robust-determinant/robust-determinant.js

General purpose robust determinant computation

"use strict"

var twoProduct = require("two-product")
var robustSum = require("robust-sum")
var robustScale = require("robust-scale")
var compress = require("robust-compress")

var NUM_EXPANDED = 6

function cofactor(m, c) {
  var result = new Array(m.length-1)
  for(var i=1; i<m.length; ++i) {
    var r = result[i-1] = new Array(m.length-1)
    for(var j=0,k=0; j<m.length; ++j) {
      if(j === c) {
        continue
      }
      r[k++] = m[i][j]
    }
  }
  return result
}

function matrix(n) {
  var result = new Array(n)
  for(var i=0; i<n; ++i) {
    result[i] = new Array(n)
    for(var j=0; j<n; ++j) {
      result[i][j] = ["m[", i, "][", j, "]"].join("")
    }
  }
  return result
}

function sign(n) {
  if(n & 1) {
    return "-"
  }
  return ""
}

function generateSum(expr) {
  if(expr.length === 1) {
    return expr[0]
  } else if(expr.length === 2) {
    return ["sum(", expr[0], ",", expr[1], ")"].join("")
  } else {
    var m = expr.length>>1
    return ["sum(", generateSum(expr.slice(0, m)), ",", generateSum(expr.slice(m)), ")"].join("")
  }
}

function determinant(m) {
  if(m.length === 2) {
    return ["sum(prod(", m[0][0], ",", m[1][1], "),prod(-", m[0][1], ",", m[1][0], "))"].join("")
  } else {
    var expr = []
    for(var i=0; i<m.length; ++i) {
      expr.push(["scale(", determinant(cofactor(m, i)), ",", sign(i), m[0][i], ")"].join(""))
    }
    return generateSum(expr)
  }
}

function compileDeterminant(n) {
  var proc = new Function("sum", "scale", "prod", "compress", [
    "function robustDeterminant",n, "(m){return compress(", 
      determinant(matrix(n)),
    ")};return robustDeterminant", n].join(""))
  return proc(robustSum, robustScale, twoProduct, compress)
}

var CACHE = [
  function robustDeterminant0() { return [0] },
  function robustDeterminant1(m) { return [m[0][0]] }
]

function generateDispatch() {
  while(CACHE.length < NUM_EXPANDED) {
    CACHE.push(compileDeterminant(CACHE.length))
  }
  var procArgs = []
  var code = ["function robustDeterminant(m){switch(m.length){"]
  for(var i=0; i<NUM_EXPANDED; ++i) {
    procArgs.push("det" + i)
    code.push("case ", i, ":return det", i, "(m);")
  }
  code.push("}\
var det=CACHE[m.length];\
if(!det)\
det=CACHE[m.length]=gen(m.length);\
return det(m);\
}\
return robustDeterminant")
  procArgs.push("CACHE", "gen", code.join(""))
  var proc = Function.apply(undefined, procArgs)
  module.exports = proc.apply(undefined, CACHE.concat([CACHE, compileDeterminant]))
  for(var i=0; i<CACHE.length; ++i) {
    module.exports[i] = CACHE[i]
  }
}

generateDispatch()