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# Identity matrix

Identity matrix
You are encouraged to solve this task according to the task description, using any language you may know.

Build an   identity matrix   of a size known at run-time.

An identity matrix is a square matrix of size n × n,
where the diagonal elements are all 1s (ones),
and all the other elements are all 0s (zeroes).

${\displaystyle I_{n}={\begin{bmatrix}1&0&0&\cdots &0\\0&1&0&\cdots &0\\0&0&1&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\cdots &1\\\end{bmatrix}}}$

## 11l

Translation of: Python
F identity_matrix(size)
V matrix = [[0] * size] * size
L(i) 0 .< size
matrix[i][i] = 1
R matrix

L(row) identity_matrix(3)
print(row)
Output:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]

## 360 Assembly

*        Identity matrix           31/03/2017
INDENMAT CSECT
USING INDENMAT,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
L R1,N n
MH R1,N+2 n*n
SLA R1,2 *4
ST R1,LL amount of storage required
GETMAIN RU,LV=(R1) allocate storage for matrix
LA R6,1 i=1
DO WHILE=(C,R6,LE,N) do i=1 to n
LA R7,1 j=1
DO WHILE=(C,R7,LE,N) do j=1 to n
IF CR,R6,EQ,R7 THEN if i=j then
LA R2,1 k=1
ELSE , else
LA R2,0 k=0
ENDIF , endif
LR R1,R6 i
BCTR R1,0 -1
MH R1,N+2 *n
AR R1,R7 (i-1)*n+j
BCTR R1,0 -1
SLA R1,2 *4
ST R2,A(R1) a(i,j)=k
LA R7,1(R7) j++
ENDDO , enddo j
LA R6,1(R6) i++
ENDDO , enddo i
LA R6,1 i=1
DO WHILE=(C,R6,LE,N) do i=1 to n
LA R10,PG pgi=0
LA R7,1 j=1
DO WHILE=(C,R7,LE,N) do j=1 to n
LR R1,R6 i
BCTR R1,0 -1
MH R1,N+2 *n
AR R1,R7 (i-1)*n+j
BCTR R1,0 -1
SLA R1,2 *4
L R2,A(R1) a(i,j)
XDECO R2,XDEC edit
MVC 0(1,R10),XDEC+11 output
LA R10,1(R10) pgi+=1
LA R7,1(R7) j++
ENDDO , enddo j
XPRNT PG,L'PG print
LA R6,1(R6) i++
ENDDO , enddo i
LA R2,LL amount of storage to free
FREEMAIN A=(R1),LV=(R2) free allocated storage
DROP R11 drop register
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
NN EQU 10 parameter n (90=>32K)
N DC A(NN) n
LL DS F n*n*4
PG DC CL(NN)' ' buffer
XDEC DS CL12 temp
DYNA DSECT
A DS F a(n,n)
YREGS
END INDENMAT
Output:
1000000000
0100000000
0010000000
0001000000
0000100000
0000010000
0000001000
0000000100
0000000010
0000000001

When using floating point matrices in Ada 2005+ the function is defined as "Unit_Matrix" in Ada.Numerics.Generic_Real_Arrays. As a generic package it can work with user defined floating point types, or the predefined Short_Real_Arrays, Real_Arrays, and Long_Real_Arrays initializations. As seen below, the first indices of both dimensions can also be set since Ada array indices do not arbitrarily begin with a particular number.

--  As prototyped in the Generic_Real_Arrays specification:
-- function Unit_Matrix (Order : Positive; First_1, First_2 : Integer := 1) return Real_Matrix;
mat : Real_Matrix := Unit_Matrix(5);

For prior versions of Ada, or non floating point types its back to basics:

type Matrix is array(Positive Range <>, Positive Range <>) of Integer;
mat : Matrix(1..5,1..5) := (others => (others => 0));
-- then after the declarative section:
for i in mat'Range(1) loop mat(i,i) := 1; end loop;

## ALGOL 68

Works with: ALGOL 68 version Revision 1 - one extension to language used - PRAGMA READ - a non standard feature similar to C's #include directive.
Works with: ALGOL 68G version Any - tested with release algol68g-2.8.

Note: The generic vector and matrix code should be moved to a more generic page.

File: prelude/vector_base.a68
#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #

# Define some generic vector initialisation and printing operations #

COMMENT REQUIRES:
MODE SCAL = ~ # a scalar, eg REAL #;
FORMAT scal fmt := ~;
END COMMENT

INT vec lwb := 1, vec upb := 0;
MODE VECNEW = [vec lwb:vec upb]SCAL; MODE VEC = REF VECNEW;
FORMAT vec fmt := $"("n(vec upb-vec lwb)(f(scal fmt)", ")f(scal fmt)")"$;

PRIO INIT = 1;

OP INIT = (VEC self, SCAL scal)VEC: (
FOR col FROM LWB self TO UPB self DO self[col]:= scal OD;
self
);

# ZEROINIT: defines the additive identity #
OP ZEROINIT = (VEC self)VEC:
self INIT SCAL(0);

OP REPR = (VEC self)STRING: (
FILE f; STRING s; associate(f,s);
vec lwb := LWB self; vec upb := UPB self;
putf(f, (vec fmt, self)); close(f);
s
);

SKIP
File: prelude/matrix_base.a68
# -*- coding: utf-8 -*- #

# Define some generic matrix initialisation and printing operations #

COMMENT REQUIRES:
MODE SCAL = ~ # a scalar, eg REAL #;
MODE VEC = []SCAL;
FORMAT scal fmt := ~;
et al.
END COMMENT

INT mat lwb := 1, mat upb := 0;
MODE MATNEW = [mat lwb:mat upb, vec lwb: vec upb]SCAL; MODE MAT = REF MATNEW;
FORMAT mat fmt = $"("n(vec upb-vec lwb)(f(vec fmt)","lx)f(vec fmt)")"l$;

PRIO DIAGINIT = 1;

OP INIT = (MAT self, SCAL scal)MAT: (
FOR row FROM LWB self TO UPB self DO self[row,] INIT scal OD;
self
);

# ZEROINIT: defines the additive identity #
OP ZEROINIT = (MAT self)MAT:
self INIT SCAL(0);

OP REPR = (MATNEW self)STRING: (
FILE f; STRING s; associate(f,s);
vec lwb := 2 LWB self; vec upb := 2 UPB self;
mat lwb := LWB self; mat upb := UPB self;
putf(f, (mat fmt, self)); close(f);
s
);

OP DIAGINIT = (MAT self, VEC diag)MAT: (
ZEROINIT self;
FOR d FROM LWB diag TO UPB diag DO self[d,d]:= diag[d] OD;
# or alternatively using TORRIX ...
DIAG self := diag;
#

self
);

# ONEINIT: defines the multiplicative identity #
OP ONEINIT = (MAT self)MAT: (
ZEROINIT self DIAGINIT (LOC[LWB self:UPB self]SCAL INIT SCAL(1))
# or alternatively using TORRIX ...
(DIAG out) VECINIT SCAL(1)
#

);

SKIP
File: prelude/matrix_ident.a68
# -*- coding: utf-8 -*- #

PRIO IDENT = 9; # The same as I for COMPLex #

OP IDENT = (INT lwb, upb)MATNEW:
ONEINIT LOC [lwb:upb,lwb:upb]SCAL;

OP IDENT = (INT upb)MATNEW: # default lwb is 1 #
1 IDENT upb;

SKIP
File: prelude/matrix.a68
#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #

SKIP
File: test/matrix_ident.a68
#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #

MODE SCAL = REAL;
FORMAT scal fmt := $g(-3,1)$;

print(REPR IDENT 4)
Output:
((1.0, 0.0, 0.0, 0.0),
(0.0, 1.0, 0.0, 0.0),
(0.0, 0.0, 1.0, 0.0),
(0.0, 0.0, 0.0, 1.0))

## ALGOL W

begin
% set m to an identity matrix of size s  %
procedure makeIdentity( real array m ( *, * )
; integer value s
) ;
for i := 1 until s do begin
for j := 1 until s do m( i, j ) := 0.0;
m( i, i ) := 1.0
end makeIdentity ;

% test the makeIdentity procedure  %
begin
real array id5( 1 :: 5, 1 :: 5 );
makeIdentity( id5, 5 );
r_format := "A"; r_w := 6; r_d := 1; % set output format for reals  %
for i := 1 until 5 do begin
write();
for j := 1 until 5 do writeon( id5( i, j ) )
end for_i ;
end text

end.

## APL

Making an identity matrix in APL involves the outer product of the equality function.

For a square matrix of 3:

∘.=⍨⍳3
1 0 0
0 1 0
0 0 1

For a function that makes an identity matrix:

ID←{∘.=⍨⍳⍵}
ID 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

An tacit function can be defined with one of the following equivalent lines:

ID←∘.=⍨⍳
ID←⍳∘.=⍳

There is a more idomatic way however:

ID←{⍵ ⍵ ρ 1, ⍵ρ0}

## AppleScript

--------------------- IDENTITY MATRIX ----------------------

-- identityMatrix :: Int -> [(0|1)]
on identityMatrix(n)
set xs to enumFromTo(1, n)

script row
on |λ|(x)
script col
on |λ|(i)
if i = x then
1
else
0
end if
end |λ|
end script
map(col, xs)
end |λ|
end script

map(row, xs)
end identityMatrix

--------------------------- TEST ---------------------------
on run

unlines(map(showList, ¬
identityMatrix(5)))

end run

-------------------- GENERIC FUNCTIONS ---------------------

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
lst
else
{}
end if
end enumFromTo

-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set s to xs as text
set my text item delimiters to dlm
s
end intercalate

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- showList :: [a] -> String
on showList(xs)
"[" & intercalate(", ", map(my str, xs)) & "]"
end showList

-- str :: a -> String
on str(x)
x as string
end str

-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines
Output:
[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]

## Applesoft BASIC

100 INPUT "MATRIX SIZE:"; SIZE%
110 GOSUB 200"IDENTITYMATRIX
120 FOR R = 0 TO SIZE%
130 FOR C = 0 TO SIZE%
140 LET S$= CHR$(13)
150 IF C < SIZE% THEN S$= " " 160 PRINT IM(R, C) S$; : NEXT C, R
170 END

200 REMIDENTITYMATRIX SIZE%
210 LET SIZE% = SIZE% - 1
220 DIM IM(SIZE%, SIZE%)
230 FOR I = 0 TO SIZE%
240 LET IM(I, I) = 1 : NEXT I
250 RETURN :IM

## ATS

(* ****** ****** *)
//
// How to compile:
//
// patscc -DATS_MEMALLOC_LIBC -o idmatrix idmatrix.dats
//
(* ****** ****** *)
//
#include
//
(* ****** ****** *)

extern
fun
idmatrix{n:nat}(n: size_t(n)): matrixref(int, n, n)
implement
idmatrix(n) =
matrixref_tabulate_cloref<int> (n, n, lam(i, j) => bool2int0(i = j))

(* ****** ****** *)

implement
main0 () =
{
//
val N = 5
//
val M = idmatrix(i2sz(N))
val () = fprint_matrixref_sep (stdout_ref, M, i2sz(N), i2sz(N), " ", "\n")
val () = fprint_newline (stdout_ref)
//
} (* end of [main0] *)

## AutoHotkey

msgbox % Clipboard := I(6)
return

I(n){
r := "--n" , s := " "
loop % n
{
k := A_index , r .= "| "
loop % n
r .= A_index=k ? "1, " : "0, "
r := RTrim(r, " ,") , r .= " |n"
}
loop % 4*n
s .= " "
return Rtrim(r,"n") "n" s "--"
}
Output:
--
|  1, 0, 0, 0, 0, 0  |
|  0, 1, 0, 0, 0, 0  |
|  0, 0, 1, 0, 0, 0  |
|  0, 0, 0, 1, 0, 0  |
|  0, 0, 0, 0, 1, 0  |
|  0, 0, 0, 0, 0, 1  |
--

## AWK

# syntax: GAWK -f IDENTITY_MATRIX.AWK size
BEGIN {
size = ARGV[1]
if (size !~ /^[0-9]+$/) { print("size invalid or missing from command line") exit(1) } for (i=1; i<=size; i++) { for (j=1; j<=size; j++) { x = (i == j) ? 1 : 0 printf("%2d",x) # print arr[i,j] = x # build } printf("\n") } exit(0) } Output: for command: GAWK -f IDENTITY_MATRIX.AWK 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 ## Bash for i in seq$1;do printf '%*s\n' $1|tr ' ' '0'|sed "s/0/1/$i";done

Output:
for command: ./scriptname 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

## BBC BASIC

INPUT "Enter size of matrix: " size%
PROCidentitymatrix(size%, im())
FOR r% = 0 TO size%-1
FOR c% = 0 TO size%-1
PRINT im(r%, c%),;
NEXT
PRINT
NEXT r%
END

DEF PROCidentitymatrix(s%, RETURN m())
LOCAL i%
DIM m(s%-1, s%-1)
FOR i% = 0 TO s%-1
m(i%,i%) = 1
NEXT
ENDPROC

## Burlesque

Neither very elegant nor short but it'll do

blsq ) 6 -.^^0\/[email protected]\/'0\/.*'1+]\/{\/{rt}\/E!XX}x/+]m[sp
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

The example above uses strings to generate the identity matrix. If you need a matrix with real numbers (Integers) then use:

6hd0bx#a.*\[#a.*0#[email protected]{(D!)\/1\/^^bx\/[+}m[e!

Shorter alternative:

blsq ) 6 ^^^^10\/**XXcy\/co.+sp

## C

#include <stdlib.h>
#include <stdio.h>
int main(int argc, char** argv) {
if (argc < 2) {
printf("usage: identitymatrix <number of rows>\n");
exit(EXIT_FAILURE);
}
signed int rowsize = atoi(argv[1]);
if (rowsize < 0) {
printf("Dimensions of matrix cannot be negative\n");
exit(EXIT_FAILURE);
}
volatile int numElements = rowsize * rowsize;
if (numElements < rowsize) {
printf("Squaring %d caused result to overflow to %d.\n", rowsize, numElements);
abort();
}
int** matrix = calloc(numElements, sizeof(int*));
if (!matrix) {
printf("Failed to allocate %d elements of %d bytes each\n", numElements, sizeof(int*));
abort();
}
for (unsigned int row = 0;row < rowsize;row++) {
matrix[row] = calloc(numElements, sizeof(int));
if (!matrix[row]) {
printf("Failed to allocate %d elements of %d bytes each\n", numElements, sizeof(int));
abort();
}
matrix[row][row] = 1;
}
printf("Matrix is: \n");
for (unsigned int row = 0;row < rowsize;row++) {
for (unsigned int column = 0;column < rowsize;column++) {
printf("%d ", matrix[row][column]);
}
printf("\n");
}
}

## C#

using System;
using System.Linq;

namespace IdentityMatrix
{
class Program
{
static void Main(string[] args)
{
if (args.Length != 1)
{
Console.WriteLine("Requires exactly one argument");
return;
}
int n;
if (!int.TryParse(args[0], out n))
{
Console.WriteLine("Requires integer parameter");
return;
}

var identity =
Enumerable.Range(0, n).Select(i => Enumerable.Repeat(0, n).Select((z,j) => j == i ? 1 : 0).ToList()).ToList();
foreach (var row in identity)
{
foreach (var elem in row)
{
Console.Write(" " + elem);
}
Console.WriteLine();
}
}
}
}

Output:
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

## C++

Library: STL
template<class T>
class matrix
{
public:
matrix( unsigned int nSize ) :
m_oData(nSize * nSize, 0), m_nSize(nSize) {}

inline T& operator()(unsigned int x, unsigned int y)
{
return m_oData[x+m_nSize*y];
}

void identity()
{
int nCount = 0;
int nStride = m_nSize + 1;
std::generate( m_oData.begin(), m_oData.end(),
[&]() { return !(nCount++%nStride); } );
}

inline unsigned int size() { return m_nSize; }

private:
std::vector<T> m_oData;
unsigned int m_nSize;
};

int main()
{
int nSize;
std::cout << "Enter matrix size (N): ";
std::cin >> nSize;

matrix<int> oMatrix( nSize );

oMatrix.identity();

for ( unsigned int y = 0; y < oMatrix.size(); y++ )
{
for ( unsigned int x = 0; x < oMatrix.size(); x++ )
{
std::cout << oMatrix(x,y) << " ";
}
std::cout << std::endl;
}
return 0;
}

Library: boost

#include <boost/numeric/ublas/matrix.hpp>

int main()
{
using namespace boost::numeric::ublas;

int nSize;
std::cout << "Enter matrix size (N): ";
std::cin >> nSize;

identity_matrix<int> oMatrix( nSize );

for ( unsigned int y = 0; y < oMatrix.size2(); y++ )
{
for ( unsigned int x = 0; x < oMatrix.size1(); x++ )
{
std::cout << oMatrix(x,y) << " ";
}
std::cout << std::endl;
}

return 0;
}

Output:
Enter matrix size (N): 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

## Clio

fn identity-matrix n:
[0:n] -> * fn i:
[0:n] -> * if = i: 1
else: 0

5 -> identity-matrix -> * print

## Clojure

Translation of: PicoLisp

The (vec ) function in the following solution is with respect to vector matrices. If dealing with normal lists matrices (e.g.

'( (0 1) (2 3) )

, then care to remove the vec function.

(defn identity-matrix [n]
(let [row (conj (repeat (dec n) 0) 1)]
(vec
(for [i (range 1 (inc n))]
(vec
(reduce conj (drop i row ) (take i row)))))))

Output:
=> (identity-matrix 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]]

The following is a more idomatic definition that utilizes infinite lists and cycling.

(defn identity-matrix [n]
(take n
(partition n (dec n)
(cycle (conj (repeat (dec n) 0) 1)))))

## Common Lisp

Common Lisp provides multi-dimensional arrays.

(defun make-identity-matrix (n)
(let ((array (make-array (list n n) :initial-element 0)))
(loop for i below n do (setf (aref array i i) 1))
array))

Output:
* (make-identity-matrix 5)
#2A((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))
(defun identity-matrix (n)
(loop for a from 1 to n
collect (loop for e from 1 to n
if (= a e) collect 1
else collect 0)))

Output:
> (identity-matrix 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))

## Component Pascal

BlackBox Component Builder

MODULE Algebras;
IMPORT StdLog,Strings;

TYPE
Matrix = POINTER TO ARRAY OF ARRAY OF INTEGER;

PROCEDURE NewIdentityMatrix(n: INTEGER): Matrix;
VAR
m: Matrix;
i: INTEGER;
BEGIN
NEW(m,n,n);
FOR i := 0 TO n - 1 DO
m[i,i] := 1;
END;
RETURN m;
END NewIdentityMatrix;

PROCEDURE Show(m: Matrix);
VAR
i,j: INTEGER;
BEGIN
FOR i := 0 TO LEN(m,0) - 1 DO
FOR j := 0 TO LEN(m,1) - 1 DO
StdLog.Int(m[i,j]);
END;
StdLog.Ln
END
END Show;

PROCEDURE Do*;
BEGIN
Show(NewIdentityMatrix(5));
END Do;
END Algebras.

Execute: ^Q Algebras.Do

Output:
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

## D

import std.traits;

T[][] matId(T)(in size_t n) pure nothrow if (isAssignable!(T, T)) {
auto Id = new T[][](n, n);

foreach (r, row; Id) {
static if (__traits(compiles, {row[] = 0;})) {
row[] = 0; // vector op doesn't work with T = BigInt
row[r] = 1;
} else {
foreach (c; 0 .. n)
row[c] = (c == r) ? 1 : 0;
}
}

return Id;
}

void main() {
import std.stdio, std.bigint;
enum form = "[%([%(%s, %)],\n %)]]";

immutable id1 = matId!real(5);
writefln(form ~ "\n", id1);

immutable id2 = matId!BigInt(3);
writefln(form ~ "\n", id2);

// auto id3 = matId!(const int)(2); // cant't compile
}
Output:
[[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]]

[[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]

## Delphi

program IdentityMatrix;

// Modified from the Pascal version

{$APPTYPE CONSOLE} var matrix: array of array of integer; n, i, j: integer; begin write('Size of matrix: '); readln(n); setlength(matrix, n, n); for i := 0 to n - 1 do matrix[i,i] := 1; for i := 0 to n - 1 do begin for j := 0 to n - 1 do write (matrix[i,j], ' '); writeln; end; end. Output: Size of matrix: 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 ## Eiffel class APPLICATION inherit ARGUMENTS create make feature {NONE} -- Initialization make -- Run application. local dim : INTEGER -- Dimension of the identity matrix do from dim := 1 until dim > 10 loop print_matrix( identity_matrix(dim) ) dim := dim + 1 io.new_line end end feature -- Access identity_matrix(dim : INTEGER) : ARRAY2[REAL_64] require dim > 0 local matrix : ARRAY2[REAL_64] i : INTEGER do create matrix.make_filled (0.0, dim, dim) from i := 1 until i > dim loop matrix.put(1.0, i, i) i := i + 1 end Result := matrix end print_matrix(matrix : ARRAY2[REAL_64]) local i, j : INTEGER do from i := 1 until i > matrix.height loop print("[ ") from j := 1 until j > matrix.width loop print(matrix.item (i, j)) print(" ") j := j + 1 end print("]%N") i := i + 1 end end end Output: [ 1 0 0 0 0 0 0 0 0 0 ] [ 0 1 0 0 0 0 0 0 0 0 ] [ 0 0 1 0 0 0 0 0 0 0 ] [ 0 0 0 1 0 0 0 0 0 0 ] [ 0 0 0 0 1 0 0 0 0 0 ] [ 0 0 0 0 0 1 0 0 0 0 ] [ 0 0 0 0 0 0 1 0 0 0 ] [ 0 0 0 0 0 0 0 1 0 0 ] [ 0 0 0 0 0 0 0 0 1 0 ] [ 0 0 0 0 0 0 0 0 0 1 ] ## Elena ELENA 4.x : import extensions; import system'routines; import system'collections; public program() { var n := console.write:"Enter the matrix size:".readLine().toInt(); var identity := new Range(0, n).selectBy:(i => new Range(0,n).selectBy:(j => (i == j).iif(1,0) ).summarize(new ArrayList())) .summarize(new ArrayList()); identity.forEach: (row) { console.printLine(row.asEnumerable()) } } Output: Enter the matrix size:3 1,0,0 0,1,0 0,0,1 ## Elixir defmodule Matrix do def identity(n) do Enum.map(0..n-1, fn i -> for j <- 0..n-1, do: (if i==j, do: 1, else: 0) end) end end IO.inspect Matrix.identity(5) Output: [[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]] ## Erlang %% Identity Matrix in Erlang for the Rosetta Code Wiki. %% Implemented by Arjun Sunel -module(identity_matrix). -export([square_matrix/2 , identity/1]). square_matrix(Size, Elements) -> [[Elements(Column, Row) || Column <- lists:seq(1, Size)] || Row <- lists:seq(1, Size)]. identity(Size) -> square_matrix(Size, fun(Column, Row) -> case Column of Row -> 1; _ -> 0 end end). ## ERRE PROGRAM IDENTITY !$DYNAMIC
DIM A[0,0]

BEGIN
PRINT(CHR$(12);) ! CLS INPUT("Matrix size",N%) !$DIM A[N%,N%]
FOR I%=1 TO N% DO
A[I%,I%]=1
END FOR
! print matrix
FOR I%=1 TO N% DO
FOR J%=1 TO N% DO
WRITE("###";A[I%,J%];)
END FOR
PRINT
END FOR
END PROGRAM

## Euler Math Toolbox

function IdentityMatrix(n)
$X:=zeros(n,n);$ for i=1 to n
$X[i,i]:=1;$ end;
$return X;$endfunction

>function IdentityMatrix (n:index)
$return setdiag(zeros(n,n),0,1);$endfunction

>id(5)

## F#

Builds a 2D matrix with the given square size.

let ident n = Array2D.init n n (fun i j -> if i = j then 1 else 0)

Output:

ident 10;;
val it : int [,] = [[1; 0; 0; 0; 0; 0; 0; 0; 0; 0]
[0; 1; 0; 0; 0; 0; 0; 0; 0; 0]
[0; 0; 1; 0; 0; 0; 0; 0; 0; 0]
[0; 0; 0; 1; 0; 0; 0; 0; 0; 0]
[0; 0; 0; 0; 1; 0; 0; 0; 0; 0]
[0; 0; 0; 0; 0; 1; 0; 0; 0; 0]
[0; 0; 0; 0; 0; 0; 1; 0; 0; 0]
[0; 0; 0; 0; 0; 0; 0; 1; 0; 0]
[0; 0; 0; 0; 0; 0; 0; 0; 1; 0]
[0; 0; 0; 0; 0; 0; 0; 0; 0; 1]]

## Factor

Works with: Factor version 0.99 2020-07-03
USING: math.matrices prettyprint ;

6 <identity-matrix> .
Output:
{
{ 1 0 0 0 0 0 }
{ 0 1 0 0 0 0 }
{ 0 0 1 0 0 0 }
{ 0 0 0 1 0 0 }
{ 0 0 0 0 1 0 }
{ 0 0 0 0 0 1 }
}

## FBSL

FBSL's BASIC layer can easily manipulate square matrices of arbitrary sizes and data types in ways similar to e.g. BBC BASIC or OxygenBasic as shown elsewhere on this page. But FBSL has also an extremely fast built-in single-precision vector2f/3f/4f, plane4f, quaternion4f, and matrix4f math library totaling 150 functions and targeting primarily 3D rendering tasks:

#APPTYPE CONSOLE

TYPE M4F ' Matrix 4F

m11 AS SINGLE
m12 AS SINGLE
m13 AS SINGLE
m14 AS SINGLE
m21 AS SINGLE
m22 AS SINGLE
m23 AS SINGLE
m24 AS SINGLE
m31 AS SINGLE
m32 AS SINGLE
m33 AS SINGLE
m34 AS SINGLE
m41 AS SINGLE
m42 AS SINGLE
m43 AS SINGLE
m44 AS SINGLE

END TYPE

DIM m AS M4F ' DIM zeros out any variable automatically

PRINT "Matrix 'm' is identity: ", IIF(MATRIXISIDENTITY(@m), "TRUE", "FALSE") ' is matrix an identity?
MATRIXIDENTITY(@m) ' set matrix to identity
PRINT "Matrix 'm' is identity: ", IIF(MATRIXISIDENTITY(@m), "TRUE", "FALSE") ' is matrix an identity?

PAUSE

Output:

Matrix 'm' is identity: FALSE
Matrix 'm' is identity: TRUE

Press any key to continue...

## Forth

Works with: gforth version 0.7.9_20170308
S" fsl-util.fs" REQUIRED

: build-identity ( 'p n -- 'p ) \ make an NxN identity matrix
0 DO
I 1+ 0 DO
I J = IF 1.0E0 DUP I J }} F!
ELSE
0.0E0 DUP J I }} F!
0.0E0 DUP I J }} F!
THEN
LOOP
LOOP ;

6 6 float matrix a{{
a{{ 6 build-identity
6 6 a{{ }}fprint

## Fortran

Works with: Fortran version 95

program identitymatrix

real, dimension(:, :), allocatable :: I
character(len=8) :: fmt
integer :: ms, j

ms = 10 ! the desired size

allocate(I(ms,ms))
I = 0 ! Initialize the array.
forall(j = 1:ms) I(j,j) = 1 ! Set the diagonal.

! I is the identity matrix, let's show it:

write (fmt, '(A,I2,A)') '(', ms, 'F6.2)'
! if you consider to have used the (row, col) convention,
! the following will print the transposed matrix (col, row)
! but I' = I, so it's not important here
write (*, fmt) I(:,:)

deallocate(I)

end program identitymatrix

### Notorious trick

The objective is to do the assignment in one fell swoop, rather than separately setting the 0 values and the 1 values. It works because, with integer arithmetic, the only way that both i/j and j/i are one is when they are equal - thus one on the diagonal elements, and zero elsewhere because either i < j so that i/j = 0, or i > j so that j/i = 0. While this means two divides and a multiply per element instead of simply transferring a constant, the constraint on speed is likely to be the limited bandwidth from cpu to memory. The expression's code would surely fit in the cpu's internal memory, and registers would be used for the variables.

Program Identity
Integer N
Parameter (N = 666)
Real A(N,N)
Integer i,j

ForAll(i = 1:N, j = 1:N) A(i,j) = (i/j)*(j/i)

END

The ForAll statement is a feature of F90, and carries the implication that the assignments may be done in any order, even "simultaneously" (as with multiple cpus), plus that all RHS values are calculated before any LHS part receives a value - not relevant here since the RHS makes no reference to items altered in the LHS. Earlier Fortran compilers lack this statement and so one must use explicit DO-loops:

DO 1 I = 1,N
DO 1 J = 1,N
1 A(I,J) = (I/J)*(J/I)

Array assignment statements are also a feature of F90 and later.

An alternative might be a simpler logical expression testing i = j except that the numerical values for true and false on a particular system may well not be 1 and 0 but (for instance, via Compaq F90/95 on Windows XP) 0 and -1 instead. On an IBM 390 mainframe, pl/i and Fortran used different values. The Burroughs 6700 inspected the low-order bit only, with the intriguing result that odd integers would be deemed true and even false. Integer arithmetic can't be relied upon across languages either, because in pl/i, integer division doesn't truncate.

## FreeBASIC

' FB 1.05.0 Win64

Dim As Integer n

Do
Input "Enter size of matrix "; n
Loop Until n > 0

Dim identity(1 To n, 1 To n) As Integer '' all zero by default

' enter 1s in diagonal elements
For i As Integer = 1 To n
identity(i, i) = 1
Next

' print identity matrix if n < 40
Print

If n < 40 Then
For i As Integer = 1 To n
For j As Integer = 1 To n
Print identity(i, j);
Next j
Print
Next i
Else
Print "Matrix is too big to display on 80 column console"
End If

Print
Print "Press any key to quit"
Sleep

Sample input/output

Output:
Enter size of matrix ? 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

## Frink

This does not use the Matrix.frink library, which has methods to create an identity matrix, but shows how to build a "raw" identity matrix as a two-dimensional array.

n = parseInt[input["Enter matrix dimension as an integer: "]]
println[joinln[makeArray[[n, n], {|a,b| a==b ? 1 : 0}]]]
Output:
Enter matrix dimension as an integer:  3
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]

## FunL

def identity( n ) = vector( n, n, \r, c -> if r == c then 1 else 0 )

println( identity(3) )
Output:
((1, 0, 0), (0, 1, 0), (0, 0, 1))

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

## GAP

# Built-in
IdentityMat(3);

# One can also specify the base ring
IdentityMat(3, Integers mod 10);

## Go

### Library gonum/mat

package main

import (
"fmt"

"gonum.org/v1/gonum/mat"
)

func eye(n int) *mat.Dense {
m := mat.NewDense(n, n, nil)
for i := 0; i < n; i++ {
m.Set(i, i, 1)
}
return m
}

func main() {
fmt.Println(mat.Formatted(eye(3)))
}
Output:
⎡1  0  0⎤
⎢0  1  0⎥
⎣0  0  1⎦

### Library go.matrix

A somewhat earlier matrix library for Go.

package main

import (
"fmt"

mat "github.com/skelterjohn/go.matrix"
)

func main() {
fmt.Println(mat.Eye(3))
}
Output:
{1, 0, 0,
0, 1, 0,
0, 0, 1}

### From scratch

Simplest: A matrix as a slice of slices, allocated separately.

package main

import "fmt"

func main() {
fmt.Println(I(3))
}

func I(n int) [][]float64 {
m := make([][]float64, n)
for i := 0; i < n; i++ {
a := make([]float64, n)
a[i] = 1
m[i] = a
}
return m
}
Output:

No special formatting method used.

[[1 0 0] [0 1 0] [0 0 1]]

2D, resliced: Representation as a slice of slices still, but with all elements based on single underlying slice. Might save a little memory management, might have a little better locality.

package main

import "fmt"

func main() {
fmt.Println(I(3))
}

func I(n int) [][]float64 {
m := make([][]float64, n)
a := make([]float64, n*n)
for i := 0; i < n; i++ {
a[i] = 1
m[i] = a[:n]
a = a[n:]
}
return m
}
Output:

Same as previous.

Flat: Representation as a single flat slice. You just have to know to handle it as a square matrix. In many cases that's not a problem and the code is simpler this way. If you want to add a little bit of type checking, you can define a matrix type as shown here.

package main

import "fmt"

type matrix []float64

func main() {
n := 3
m := I(n)
// dump flat represenation
fmt.Println(m)

// function x turns a row and column into an index into the
// flat representation.
x := func(r, c int) int { return r*n + c }

// access m by row and column.
for r := 0; r < n; r++ {
for c := 0; c < n; c++ {
fmt.Print(m[x(r, c)], " ")
}
fmt.Println()
}
}

func I(n int) matrix {
m := make(matrix, n*n)
// a fast way to initialize the flat representation
n++
for i := 0; i < len(m); i += n {
m[i] = 1
}
return m
}
Output:
[1 0 0 0 1 0 0 0 1]
1 0 0
0 1 0
0 0 1

## Groovy

Solution:

def makeIdentityMatrix = { n ->
(0..<n).collect { i -> (0..<n).collect { j -> (i == j) ? 1 : 0 } }
}

Test:

(2..6).each { order ->
def iMatrix = makeIdentityMatrix(order)
iMatrix.each { println it }
println()
}
Output:
[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]

[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]

[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]

| reduce range(0;n) as $i ([]; . + [$row | .[$i] = 1 ] ); Example: identity(4) produces: [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] ### Using matrix/2 Using the definition of matrix/2 at Create_a_two-dimensional_array_at_runtime#jq: def identity(n): reduce range(0;n) as$i
(0 | matrix(n;n); .[$i][$i] = 1);

## Jsish

/* Identity matrix, in Jsish */
function identityMatrix(n) {
var mat = new Array(n).fill(0);
for (var r in mat) {
mat[r] = new Array(n).fill(0);
mat[r][r] = 1;
}
return mat;
}

provide('identityMatrix', 1);

if (Interp.conf('unitTest')) {
; identityMatrix(0);
; identityMatrix(1);
; identityMatrix(2);
; identityMatrix(3);
var mat = identityMatrix(4);
for (var r in mat) puts(mat[r]);
}

/*
=!EXPECTSTART!=
identityMatrix(0) ==> []
identityMatrix(1) ==> [ [ 1 ] ]
identityMatrix(2) ==> [ [ 1, 0 ], [ 0, 1 ] ]
identityMatrix(3) ==> [ [ 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 ]
=!EXPECTEND!=
*/
Output:
promt$jsish -u identityMatrix.jsi [PASS] identityMatrix.jsi ## Julia The I function takes an integer argument and returns a square identity matrix of that size. using LinearAlgebra I(3) This returns: 3x3 Float64 Array: 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 If you want to take the size from the commandline: I(parse(Int, readline(stdin))) ## K =4 (1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1) =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) ## Kotlin // version 1.0.6 fun main(args: Array<String>) { print("Enter size of matrix : ") val n = readLine()!!.toInt() println() val identity = Array(n) { IntArray(n) } // create n x n matrix of integers // enter 1s in diagonal elements for(i in 0 until n) identity[i][i] = 1 // print identity matrix if n <= 40 if (n <= 40) for (i in 0 until n) println(identity[i].joinToString(" ")) else println("Matrix is too big to display on 80 column console") } Sample input/output Output: Enter size of matrix : 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 ## Lang5 : identity-matrix dup iota 'A set : i.(*) A in ; [1] swap append reverse A swap reshape 'i. apply ; 5 identity-matrix . Output: [ [ 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 ] ] ## LFE (defun identity ((`(,m ,n)) (identity m n)) ((m) (identity m m))) (defun identity (m n) (lists:duplicate m (lists:duplicate n 1))) From the LFE REPL; note that the last two usage examples demonstrate how identify could be used when composed with functions that get the dimension of a matrix: > (identity 3) ((1 1 1) (1 1 1) (1 1 1)) > (identity 3 3) ((1 1 1) (1 1 1) (1 1 1)) > (identity '(3 3)) ((1 1 1) (1 1 1) (1 1 1)) ## LSL To test it yourself; rez a box on the ground, and add the following as a New Script. default { state_entry() { llListen(PUBLIC_CHANNEL, "", llGetOwner(), ""); llOwnerSay("Please Enter a Dimension for an Identity Matrix."); } listen(integer iChannel, string sName, key kId, string sMessage) { llOwnerSay("You entered "+sMessage+"."); list lMatrix = []; integer x = 0; integer n = (integer)sMessage; for(x=0 ; x<n*n ; x++) { lMatrix += [(integer)(((x+1)%(n+1))==1)]; } //llOwnerSay("["+llList2CSV(lMatrix)+"]"); for(x=0 ; x<n ; x++) { llOwnerSay("["+llList2CSV(llList2ListStrided(lMatrix, x*n, (x+1)*n-1, 1))+"]"); } } } Output: You: 0 Identity_Matrix: You entered 0. You: 1 Identity_Matrix: You entered 1. Identity_Matrix: [1] You: 3 Identity_Matrix: You entered 3. Identity_Matrix: [1, 0, 0] Identity_Matrix: [0, 1, 0] Identity_Matrix: [0, 0, 1] You: 5 Identity_Matrix: You entered 5. Identity_Matrix: [1, 0, 0, 0, 0] Identity_Matrix: [0, 1, 0, 0, 0] Identity_Matrix: [0, 0, 1, 0, 0] Identity_Matrix: [0, 0, 0, 1, 0] Identity_Matrix: [0, 0, 0, 0, 1] ## Lua function identity_matrix (size) local m = {} for i = 1, size do m[i] = {} for j = 1, size do m[i][j] = i == j and 1 or 0 end end return m end function print_matrix (m) for i = 1, #m do print(table.concat(m[i], " ")) end end print_matrix(identity_matrix(5)) Output: 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 ## Maple One of a number of ways to do this: > LinearAlgebra:-IdentityMatrix( 4 ); [1 0 0 0] [ ] [0 1 0 0] [ ] [0 0 1 0] [ ] [0 0 0 1] Here, for instance, is another, in which the entries are (4-byte) floats. > Matrix( 4, shape = scalar[1], datatype = float[4] ); [1. 0. 0. 0.] [ ] [0. 1. 0. 0.] [ ] [0. 0. 1. 0.] [ ] [0. 0. 0. 1.] Yet another, with 2-byte integer entries: > Matrix( 4, shape = identity, datatype = integer[ 2 ] ); [1 0 0 0] [ ] [0 1 0 0] [ ] [0 0 1 0] [ ] [0 0 0 1] ## MathCortex I = eye(10) ## Mathematica / Wolfram Language IdentityMatrix[4] ## MATLAB / Octave The eye function create the identity (I) matrix, e.g.: I = eye(10) ## Maxima ident(4); /* matrix([1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]) */ ## NetRexx ### Using int Array Translation of: REXX /* NetRexx ************************************************************ * show identity matrix of size n * I consider m[i,j] to represent the matrix * 09.07.2013 Walter Pachl (translated from REXX Version 2) **********************************************************************/ options replace format comments java crossref symbols binary Parse Arg n . If n='' then n=5 Say 'Identity Matrix of size' n '(m[i,j] IS the Matrix)' m=int[n,n] -- Allocate 2D square array at run-time Loop i=0 To n-1 -- Like Java, arrays in NetRexx start at 0 ol='' Loop j=0 To n-1 m[i,j]=(i=j) ol=ol m[i,j] End Say ol End ### Using Indexed String /* NetRexx */ options replace format comments java crossref symbols nobinary runSample(arg) return -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method createIdMatrix(n) public static DIM_ = 'DIMENSION' m = 0 -- Indexed string to hold matrix; default value for all elements is zero m[DIM_] = n loop i = 1 to n -- NetRexx indexed strings don't have to start at zero m[i, i] = 1 -- set this diagonal element to 1 end i return m -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method displayIdMatrix(m) public static DIM_ = 'DIMENSION' if \m.exists(DIM_) then signal RuntimeException('Matrix dimension not set') n = m[DIM_] loop i = 1 to n ol = '' loop j = 1 To n ol = ol m[i, j] end j say ol end i return -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method runSample(arg) public static parse arg n . if n = '' then n = 5 say 'Identity Matrix of size' n displayIdMatrix(createIdMatrix(n)) return ## Nim proc identityMatrix(n): auto = result = newSeq[seq[int]](n) for i in 0 .. < result.len: result[i] = newSeq[int](n) result[i][i] = 1 ## Objeck class IdentityMatrix { function : Matrix(n : Int) ~ Int[,] { array := Int->New[n,n]; for(row:=0; row<n; row+=1;){ for(col:=0; col<n; col+=1;){ if(row = col){ array[row, col] := 1; } else{ array[row,col] := 0; }; }; }; return array; } function : PrintMatrix(array : Int[,]) ~ Nil { sizes := array->Size(); for(row:=0; row<sizes[0]; row+=1;){ for(col:=0; col<sizes[1]; col+=1;){ value := array[row,col]; "{$value} \t"->Print();
};
'\n'->PrintLine();
};
}

function : Main(args : String[]) ~ Nil {
PrintMatrix(Matrix(5));
}
}

## OCaml

From the interactive loop (that we call the "toplevel"):

$ocaml # let make_id_matrix n = let m = Array.make_matrix n n 0.0 in for i = 0 to pred n do m.(i).(i) <- 1.0 done; (m) ;; val make_id_matrix : int -> float array array = <fun> # make_id_matrix 4 ;; - : float array array = [| [|1.; 0.; 0.; 0.|]; [|0.; 1.; 0.; 0.|]; [|0.; 0.; 1.; 0.|]; [|0.; 0.; 0.; 1.|] |] another way: # let make_id_matrix n = Array.init n (fun i -> Array.init n (fun j -> if i = j then 1.0 else 0.0)) ;; val make_id_matrix : int -> float array array = <fun> # make_id_matrix 4 ;; - : float array array = [| [|1.; 0.; 0.; 0.|]; [|0.; 1.; 0.; 0.|]; [|0.; 0.; 1.; 0.|]; [|0.; 0.; 0.; 1.|] |] When we write a function in the toplevel, it returns us its signature (the prototype), and when we write a variable (or a function call), it returns its type and its value. ## Octave The eye function create the identity (I) matrix, e.g.: I = eye(10) ## Ol (define (make-identity-matrix n) (map (lambda (i) (append (repeat 0 i) '(1) (repeat 0 (- n i 1)))) (iota n))) (for-each print (make-identity-matrix 3)) (for-each print (make-identity-matrix 17)) Output: (1 0 0) (0 1 0) (0 0 1) (1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) (0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) (0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1) ## ooRexx ooRexx doesn't have a proper matrix class, but it does have multidimensional arrays. say "a 3x3 identity matrix" say call printMatrix createIdentityMatrix(3) say say "a 5x5 identity matrix" say call printMatrix createIdentityMatrix(5) ::routine createIdentityMatrix use arg size matrix = .array~new(size, size) loop i = 1 to size loop j = 1 to size if i == j then matrix[i, j] = 1 else matrix[i, j] = 0 end j end i return matrix ::routine printMatrix use arg matrix loop i = 1 to matrix~dimension(1) line = "" loop j = 1 to matrix~dimension(2) line = line matrix[i, j] end j say line end i Output: a 3x3 identity matrix 1 0 0 0 1 0 0 0 1 a 5x5 identity matrix 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 ## OxygenBasic Class SquareMatrix '================= double *Cell sys size method SetIdentity() indexbase 0 sys e,i,j e=size*size for i=0 to <size cell(i*size+j)=1 : j++ next end method method constructor(sys n) @cell=getmemory n*n*sizeof double size=n end method method destructor() freememory @cell end method end class new SquareMatrix M(8) M.SetIdentity '... del M ## PARI/GP Built-in: matid(9) Custom: matrix(9,9,i,j,i==j) ## Pascal program IdentityMatrix(input, output); var matrix: array of array of integer; n, i, j: integer; begin write('Size of matrix: '); readln(n); setlength(matrix, n, n); for i := 0 to n - 1 do matrix[i,i] := 1; for i := 0 to n - 1 do begin for j := 0 to n - 1 do write (matrix[i,j], ' '); writeln; end; end. Output: % ./IdentityMatrix Size of matrix: 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 ## Perl sub identity_matrix { my$n = shift;
map {
my $i =$_;
[ map { ($_ ==$i) - 0 } 1 .. $n ] } 1 ..$n;
}

@ARGV = (4, 5, 6) unless @ARGV;

for (@ARGV) {
my @id = identity_matrix $_; print "$_:\n";
for (my $i=0;$i<@id; ++$i) { print join ' ', @{$id[$i]}, "\n"; } print "\n"; } Output: 4: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 5: 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 6: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ## Phix function identity(integer n) sequence res = repeat(repeat(0,n),n) for i=1 to n do res[i][i] = 1 end for return res end function ppOpt({pp_Nest,1}) pp(identity(3)) pp(identity(5)) pp(identity(7)) pp(identity(9)) Output: {{1,0,0}, {0,1,0}, {0,0,1}} {{1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0,0}, {0,0,0,1,0}, {0,0,0,0,1}} {{1,0,0,0,0,0,0}, {0,1,0,0,0,0,0}, {0,0,1,0,0,0,0}, {0,0,0,1,0,0,0}, {0,0,0,0,1,0,0}, {0,0,0,0,0,1,0}, {0,0,0,0,0,0,1}} {{1,0,0,0,0,0,0,0,0}, {0,1,0,0,0,0,0,0,0}, {0,0,1,0,0,0,0,0,0}, {0,0,0,1,0,0,0,0,0}, {0,0,0,0,1,0,0,0,0}, {0,0,0,0,0,1,0,0,0}, {0,0,0,0,0,0,1,0,0}, {0,0,0,0,0,0,0,1,0}, {0,0,0,0,0,0,0,0,1}} ## PHP function identity($length) {
return array_map(function($key,$value) {$value[$key] = 1; return $value;}, range(0,$length-1),
array_fill(0, $length, array_fill(0,$length, 0)));
}
function print_identity($identity) { echo implode(PHP_EOL, array_map(function ($value) {return implode(' ', $value);},$identity));
}
print_identity(identity(10));

Output:
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1

## PicoLisp

(de identity (Size)
(let L (need Size (1) 0)
(make
(do Size
(link (copy (rot L))) ) ) ) )

Test:

: (identity 3)
-> ((1 0 0) (0 1 0) (0 0 1))

: (mapc println (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)

## PL/I

identity: procedure (A, n);
declare A(n,n) fixed controlled;
declare (i,n) fixed binary;
allocate A; A = 0;
do i = 1 to n; A(i,i) = 1; end;
end identity;

## PostScript

% n ident [identity-matrix]
% create an identity matrix of dimension n*n.
% Uses a local dictionary for its one parameter, perhaps overkill.
% Constructs arrays of arrays of integers using [], for loops, and stack manipulation.
/ident { 1 dict begin /n exch def
[
1 1 n {  % [ i
[ exch  % [ [ i
1 1 n {  % [ [ i j
1 index eq { 1 }{ 0 } ifelse % [ [ i b
exch  % [ [ b i
} for  % [ [ b+ i
pop ]  % [ [ b+ ]
} for  % [ [b+]+ ]
]
end } def

## PowerShell

function identity($n) { 0..($n-1) | foreach{$row = @(0) *$n; $row[$_] = 1; ,$row} } function show($a) { $a | foreach{ "$_"} }
$array = identity 4 show$array

Output:

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

$array[0][0]$array[0][1]

Output:

1
0

## PureBasic

>Procedure identityMatrix(Array i(2), size) ;valid only for size >= 0
;formats array i() as an identity matrix of size x size
Dim i(size - 1, size - 1)

Protected j
For j = 0 To size - 1
i(j, j) = 1
Next
EndProcedure

Procedure displayMatrix(Array a(2))
Protected rows = ArraySize(a(), 2), columns = ArraySize(a(), 1)
Protected i, j

For i = 0 To rows
For j = 0 To columns
Print(RSet(Str(a(i, j)), 3, " "))
Next
PrintN("")
Next
EndProcedure

If OpenConsole()
Dim i3(0, 0)
Dim i4(0, 0)

identityMatrix(i3(), 3)
identityMatrix(i4(), 4)

displayMatrix(i3())
PrintN("")
displayMatrix(i4())

Print(#CRLF$+ #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
Output:
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

## Python

### Nested lists

A simple solution, using nested lists to represent the matrix.

def identity(size):
matrix = [[0]*size for i in range(size)]
#matrix = [[0] * size] * size #Has a flaw. See http://stackoverflow.com/questions/240178/unexpected-feature-in-a-python-list-of-lists

for i in range(size):
matrix[i][i] = 1

for rows in matrix:
for elements in rows:
print elements,
print ""

### Nested maps and comprehensions

Works with: Python version 3.7
'''Identity matrices by maps and equivalent list comprehensions'''

import operator

# idMatrix :: Int -> [[Int]]
def idMatrix(n):
'''Identity matrix of order n,
expressed as a nested map.
'''

eq = curry(operator.eq)
xs = range(0, n)
return list(map(
lambda x: list(map(
compose(int)(eq(x)),
xs
)),
xs
))

# idMatrix3 :: Int -> [[Int]]
def idMatrix2(n):
'''Identity matrix of order n,
expressed as a nested comprehension.
'''

xs = range(0, n)
return ([int(x == y) for x in xs] for y in xs)

# TEST ----------------------------------------------------
def main():
'''
Identity matrix of dimension five,
by two different routes.
'''

for f in [idMatrix, idMatrix2]:
print(
'\n' + f.__name__ + ':',
'\n\n' + '\n'.join(map(str, f(5))),
)

# GENERIC -------------------------------------------------

# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))

# curry :: ((a, b) -> c) -> a -> b -> c
def curry(f):
'''A curried function derived
from an uncurried function.'''

return lambda a: lambda b: f(a, b)

# MAIN ---
if __name__ == '__main__':
main()
Output:
idMatrix:

[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]

idMatrix2:

[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]

### Dict of points

A dict of tuples of two ints (x, y) are used to represent the matrix.

>>> def identity(size):
... return {(x, y):int(x == y) for x in range(size) for y in range(size)}
...
>>> size = 4
>>> matrix = identity(size)
>>> print('\n'.join(' '.join(str(matrix[(x, y)]) for x in range(size)) for y in range(size)))
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
>>>

### Numpy

A solution using the numpy library

np.mat(np.eye(size))

## R

When passed a single scalar argument, diag produces an identity matrix of size given by the scalar. For example:

diag(3)

produces:

[,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1

Or you can also use the method that is shown below

Identity_matrix=function(size){
x=matrix(0,size,size)
for (i in 1:size) {
x[i,i]=1
}
return(x)
}

## Racket

#lang racket
(require math)
(identity-matrix 5)

Output:
(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]])

## Raku

(formerly Perl 6)

Works with: rakudo version 2015-09-15
sub identity-matrix($n) { my @id; for flat ^$n X ^$n ->$i, $j { @id[$i][$j] = +($i == $j); } @id; } .say for identity-matrix(5); Output: [1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] On the other hand, this may be clearer and/or faster: sub identity-matrix($n) {
my @id = [0 xx $n] xx$n;
@id[$_][$_] = 1 for ^$n; @id; } Here is yet an other way to do it: sub identity-matrix($n) {
[1, |(0 xx n-1)], *.rotate(-1) ... *[*-1] } ## REXX ### version 1 The REXX language doesn't have matrices as such, so the problem is largely how to display the "matrix". The code to display the matrices was kept as a stand-alone general-purpose (square) matrix display subroutine, which, in part, determines if the square matrix is indeed a square matrix based on the number of elements given. It also finds the maximum widths of the integer and decimal fraction parts (if any) and uses those widths to align (right-justify according to the [possibly implied] decimal point) the columns of the square matrix. It also tries to display a centered (and easier to read) matrix, along with a title. /*REXX program creates and displays any sized identity matrix (centered, with title).*/ do k=3 to 6 /* [↓] build and display a sq. matrix.*/ call ident_mat k /*build & display a KxK square matrix. */ end /*k*/ /* [↑] use general─purpose display sub*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ ident_mat: procedure; parse arg n;=
do r=1 for n /*build identity matrix, by row and col*/
do c=1 for n; $=$ (r==c) /*append zero or one (if on diag). */
end /*c*/
end /*r*/
call showMat 'identity matrix of size' n, $return /*──────────────────────────────────────────────────────────────────────────────────────*/ showMat: procedure; parse arg hdr,x; #=words(x) /*# is the number of matrix elements. */ dp= 0 /*DP: max width of decimal fractions. */ w= 0 /*W: max width of integer part. */ do n=1 until n*n>=#; _= word(x,n) /*determine the matrix order. */ parse var _ y '.' f; w= max(w, length(y)); dp= max(dp, length(f) ) end /*n*/ /* [↑] idiomatically find the widths. */ w= w +1 say; say center(hdr, max(length(hdr)+8, (w+1)*#%n), '─'); say #= 0 /*#: element #.*/ do row=1 for n; _= left('', n+w) /*indentation. */ do col=1 for n; #= # + 1 /*bump element.*/ _=_ right(format(word(x, #), , dp)/1, w) end /*col*/ /* [↑] division by unity normalizes #.*/ say _ /*display a single line of the matrix. */ end /*row*/ return output when using the default sizes (3 ──► 6) for generating four matrices: ────identity matrix of size 3──── 1 0 0 0 1 0 0 0 1 ────identity matrix of size 4──── 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ────identity matrix of size 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 ────identity matrix of size 6──── 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ### version 2 An alternative?! /* REXX *************************************************************** * show identity matrix of size n * I consider m.i.j to represent the matrix (not needed for showing) * 06.07.2012 Walter Pachl **********************************************************************/ Parse Arg n Say 'Identity Matrix of size' n '(m.i.j IS the Matrix)' m.=0 Do i=1 To n ol='' Do j=1 To n m.i.j=(i=j) ol=ol''format(m.i.j,2) /* or ol=ol (i=j) */ End Say ol End Output: Identity Matrix of size 3 (m.i.j IS the Matrix) 1 0 0 0 1 0 0 0 1 This could be a 3-dimensional sparse matrix with one element set: m.=0 m.0=1000 /* the matrix' size */ m.4.17.333='Walter' ## Ring size = 5 im = newlist(size, size) identityMatrix(size, im) for r = 1 to size for c = 1 to size see im[r][c] next see nl next func identityMatrix s, m m = newlist(s, s) for i = 1 to s m[i][i] = 1 next return m func newlist x, y if isstring(x) x=0+x ok if isstring(y) y=0+y ok alist = list(x) for t in alist t = list(y) next return alist Output: 10000 01000 00100 00010 00001 ## Ruby ### Using Array def identity(size) Array.new(size){|i| Array.new(size){|j| i==j ? 1 : 0}} end [4,5,6].each do |size| puts size, identity(size).map {|r| r.to_s}, "" end Output: 4 [1, 0, 0, 0] [0, 1, 0, 0] [0, 0, 1, 0] [0, 0, 0, 1] 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] 6 [1, 0, 0, 0, 0, 0] [0, 1, 0, 0, 0, 0] [0, 0, 1, 0, 0, 0] [0, 0, 0, 1, 0, 0] [0, 0, 0, 0, 1, 0] [0, 0, 0, 0, 0, 1] ### Using Matrix 2.1.1 :001 > require "matrix" => true 2.1.1 :002 > Matrix.identity(5) => Matrix[[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]] ## Run BASIC ' formats array im() of size ims for ims = 4 to 6 print :print "--- Size: ";ims;" ---" Dim im(ims,ims) For i = 1 To ims im(i,i) = 1 next For row = 1 To ims print "["; cma$ = ""
For col = 1 To ims
print cma$;im(row, col); cma$ = ", "
next
print "]"
next
next ims
Output:
--- Size: 4 ---
[1, 0, 0, 0]
[0, 1, 0, 0]
[0, 0, 1, 0]
[0, 0, 0, 1]

--- Size: 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]

--- Size: 6 ---
[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]

## Rust

Run with command-line containing the matrix size.

extern crate num;
struct Matrix<T> {
data: Vec<T>,
size: usize,
}

impl<T> Matrix<T>
where
T: num::Num + Clone + Copy,
{
fn new(size: usize) -> Self {
Self {
data: vec![T::zero(); size * size],
size: size,
}
}
fn get(&mut self, x: usize, y: usize) -> T {
self.data[x + self.size * y]
}
fn identity(&mut self) {
for (i, item) in self.data.iter_mut().enumerate() {
*item = if i % (self.size + 1) == 0 {
T::one()
} else {
T::zero()
}
}
}
}

fn main() {
let size = std::env::args().nth(1).unwrap().parse().unwrap();
let mut matrix = Matrix::<i32>::new(size);
matrix.identity();
for y in 0..size {
for x in 0..size {
print!("{} ", matrix.get(x, y));
}
println!();
}
}

## Scala

def identityMatrix(n:Int)=Array.tabulate(n,n)((x,y) => if(x==y) 1 else 0)
def printMatrix[T](m:Array[Array[T]])=m map (_.mkString("[", ", ", "]")) mkString "\n"

printMatrix(identityMatrix(5))
Output:
[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]

## Scheme

When representing a matrix as a collection of nested lists:

(define (identity n)
(letrec
((uvec
(lambda (m i acc)
(if (= i n)
acc
(uvec m (+ i 1)
(cons (if (= i m) 1 0) acc)))))
(idgen
(lambda (i acc)
(if (= i n)
acc
(idgen (+ i 1)
(cons (uvec i 0 '()) acc))))))
(idgen 0 '())))

Test program:

(display (identity 4))

Output:
((1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1))

## Seed7

$include "seed7_05.s7i"; const type: matrix is array array integer; const func matrix: identity (in integer: size) is func result var matrix: identity is matrix.value; local var integer: index is 0; begin identity := size times size times 0; for index range 1 to size do identity[index][index] := 1; end for; end func; const proc: writeMat (in matrix: a) is func local var integer: i is 0; var integer: num is 0; begin for key i range a do for num range a[i] do write(num lpad 2); end for; writeln; end for; end func; const proc: main is func begin writeMat(identity(6)); end func; Output: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ## SenseTalk set matrix to buildIdentityMatrix(3) repeat for each item in matrix put it end repeat set matrix to buildIdentityMatrix(17) repeat for each item in matrix put it end repeat function buildIdentityMatrix matrixSize set matrixList to () repeat matrixSize times set rowMatrixIndex to the counter set rowMatrix to () repeat matrixSize times if the counter equals rowMatrixIndex insert 1 after rowMatrix else insert 0 after rowMatrix end if end repeat insert rowMatrix nested after matrixList end repeat return matrixList end buildIdentityMatrix Output for n 3 (1,0,0) (0,1,0) (0,0,1) Output for n 17 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) (0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) (0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0) (0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0) (0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0) (0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0) (0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0) (0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0) (0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0) (0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0) (0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0) (0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0) (0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0) (0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0) (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0) (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0) (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1) ## Sidef func identity_matrix(n) { n.of { |i| n.of { |j| i == j ? 1 : 0 } } } for n (ARGV ? ARGV.map{.to_i} : [4, 5, 6]) { say "\n#{n}:" for row (identity_matrix(n)) { say row.join(' ') } } Output: 4: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 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 6: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ## Sinclair ZX81 BASIC Works with 1k of RAM, but for a larger matrix you'll want at least 2k. 10 INPUT S 20 DIM M(S,S) 30 FOR I=1 TO S 40 LET M(I,I)=1 50 NEXT I 60 FOR I=1 TO S 70 SCROLL 80 FOR J=1 TO S 90 PRINT M(I,J); 100 NEXT J 110 PRINT 120 NEXT I Input: 10 Output: 1000000000 0100000000 0010000000 0001000000 0000100000 0000010000 0000001000 0000000100 0000000010 0000000001 ## Smalltalk Works with: Pharo Smalltalk (Array2D identity: (UIManager default request: 'Enter size of the matrix:') asInteger) asString Output: '(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )' ## Sparkling function unitMatrix(n) { return map(range(n), function(k1, v1) { return map(range(n), function(k2, v2) { return v2 == v1 ? 1 : 0; }); }); } ## Standard ML val eye= fn n => List.tabulate( n, fn i => List.tabulate( n, fn j=> if j=i then 1.0 else 0.0)); ## Stata ### Stata matrix . mat a = I(3) . mat list a symmetric a[3,3] c1 c2 c3 r1 1 r2 0 1 r3 0 0 1 ### Mata : I(3) [symmetric] 1 2 3 +-------------+ 1 | 1 | 2 | 0 1 | 3 | 0 0 1 | +-------------+ ## Swift Translation of: Elixir func identityMatrix(size: Int) -> [[Int]] { return (0..<size).map({i in return (0..<size).map({$0 == i ? 1 : 0})
})
}

print(identityMatrix(size: 5))
Output:
[[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]]

## Tailspin

templates identityMatrix
def n: $; [1..$n -> $$def i: ; [1..n -> \(<=i> 1 ! <> 0 !$$] !\)] !
end identityMatrix

def identity: 5 -> identityMatrix;
$identity... -> '|$(1);$(2..last)... -> ',$;';|
' -> !OUT::write

Output:
|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|

## Tcl

When representing a matrix as a collection of nested lists:

proc I {rank {zero 0.0} {one 1.0}} {
set m [lrepeat $rank [lrepeat$rank $zero]] for {set i 0} {$i < $rank} {incr i} { lset m$i $i$one
}
return $m } Or alternatively with the help of the tcllib package for rectangular data structures: Library: Tcllib (Package: struct::matrix) package require struct::matrix proc I {rank {zero 0.0} {one 1.0}} { set m [struct::matrix]$m add columns $rank$m add rows $rank for {set i 0} {$i < $rank} {incr i} { for {set j 0} {$j < $rank} {incr j} {$m set cell $i$j [expr {$i==$j ? $one :$zero}]
}
}
return $m } Demonstrating the latter: set m [I 5 0 1] ;# Integer 0/1 for clarity of presentation puts [$m format 2string]
Output:
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

## TypeScript

function identity(n) {
if (n < 1) return "Not defined";
else if (n == 1) return 1;
else {
var idMatrix:number[][];
for (var i: number = 0; i < n; i++) {
for (var j: number = 0; j < n; j++) {
if (i != j) idMatrix[i][j] = 0;
else idMatrix[i][j] = 1;
}
}
return idMatrix;
}
}

## Vala

int main (string[] args) {
if (args.length < 2) {
print ("Please, input an integer > 0.\n");
return 0;
}
var n = int.parse (args[1]);
if (n <= 0) {
print ("Please, input an integer > 0.\n");
return 0;
}
int[,] array = new int[n, n];
for (var i = 0; i < n; i ++) {
for (var j = 0; j < n; j ++) {
if (i == j) array[i,j] = 1;
else array[i,j] = 0;
}
}
for (var i = 0; i < n; i ++) {
for (var j = 0; j < n; j ++) {
print ("%d ", array[i,j]);
}
print ("\b\n");
}
return 0;
}

## VBA

Private Function Identity(n As Integer) As Variant
Dim I() As Integer
ReDim I(n - 1, n - 1)
For j = 0 To n - 1
I(j, j) = 1
Next j
Identity = I
End Function

## VBScript

build_matrix(7)

Sub build_matrix(n)
Dim matrix()
ReDim matrix(n-1,n-1)
i = 0
'populate the matrix
For row = 0 To n-1
For col = 0 To n-1
If col = i Then
matrix(row,col) = 1
Else
matrix(row,col) = 0
End If
Next
i = i + 1
Next
'display the matrix
For row = 0 To n-1
For col = 0 To n-1
If col < n-1 Then
WScript.StdOut.Write matrix(row,col) & " "
Else
WScript.StdOut.Write matrix(row,col)
End If
Next
WScript.StdOut.WriteLine
Next
End Sub

Output:
1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1

Alternate version

n = 8

arr = Identity(n)

for i = 0 to n-1
for j = 0 to n-1
wscript.stdout.Write arr(i,j) & " "
next
wscript.stdout.writeline
next

Function Identity (size)
Execute Replace("dim a(#,#):for i=0 to #:for j=0 to #:a(i,j)=0:next:a(i,i)=1:next","#",size-1)
Identity = a
End Function

Output:
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1

## Visual Basic

Works with: Visual Basic version 6
Option Explicit
'------------
Public Function BuildIdentityMatrix(ByVal Size As Long) As Byte()
Dim i As Long
Dim b() As Byte

Size = Size - 1
ReDim b(0 To Size, 0 To Size)
'at this point, the matrix is allocated and
'all elements are initialized to 0 (zero)
For i = 0 To Size
b(i, i) = 1 'set diagonal elements to 1
Next i
BuildIdentityMatrix = b

End Function
'------------
Sub IdentityMatrixDemo(ByVal Size As Long)
Dim b() As Byte
Dim i As Long, j As Long

b() = BuildIdentityMatrix(Size)
For i = LBound(b(), 1) To UBound(b(), 1)
For j = LBound(b(), 2) To UBound(b(), 2)
Debug.Print CStr(b(i, j));
Next j
Debug.Print
Next i

End Sub
'------------
Sub Main()

IdentityMatrixDemo 5
Debug.Print
IdentityMatrixDemo 10

End Sub

Output:
10000
01000
00100
00010
00001

1000000000
0100000000
0010000000
0001000000
0000100000
0000010000
0000001000
0000000100
0000000010
0000000001

## Wortel

@let {
im ^(%^\@table ^(@+ =) @to)

!im 4
}

Returns:

[[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]]

## XPL0

include c:\cxpl\codes;
def IntSize = 4; \number of bytes in an integer
int Matrix, Size, I, J;

[Text(0, "Size: "); Size:= IntIn(0);
Matrix:= Reserve(Size*IntSize); \reserve memory for 2D integer array
for I:= 0 to Size-1 do
Matrix(I):= Reserve(Size*IntSize);
for J:= 0 to Size-1 do \make array an identity matrix
for I:= 0 to Size-1 do
Matrix(I,J):= if I=J then 1 else 0;
for J:= 0 to Size-1 do \display the result
[for I:= 0 to Size-1 do
[IntOut(0, Matrix(I,J)); ChOut(0, ^ )];
CrLf(0);
];
]
Output:
Size: 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

## zkl

Using lists of lists:

fcn idMatrix(n){
m:=(0).pump(n,List.createLong(n).write,0)*n;
m.apply2(fcn(row,rc){ row[rc.inc()]=1 },Ref(0));
m
}
idMatrix(5).println();
idMatrix(5).pump(Console.println);
Output:
L(L(1,0,0,0,0),L(0,1,0,0,0),L(0,0,1,0,0),L(0,0,0,1,0),L(0,0,0,0,1))
L(1,0,0,0,0)
L(0,1,0,0,0)
L(0,0,1,0,0)
L(0,0,0,1,0)
L(0,0,0,0,1)

## ZX Spectrum Basic

Translation of: Applesoft_BASIC
10 INPUT "Matrix size: ";size
20 GO SUB 200: REM Identity matrix
30 FOR r=1 TO size
40 FOR c=1 TO size
50 LET s$=CHR$ 13
60 IF c<size THEN LET s$=" " 70 PRINT i(r,c);s$;
80 NEXT c
90 NEXT r
100 STOP
200 REM Identity matrix size
220 DIM i(size,size)
230 FOR i=1 TO size
240 LET i(i,i)=1
250 NEXT i
260 RETURN