Fix proptest functionality test

The previous test claimed to verify that all possible outputs
are sampled, but it didn't. This commits fixes this issue
by actually computing all possible combinations.
However, to accomplish this we needed to add itertools as a test
dependency. Otherwise we'd have to implement our own way of
generating the Cartesian product of an arbitrary number
of sets.

Cargo.toml

@@ -73,6 +73,7 @@ matrixcompare = "0.1.3"
 # RNG for certain tests. However, different versions of proptest may give different sequences of numbers,
 # which may cause more brittle tests (although ideally they should take enough samples for it not to matter).
 proptest = { version = "=0.10.1" }
+itertools = "0.9"
 
 [workspace]
 members = [ "nalgebra-lapack", "nalgebra-glm" ]

tests/proptest/mod.rs

@@ -1,10 +1,13 @@
 //! Tests for proptest-related functionality.
 use nalgebra::base::dimension::*;
 use nalgebra::proptest::{matrix, DimRange, MatrixStrategy};
-use nalgebra::{DMatrix, DVector, Dim, Matrix3, Matrix4, MatrixMN, Vector3};
+use nalgebra::{DMatrix, DVector, Dim, Matrix3, MatrixMN, Vector3};
 use proptest::prelude::*;
 use proptest::strategy::ValueTree;
 use proptest::test_runner::TestRunner;
+use itertools::Itertools;
+use std::iter::repeat;
+use std::collections::HashSet;
 
 /// Generate a proptest that tests that all matrices generated with the
 /// provided rows and columns conform to the constraints defined by the
@@ -97,35 +100,51 @@ fn matrix_samples_all_possible_outputs() {
     // We use a deterministic test runner to make the test "stable".
     let mut runner = TestRunner::deterministic();
 
-    let strategy = matrix(0..=2usize, 0..=3, 0..=3);
+    // This number needs to be high enough so that we with high probability sample
+    // all possible cases
+    let num_generated_matrices = 200000;
 
-    // We use flags to record whether values and combinations of dimensions were encountered.
-    // For example, if we encounter value 1, we set the value flag of 1 to true,
-    // and if we encounted matrix dimensions 4x3, we set the flag of [4, 3] to true.
-    let mut value_encountered = Vector3::new(false, false, false);
-    let mut dimensions_encountered = Matrix4::repeat(false);
+    let values = -1..=1;
+    let rows = 0..=2;
+    let cols = 0..=3;
+    let strategy = matrix(values.clone(), rows.clone(), cols.clone());
 
-    for _ in 0..1000 {
+    // Enumerate all possible combinations
+    let mut all_combinations = HashSet::new();
+    for nrows in rows {
+        for ncols in cols.clone() {
+            // For the given number of rows and columns
+            let n_values = nrows * ncols;
+
+            if n_values == 0 {
+                // If we have zero rows or columns, the set of matrices with the given
+                // rows and columns is a single element: an empty matrix
+                all_combinations.insert(DMatrix::from_row_slice(nrows, ncols, &[]));
+            } else {
+                // Otherwise, we need to sample all possible matrices.
+                // To do this, we generate the values as the (multi) Cartesian product
+                // of the value sets. For example, for a 2x2 matrices, we consider
+                // all possible 4-element arrays that the matrices can take by
+                // considering all elements in the cartesian product
+                //  V x V x V x V
+                // where V is the set of eligible values, e.g. V := -1 ..= 1
+                for matrix_values in repeat(values.clone()).take(n_values).multi_cartesian_product() {
+                    all_combinations.insert(DMatrix::from_row_slice(nrows, ncols, &matrix_values));
+                }
+            }
+        }
+    }
+
+    let mut visited_combinations = HashSet::new();
+    for _ in 0..num_generated_matrices {
         let tree = strategy
             .new_tree(&mut runner)
             .expect("Tree generation should not fail");
         let matrix = tree.current();
-
-        dimensions_encountered[(matrix.nrows(), matrix.ncols())] = true;
-
-        for &value in matrix.iter() {
-            value_encountered[value] = true;
-        }
+        visited_combinations.insert(matrix.clone());
     }
 
-    assert!(
-        value_encountered.iter().all(|v| *v),
-        "Did not sample all possible values."
-    );
-    assert!(
-        dimensions_encountered.iter().all(|v| *v),
-        "Did not sample all possible matrix dimensions."
-    );
+    assert_eq!(visited_combinations, all_combinations, "Did not sample all possible values.");
 }
 
 #[test]