89 lines
1.7 KiB
Markdown
89 lines
1.7 KiB
Markdown
|
---
|
||
|
|
id: 5a23c84252665b21eecc7eb1
|
||
|
|
title: Identity matrix
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302290
|
||
|
|
dashedName: identity-matrix
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
An *identity matrix* is a square matrix of size \\( n \\times n \\), where the diagonal elements are all `1`s (ones), and all the other elements are all `0`s (zeroes).
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li style='list-style: none;'>\(\displaystyle I_{n}=\begin{bmatrix} 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr \end{bmatrix}\)</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
# --instructions--
|
||
|
|
|
||
|
|
Write a function that takes a number `n` as a parameter and returns the identity matrix of order \\( n \\times n \\).
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`idMatrix` should be a function.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert(typeof idMatrix == 'function');
|
||
|
|
```
|
||
|
|
|
||
|
|
`idMatrix(1)` should return an array.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert(Array.isArray(idMatrix(1)));
|
||
|
|
```
|
||
|
|
|
||
|
|
`idMatrix(1)` should return `[ [ 1 ] ]`.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.deepEqual(idMatrix(1), results[0]);
|
||
|
|
```
|
||
|
|
|
||
|
|
`idMatrix(2)` should return `[ [ 1, 0 ], [ 0, 1 ] ]`.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.deepEqual(idMatrix(2), results[1]);
|
||
|
|
```
|
||
|
|
|
||
|
|
`idMatrix(3)` should return `[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ]`.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.deepEqual(idMatrix(3), results[2]);
|
||
|
|
```
|
||
|
|
|
||
|
|
`idMatrix(4)` should return `[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]`.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.deepEqual(idMatrix(4), results[3]);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --after-user-code--
|
||
|
|
|
||
|
|
```js
|
||
|
|
let results=[[ [ 1 ] ],
|
||
|
|
[ [ 1, 0 ], [ 0, 1 ] ],
|
||
|
|
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ],
|
||
|
|
[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]]
|
||
|
|
```
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function idMatrix(n) {
|
||
|
|
|
||
|
|
}
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function idMatrix(n) {
|
||
|
|
return Array.apply(null, new Array(n)).map(function (x, i, xs) {
|
||
|
|
return xs.map(function (_, k) {
|
||
|
|
return i === k ? 1 : 0;
|
||
|
|
})
|
||
|
|
});
|
||
|
|
}
|
||
|
|
```
|