diff --git a/ndarray-rand/src/lib.rs b/ndarray-rand/src/lib.rs
index 19235237f..63cf1c397 100644
--- a/ndarray-rand/src/lib.rs
+++ b/ndarray-rand/src/lib.rs
@@ -246,7 +246,7 @@ where
         R: Rng + ?Sized,
         Sh: ShapeBuilder<Dim = D>,
     {
-        Self::from_shape_fn(shape, |_| dist.sample(rng))
+        Self::from_shape_simple_fn(shape, move || dist.sample(rng))
     }
 
     fn sample_axis(&self, axis: Axis, n_samples: usize, strategy: SamplingStrategy) -> Array<A, D>
diff --git a/ndarray-rand/tests/tests.rs b/ndarray-rand/tests/tests.rs
index 52de74595..f7860ac12 100644
--- a/ndarray-rand/tests/tests.rs
+++ b/ndarray-rand/tests/tests.rs
@@ -1,6 +1,8 @@
 use ndarray::{Array, Array2, ArrayView1, Axis};
 #[cfg(feature = "quickcheck")]
 use ndarray_rand::rand::{distributions::Distribution, thread_rng};
+
+use ndarray::ShapeBuilder;
 use ndarray_rand::rand_distr::Uniform;
 use ndarray_rand::{RandomExt, SamplingStrategy};
 use quickcheck::quickcheck;
@@ -14,6 +16,21 @@ fn test_dim() {
             assert_eq!(a.shape(), &[m, n]);
             assert!(a.iter().all(|x| *x < 2.));
             assert!(a.iter().all(|x| *x >= 0.));
+            assert!(a.is_standard_layout());
+        }
+    }
+}
+
+#[test]
+fn test_dim_f() {
+    let (mm, nn) = (5, 5);
+    for m in 0..mm {
+        for n in 0..nn {
+            let a = Array::random((m, n).f(), Uniform::new(0., 2.));
+            assert_eq!(a.shape(), &[m, n]);
+            assert!(a.iter().all(|x| *x < 2.));
+            assert!(a.iter().all(|x| *x >= 0.));
+            assert!(a.t().is_standard_layout());
         }
     }
 }
diff --git a/src/impl_constructors.rs b/src/impl_constructors.rs
index 4c35bbfb3..cb39f8e9b 100644
--- a/src/impl_constructors.rs
+++ b/src/impl_constructors.rs
@@ -305,10 +305,28 @@ where
     where
         A: Default,
         Sh: ShapeBuilder<Dim = D>,
+    {
+        Self::from_shape_simple_fn(shape, A::default)
+    }
+
+    /// Create an array with values created by the function `f`.
+    ///
+    /// `f` is called with no argument, and it should return the element to
+    /// create. If the precise index of the element to create is needed,
+    /// use [`from_shape_fn`](ArrayBase::from_shape_fn) instead.
+    ///
+    /// This constructor can be useful if the element order is not important,
+    /// for example if they are identical or random.
+    ///
+    /// **Panics** if the product of non-zero axis lengths overflows `isize`.
+    pub fn from_shape_simple_fn<Sh, F>(shape: Sh, mut f: F) -> Self
+    where
+        Sh: ShapeBuilder<Dim = D>,
+        F: FnMut() -> A,
     {
         let shape = shape.into_shape();
-        let size = size_of_shape_checked_unwrap!(&shape.dim);
-        let v = to_vec((0..size).map(|_| A::default()));
+        let len = size_of_shape_checked_unwrap!(&shape.dim);
+        let v = to_vec_mapped(0..len, move |_| f());
         unsafe { Self::from_shape_vec_unchecked(shape, v) }
     }
 
@@ -318,6 +336,20 @@ where
     /// visited in arbitrary order.
     ///
     /// **Panics** if the product of non-zero axis lengths overflows `isize`.
+    ///
+    /// ```
+    /// use ndarray::{Array, arr2};
+    ///
+    /// // Create a table of i × j (with i and j from 1 to 3)
+    /// let ij_table = Array::from_shape_fn((3, 3), |(i, j)| (1 + i) * (1 + j));
+    ///
+    /// assert_eq!(
+    ///     ij_table,
+    ///     arr2(&[[1, 2, 3],
+    ///            [2, 4, 6],
+    ///            [3, 6, 9]])
+    /// );
+    /// ```
     pub fn from_shape_fn<Sh, F>(shape: Sh, f: F) -> Self
     where
         Sh: ShapeBuilder<Dim = D>,
diff --git a/src/impl_methods.rs b/src/impl_methods.rs
index 5caa11b81..97193de36 100644
--- a/src/impl_methods.rs
+++ b/src/impl_methods.rs
@@ -2187,7 +2187,7 @@ where
         let view_stride = self.strides.axis(axis);
         if view_len == 0 {
             let new_dim = self.dim.remove_axis(axis);
-            Array::from_shape_fn(new_dim, move |_| mapping(ArrayView::from(&[])))
+            Array::from_shape_simple_fn(new_dim, move || mapping(ArrayView::from(&[])))
         } else {
             // use the 0th subview as a map to each 1d array view extended from
             // the 0th element.
@@ -2218,7 +2218,7 @@ where
         let view_stride = self.strides.axis(axis);
         if view_len == 0 {
             let new_dim = self.dim.remove_axis(axis);
-            Array::from_shape_fn(new_dim, move |_| mapping(ArrayViewMut::from(&mut [])))
+            Array::from_shape_simple_fn(new_dim, move || mapping(ArrayViewMut::from(&mut [])))
         } else {
             // use the 0th subview as a map to each 1d array view extended from
             // the 0th element.