Initial vendor packages

Signed-off-by: Valentin Popov <valentin@popov.link>

vendor/smawk/tests/agreement.rs

@@ -0,0 +1,104 @@
+#![cfg(feature = "ndarray")]
+
+use ndarray::{s, Array2};
+use rand::SeedableRng;
+use rand_chacha::ChaCha20Rng;
+use smawk::{brute_force, online_column_minima, recursive};
+
+mod random_monge;
+use random_monge::random_monge_matrix;
+
+/// Check that the brute force, recursive, and SMAWK functions
+/// give identical results on a large number of randomly generated
+/// Monge matrices.
+#[test]
+fn column_minima_agree() {
+    let sizes = vec![1, 2, 3, 4, 5, 10, 15, 20, 30];
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    for _ in 0..4 {
+        for m in sizes.clone().iter() {
+            for n in sizes.clone().iter() {
+                let matrix: Array2<i32> = random_monge_matrix(*m, *n, &mut rng);
+
+                // Compute and test row minima.
+                let brute_force = brute_force::row_minima(&matrix);
+                let recursive = recursive::row_minima(&matrix);
+                let smawk = smawk::row_minima(&matrix);
+                assert_eq!(
+                    brute_force, recursive,
+                    "recursive and brute force differs on:\n{:?}",
+                    matrix
+                );
+                assert_eq!(
+                    brute_force, smawk,
+                    "SMAWK and brute force differs on:\n{:?}",
+                    matrix
+                );
+
+                // Do the same for the column minima.
+                let brute_force = brute_force::column_minima(&matrix);
+                let recursive = recursive::column_minima(&matrix);
+                let smawk = smawk::column_minima(&matrix);
+                assert_eq!(
+                    brute_force, recursive,
+                    "recursive and brute force differs on:\n{:?}",
+                    matrix
+                );
+                assert_eq!(
+                    brute_force, smawk,
+                    "SMAWK and brute force differs on:\n{:?}",
+                    matrix
+                );
+            }
+        }
+    }
+}
+
+/// Check that the brute force and online SMAWK functions give
+/// identical results on a large number of randomly generated
+/// Monge matrices.
+#[test]
+fn online_agree() {
+    let sizes = vec![1, 2, 3, 4, 5, 10, 15, 20, 30, 50];
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    for _ in 0..5 {
+        for &size in &sizes {
+            // Random totally monotone square matrix of the
+            // desired size.
+            let mut matrix: Array2<i32> = random_monge_matrix(size, size, &mut rng);
+
+            // Adjust matrix so the column minima are above the
+            // diagonal. The brute_force::column_minima will still
+            // work just fine on such a mangled Monge matrix.
+            let max = *matrix.iter().max().unwrap_or(&0);
+            for idx in 0..(size as isize) {
+                // Using the maximum value of the matrix instead
+                // of i32::max_value() makes for prettier matrices
+                // in case we want to print them.
+                matrix.slice_mut(s![idx..idx + 1, ..idx + 1]).fill(max);
+            }
+
+            // The online algorithm always returns the initial
+            // value for the left-most column -- without
+            // inspecting the column at all. So we fill the
+            // left-most column with this value to have the brute
+            // force algorithm do the same.
+            let initial = 42;
+            matrix.slice_mut(s![0.., ..1]).fill(initial);
+
+            // Brute-force computation of column minima, returned
+            // in the same form as online_column_minima.
+            let brute_force = brute_force::column_minima(&matrix)
+                .iter()
+                .enumerate()
+                .map(|(j, &i)| (i, matrix[[i, j]]))
+                .collect::<Vec<_>>();
+            let online = online_column_minima(initial, size, |_, i, j| matrix[[i, j]]);
+            assert_eq!(
+                brute_force, online,
+                "brute force and online differ on:\n{:3?}",
+                matrix
+            );
+        }
+    }
+}

vendor/smawk/tests/complexity.rs

@@ -0,0 +1,83 @@
+#![cfg(feature = "ndarray")]
+
+use ndarray::{Array1, Array2};
+use rand::SeedableRng;
+use rand_chacha::ChaCha20Rng;
+use smawk::online_column_minima;
+
+mod random_monge;
+use random_monge::random_monge_matrix;
+
+#[derive(Debug)]
+struct LinRegression {
+    alpha: f64,
+    beta: f64,
+    r_squared: f64,
+}
+
+/// Square an expression. Works equally well for floats and matrices.
+macro_rules! squared {
+    ($x:expr) => {
+        $x * $x
+    };
+}
+
+/// Compute the mean of a 1-dimensional array.
+macro_rules! mean {
+    ($a:expr) => {
+        $a.mean().expect("Mean of empty array")
+    };
+}
+
+/// Compute a simple linear regression from the list of values.
+///
+/// See <https://en.wikipedia.org/wiki/Simple_linear_regression>.
+fn linear_regression(values: &[(usize, i32)]) -> LinRegression {
+    let xs = values.iter().map(|&(x, _)| x as f64).collect::<Array1<_>>();
+    let ys = values.iter().map(|&(_, y)| y as f64).collect::<Array1<_>>();
+
+    let xs_mean = mean!(&xs);
+    let ys_mean = mean!(&ys);
+    let xs_ys_mean = mean!(&xs * &ys);
+
+    let cov_xs_ys = ((&xs - xs_mean) * (&ys - ys_mean)).sum();
+    let var_xs = squared!(&xs - xs_mean).sum();
+
+    let beta = cov_xs_ys / var_xs;
+    let alpha = ys_mean - beta * xs_mean;
+    let r_squared = squared!(xs_ys_mean - xs_mean * ys_mean)
+        / ((mean!(&xs * &xs) - squared!(xs_mean)) * (mean!(&ys * &ys) - squared!(ys_mean)));
+
+    LinRegression {
+        alpha: alpha,
+        beta: beta,
+        r_squared: r_squared,
+    }
+}
+
+/// Check that the number of matrix accesses in `online_column_minima`
+/// grows as O(*n*) for *n* ✕ *n* matrix.
+#[test]
+fn online_linear_complexity() {
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    let mut data = vec![];
+
+    for &size in &[1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100] {
+        let matrix: Array2<i32> = random_monge_matrix(size, size, &mut rng);
+        let count = std::cell::RefCell::new(0);
+        online_column_minima(0, size, |_, i, j| {
+            *count.borrow_mut() += 1;
+            matrix[[i, j]]
+        });
+        data.push((size, count.into_inner()));
+    }
+
+    let lin_reg = linear_regression(&data);
+    assert!(
+        lin_reg.r_squared > 0.95,
+        "r² = {:.4} is lower than expected for a linear fit\nData points: {:?}\n{:?}",
+        lin_reg.r_squared,
+        data,
+        lin_reg
+    );
+}

vendor/smawk/tests/monge.rs

@@ -0,0 +1,83 @@
+#![cfg(feature = "ndarray")]
+
+use ndarray::{arr2, Array, Array2};
+use rand::SeedableRng;
+use rand_chacha::ChaCha20Rng;
+use smawk::monge::is_monge;
+
+mod random_monge;
+use random_monge::{random_monge_matrix, MongePrim};
+
+#[test]
+fn random_monge() {
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    let matrix: Array2<u8> = random_monge_matrix(5, 5, &mut rng);
+
+    assert!(is_monge(&matrix));
+    assert_eq!(
+        matrix,
+        arr2(&[
+            [2, 3, 4, 4, 5],
+            [5, 5, 6, 6, 7],
+            [3, 3, 4, 4, 5],
+            [5, 2, 3, 3, 4],
+            [5, 2, 3, 3, 4]
+        ])
+    );
+}
+
+#[test]
+fn monge_constant_rows() {
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    let matrix: Array2<u8> = MongePrim::ConstantRows.to_matrix(5, 4, &mut rng);
+    assert!(is_monge(&matrix));
+    for row in matrix.rows() {
+        let elem = row[0];
+        assert_eq!(row, Array::from_elem(matrix.ncols(), elem));
+    }
+}
+
+#[test]
+fn monge_constant_cols() {
+    let mut rng = ChaCha20Rng::seed_from_u64(0);
+    let matrix: Array2<u8> = MongePrim::ConstantCols.to_matrix(5, 4, &mut rng);
+    assert!(is_monge(&matrix));
+    for column in matrix.columns() {
+        let elem = column[0];
+        assert_eq!(column, Array::from_elem(matrix.nrows(), elem));
+    }
+}
+
+#[test]
+fn monge_upper_right_ones() {
+    let mut rng = ChaCha20Rng::seed_from_u64(1);
+    let matrix: Array2<u8> = MongePrim::UpperRightOnes.to_matrix(5, 4, &mut rng);
+    assert!(is_monge(&matrix));
+    assert_eq!(
+        matrix,
+        arr2(&[
+            [0, 0, 1, 1],
+            [0, 0, 1, 1],
+            [0, 0, 1, 1],
+            [0, 0, 0, 0],
+            [0, 0, 0, 0]
+        ])
+    );
+}
+
+#[test]
+fn monge_lower_left_ones() {
+    let mut rng = ChaCha20Rng::seed_from_u64(1);
+    let matrix: Array2<u8> = MongePrim::LowerLeftOnes.to_matrix(5, 4, &mut rng);
+    assert!(is_monge(&matrix));
+    assert_eq!(
+        matrix,
+        arr2(&[
+            [0, 0, 0, 0],
+            [0, 0, 0, 0],
+            [1, 1, 0, 0],
+            [1, 1, 0, 0],
+            [1, 1, 0, 0]
+        ])
+    );
+}

vendor/smawk/tests/random_monge/mod.rs

@@ -0,0 +1,83 @@
+//! Test functionality for generating random Monge matrices.
+
+// The code is put here so we can reuse it in different integration
+// tests, without Cargo finding it when `cargo test` is run. See the
+// section on "Submodules in Integration Tests" in
+// https://doc.rust-lang.org/book/ch11-03-test-organization.html
+
+use ndarray::{s, Array2};
+use num_traits::PrimInt;
+use rand::distributions::{Distribution, Standard};
+use rand::Rng;
+
+/// A Monge matrix can be decomposed into one of these primitive
+/// building blocks.
+#[derive(Copy, Clone)]
+pub enum MongePrim {
+    ConstantRows,
+    ConstantCols,
+    UpperRightOnes,
+    LowerLeftOnes,
+}
+
+impl MongePrim {
+    /// Generate a Monge matrix from a primitive.
+    pub fn to_matrix<T: PrimInt, R: Rng>(&self, m: usize, n: usize, rng: &mut R) -> Array2<T>
+    where
+        Standard: Distribution<T>,
+    {
+        let mut matrix = Array2::from_elem((m, n), T::zero());
+        // Avoid panic in UpperRightOnes and LowerLeftOnes below.
+        if m == 0 || n == 0 {
+            return matrix;
+        }
+
+        match *self {
+            MongePrim::ConstantRows => {
+                for mut row in matrix.rows_mut() {
+                    if rng.gen::<bool>() {
+                        row.fill(T::one())
+                    }
+                }
+            }
+            MongePrim::ConstantCols => {
+                for mut col in matrix.columns_mut() {
+                    if rng.gen::<bool>() {
+                        col.fill(T::one())
+                    }
+                }
+            }
+            MongePrim::UpperRightOnes => {
+                let i = rng.gen_range(0..(m + 1) as isize);
+                let j = rng.gen_range(0..(n + 1) as isize);
+                matrix.slice_mut(s![..i, -j..]).fill(T::one());
+            }
+            MongePrim::LowerLeftOnes => {
+                let i = rng.gen_range(0..(m + 1) as isize);
+                let j = rng.gen_range(0..(n + 1) as isize);
+                matrix.slice_mut(s![-i.., ..j]).fill(T::one());
+            }
+        }
+
+        matrix
+    }
+}
+
+/// Generate a random Monge matrix.
+pub fn random_monge_matrix<R: Rng, T: PrimInt>(m: usize, n: usize, rng: &mut R) -> Array2<T>
+where
+    Standard: Distribution<T>,
+{
+    let monge_primitives = [
+        MongePrim::ConstantRows,
+        MongePrim::ConstantCols,
+        MongePrim::LowerLeftOnes,
+        MongePrim::UpperRightOnes,
+    ];
+    let mut matrix = Array2::from_elem((m, n), T::zero());
+    for _ in 0..(m + n) {
+        let monge = monge_primitives[rng.gen_range(0..monge_primitives.len())];
+        matrix = matrix + monge.to_matrix(m, n, rng);
+    }
+    matrix
+}

vendor/smawk/tests/version-numbers.rs

@@ -0,0 +1,9 @@
+#[test]
+fn test_readme_deps() {
+    version_sync::assert_markdown_deps_updated!("README.md");
+}
+
+#[test]
+fn test_html_root_url() {
+    version_sync::assert_html_root_url_updated!("src/lib.rs");
+}