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matrix_identity.md

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Creating an Identity Matrix

Summary

Identity Matrix
APL ∘.=⍨⍳
Kap =⌻⍨⍳
TinyAPL =⊞⍨⍤⍳
J e.@i.
BQN =⌜˜↕
Uiua ⊞=.⇡
Q {(til x) =/: (til x)}
Julia ⬇️⬇️
MATLAB eye(n)
NumPy np.identity(n, int)
np.equal.outer(np.arange(n), np.arange(n)).astype(int)
R diag(n)
outer(1:n, 1:n, "==")
Nial ⬇️⬇️
Futhark ⬇️⬇️
Ivy (iota n) o.== iota n
SaC ⬇️⬇️
ArrayFire identity(dim4(n, n), s32)
MatX ⬇️

APL

      Identity ← ∘.=⍨⍳

      ⍝ Example usage
      Identity 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

J

Essay on Identity Matrix in J

   Identity =. e.@i. 
   Identity =. =/~@i. NB. This one is for comparison with APL & BQN

   NB. Example usage
   Identity 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

BQN

   Identity ← =⌜˜↕

   # Example Usage
   Identity 5
┌─           
╵ 1 0 0 0 0  
  0 1 0 0 0  
  0 0 1 0 0  
  0 0 0 1 0  
  0 0 0 0 1  
            ┘

Uiua

   Identity ← ⊞=.⇡

   # Example Usage
   Identity 5
┌─           
╵ 1 0 0 0 0  
  0 1 0 0 0  
  0 0 1 0 0  
  0 0 0 1 0  
  0 0 0 0 1  
            ┘

Q

identity: {(til x) =/: (til x)}

/ Example usage
identity 5
10000b
01000b
00100b
00010b
00001b

Julia

function identity(n)
    Int.(1:n .== (1:n) |> transpose)
end

# Example usage (in REPL)
julia> identity(5)
5×5 Array{Int32,2}:
 1  0  0  0  0
 0  1  0  0  0
 0  0  1  0  0
 0  0  0  1  0
 0  0  0  0  1

MATB

>> eye(5)

ans =

     1     0     0     0     0
     0     1     0     0     0
     0     0     1     0     0
     0     0     0     1     0
     0     0     0     0     1

NumPy

import numpy as np # just use np.identity

# Example usage (in ipython)
In : np.identity(5, int)
Out: 
array([[1, 0, 0, 0, 0],
       [0, 1, 0, 0, 0],
       [0, 0, 1, 0, 0],
       [0, 0, 0, 1, 0],
       [0, 0, 0, 0, 1]])

R

# Example usage (in REPL)
> diag(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    0    0    0    0
[2,]    0    1    0    0    0
[3,]    0    0    1    0    0
[4,]    0    0    0    1    0
[5,]    0    0    0    0    1

Nial

identity is op n {
    (count n) OUTER = count n
}

% Example usage ;
     identity(5)
loooo
olooo
ooloo
ooolo
ooool

Futhark

Outer product in Futhark.

def outer_prod op A B = map (\a -> map (\b -> a `op` b) B) A
def identity n = outer_product (==) (iota n) (iota n)

-- Example usage
> identity 5
[[1i32, 0i32, 0i32, 0i32, 0i32],
 [0i32, 1i32, 0i32, 0i32, 0i32],
 [0i32, 0i32, 1i32, 0i32, 0i32],
 [0i32, 0i32, 0i32, 1i32, 0i32],
 [0i32, 0i32, 0i32, 0i32, 1i32]]

Ivy

(iota 5) o.== iota 5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

SaC

use StdIO: all;
use Array: all;

int[.,.] identity(int n) {
    arr = genarray([5, 5], 1);
    return {[i,j] -> where(i == j, arr[[i,j]], 0)};
}

int main() {
    print(identity(5));
    return 0;
}

// Outputs
Dimension:  2
Shape    : <  5,  5>
| 1  0  0  0  0 | 
| 0  1  0  0  0 | 
| 0  0  1  0  0 | 
| 0  0  0  1  0 | 
| 0  0  0  0  1 |

ArrayFire

#include <arrayfire.h>

auto main() -> int {
  af::array const arr = af::identity(af::dim4(4, 4), s32);
  af::print("Identity Matrix", arr);
  return 0;
}

// Outputs
Identity Matrix
[4 4 1 1]
         1          0          0          0 
         0          1          0          0 
         0          0          1          0 
         0          0          0          1

MatX

#include <matx.h>

auto main() -> int {
  auto t = matx::make_tensor<int32_t>({3, 3});
  (t = matx::eye(t.Shape())).run();
  t.Print();
  return 0;
}

// Outputs
Tensor{int32_t} Rank: 2, Sizes:[3, 3], Strides:[3,1]
000000: 1 0 0 
000001: 0 1 0 
000002: 0 0 1