ListCorrelate

Usage

• ListCorrelate[ker, list] forms the correlation of the kernel ker with list.
• ListCorrelate[ker, list, k] forms the cyclic correlation in which the k element of ker is aligned with each element in list.
• ListCorrelate[ker, list, {, }] forms the cyclic correlation whose first element contains list[[1]] ker[[]] and whose last element contains list[[-1]] ker[[]].
• ListCorrelate[ker, list, klist, p] forms the correlation in which list is padded at each end with repetitions of the element p.
• ListCorrelate[ker, list, klist, {, , ... }] forms the correlation in which list is padded at each end with cyclic repetitions of the .
• ListCorrelate[ker, list, klist, padding, g, h] forms a generalized correlation in which g is used in place of Times and h in place of Plus.
• ListCorrelate[ker, list, klist, padding, g, h, lev] forms a correlation using elements at level lev in ker and list.

Notes

• With kernel

and list

, ListCorrelate[ker, list] computes

, where the limits of the sum are such that the kernel never overhangs either end of the list.

• Example: ListCorrelate[

x,y

a,b,c

]

• For a one-dimensional list ListCorrelate[ker, list] is equivalent to ListConvolve[Reverse[ker], list].

• For higher-dimensional lists, ker must be reversed at every level.

• See notes for ListConvolve.

• Settings for

and

are negated in ListConvolve relative to ListCorrelate.

• Common settings for {

} in ListCorrelate are:

{1, -1}	no overhangs (default)
{1, 1}	maximal overhang at the right-hand end
{-1, -1}	maximal overhang at the left-hand end
{-1, 1}	maximal overhangs at both beginning and end

• See Section 3.8.5.

• Implementation notes: see Section A.9.4.

• See also: ListConvolve, Partition, Inner, CellularAutomaton, PadLeft.

• New in Version 4.

Further Examples