implement scalar_prod

Author: sebasv

src/numeric/impl_numeric.rs

@@ -6,7 +6,7 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-use std::ops::{Add, Div};
+use std::ops::{Add, Div, Mul};
 use libnum::{self, One, Zero, Float};
 use itertools::free::enumerate;
 
@@ -33,19 +33,45 @@ impl<A, S, D> ArrayBase<S, D>
         where A: Clone + Add<Output=A> + libnum::Zero,
     {
         if let Some(slc) = self.as_slice_memory_order() {
-            return numeric_util::unrolled_sum(slc);
+            return numeric_util::unrolled_fold(slc, A::zero, A::add);
         }
         let mut sum = A::zero();
         for row in self.inner_rows() {
             if let Some(slc) = row.as_slice() {
-                sum = sum + numeric_util::unrolled_sum(slc);
+                sum = sum + numeric_util::unrolled_fold(slc, A::zero, A::add);
             } else {
                 sum = sum + row.iter().fold(A::zero(), |acc, elt| acc + elt.clone());
             }
         }
         sum
     }
 
+    /// Return the product of all elements in the array.
+    ///
+    /// ```
+    /// use ndarray::arr2;
+    ///
+    /// let a = arr2(&[[1., 2.],
+    ///                [3., 4.]]);
+    /// assert_eq!(a.scalar_prod(), 24.);
+    /// ```
+    pub fn scalar_prod(&self) -> A
+        where A: Clone + Mul<Output=A> + libnum::One,
+    {
+        if let Some(slc) = self.as_slice_memory_order() {
+            return numeric_util::unrolled_fold(slc, A::one, A::mul);
+        }
+        let mut sum = A::one();
+        for row in self.inner_rows() {
+            if let Some(slc) = row.as_slice() {
+                sum = sum * numeric_util::unrolled_fold(slc, A::one, A::mul);
+            } else {
+                sum = sum * row.iter().fold(A::one(), |acc, elt| acc * elt.clone());
+            }
+        }
+        sum
+    }
+
     /// Return sum along `axis`.
     ///
     /// ```

src/numeric_util.rs

@@ -5,50 +5,47 @@
 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
-use libnum;
-
 use std::cmp;
-use std::ops::{
-    Add,
-};
 
 use LinalgScalar;
 
-/// Compute the sum of the values in `xs`
-pub fn unrolled_sum<A>(mut xs: &[A]) -> A
-    where A: Clone + Add<Output=A> + libnum::Zero,
+/// Fold over the manually unrolled `xs` with `f`
+pub fn unrolled_fold<A, I, F>(mut xs: &[A], init: I, f: F) -> A
+    where A: Clone,
+    I: Fn() -> A,
+    F: Fn(A, A) -> A,
 {
     // eightfold unrolled so that floating point can be vectorized
     // (even with strict floating point accuracy semantics)
-    let mut sum = A::zero();
+    let mut acc = init();
     let (mut p0, mut p1, mut p2, mut p3,
          mut p4, mut p5, mut p6, mut p7) =
-        (A::zero(), A::zero(), A::zero(), A::zero(),
-         A::zero(), A::zero(), A::zero(), A::zero());
+        (init(), init(), init(), init(),
+         init(), init(), init(), init());
     while xs.len() >= 8 {
-        p0 = p0 + xs[0].clone();
-        p1 = p1 + xs[1].clone();
-        p2 = p2 + xs[2].clone();
-        p3 = p3 + xs[3].clone();
-        p4 = p4 + xs[4].clone();
-        p5 = p5 + xs[5].clone();
-        p6 = p6 + xs[6].clone();
-        p7 = p7 + xs[7].clone();
+        p0 = f(p0, xs[0].clone());
+        p1 = f(p1, xs[1].clone());
+        p2 = f(p2, xs[2].clone());
+        p3 = f(p3, xs[3].clone());
+        p4 = f(p4, xs[4].clone());
+        p5 = f(p5, xs[5].clone());
+        p6 = f(p6, xs[6].clone());
+        p7 = f(p7, xs[7].clone());
 
         xs = &xs[8..];
     }
-    sum = sum.clone() + (p0 + p4);
-    sum = sum.clone() + (p1 + p5);
-    sum = sum.clone() + (p2 + p6);
-    sum = sum.clone() + (p3 + p7);
+    acc = f(acc.clone(), f(p0, p4));
+    acc = f(acc.clone(), f(p1, p5));
+    acc = f(acc.clone(), f(p2, p6));
+    acc = f(acc.clone(), f(p3, p7));
 
     // make it clear to the optimizer that this loop is short
     // and can not be autovectorized.
     for i in 0..xs.len() {
         if i >= 7 { break; }
-        sum = sum.clone() + xs[i].clone()
+        acc = f(acc.clone(), xs[i].clone())
     }
-    sum
+    acc
 }
 
 /// Compute the dot product.

tests/oper.rs

@@ -271,6 +271,26 @@ fn fold_and_sum() {
     }
 }
 
+#[test]
+fn scalar_prod() {
+    let a = Array::linspace(0.5, 2., 128).into_shape((8, 16)).unwrap();
+    assert_approx_eq(a.fold(1., |acc, &x| acc * x), a.scalar_prod(), 1e-5);
+
+    // test different strides
+    let max = 8 as Ixs;
+    for i in 1..max {
+        for j in 1..max {
+            let a1 = a.slice(s![..;i, ..;j]);
+            let mut prod = 1.;
+            for elt in a1.iter() {
+                prod *= *elt;
+            }
+            assert_approx_eq(a1.fold(1., |acc, &x| acc * x), prod, 1e-5);
+            assert_approx_eq(prod, a1.scalar_prod(), 1e-5);
+        }
+    }
+}
+
 fn range_mat(m: Ix, n: Ix) -> Array2<f32> {
     Array::linspace(0., (m * n) as f32 - 1., m * n).into_shape((m, n)).unwrap()
 }