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#![cfg_attr(all(feature = "nightly", test), feature(test))]
extern crate ndarray;
extern crate rand;
extern crate num_traits;
#[macro_use] extern crate log;
#[cfg(all(feature = "nightly", test))]
extern crate test;
use num_traits::Float;
use std::ops;
use std::fmt;
pub type Matrix<T> = ndarray::Array2<T>;
pub trait LapJVCost: Float + ops::AddAssign + ops::SubAssign + std::fmt::Debug {}
impl <T>LapJVCost for T where T: Float + ops::AddAssign + ops::SubAssign + std::fmt::Debug {}
#[derive(Debug)]
pub struct LapJVError(&'static str);
impl std::fmt::Display for LapJVError {
fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
write!(f, "{}", self.0)
}
}
impl std::error::Error for LapJVError {
fn description(&self) -> &str {
self.0
}
}
pub struct LapJV<'a, T: 'a> {
costs: &'a Matrix<T>,
dim: usize,
free_rows: Vec<usize>,
v: Vec<T>,
in_col: Vec<usize>,
in_row: Vec<usize>
}
pub fn lapjv<T>(costs: &Matrix<T>) -> Result<(Vec<usize>, Vec<usize>), LapJVError> where T: LapJVCost {
LapJV::new(costs).solve()
}
pub fn cost<T>(input: &Matrix<T>, x: &[usize]) -> T where T: LapJVCost {
(0..x.len()).into_iter().fold(T::zero(), |acc, i| acc + input[(i, x[i])])
}
impl <'a, T>LapJV<'a, T> where T: LapJVCost {
pub fn new(costs: &'a Matrix<T>) -> Self {
let dim = costs.dim().0;
let free_rows = Vec::with_capacity(dim);
let v = Vec::with_capacity(dim);
let in_row = vec![0; dim];
let in_col = Vec::with_capacity(dim);
Self {
costs,
dim,
free_rows,
v,
in_col,
in_row
}
}
pub fn solve(mut self) -> Result<(Vec<usize>, Vec<usize>), LapJVError> {
if self.costs.dim().0 != self.costs.dim().1 {
return Err(LapJVError("Input error: matrix is not square"))
}
self.ccrrt_dense();
let mut i = 0;
while !self.free_rows.is_empty() && i < 2 {
self.carr_dense();
i+= 1;
}
if !self.free_rows.is_empty() {
self.ca_dense()?;
}
Ok((self.in_row, self.in_col))
}
fn ccrrt_dense(&mut self) {
let mut unique = vec![true; self.dim];
let mut in_row_not_set = vec![true; self.dim];
for row in self.costs.lanes(ndarray::Axis(0)) {
let (min_index, min_value) = row.indexed_iter()
.skip(1)
.fold((0, row[0]), |(old_idx, old_min), (new_idx, &new_min)| if new_min < old_min { (new_idx, new_min) } else { (old_idx, old_min) });
self.in_col.push(min_index);
self.v.push(min_value);
}
for j in (0..self.dim).into_iter().rev() {
let i = self.in_col[j];
if in_row_not_set[i] {
self.in_row[i] = j;
in_row_not_set[i] = false;
} else {
unique[i] = false;
self.in_col[j] = std::usize::MAX;
}
}
for i in 0..self.dim {
if in_row_not_set[i] {
self.free_rows.push(i);
} else if unique[i] {
let j = self.in_row[i];
let mut min = T::max_value();
for j2 in 0..self.dim {
if j2 == j {
continue;
}
let c = self.reduced_cost(i, j2);
if c < min {
min = c;
}
}
self.v[j] -= min;
}
}
}
fn carr_dense(&mut self) {
let dim = self.dim;
let mut current = 0;
let mut new_free_rows = 0;
let mut rr_cnt = 0;
let num_free_rows = self.free_rows.len();
while current < num_free_rows {
rr_cnt += 1;
let free_i = self.free_rows[current];
current += 1;
let (v1, v2, mut j1, j2) = find_umins_plain(self.costs.row(free_i), &self.v);
let mut i0 = self.in_col[j1];
let v1_new = self.v[j1] - (v2 - v1);
let v1_lowers = v1_new < self.v[j1];
if rr_cnt < current * dim {
if v1_lowers {
self.v[j1] = v1_new;
} else if i0 != std::usize::MAX && j2.is_some() {
j1 = j2.unwrap();
i0 = self.in_col[j1];
}
if i0 != std::usize::MAX {
if v1_lowers {
current -= 1;
self.free_rows[current] = i0;
} else {
self.free_rows[new_free_rows] = i0;
new_free_rows += 1;
}
}
} else {
if i0 != std::usize::MAX {
self.free_rows[new_free_rows] = i0;
new_free_rows += 1;
}
}
self.in_row[free_i] = j1;
self.in_col[j1] = free_i;
}
self.free_rows.truncate(new_free_rows);
}
fn ca_dense(&mut self) -> Result<(), LapJVError> {
let dim = self.dim;
let mut pred = vec![0; dim];
let free_rows = std::mem::replace(&mut self.free_rows, vec![]);
for freerow in free_rows {
trace!("looking at free_i={}", freerow);
let mut i = std::usize::MAX;
let mut k = 0;
let mut j = self.find_path_dense(freerow, &mut pred);
assert!(j < dim);
while i != freerow {
i = pred[j];
self.in_col[j] = i;
std::mem::swap(&mut j, &mut self.in_row[i]);
k += 1;
if k >= dim {
return Err(LapJVError("Error: ca_dense will not finish"))
}
}
}
Ok(())
}
fn find_path_dense(&mut self, start_i: usize, pred: &mut [usize]) -> usize {
let dim = self.dim;
let mut collist = Vec::with_capacity(dim);
let mut d = Vec::with_capacity(dim);
let mut lo = 0;
let mut hi = 0;
let mut n_ready = 0;
for i in 0..dim {
collist.push(i);
d.push(self.reduced_cost(start_i, i));
pred[i] = start_i;
}
trace!("d: {:?}", d);
let mut final_j = None;
while final_j.is_none() {
if lo == hi {
trace!("{}..{} -> find", lo, hi);
n_ready = lo;
hi = find_dense(dim, lo, &d, &mut collist);
trace!("check {}..{}", lo, hi);
for &j in collist.iter().take(hi).skip(lo) {
if self.in_col[j] == std::usize::MAX {
final_j = Some(j);
}
}
}
if final_j.is_none() {
trace!("{}..{} -> scan", lo, hi);
let maybe_final_j = self.scan_dense(&mut lo, &mut hi, &mut d, &mut collist, pred);
if let Some(val) = maybe_final_j {
final_j = Some(val);
}
}
}
trace!("found final_j={:?}", final_j);
let mind = d[collist[lo]];
for &j in collist.iter().take(n_ready) {
self.v[j] += d[j] - mind;
}
final_j.unwrap()
}
fn scan_dense(&self, plo: &mut usize, phi: &mut usize, d: &mut [T], collist: &mut [usize], pred: &mut [usize]) -> Option<usize> {
let mut lo = *plo;
let mut hi = *phi;
while lo != hi {
let j = collist[lo];
lo += 1;
let i = self.in_col[j];
let mind = d[j];
let h = self.reduced_cost(i, j) - mind;
for k in hi..collist.len() {
let j = collist[k];
let cred_ij = self.reduced_cost(i, j) - h;
if cred_ij < d[j] {
d[j] = cred_ij;
pred[j] = i;
if (cred_ij - mind).abs() < T::epsilon() {
if self.in_col[j] == std::usize::MAX {
return Some(j);
}
collist[k] = collist[hi];
collist[hi] = j;
hi += 1;
}
}
}
}
*plo = lo;
*phi = hi;
None
}
#[inline(always)]
fn cost(&self, i: usize, j: usize) -> T {
self.costs[(i, j)]
}
#[inline(always)]
fn reduced_cost(&self, i: usize, j: usize) -> T {
self.cost(i, j) - self.v[j]
}
}
fn find_dense<T>(dim: usize, lo: usize, d: &[T], collist: &mut [usize]) -> usize where T: LapJVCost {
let mut hi = lo + 1;
let mut mind = d[collist[lo]];
for k in hi..dim {
let j = collist[k];
let h = d[j];
if h <= mind {
if h < mind {
hi = lo;
mind = h;
}
collist[k] = collist[hi];
collist[hi] = j;
hi += 1;
}
}
hi
}
#[inline(always)]
fn find_umins_plain<T>(local_cost: ndarray::ArrayView1<T>, v: &[T]) -> (T, T, usize, Option<usize>) where T: LapJVCost{
let mut umin = local_cost[0] - v[0];
let mut usubmin = T::max_value();
let mut j1 = 0;
let mut j2 = None;
for j in 1..local_cost.dim() {
let h = local_cost[j] - v[j];
if h < usubmin {
if h >= umin {
usubmin = h;
j2 = Some(j);
} else {
usubmin = umin;
umin = h;
j2 = Some(j1);
j1 = j;
}
}
}
(umin, usubmin, j1, j2)
}
#[cfg(test)]
mod tests {
use super::*;
use rand;
#[test]
fn it_works() {
let m = Matrix::from_shape_vec((3,3), vec![1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0]).unwrap();
let result = lapjv(&m).unwrap();
assert_eq!(result.0, vec![2, 0, 1]);
assert_eq!(result.1, vec![1, 2, 0]);
}
#[test]
fn test_solve_random10() {
let (m, result) = solve_random10();
let cost = cost(&m, &result.0);
assert_eq!(cost, 1071.0);
assert_eq!(result.0, vec![7,9,3,4,1,0,5,6,2,8]);
}
#[test]
fn test_solve_inf1() {
let c = vec![
std::f64::INFINITY, 643.0, 717.0, 2.0, 946.0, 534.0, 242.0, 235.0, 376.0, 839.0,
std::f64::INFINITY, 141.0, 799.0, 180.0, 386.0, 745.0, 592.0, 822.0, 421.0, 42.0,
std::f64::INFINITY, 369.0, 831.0, 67.0, 258.0, 549.0, 615.0, 529.0, 458.0, 524.0,
std::f64::INFINITY, 649.0, 287.0, 910.0, 12.0, 820.0, 31.0, 92.0, 217.0, 555.0,
std::f64::INFINITY, 81.0, 568.0, 241.0, 292.0, 653.0, 417.0, 652.0, 630.0, 788.0,
std::f64::INFINITY, 822.0, 788.0, 166.0, 122.0, 690.0, 304.0, 568.0, 449.0, 214.0,
std::f64::INFINITY, 469.0, 584.0, 633.0, 213.0, 414.0, 498.0, 500.0, 317.0, 391.0,
std::f64::INFINITY, 581.0, 183.0, 420.0, 16.0, 748.0, 35.0, 516.0, 639.0, 356.0,
std::f64::INFINITY, 921.0, 67.0, 33.0, 592.0, 775.0, 780.0, 335.0, 464.0, 788.0,
123.0, 455.0, 950.0, 25.0, 22.0, 576.0, 969.0, 122.0, 86.0, 74.0,
];
let m = Matrix::from_shape_vec((10,10), c).unwrap();
let result = lapjv(&m).unwrap();
let cost = cost(&m, &result.0);
assert_eq!(cost, 1403.0);
assert_eq!(result.0, vec![7, 9, 3, 8, 1, 4, 5, 6, 2, 0]);
}
#[test]
fn test_find_umins() {
let m = Matrix::from_shape_vec((3,3), vec![25.0,0.0,15.0,4.0,5.0,6.0,7.0,8.0,9.0]).unwrap();
let result = find_umins_plain(m.row(0), &vec![0.0,0.0,0.0]);
println!("Result: {:?}", result);
assert_eq!(result,(0.0, 15.0, 1, Some(2)));
}
#[test]
fn test_random() {
use rand::Rng;
let mut rng = rand::thread_rng();
const DIM: usize = 512;
let mut m = Vec::with_capacity(DIM*DIM);
for _ in 0..DIM*DIM {
m.push(rng.next_f64()*100.0);
}
let m = Matrix::from_shape_vec((DIM,DIM), m).unwrap();
let _result = lapjv(&m).unwrap();
}
fn solve_random10() -> (Matrix<f64>, (Vec<usize>, Vec<usize>)) {
const N: usize = 10;
let c = vec![
612.0, 643.0, 717.0, 2.0, 946.0, 534.0, 242.0, 235.0, 376.0, 839.0,
224.0, 141.0, 799.0, 180.0, 386.0, 745.0, 592.0, 822.0, 421.0, 42.0,
241.0, 369.0, 831.0, 67.0, 258.0, 549.0, 615.0, 529.0, 458.0, 524.0,
231.0, 649.0, 287.0, 910.0, 12.0, 820.0, 31.0, 92.0, 217.0, 555.0,
912.0, 81.0, 568.0, 241.0, 292.0, 653.0, 417.0, 652.0, 630.0, 788.0,
32.0, 822.0, 788.0, 166.0, 122.0, 690.0, 304.0, 568.0, 449.0, 214.0,
441.0, 469.0, 584.0, 633.0, 213.0, 414.0, 498.0, 500.0, 317.0, 391.0,
798.0, 581.0, 183.0, 420.0, 16.0, 748.0, 35.0, 516.0, 639.0, 356.0,
351.0, 921.0, 67.0, 33.0, 592.0, 775.0, 780.0, 335.0, 464.0, 788.0,
771.0, 455.0, 950.0, 25.0, 22.0, 576.0, 969.0, 122.0, 86.0, 74.0,
];
let m = Matrix::from_shape_vec((N,N), c).unwrap();
let result = lapjv(&m).unwrap();
(m, result)
}
#[cfg(feature = "nightly")]
mod benches {
use test::Bencher;
use super::*;
#[bench]
fn bench_solve_random10(b: &mut Bencher) {
b.iter(|| test_solve_random10());
}
#[bench]
fn bench_solve_random_inf1(b: &mut Bencher) {
b.iter(|| test_solve_random10());
}
}
}