fields (version 1.0)

grid list: Grid list for describing equally spaced grids

Description

The object grid.list refers to a list that contains information for evaluating a function on a 2-dimensional grid of points. If a function has more than two independent variables then one also needs to specify the constant levels for the variables that are not being varied. Also one needs to be able to specify which variable should be identified with the horizontal or "X" axis and which variable should be associated with the vertical or "Y" axis when the surface is plotted using contour or persp. This format is used extensively in the FUNFITS/FIELDS functions that evaluate function estimates and plot surfaces. The form of a grid.list is list( var.name1= what , var.name2=what , ... var.nameN=what) Here var.names are the names of the independent variables. The what options describe what should be done with this variable when generating the grid. The options are numerous reflecting some laziness in not wanting to type too much.

The argument what can take on the following values: "x" Generate the grid using this variable as the horizontal axis for a contour plot. "y" Take this variable to be the vertical axis for a contour plot. Numerical vector with two or more elements. If only two elements these are interpreted as the range for the grid. ( make.surface.grid has an option for specifying the number of grid points in this range with the default being 30.) If the vector has more than two elements these are assumed to be the actual grid values. Most of time these are equally spaced and are easily generated using the seq function. If two vectors are used to specify the x and y grids the first variable mentioned in the list is assumed as the x coordinate for contour and the second variable in order is the y coordinate. (There is an option in the as.surface function to flip these before plotting.) "c" This variable is held constant at its mean level. Numerical value. This variable held constant at the specified value. There are are some important defaults that are assumed in this format. If a variable is omitted in the grid.list it is assumed to have value "c". If the variable names are omitted then the components are assumed to be in the same order as the variables. In this case one is not legal to omit a variable. Finally if a plotting or predict function takes a grid.list as an argument the default object when it is not specified is list("x","y"). Sometimes it is easier not to specify either columns names for the X matrix paired with a grid list or for the grid list itself. In this case names are assigned as X1, X2, .... So for in the example below: dimnames( X)<- list(NULL, c("X1","X2","X3")) this line is not needed because X does not have names for its columns and these will be assigned within the surface function.

See Also

make.surface.grid, as.surface, predict.surface, plot.surface, surface

Examples

#Given below are some examples of grid.list objects and the results  
#when they are used with make.surface.grid. Note that  
#make.surface.grid returns a matrix that retains the grid.list  
#information as an attribute. 

grid.l<- list( 1:3, 2:5) 
make.surface.grid(grid.l)
  
grid.l <- list( 1:3, 10, 1:3) 
make.surface.grid(grid.l) 

#The next set of examples show how the grid.list can be used to  
#control surface plotting and evaluation of an estimated function. 

# first create a test function  
X<- 2*cbind( runif(50), runif(50), runif(50))  
dimnames( X)<- list(NULL, c("X1","X2","X3")) 
y<- X[,1]**2 + X[,2]**2 + exp(X[,3])   

# fit an  interpolating thin plate spline  
out<- Tps( X,y,lambda=1e-8) 
grid.l<- list( X1="x", X2="y") 
surface( out, grid.l, type="I") # surface plot of estimated surface with  
#                       X3= mean value 


grid.l<- list( X1= seq( 0,2,,25), X2=1.0, X3=seq(0,2,,25)) 
surface( out,grid.l, type="I") 
#  surface plot based on a 25X25 grid in X1 an X3  
#                       over the square [0,2] and [0,2]   
#                       holding X2 equal to 1.0. 
#