Update to ndarray 0.13 (#560)

Cargo.toml

@@ -29,7 +29,7 @@ log4rs = "0.8"
 memmap = "0.7"
 mime = "0.3"
 nalgebra = "0.16.12"
-ndarray = "0.12"
+ndarray = { version = "0.13", features = ["approx"] }
 num = "0.2"
 num_cpus = "1.8"
 percent-encoding = "2.1"

src/science/mathematics/linear_algebra.md

@@ -1,10 +1,10 @@
 # Linear Algebra
 
-{{#include linear_algebra/vector-sum.md}}
-{{#include linear_algebra/vector-norm.md}}
 {{#include linear_algebra/add-matrices.md}}
 {{#include linear_algebra/multiply-matrices.md}}
 {{#include linear_algebra/multiply-scalar-vector-matrix.md}}
+{{#include linear_algebra/vector-comparison.md}}
+{{#include linear_algebra/vector-norm.md}}
 {{#include linear_algebra/invert-matrix.md}}
 
 {{#include ../../links.md}}

src/science/mathematics/linear_algebra/add-matrices.md

@@ -1,7 +1,9 @@
 ## Adding matrices
 [![ndarray-badge]][ndarray] [![cat-science-badge]][cat-science]
 
-Creates two matrices with [`ndarray::arr2`] and adds them together.
+Creates two 2-D matrices with [`ndarray::arr2`] and sums them element-wise.
+
+Note the sum is computed as `let sum = &a + &b`. The `&` operator is used to avoid consuming `a` and `b`, making them available later for display. A new array is created containing their sum.
 
 ```rust
 extern crate ndarray;
@@ -15,7 +17,13 @@ fn main() {
     let b = arr2(&[[6, 5, 4],
                    [3, 2, 1]]);
 
-    println!("Sum: {}", a + b);
+    let sum = &a + &b;
+
+    println!("{}", a);
+    println!("+");
+    println!("{}", b);
+    println!("=");
+    println!("{}", sum);
 }
 ```
 

src/science/mathematics/linear_algebra/multiply-scalar-vector-matrix.md

@@ -2,14 +2,18 @@
 [![ndarray-badge]][ndarray] [![cat-science-badge]][cat-science]
 
 Creates a 1-D array (vector) with [`ndarray::arr1`] and a 2-D array (matrix)
-with [`ndarray::arr2`]. First, a scalar is multiplied by the vector to get
+with [`ndarray::arr2`].
+
+First, a scalar is multiplied by the vector to get
 another vector. Then, the matrix is multiplied by the new vector with
-[`ndarray::Array2::dot`]. (`dot` performs matrix multiplication, while the `*`
+[`ndarray::Array2::dot`]. (Matrix multiplication is performed using `dot`, while 
-operator performs element-wise multiplication.) In `ndarray`, 1-D arrays can be
+the `*` operator performs element-wise multiplication.)
-interpreted as either row or column vectors depending on context. If
+
-representing the orientation of a vector is important, a 2-D array with one row
+In `ndarray`, 1-D arrays can be interpreted as either row or column vectors 
-or one column must be used instead. In this example, the vector is a 1-D array
+depending on context. If representing the orientation of a vector is important, 
-on the right-hand side, so `dot` handles it as a column vector.
+a 2-D array with one row or one column must be used instead. In this example, 
+the vector is a 1-D array on the right-hand side, so `dot` handles it as a column 
+vector.
 
 ```rust
 extern crate ndarray;
@@ -32,6 +36,6 @@ fn main() {
 }
 ```
 
-[`ndarray::Array2::dot`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.dot-1
 [`ndarray::arr1`]: https://docs.rs/ndarray/*/ndarray/fn.arr1.html
 [`ndarray::arr2`]: https://docs.rs/ndarray/*/ndarray/fn.arr2.html
+[`ndarray::Array2::dot`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.dot-1

src/science/mathematics/linear_algebra/vector-comparison.md

@@ -0,0 +1,50 @@
+## Vector comparison
+[![ndarray-badge]][ndarray]
+
+The [ndarray] crate supports a number of ways to create arrays -- this recipe creates 
+[`ndarray::Array`]s from `std::Vec` using `from`. Then, it sums the arrays element-wise.
+
+This recipe contains an example of comparing two floating-point vectors element-wise. 
+Floating-point numbers are often stored inexactly, making exact comparisons difficult. 
+However, the [`assert_abs_diff_eq!`] macro from the [`approx`] crate allows for convenient 
+element-wise comparisons. To use the `approx` crate with `ndarray`, the `approx` 
+feature must be added to the `ndarray` dependency in `Cargo.toml`. For example, 
+`ndarray = { version = "0.13", features = ["approx"] }`.
+
+This recipe also contains additional ownership examples. Here, `let z = a + b` consumes 
+`a` and `b`, updates `a` with the result, then moves ownership to `z`. Alternatively, 
+`let w = &c + &d` creates a new vector without consuming `c` or `d`, allowing 
+their modification later. See [Binary Operators With Two Arrays] for additional detail.
+
+```rust
+#[macro_use(assert_abs_diff_eq)]
+extern crate approx;
+extern crate ndarray;
+
+use ndarray::Array;
+
+fn main() {
+  let a = Array::from(vec![1., 2., 3., 4., 5.]);
+  let b = Array::from(vec![5., 4., 3., 2., 1.]);
+  let mut c = Array::from(vec![1., 2., 3., 4., 5.]);
+  let mut d = Array::from(vec![5., 4., 3., 2., 1.]);
+
+  let z = a + b;
+  let w =  &c + &d;
+
+  assert_abs_diff_eq!(z, Array::from(vec![6., 6., 6., 6., 6.]));
+
+  println!("c = {}", c);
+  c[0] = 10.;
+  d[1] = 10.;
+
+  assert_abs_diff_eq!(w, Array::from(vec![6., 6., 6., 6., 6.]));
+
+}
+```
+
+[`approx`]: https://docs.rs/approx/*/approx/index.html
+[`assert_abs_diff_eq!`]: https://docs.rs/approx/*/approx/macro.assert_abs_diff_eq.html
+[Binary Operators With Two Arrays]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#binary-operators-with-two-arrays
+[ndarray]: https://docs.rs/crate/ndarray/*
+[`ndarray::Array`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html

src/science/mathematics/linear_algebra/vector-norm.md

@@ -1,26 +1,30 @@
-## Vector Norm
+## Vector norm
 [![ndarray-badge]][ndarray]
 
 This recipe demonstrates use of the [`Array1`] type, [`ArrayView1`] type,
 [`fold`] method, and [`dot`] method in computing the [l1] and [l2] norms of a
-given vector. The l2 norm calculation is the simpler of the two, as it is the
+given vector. 
-square root of the dot product of a vector with itself, shown in the function
++ The `l2_norm` function is the simpler of the two, as it computes the
-`l2_norm`. The l1 norm, shown in the function `l1_norm`, is computed by a `fold`
+square root of the dot product of a vector with itself.
++ The `l1_norm` function is computed by a `fold`
 operation that sums the absolute values of the elements. (This could also be
 performed with `x.mapv(f64::abs).scalar_sum()`, but that would allocate a new
 array for the result of the `mapv`.)
 
 Note that both `l1_norm` and `l2_norm` take the [`ArrayView1`] type. This recipe
-considers vector norms, so the norm functions only need to accept one
+considers vector norms, so the norm functions only need to accept one-dimensional 
-dimensional views (hence [`ArrayView1`]). While the functions could take a
+views (hence [`ArrayView1`]). While the functions could take a
 parameter of type `&Array1<f64>` instead, that would require the caller to have
 a reference to an owned array, which is more restrictive than just having access
 to a view (since a view can be created from any array or view, not just an owned
-array). The most convenient argument type for the caller would be
+array).
-`&ArrayBase<S, Ix1> where S: Data`, because then the caller could use `&array`
+
-or `&view` instead of `x.view()`. If the function is part of your public API,
+`Array` and `ArrayView` are both type aliases for `ArrayBase`. So, the most 
-that may be a better choice for the benefit of your users, but for internal
+general argument type for the caller would be `&ArrayBase<S, Ix1> where S: Data`, 
-functions, the more concise `ArrayView1<f64>` may be preferable.
+because then the caller could use `&array` or `&view` instead of `x.view()`. 
+If the function is part of a public API, that may be a better choice for the 
+benefit of users. For internal functions, the more concise `ArrayView1<f64>` 
+may be preferable.
 
 ```rust
 #[macro_use(array)]
@@ -50,9 +54,9 @@ fn main() {
 }
 ```
 
-[l1]: http://mathworld.wolfram.com/L1-Norm.html
-[l2]: http://mathworld.wolfram.com/L2-Norm.html
 [`Array1`]: https://docs.rs/ndarray/*/ndarray/type.Array1.html
 [`ArrayView1`]: https://docs.rs/ndarray/*/ndarray/type.ArrayView1.html
 [`dot`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.dot
 [`fold`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.fold
+[l1]: http://mathworld.wolfram.com/L1-Norm.html
+[l2]: http://mathworld.wolfram.com/L2-Norm.html

src/science/mathematics/linear_algebra/vector-sum.md

@@ -1,51 +0,0 @@
-## Vector Sum
-[![ndarray-badge]][ndarray]
-
-The [ndarray] crate supports a number of ways to create arrays -- this recipe
-focuses on creating [`ndarray::Array`]s from `std::Vec` via [`from_vec`]. Adding two
-arrays together is no different than adding two numbers together. Using the `&`
-operand on the arrays within an arithmetic operation prevents the operation from
-consuming the arrays. Without `&`, the arrays are consumed.
-
-In the first example, arrays `a` and `b` are moved in the let-statement `z = a +
-b`. In the second example, the arrays `c` and `d` are not moved and instead, a
-new array is created for `w`. Updating either of `c` or `d` after the vector sum
-has no effect the value of `w`. Additionally, while printing `c` works as
-expected, it would be an error to print `b` due to the move. See [Binary
-Operators With Two Arrays] for additional detail.
-
-```rust
-extern crate ndarray;
-use ndarray::Array;
-
-fn main() {
-  let a = Array::from_vec(vec![1., 2., 3., 4., 5.]);
-  let b = Array::from_vec(vec![5., 4., 3., 2., 1.]);
-  let mut c = Array::from_vec(vec![1., 2., 3., 4., 5.]);
-  let mut d = Array::from_vec(vec![5., 4., 3., 2., 1.]);
-
-  let z = a + b;
-  let w =  &c + &d;
-
-  let epsilon = 1e-8;
-  for elem in z.iter() {
-    let diff: f32 = *elem - 6.;
-    assert!(diff.abs() < epsilon);
-  }
-
-  println!("c = {}", c);
-  c[0] = 10.;
-  d[1] = 10.;
-
-  for elem in w.iter() {
-    let diff: f32 = *elem - 6.;
-    assert!(diff.abs() < epsilon);
-  }
-
-}
-```
-
-[Binary Operators With Two Arrays]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#binary-operators-with-two-arrays
-[`from_vec`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.from_vec
-[ndarray]: https://docs.rs/crate/ndarray/*
-[`ndarray::Array`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html