The window operator produces a result array where each output cell is some aggregate function calculated over the cells contained in a N-dimensional rectangle around the corresponding cell in the source array.

Synopsis

window(array, dim1_preceding, dim1_following, [dim2_low,dim2_high[, ...]], aggregate1(attr_name1)[,aggrgegate2(attr_name2)[, ...]])

Summary

The window operator computes one or more aggregate functions of specified attributes over a fixed-size moving window. The result array has the same size and number of cells as the source array.

Inputs

The window operator takes the following arguments:

• array:  A source array.

• dimN_preceding:  For each dimension, 1 ... n, these arguments specify the number of cells before the current cell to include in the window.

• dimN_following: For each dimension, 1 ... n, these argument specifiy the number of cells after of the current cell to include in the window.

• aggregateN(attr_nameN): The aggregate function to use to compute the aggregate of the specified attribute.

Example

To calculate a running average for a 3x3 window on a 4x3 array, do the following:

1. Create an array M with constant values on each diagonal:

   AFL% create array M <val:double>[row=1:4; col=1:3]; AFL% store(build(M, row+col), M);

   The output is:

   {row,col} val {1,1} 2 {1,2} 3 {1,3} 4 {2,1} 3 {2,2} 4 {2,3} 5 {3,1} 4 {3,2} 5 {3,3} 6 {4,1} 5 {4,2} 6 {4,3} 7

2. Return the average (mean) values over a  3×3 rectangle moving over M.  The center of the rectangle is the left corner of the input.

   AFL% window(M, 0, 2, 0, 2, avg(val)); 

   
   The output is:

   {row,col} val_avg {1,1} 4 {1,2} 4.5 {1,3} 5 {2,1} 5 {2,2} 5.5 {2,3} 6 {3,1} 5.5 {3,2} 6 {3,3} 6.5 {4,1} 6 {4,2} 6.5 {4,3} 7

When the Window goes Beyond the End of the Array

To see what happens when the window goes beyond the end of the array, do the following:

1. Consider the following array, A:

   [(),(2),(3),(4),(5)] 

2. Use a window that goes outside the boundary of the array, and join it to A, to construct a new array that has a lag:

   AFL% join(A,window(A,1,0,first_value(x) as lag)); 

   
   The output is:

   i,x,lag 2,2,2 3,3,2 4,4,3 5,5,4