Merge branch 'dimforge:dev' into dev

CHANGELOG.md

@@ -4,6 +4,10 @@ documented here.
 
 This project adheres to [Semantic Versioning](https://semver.org/).
 
+## Unreleased
+
+### Fixed
+- Fixed severe catastrophic cancellation issue in variance calculation.
 
 ## [0.32.2] (07 March 2023)
 

Cargo.toml

@@ -111,6 +111,7 @@ serde_json = "1.0"
 rand_xorshift = "0.3"
 rand_isaac = "0.3"
 criterion = { version = "0.4", features = ["html_reports"] }
+nalgebra = { path = ".", features = ["debug", "compare", "rand", "macros"]}
 
 # For matrix comparison macro
 matrixcompare = "0.3.0"

src/base/alias.rs

@@ -81,32 +81,32 @@ pub type MatrixXx5<T> = Matrix<T, Dyn, U5, VecStorage<T, Dyn, U5>>;
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type MatrixXx6<T> = Matrix<T, Dyn, U6, VecStorage<T, Dyn, U6>>;
 
-/// A heap-allocated, row-major, matrix with 1 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 1 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix1xX<T> = Matrix<T, U1, Dyn, VecStorage<T, U1, Dyn>>;
-/// A heap-allocated, row-major, matrix with 2 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 2 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix2xX<T> = Matrix<T, U2, Dyn, VecStorage<T, U2, Dyn>>;
-/// A heap-allocated, row-major, matrix with 3 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 3 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix3xX<T> = Matrix<T, U3, Dyn, VecStorage<T, U3, Dyn>>;
-/// A heap-allocated, row-major, matrix with 4 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 4 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix4xX<T> = Matrix<T, U4, Dyn, VecStorage<T, U4, Dyn>>;
-/// A heap-allocated, row-major, matrix with 5 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 5 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]
 pub type Matrix5xX<T> = Matrix<T, U5, Dyn, VecStorage<T, U5, Dyn>>;
-/// A heap-allocated, row-major, matrix with 6 rows and a dynamic number of columns.
+/// A heap-allocated, column-major, matrix with 6 rows and a dynamic number of columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 #[cfg(any(feature = "std", feature = "alloc"))]

src/base/matrix.rs

@@ -2255,3 +2255,102 @@ where
         Unit::new_unchecked(crate::convert_ref(self.as_ref()))
     }
 }
+
+impl<T, S> Matrix<T, U1, U1, S>
+where
+    S: RawStorage<T, U1, U1>,
+{
+    /// Returns a reference to the single element in this matrix.
+    ///
+    /// As opposed to indexing, using this provides type-safety
+    /// when flattening dimensions.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let inner_product: f32 = *(v.transpose() * v).as_scalar();
+    /// ```
+    ///
+    ///```compile_fail
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let inner_product = (v * v.transpose()).item(); // Typo, does not compile.
+    ///```
+    pub fn as_scalar(&self) -> &T {
+        &self[(0, 0)]
+    }
+    /// Get a mutable reference to the single element in this matrix
+    ///
+    /// As opposed to indexing, using this provides type-safety
+    /// when flattening dimensions.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let mut inner_product = (v.transpose() * v);
+    /// *inner_product.as_scalar_mut() = 3.;
+    /// ```
+    ///
+    ///```compile_fail
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let mut inner_product = (v * v.transpose());
+    /// *inner_product.as_scalar_mut() = 3.;
+    ///```
+    pub fn as_scalar_mut(&mut self) -> &mut T
+    where
+        S: RawStorageMut<T, U1>,
+    {
+        &mut self[(0, 0)]
+    }
+    /// Convert this 1x1 matrix by reference into a scalar.
+    ///
+    /// As opposed to indexing, using this provides type-safety
+    /// when flattening dimensions.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let mut inner_product: f32 = (v.transpose() * v).to_scalar();
+    /// ```
+    ///
+    ///```compile_fail
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let mut inner_product: f32 = (v * v.transpose()).to_scalar();
+    ///```
+    pub fn to_scalar(&self) -> T
+    where
+        T: Clone,
+    {
+        self.as_scalar().clone()
+    }
+}
+
+impl<T> super::alias::Matrix1<T> {
+    /// Convert this 1x1 matrix into a scalar.
+    ///
+    /// As opposed to indexing, using this provides type-safety
+    /// when flattening dimensions.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Vector3, Matrix2, U1};
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let inner_product: f32 = (v.transpose() * v).into_scalar();
+    /// assert_eq!(inner_product, 1.);
+    /// ```
+    ///
+    ///```compile_fail
+    /// # use nalgebra::Vector3;
+    /// let v = Vector3::new(0., 0., 1.);
+    /// let mut inner_product: f32 = (v * v.transpose()).into_scalar();
+    ///```
+    pub fn into_scalar(self) -> T {
+        let [[scalar]] = self.data.0;
+        scalar
+    }
+}

src/base/statistics.rs

@@ -335,12 +335,12 @@ impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
         if self.is_empty() {
             T::zero()
         } else {
-            let val = self.iter().cloned().fold((T::zero(), T::zero()), |a, b| {
-                (a.0 + b.clone() * b.clone(), a.1 + b)
-            });
-            let denom = T::one() / crate::convert::<_, T>(self.len() as f64);
-            let vd = val.1 * denom.clone();
-            val.0 * denom - vd.clone() * vd
+            let n_elements: T = crate::convert(self.len() as f64);
+            let mean = self.mean();
+
+            self.iter().cloned().fold(T::zero(), |acc, x| {
+                acc + (x.clone() - mean.clone()) * (x.clone() - mean.clone())
+            }) / n_elements
         }
     }
 

tests/core/mod.rs

@@ -11,6 +11,7 @@ mod reshape;
 #[cfg(feature = "rkyv-serialize-no-std")]
 mod rkyv;
 mod serde;
+mod variance;
 
 #[cfg(feature = "compare")]
 mod matrixcompare;

tests/core/variance.rs

@@ -0,0 +1,18 @@
+use nalgebra::DVector;
+
+#[test]
+fn test_variance_catastrophic_cancellation() {
+    let long_repeating_vector = DVector::repeat(10_000, 100000000.0);
+    assert_eq!(long_repeating_vector.variance(), 0.0);
+
+    let short_vec = DVector::from_vec(vec![1., 2., 3.]);
+    assert_eq!(short_vec.variance(), 2.0 / 3.0);
+
+    let short_vec =
+        DVector::<f64>::from_vec(vec![1.0e8 + 4.0, 1.0e8 + 7.0, 1.0e8 + 13.0, 1.0e8 + 16.0]);
+    assert_eq!(short_vec.variance(), 22.5);
+
+    let short_vec =
+        DVector::<f64>::from_vec(vec![1.0e9 + 4.0, 1.0e9 + 7.0, 1.0e9 + 13.0, 1.0e9 + 16.0]);
+    assert_eq!(short_vec.variance(), 22.5);
+}