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LURE: row

Rows in a table

tim@menzies.us
August, 2017

A row is a slave module to tbl. Rows are where tbls store one line of data. Note that it is not possible to test rows without also testing tbls.

 
local ID=  require "id"
local LST= require "lists"
local NUM= require "num"

Rows have a unique id and cells of data.

 
local function create()
  return {id=ID.new(),   cells={}} end

When row data is added, go to the tbl headers and update their counts of what numbers and symbols have been seen

 
local function update(i,cells,t)
  i.cells=LST.copy(cells)
  for _,head in pairs(t.all.cols) do
    head.what.update(head, cells[head.pos]) end
  return i end

Copied rows have the same unique id but their cells are held in a different container.

 
local function copy(i)
  local j = create()
  j.cells = LST.copy(i.cells) -- get different cells
  j.id = i.id -- keep their same id (for reference purposes)
  return j end

The distance between two rows is normalized 0..1 by dividing it by the maximum possible distance. To compute that distance, rows ask each column for a function f that determines the distance between two values in that kind of column (to see how that works, look at distance in num.lua and sym.lua).

 
local function distance(i,j,t)
  local d,n,p=0,10^-64,0.5
  for _,col in pairs(t.x.cols) do
    local f = col.what.distance
    local d1,n1 = f(col, i.cells[col.pos], j.cells[col.pos])
    d = d + d1
    n = n + n1 end
  return d^p / n^p end

A rows position can be projected using the cosine rule onto a line running between two other points (called west and east).

 
local function x(i,west,east,t,      c)
  local c= c or distance(west,east,t)
  local b= distance(i,east,t)
  local a= distance(i,west, t)
  return (a^2 + c^2 - b^2) / (2*c),c  
end

Imagine we have some function f that inputs a row, and outputs some value calulated for that row. Then, given a new row (without that value), then that value can be extraloated from two other rows. Note that the following code assumes f(west) ≤ f(east).

 
local function extrapolate(i,west, east,f,t,c)
  local x0,c = x(i,west,east,t,c)
  local x1,x2,y1,y2 = 0,c,f(west,t), f(east,t)
  local m  = (y2 - y1) / (x2 - x1) -- rise/run
  local b  = y2 - m*x2  -- the slope
  return m * x0 + b end

To see if row i dominates rows j in table t, then sum the difference in the goal values between the two rows (we raise that difference to an exponent to make any such difference "shout load").

 
local function dominate1(i,j,t)
  local e,n = 2.71828,#t.goals
  local sum1,sum2=0,0
  for _,col in pairs(t.goals)  do
    local w= col.weight
    local x= NUM.norm(col, i.cells[col.pos])
    local y= NUM.norm(col, j.cells[col.pos])
    sum1 = sum1 - e^(w * (x-y)/n)
    sum2 = sum2 - e^(w * (y-x)/n) 
  end 
  return sum1/n < sum2/n end

Count how many times row i dominates row j (where "domination" is computed by the function f).

 
local function dominate(i,t,f) 
  f = f or dominate1
  local tmp = 0
  for x,j in pairs(t.rows) do
    if i.id ~= j.id then 
      if f(i,j,t) then
        tmp= tmp + 1  end end end 
  return tmp end

External Interface

 
return {create=create, update=update,distance=distance,dominate=dominate,copy=copy}

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