Support for disallowed assignments.

Add support for disallowed assignments, and include a check to avoid
attempting to solve unsolvable matrices (where a row only has disallowed
values).

For now only allow `f32`/`f64`, as we can use `INFINITY` to encode a
disallowed assignment.

This is a re-implementation of most of bmc/munkres#20, but is missing
the changes to `step6`, which attempt to detect when we're not making
progress. I couldn't implement this without regressing performance and I
am not sure they add much given we're checking `is_solvable()` before
attempting to solve.

src/lib.rs

@@ -21,7 +21,9 @@ extern crate ndarray;
 #[cfg(test)]
 extern crate test;
 
+use std::{f32, f64};
 use std::ops::{Add, Sub};
+
 use coverage::Coverage;
 use mark_matrix::MarkMatrix;
 pub use weight_matrix::WeightMatrix;
@@ -36,6 +38,7 @@ pub mod weight_matrix;
 
 pub trait WeightNum: PartialOrd + Copy + Sub<Output=Self> + Add<Output=Self> {
     fn is_zero(&self) -> bool;
+    fn is_disallowed(&self) -> bool { false }
 }
 
 impl WeightNum for usize { #[inline(always)] fn is_zero(&self) -> bool { *self == 0 } }
@@ -48,8 +51,28 @@ impl WeightNum for u16 { #[inline(always)] fn is_zero(&self) -> bool { *self ==
 impl WeightNum for i16 { #[inline(always)] fn is_zero(&self) -> bool { *self == 0 } }
 impl WeightNum for u8 { #[inline(always)] fn is_zero(&self) -> bool { *self == 0 } }
 impl WeightNum for i8 { #[inline(always)] fn is_zero(&self) -> bool { *self == 0 } }
-impl WeightNum for f64 { #[inline(always)] fn is_zero(&self) -> bool { *self == 0.0 } }
+
-impl WeightNum for f32 { #[inline(always)] fn is_zero(&self) -> bool { *self == 0.0 } }
+impl WeightNum for f64 {
+    #[inline(always)]
+    fn is_zero(&self) -> bool {
+        *self == 0.0
+    }
+
+    fn is_disallowed(&self) -> bool {
+        *self == f64::INFINITY
+    }
+}
+
+impl WeightNum for f32 {
+    #[inline(always)]
+    fn is_zero(&self) -> bool {
+        *self == 0.0
+    }
+
+    fn is_disallowed(&self) -> bool {
+        *self == f32::INFINITY
+    }
+}
 
 pub trait Weights {
     type T: WeightNum;
@@ -64,6 +87,8 @@ pub trait Weights {
     fn is_element_zero(&self, pos: (usize, usize)) -> bool {
         self.element_at(pos).is_zero()
     }
+
+    fn is_solvable(&self) -> bool;
 }
 
 #[derive(Debug, Eq, PartialEq)]
@@ -275,6 +300,10 @@ fn step6<W>(c: &mut W, cov: &Coverage) -> Step
 pub fn solve_assignment<W>(weights: &mut W) -> Vec<(usize, usize)>
     where W: Weights
 {
+    if !weights.is_solvable() {
+        panic!("Matrix can not be solved");
+    }
+
     let n = weights.n();
 
     let mut marks = MarkMatrix::new(n);
@@ -719,6 +748,34 @@ fn test_solve_random10() {
     assert_eq!(exp, &matching[..]);
 }
 
+#[test]
+fn test_disallowed() {
+    let c = vec![
+        250.0, 400.0, 350.0,
+        400.0, 600.0, f32::INFINITY,
+        200.0, 400.0, 250.0
+    ];
+
+    let mut weights: WeightMatrix<f32> = WeightMatrix::from_row_vec(3, c);
+    let matching = solve_assignment(&mut weights);
+
+    assert_eq!(vec![(0, 1), (1, 0), (2, 2)], matching);
+}
+
+#[test]
+#[should_panic]
+fn test_unsolvable() {
+    const N: usize = 3;
+    let c = vec![
+         1.0, 1.0, 1.0,
+         f32::INFINITY, f32::INFINITY, f32::INFINITY,
+         1.0, 1.0, 1.0,
+    ];
+
+    let mut weights: WeightMatrix<f32> = WeightMatrix::from_row_vec(N, c.clone());
+    solve_assignment(&mut weights);
+}
+
 #[cfg(test)]
 fn gen_matrix(n: usize) -> Vec<i32> {
     (0..n * n)

src/weight_matrix.rs

@@ -31,12 +31,33 @@ impl<T: WeightNum> Weights for WeightMatrix<T> {
 
     // Add `val` to every element in row `row`.
     fn add_row(&mut self, row: usize, val: T) {
-        self.c.row_mut(row).mapv_inplace(|cur| cur + val);
+        self.c.row_mut(row).mapv_inplace(|cur| {
+            if cur.is_disallowed() {
+                cur
+            } else {
+                cur + val
+            }
+        });
     }
 
     // Subtract `val` from every element in column `col`.
     fn sub_col(&mut self, col: usize, val: T) {
-        self.c.column_mut(col).mapv_inplace(|cur| cur - val);
+        self.c.column_mut(col).mapv_inplace(|cur| {
+            if cur.is_disallowed() {
+                cur
+            } else {
+                cur - val
+            }
+        });
+    }
+
+    fn is_solvable(&self) -> bool {
+        for row in 0..self.n() {
+            if self.c.row(row).iter().all(|c| c.is_disallowed()) {
+                return false;
+            }
+        }
+        true
     }
 }
 
@@ -55,7 +76,7 @@ impl<T: WeightNum> WeightMatrix<T> {
         let row_slice = self.c.row(row);
         let mut min = row_slice[0];
         for &val in row_slice.iter().skip(1) {
-            if val < min {
+            if !val.is_disallowed() && val < min {
                 min = val;
             }
         }
@@ -64,7 +85,13 @@ impl<T: WeightNum> WeightMatrix<T> {
 
     // Subtract `val` from every element in row `row`.
     fn sub_row(&mut self, row: usize, val: T) {
-        self.c.row_mut(row).mapv_inplace(|cur| cur - val);
+        self.c.row_mut(row).mapv_inplace(|cur| {
+            if cur.is_disallowed() {
+                cur
+            } else {
+                cur - val
+            }
+        });
     }
 
     pub fn as_slice(&self) -> &[T] {