import std/random
import std/os
import std/parseutils
from mmath/rational import Rational, newRational, `$`, zero, abs, `<`, `*`, `-`, `/=`, `+`, `+=`
from mmath/hmatrix import newHMatrix, clone, lup, lu_solve, `*`, `-`, `$`
from mmath/hvector import newHvector, `-`, norm
from mmath/bigint import BigInt, newBigInt, `of`, one, zero, abs, `*`, `mod`, `div`, `-`, `+`, `$`, `==`

let argv = commandLineParams()

let size = block:
        var n : int = 0
        if argv.len() > 0: 
                discard parseInt(argv[0], n) 
        else: 
                n = 3
        n

proc nextInt(r : var Rand, min : int, max : int) : int = min + r.rand(max - min)

var rand = initRand(101325)
let mtx = block:
    let valueGenerator = proc(i : int, j : int): Rational[BigInt] =
        return newRational[BigInt](BigInt.of(rand.nextInt(-1000 * size, 1000 * size).int64), BigInt.of((1000 * size).int64))
    newHMatrix[Rational[BigInt]](size, size, valueGenerator)
var lu = mtx.clone()
let pivot = lu.lup()
let b = block:
    let generator = proc(i : int) : Rational[BigInt] = newRational(BigInt.of(rand.nextInt(0, size)), BigInt.of(size))
    newHVector[Rational[BigInt]](size, generator)
let x = lu.lu_solve(b, pivot)
let error = mtx * x - b
echo $norm(error)