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Fix multiply-scalar-vector-matrix recipe (#487)

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The original version was incorrect about `ndarray`'s treatment of 1-D
arrays as vectors, and it incorrectly indicated that `*` performed
matrix multiplication.

`ndarray` decides whether a 1-D array is a row vector or column vector
in matrix multiplication by whether it is on the left-hand side or
right-hand side. (The behavior matches NumPy. If it's on the left-hand
side, it's a row vector, while if it's on the right-hand side, it's a
column vector.) The original version incorrectly indicated that
calling `.reversed_axes()` on a 1-D array would make it into a column
vector. In fact, calling `.reversed_axes()` on a 1-D array has no
effect since a 1-D array has only 1 axis.

Matrix multiplication is performed with `.dot()`, not `*`. The `*`
operator performs element-wise multiplication.
This commit is contained in:
Jim Turner 2018-10-11 16:56:32 -04:00 committed by Andrew Gauger
parent cb852c17d8
commit 26744a77b9
1 changed files with 11 additions and 3 deletions
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14
src/science/mathematics/linear_algebra/multiply-scalar-vector-matrix.md
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@ -1,7 +1,15 @@
## Multiply a scalar with a vector with a matrix ## Multiply a scalar with a vector with a matrix
[![ndarray-badge]][ndarray] [![cat-science-badge]][cat-science] [![ndarray-badge]][ndarray] [![cat-science-badge]][cat-science]
Creates a vector with [`ndarray::arr1`] and a matrix with [`ndarray::arr2`]. First, a scalar is multiplied by the vector to get another vector. Then, convert the vector to a column vector with [`ndarray::ArrayBase::reversed_axes`] and multiply the matrix by the column vector to calculate a new matrix. 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
another vector. Then, the matrix is multiplied by the new vector with [`dot`].
([`dot`] performs matrix multiplication, while the `*` operator performs
element-wise multiplication.) In `ndarray`, 1-D arrays can be 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 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 ```rust
extern crate ndarray; extern crate ndarray;
@ -19,11 +27,11 @@ fn main() {
let new_vector: Array1<_> = scalar * vector; let new_vector: Array1<_> = scalar * vector;
println!("{}", new_vector); println!("{}", new_vector);
let new_matrix = matrix * new_vector.reversed_axes(); let new_matrix = matrix.dot(&new_vector);
println!("{}", new_matrix); println!("{}", new_matrix);
} }
``` ```
[`dot`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.dot
[`ndarray::arr1`]: https://docs.rs/ndarray/*/ndarray/fn.arr1.html [`ndarray::arr1`]: https://docs.rs/ndarray/*/ndarray/fn.arr1.html
[`ndarray::arr2`]: https://docs.rs/ndarray/*/ndarray/fn.arr2.html [`ndarray::arr2`]: https://docs.rs/ndarray/*/ndarray/fn.arr2.html
[`ndarray::ArrayBase::reversed_axes`]: https://docs.rs/ndarray/*/ndarray/struct.ArrayBase.html#method.reversed_axes