Diagonalize a vector

Question

Diagonalize a vector into a matrix.

Input

A vector, list, array, etc. of integers \$\mathbf{v}\$ of length \$n\$.

Output

A \$n \times n\$ matrix, 2D array, etc. \$A\$ such that for each element \$a_i \in \mathbf{v}\$,

$$ A = \left( \begin{array}{ccc} a_1 & 0 & \cdots & 0 \\ 0 & a_2 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & a_n \end{array} \right) $$

where the diagonal of \$A\$ is each element in \$\mathbf{v}\$.

Notes

• This is code-golf, so shortest program or function in bytes wins!
• Construct the Identity Matrix may be of use to you.
• If the length of \$\mathbf{v}\$ is 0, you may return an empty vector, or an empty matrix.
• If the length of \$\mathbf{v}\$ is 1, you must return a \$1 \times 1\$ matrix.

Not Bonus

You can receive this Not Bonus if your program is generic across any type, using the type's zero-value (if it exists) in place of \$0\$.

Test Cases

[] -> []
[0] -> [[0]]
[1] -> [[1]]
[1, 2, 3] -> [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
[1, 0, 2, 3] -> [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]
[1, -9, 1, 3, 4, -4, -5, 6, 9, -10] -> [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]

Answer 1

Racket, 97 bytes; Not Bonus

(define(f v)(let([n(length v)])(for/list([i(range n)])(list-set(make-list n 0)i(list-ref v i)))))

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---

Explanation

After reading in the input as a list called v, we obtain the length of v and store it as n.

(define (f v)
  (let ([n (length v)])
    ...))

We then loop through the range \$ 0 \le i < n \$ and for each iteration, we return a new list (a row of the matrix) of n length filled with zeros except at the index of i which is filled with the corresponding value from v at index i.

(define (f v)
  (let ([n (length v)])
    (for/list ([i (range n)])
      (list-set (make-list n 0)
                i
                (list-ref v i)))))

The for/list function returns the collected rows after each iteration.

Not Bonus

While the rows start with zeros, any data in v will still be preserved. What this means is that we can pass list of strings to f and receive a matrix with both strings and zeros as the zero-value:

; Strings
(f '("h" "e" "y"))
;;> '(("h" 0 0) (0 "e" 0) (0 0 "y"))

; Symboles
(f '(a b c))
;;> '((a 0 0) (0 b 0) (0 0 c))

; Characters
(f '(#\d #\e #\f))
;;> '((#\d 0 0) (0 #\e 0) (0 0 #\f))

Have a wonderful weekend!

Answer 2

KamilaLisp v0.3, 21 bytes

[* #0[(⌼ =)#0#0]∘⍳∘⍴]

The code generates a range vector from 0 to the size of the argument; then it computes the Cartesian product of the range vector and itself using equality as the functor, therefore computing the identity matrix. Each row of the identity matrix is then multiplied by the initial vector.

Answer 3

Japt, 7 bytes

£çT hYX

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£çT hYX     :Implicit input of array U
£           :Map each X at index Y
 ç          :  Fill U with
  T         :    0
    hYX     :  Replace the element at index Y with X

Answer 4

05AB1E, 5 bytes

āDδQ*

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Explanation:

āDδQ   # Create an identify matrix the size of the input-length:
ā      #  Push a list in the range [1, (implicit) input-length]
 D     #  Duplicate it
  δ    #  Apply double-vectorized:
   Q   #   Check whether the values are equal
    *  # Multiply the values in each row with the values of the (implicit) input-list
       # (after which the matrix is output implicitly as result)

Answer 5

Kotlin, 65 bytes

{a:IntArray->Array(a.size){i->IntArray(a.size).also{it[i]=a[i]}}}

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Answer 6

Pyth, 8 bytes

.eXmZQkb

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Explanation

.eXmZQkbQ    # implicitly add Q
             # implicitly assign Q = eval(input())
.e      Q    # enumerated map Q over lambda, b, k
   mZQ       # list of zeros the same length as Q
  X   kb     # replace position k with b

Answer 7

PowerShell Core, 77 bytes

if($l=($a=$args).count){($k=1..$l)|%{$r++
$c=1
,($k|%{$a[$_-1]*!($c++-$r)})}}

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Answer 8

BQN, 6 bytes

⊢×⍋=⌜⍋

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Explanation

⊢×⍋=⌜⍋
      ⍋  Grade up; for our purposes, gives a list of unique integers of the same
          length as the argument
  ⍋      Grade up again
    =⌜   Create an equality table
         This gives an identity matrix the same size as the length of the argument
⊢×       Multiply each row by the corresponding element of the argument

Answer 9

Scala 3, 70 bytes

x=>x.zipWithIndex.map((e:Int,i:Int)=>Seq.fill(x.size)(0).updated(i,e))

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Answer 10

Python 3.8 (pre-release), 67 bytes

lambda a:[[x*(i==j) for i,x in enumerate(a)]for j in range(len(a))]

A 42-byte solution that only works if all elements are unique:

lambda a:[[x*(x==y) for x in a]for y in a]

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