial point pattern with coordinates specified by the parameters `OLDX`

and `OLDY`

. The number of points required in the thinned pattern is specified using the `NPOINTS`

parameter which must be a positive integer. If `NPOINTS`

is equal to or greater than the number of points in the original pattern then no points will be deleted. The coordinates of the points which remain after thinning can be saved using the parameters `NEWX`

and `NEWY`

. The `SEED`

parameter allows a seed to be supplied for generating the random numbers used to select the thinned points (thereby producing reproducible results). If this is not supplied, the default of 0 initializes the random number generator (if necessary) from the system clock. The `THINNED`

parameter can be used to save a logical variable containing the value 1 when a coordinate is used within the thinned pattern and 0 if the coordinate has not been selected in the thinned pattern.

Printed output is controlled by the `PRINT`

option. The default setting of summary prints the horizontal and vertical coordinates of the points which remain after thinning under the headings `NEWX`

and `NEWY`

.

Option: `PRINT`

.

Parameters: `OLDY`

, `OLDX`

, `NPOINTS`

, `NEWY`

, `NEWX`

, `SEED`

, `THINNED`

.

### Method

A procedure `PTCHECKXY`

is called to check that `OLDX`

and `OLDY`

have identical restrictions. A dummy variate with the same number of elements as `OLDX`

and `OLDY`

and containing uniform random numbers in the interval (0,1) is created using the `URAND`

function. The `SORT`

function is then used to sort the elements of `OLDX`

and `OLDY`

`into`

the order which would put the elements of the dummy variate in ascending order. Finally, the first `NPOINTS`

elements of the sorted coordinates are transferred to the variates `NEWX`

and `NEWY`

using the `EQUATE`

directive.

### Action with `RESTRICT`

If `OLDX`

and `OLDY`

are restricted, only the subset of values specified by the restriction will be included in the calculations.

### See also

Procedures: `GRCSR`

, `GRLABEL`

, `GRTORSHIFT`

.

Commands for: Calculations and manipulation, Spatial statistics.

### Example

CAPTION 'GRTHIN example'; STYLE=meta VARIATE pinex,piney READ [SETNVALUES=yes] pinex,piney 0.09 0.91 0.02 0.71 0.03 0.62 0.18 0.61 0.03 0.52 0.02 0.41 0.16 0.35 0.13 0.33 0.13 0.27 0.03 0.21 0.13 0.14 0.08 0.11 0.02 0.02 0.18 0.98 0.31 0.89 0.22 0.58 0.13 0.52 0.21 0.38 0.23 0.27 0.23 0.11 0.41 0.98 0.44 0.97 0.42 0.93 0.42 0.48 0.43 0.36 0.59 0.92 0.63 0.92 0.63 0.88 0.66 0.88 0.58 0.83 0.53 0.69 0.52 0.68 0.49 0.58 0.52 0.48 0.52 0.09 0.58 0.06 0.68 0.66 0.68 0.63 0.67 0.53 0.67 0.48 0.67 0.41 0.68 0.34 0.66 0.24 0.73 0.27 0.74 0.11 0.78 0.06 0.79 0.02 0.86 0.03 0.84 0.88 0.94 0.89 0.95 0.83 0.79 0.79 0.84 0.71 0.83 0.68 0.86 0.65 0.79 0.61 0.93 0.48 0.83 0.42 0.93 0.31 0.93 0.23 0.97 0.64 0.96 0.64 0.96 0.61 0.96 0.57 0.97 0.38 : GRTHIN OLDY=piney; OLDX=pinex; NPOINTS=10; SEED=519352