Fix Vector::axpy for noncommutative cases (#648)

Fix Vector::axpy for noncommutative cases

src/base/blas.rs

@@ -468,21 +468,21 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
     }
 }
 
-fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
+fn array_axcpy<N>(y: &mut [N], a: N, x: &[N], c: N, beta: N, stride1: usize, stride2: usize, len: usize)
 where N: Scalar + Zero + ClosedAdd + ClosedMul {
     for i in 0..len {
         unsafe {
             let y = y.get_unchecked_mut(i * stride1);
-            *y = a * *x.get_unchecked(i * stride2) + beta * *y;
+            *y = a * *x.get_unchecked(i * stride2) * c + beta * *y;
         }
     }
 }
 
-fn array_ax<N>(y: &mut [N], a: N, x: &[N], stride1: usize, stride2: usize, len: usize)
+fn array_axc<N>(y: &mut [N], a: N, x: &[N], c: N, stride1: usize, stride2: usize, len: usize)
 where N: Scalar + Zero + ClosedAdd + ClosedMul {
     for i in 0..len {
         unsafe {
-            *y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2);
+            *y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2) * c;
         }
     }
 }
@@ -492,6 +492,40 @@ where
     N: Scalar + Zero + ClosedAdd + ClosedMul,
     S: StorageMut<N, D>,
 {
+    /// Computes `self = a * x * c + b * self`.
+    ///
+    /// If `b` is zero, `self` is never read from.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let mut vec1 = Vector3::new(1.0, 2.0, 3.0);
+    /// let vec2 = Vector3::new(0.1, 0.2, 0.3);
+    /// vec1.axcpy(5.0, &vec2, 2.0, 5.0);
+    /// assert_eq!(vec1, Vector3::new(6.0, 12.0, 18.0));
+    /// ```
+    #[inline]
+    pub fn axcpy<D2: Dim, SB>(&mut self, a: N, x: &Vector<N, D2, SB>, c: N, b: N)
+    where
+        SB: Storage<N, D2>,
+        ShapeConstraint: DimEq<D, D2>,
+    {
+        assert_eq!(self.nrows(), x.nrows(), "Axcpy: mismatched vector shapes.");
+
+        let rstride1 = self.strides().0;
+        let rstride2 = x.strides().0;
+
+        let y = self.data.as_mut_slice();
+        let x = x.data.as_slice();
+
+        if !b.is_zero() {
+            array_axcpy(y, a, x, c, b, rstride1, rstride2, x.len());
+        } else {
+            array_axc(y, a, x, c, rstride1, rstride2, x.len());
+        }
+    }
+
     /// Computes `self = a * x + b * self`.
     ///
     /// If `b` is zero, `self` is never read from.
@@ -508,22 +542,12 @@ where
     #[inline]
     pub fn axpy<D2: Dim, SB>(&mut self, a: N, x: &Vector<N, D2, SB>, b: N)
     where
+        N: One,
         SB: Storage<N, D2>,
         ShapeConstraint: DimEq<D, D2>,
     {
         assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
-
-        let rstride1 = self.strides().0;
-        let rstride2 = x.strides().0;
-
-        let y = self.data.as_mut_slice();
-        let x = x.data.as_slice();
-
-        if !b.is_zero() {
-            array_axpy(y, a, x, b, rstride1, rstride2, x.len());
-        } else {
-            array_ax(y, a, x, rstride1, rstride2, x.len());
-        }
+        self.axcpy(a, x, N::one(), b)
     }
 
     /// Computes `self = alpha * a * x + beta * self`, where `a` is a matrix, `x` a vector, and
@@ -579,13 +603,13 @@ where
         // FIXME: avoid bound checks.
         let col2 = a.column(0);
         let val = unsafe { *x.vget_unchecked(0) };
-        self.axpy(alpha * val, &col2, beta);
+        self.axcpy(alpha, &col2, val, beta);
 
         for j in 1..ncols2 {
             let col2 = a.column(j);
             let val = unsafe { *x.vget_unchecked(j) };
 
-            self.axpy(alpha * val, &col2, N::one());
+            self.axcpy(alpha, &col2, val, N::one());
         }
     }
 

tests/core/blas.rs

@@ -1,5 +1,28 @@
-#![cfg(feature = "arbitrary")]
+use na::{geometry::Quaternion, Matrix2, Vector3};
+use num_traits::{One, Zero};
 
+#[test]
+fn gemm_noncommutative() {
+    type Qf64 = Quaternion<f64>;
+    let i = Qf64::from_imag(Vector3::new(1.0, 0.0, 0.0));
+    let j = Qf64::from_imag(Vector3::new(0.0, 1.0, 0.0));
+    let k = Qf64::from_imag(Vector3::new(0.0, 0.0, 1.0));
+
+    let m1 = Matrix2::new(k, Qf64::zero(), j, i);
+    // this is the inverse of m1
+    let m2 = Matrix2::new(-k, Qf64::zero(), Qf64::one(), -i);
+
+    let mut res: Matrix2<Qf64> = Matrix2::zero();
+    res.gemm(Qf64::one(), &m1, &m2, Qf64::zero());
+    assert_eq!(res, Matrix2::identity());
+
+    let mut res: Matrix2<Qf64> = Matrix2::identity();
+    res.gemm(k, &m1, &m2, -k);
+    assert_eq!(res, Matrix2::zero());
+}
+
+#[cfg(feature = "arbitrary")]
+mod blas_quickcheck {
     use na::{DMatrix, DVector};
     use std::cmp;
 
@@ -103,3 +126,4 @@ quickcheck! {
             relative_eq!(res, expected, epsilon = 1.0e-7)
         }
     }
+}