Spline Toolbox

sorted

Locate sites with respect to mesh sites

Syntax

• pointer = sorted(meshsites,sites)
  

Description

Various commands in this toolbox need to determine the index for which a given lies in the interval , with a given nondecreasing sequence, e.g., a knot sequence. This job is done by sorted in the following fashion.

pointer=sorted(meshsites,sites) gives the integer sequence for which, for all j, pointer(j) equals the number of entries in meshsites that are  ssites(j), with ssites the vector sort(sites). Thus, if both meshsites and sites are nondecreasing, then

• meshsites(pointer(j))  sites(j) < meshsites(pointer(j)+1)
  

with the obvious interpretations when

• pointer(j) < 1    or    length(meshsites) < pointer(j) + 1
  

Specifically, having pointer(j) < 1 then corresponds to having sites(j) strictly to the left of meshsites(1), while having length(meshsites) < pointer(j)+1 then corresponds to having sites(j) at, or to the right of, meshsites(end).

Examples

The statement

• sorted([1 1 1 2 2 3 3 3],[0:4])
  

will generate the output 0 3 5 8 8, as will the statement

• sorted([3 2 1 1 3 2 3 1],[2 3 0 4 1])
  

Algorithm

The indexing output from sort([meshsites(:).',sites(:).']) is used.

slvblk

spap2