PTK3D procedure

Performs kernel smoothing of space-time data (D.A. Murray, P.J. Diggle & B.S. Rowlingson).


Option

PRINT = string
Controls printed output (grid, monitoring); default grid


Parameters

Y = variates
Vertical coordinates of the spatial point pattern

X = variates
Horizontal coordinates of the spatial point pattern

TIMES = variates
Times for each event

XGRID = variates
The values of x to compute kernel function

YGRID = variates
The values of y to compute kernel function

ZGRID = variates
The values of z, or time dimension, to compute kernel function

HXY = scalars
What quartic kernel width to use in the XY direction

HZ = scalars
What quartic kernel width to use in the Z or time direction

GRID = pointers
Pointer to matrices containing the kernel smoothed values


Description

This procedure performs kernel smoothing of 3 dimensional, or space-time data. The method implemented uses a quartic kernel function as in the PTKERNEL2D procedure.

   The data required by the procedure are the coordinates of the events in the spatial pattern (specified using the parameters X and Y) and the times of the events (specified by TIMES). The XGRID, YGRID and ZGRID parameters specify the 3 dimensions or space-time domain over which to evaluate the kernel smoothing. The kernel width must be specified for the X and Y direction using the HXY parameter, and in the Z (time) direction using the parameter HZ. The procedure calculates kernel density estimates at a grid of points spanning the specified polygon.

   The GRID parameter can be used to save the kernel density estimates as a pointer to matrices where each matrix has rows corresponding to values of the horizontal coordinate (x) arranged in ascending order, and the columns corresponding to values of the vertical coordinate (y) in ascending order. Each matrix in the pointer represents a different time-slice and are arranged in ascending order.

   Printed output is controlled using the PRINT option. The settings available are monitoring (which prints details about the parameter settings for the kernel smoothing process) and grid (which prints the grids of kernel density estimates).

 

Option: PRINT.

Parameters: Y1, X1, TIMES, XGRID, YGRID, ZGRID, HXY, HZ, GRID.


Method

A procedure PTCHECKXY is called to check that X, Y and TIMES have identical restrictions. The procedure then calls PTPASS to call a Fortran program to calculate the kernel density estimates for the grid of points spanning the 3 dimensional array.