Identity matrix
Build an identity matrix of a size known at run-time.
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
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).
- Related tasks
11l
<lang 11l>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)</lang>
- Output:
[1, 0, 0] [0, 1, 0] [0, 0, 1]
360 Assembly
<lang 360asm>* 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
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
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
USING DYNA,R11 make storage addressable
LR R11,R1 set addressability
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 R1,A address to free
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</lang>
- Output:
1000000000 0100000000 0010000000 0001000000 0000100000 0000010000 0000001000 0000000100 0000000010 0000000001
Action!
<lang Action!>PROC CreateIdentityMatrix(BYTE ARRAY mat,BYTE size)
CARD pos BYTE i,j
pos=0
FOR i=1 TO size
DO
FOR j=1 TO size
DO
IF i=j THEN
mat(pos)=1
ELSE
mat(pos)=0
FI
pos==+1
OD
OD
RETURN
PROC PrintMatrix(BYTE ARRAY mat,BYTE size)
CARD pos BYTE i,j,v
pos=0
FOR i=1 TO size
DO
FOR j=1 TO size
DO
v=mat(pos)
IF j=size THEN
PrintF("%I%E",v)
ELSE
PrintF("%I ",v)
FI
pos==+1
OD
OD
RETURN
PROC Main()
BYTE size BYTE ARRAY mat(400) BYTE LMARGIN=$52,old
old=LMARGIN LMARGIN=0 ;remove left margin on the screen
DO
Print("Get size of matrix [1-20] ")
size=InputB()
UNTIL size>=1 AND size<=20
OD
CreateIdentityMatrix(mat,size) PrintMatrix(mat,size)
LMARGIN=old ;restore left margin on the screen
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
Get size of matrix [1-20] 13 1 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 1 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 1 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 1 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 1 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 1 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 1
Ada
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. <lang Ada>-- As prototyped in the Generic_Real_Arrays specification: -- function Unit_Matrix (Order : Positive; First_1, First_2 : Integer := 1) return Real_Matrix; -- For the task: mat : Real_Matrix := Unit_Matrix(5);</lang> For prior versions of Ada, or non floating point types its back to basics: <lang Ada>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;</lang>
ALGOL 68
Note: The generic vector and matrix code should be moved to a more generic page.
File: prelude/vector_base.a68<lang algol68>#!/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</lang>File: prelude/matrix_base.a68<lang algol68># -*- 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</lang>File: prelude/matrix_ident.a68<lang algol68># -*- 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</lang>File: prelude/matrix.a68<lang algol68>#!/usr/bin/a68g --script #
- -*- coding: utf-8 -*- #
PR READ "prelude/vector_base.a68" PR; PR READ "prelude/matrix_base.a68" PR; PR READ "prelude/matrix_ident.a68" PR;
SKIP</lang>File: test/matrix_ident.a68<lang algol68>#!/usr/bin/a68g --script #
- -*- coding: utf-8 -*- #
MODE SCAL = REAL; FORMAT scal fmt := $g(-3,1)$;
PR READ "prelude/matrix.a68" PR;
print(REPR IDENT 4)</lang>
- 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
<lang algolw>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.</lang>
APL
Making an identity matrix in APL involves the outer product of the equality function.
For a square matrix of 3: <lang apl>
∘.=⍨⍳3
1 0 0 0 1 0 0 0 1 </lang>
For a function that makes an identity matrix: <lang apl>
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 </lang> An tacit function can be defined with one of the following equivalent lines: <lang apl>
ID←∘.=⍨⍳ ID←⍳∘.=⍳
</lang>
There is a more idomatic way however: <lang apl>
ID←{⍵ ⍵ ρ 1, ⍵ρ0}
</lang>
AppleScript
<lang 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</lang>
- 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
<lang 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$; : NEXT C, R 170 END
200 REMIDENTITYMATRIX SIZE% 210 LET SIZE% = SIZE% - 1 220 DIM IM(SIZE%, SIZE%) 230 FOR I = 0 TO SIZE% 240 LET IM(I, I) = 1 : NEXT I 250 RETURN :IM </lang>
ATS
<lang ATS> (* ****** ****** *) // // How to compile: // // patscc -DATS_MEMALLOC_LIBC -o idmatrix idmatrix.dats // (* ****** ****** *) //
- include
"share/atspre_staload.hats" // (* ****** ****** *)
extern fun idmatrix{n:nat}(n: size_t(n)): matrixref(int, n, n) implement idmatrix(n) = matrixref_tabulate_cloref<int> (n, n, lam(i, j) => bool2int0(i = j))
(* ****** ****** *)
implement main0 () = { // val N = 5 // val M = idmatrix(i2sz(N)) val () = fprint_matrixref_sep (stdout_ref, M, i2sz(N), i2sz(N), " ", "\n") val () = fprint_newline (stdout_ref) // } (* end of [main0] *) </lang>
AutoHotkey
<lang autohotkey>msgbox % Clipboard := I(6) return
I(n){
r := "--`n" , s := " "
loop % n
{
k := A_index , r .= "| "
loop % n
r .= A_index=k ? "1, " : "0, "
r := RTrim(r, " ,") , r .= " |`n"
}
loop % 4*n
s .= " "
return Rtrim(r,"`n") "`n" s "--"
}</lang>
- Output:
--
| 1, 0, 0, 0, 0, 0 |
| 0, 1, 0, 0, 0, 0 |
| 0, 0, 1, 0, 0, 0 |
| 0, 0, 0, 1, 0, 0 |
| 0, 0, 0, 0, 1, 0 |
| 0, 0, 0, 0, 0, 1 |
--
AWK
<lang AWK>
- syntax: GAWK -f IDENTITY_MATRIX.AWK size
BEGIN {
size = ARGV[1]
if (size !~ /^[0-9]+$/) {
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)
} </lang>
- Output:
for command
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
<lang Bash> for i in `seq $1`;do printf '%*s\n' $1|tr ' ' '0'|sed "s/0/1/$i";done </lang>
- Output:
for command
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
<lang bbcbasic> 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</lang>
Beads
<lang beads>beads 1 program 'Identity matrix'
var id : array^2 of num n = 5
calc main_init loop from:1 to:n index:i loop from:1 to:n index:j id[i,j] = 1 if i == j else 0</lang>
- 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
Burlesque
Neither very elegant nor short but it'll do
<lang burlesque> blsq ) 6 -.^^0\/r@\/'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 </lang>
The example above uses strings to generate the identity matrix. If you need a matrix with real numbers (Integers) then use:
<lang burlesque> 6hd0bx#a.*\[#a.*0#a?dr@{(D!)\/1\/^^bx\/[+}m[e! </lang>
Shorter alternative:
<lang burlesque> blsq ) 6 ^^^^10\/**XXcy\/co.+sp </lang>
BQN
<lang>⍝ Using table Eye ← =⌜˜∘↕ •Show Eye 3
⍝ Using reshape Eye1 ← {𝕩‿𝕩⥊1∾𝕩⥊0} Eye1 5</lang> <lang>┌─ ╵ 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
┘
</lang>
Eye generates an identity matrix using a table of equality for [0,n).
Eye1 reshapes a boolean vector to generate the matrix.
C
<lang 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);
}
int rowsize = atoi(argv[1]);
if (rowsize < 0) {
printf("Dimensions of matrix cannot be negative\n");
exit(EXIT_FAILURE);
}
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 %ld 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 %ld 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");
}
} </lang>
C#
<lang csharp> 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();
}
Console.ReadKey();
}
}
} </lang>
- 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++
<lang cpp>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;
} </lang>
<lang cpp>
- 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;
} </lang>
- 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
<lang clio>fn identity-matrix n:
[0:n] -> * fn i:
[0:n] -> * if = i: 1
else: 0
5 -> identity-matrix -> * print</lang>
Clojure
The (vec ) function in the following solution is with respect to vector matrices. If dealing with normal lists matrices (e.g. <lang clojure> '( (0 1) (2 3) ) </lang> , then care to remove the vec function. <lang clojure>(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)))))))
</lang>
- Output:
<lang clojure>=> (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]] </lang>
The following is a more idomatic definition that utilizes infinite lists and cycling. <lang clojure> (defn identity-matrix [n]
(take n
(partition n (dec n)
(cycle (conj (repeat (dec n) 0) 1)))))
</lang>
Common Lisp
Common Lisp provides multi-dimensional arrays.
<lang lisp>(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))
</lang>
- 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))
<lang lisp>(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)))
</lang>
- 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 <lang oberon2> 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.
</lang>
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
<lang 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
}</lang>
- 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
<lang 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.</lang>
- 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
<lang 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 </lang>
- 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 : <lang elena>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()) }
}</lang>
- Output:
Enter the matrix size:3 1,0,0 0,1,0 0,0,1
Elixir
<lang 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)</lang>
- 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
<lang 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).</lang>
ERRE
<lang 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 </lang>
Euler Math Toolbox
<lang Euler Math Toolbox> function IdentityMatrix(n)
$ X:=zeros(n,n); $ for i=1 to n $ X[i,i]:=1; $ end; $ return X; $endfunction
</lang>
<lang Euler Math Toobox> >function IdentityMatrix (n:index) $ return setdiag(zeros(n,n),0,1); $endfunction </lang>
<lang> >id(5) </lang>
Excel
LAMBDA
Excel can lift functions over scalar values to functions over two-dimensional arrays.
Here we bind the name IDMATRIX to a lambda expression in the Name Manager of the Excel WorkBook:
(See LAMBDA: The ultimate Excel worksheet function)
<lang lisp>IDMATRIX =LAMBDA(n,
LET(
ixs, SEQUENCE(n, n, 0, 1),
x, MOD(ixs, n),
y, QUOTIENT(ixs, n),
IF(x = y,
1,
0
)
)
)</lang>
- Output:
The formula in cell B2 below populates the B2:F6 grid:
| fx | =IDMATRIX(A2) | ||||||
|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | ||
| 1 | N | Identity matrix | |||||
| 2 | 5 | 1 | 0 | 0 | 0 | 0 | |
| 3 | 0 | 1 | 0 | 0 | 0 | ||
| 4 | 0 | 0 | 1 | 0 | 0 | ||
| 5 | 0 | 0 | 0 | 1 | 0 | ||
| 6 | 0 | 0 | 0 | 0 | 1 | ||
| 7 | |||||||
| 8 | 3 | 1 | 0 | 0 | |||
| 9 | 0 | 1 | 0 | ||||
| 10 | 0 | 0 | 1 | ||||
F#
Builds a 2D matrix with the given square size. <lang FSharp> let ident n = Array2D.init n n (fun i j -> if i = j then 1 else 0) </lang>
- Output:
<lang FSharp> 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]]
</lang>
Factor
<lang factor>USING: math.matrices prettyprint ;
6 <identity-matrix> .</lang>
- 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...
Fermat
<lang fermat> Func Identity(n)=Array id[n,n];[id]:=[1].
Identity(7) [id] </lang>
- 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 ]]
Forth
<lang forth>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</lang>
Fortran
<lang fortran> 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 </lang>
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. <lang Fortran> 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</lang>
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:
<lang Fortran> DO 1 I = 1,N
DO 1 J = 1,N 1 A(I,J) = (I/J)*(J/I)</lang>
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
<lang 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</lang> 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.
<lang frink>n = parseInt[input["Enter matrix dimension as an integer: "]] println[joinln[makeArray[[n, n], {|a,b| a==b ? 1 : 0}]]]</lang>
- Output:
Enter matrix dimension as an integer: 3 [1, 0, 0] [0, 1, 0] [0, 0, 1]
FunL
<lang funl>def identity( n ) = vector( n, n, \r, c -> if r == c then 1 else 0 )
println( identity(3) )</lang>
- 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. 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 storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
GAP
<lang gap># Built-in IdentityMat(3);
- One can also specify the base ring
IdentityMat(3, Integers mod 10);</lang>
Go
Library gonum/mat
<lang go>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)))
}</lang>
- Output:
⎡1 0 0⎤ ⎢0 1 0⎥ ⎣0 0 1⎦
Library go.matrix
A somewhat earlier matrix library for Go. <lang go>package main
import (
"fmt"
mat "github.com/skelterjohn/go.matrix"
)
func main() {
fmt.Println(mat.Eye(3))
}</lang>
- Output:
{1, 0, 0,
0, 1, 0,
0, 0, 1}
From scratch
Simplest: A matrix as a slice of slices, allocated separately. <lang go>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
}</lang>
- 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. <lang go>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
}</lang>
- 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. <lang go>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
}</lang>
- Output:
[1 0 0 0 1 0 0 0 1] 1 0 0 0 1 0 0 0 1
Groovy
Solution: <lang groovy>def makeIdentityMatrix = { n ->
(0..<n).collect { i -> (0..<n).collect { j -> (i == j) ? 1 : 0 } }
}</lang>
Test: <lang groovy>(2..6).each { order ->
def iMatrix = makeIdentityMatrix(order)
iMatrix.each { println it }
println()
}</lang>
- 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]
Haskell
<lang haskell>matI n = [ [fromEnum $ i == j | i <- [1..n]] | j <- [1..n]]</lang> And a function to show matrix pretty: <lang haskell>showMat :: Int -> String showMat = unlines . map (unwords . map show)</lang>
<lang haskell>*Main> putStr $ showMat $ matId 9
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
</lang>
We could alternatively bypassing the syntactic sugaring of list comprehension notation, and use a bind function directly:
<lang haskell>idMatrix :: Int -> Int idMatrix n =
let xs = [1 .. n] in xs >>= \x -> [xs >>= \y -> [fromEnum (x == y)]]</lang>
or reduce the number of terms a little to: <lang haskell>idMatrix :: Int -> Int idMatrix n =
let xs = [1 .. n] in (\x -> fromEnum . (x ==) <$> xs) <$> xs
main :: IO () main = (putStr . unlines) $ unwords . fmap show <$> idMatrix 5</lang>
- 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
Icon and Unicon
This code works for Icon and Unicon. <lang unicon>link matrix procedure main(argv)
if not (integer(argv[1]) > 0) then stop("Argument must be a positive integer.")
matrix1 := identity_matrix(argv[1], argv[1])
write_matrix(&output,matrix1)
end </lang>
- Output:
->im 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 ->
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Identity.bas" 110 INPUT PROMPT "Enter size of matrix: ":N 120 NUMERIC A(1 TO N,1 TO N) 130 CALL INIT(A) 140 CALL WRITE(A) 150 DEF INIT(REF T) 160 FOR I=LBOUND(T,1) TO UBOUND(T,1) 170 FOR J=LBOUND(T,2) TO UBOUND(T,2) 180 LET T(I,J)=0 190 NEXT 200 LET T(I,I)=1 210 NEXT 220 END DEF 230 DEF WRITE(REF T) 240 FOR I=LBOUND(T,1) TO UBOUND(T,1) 250 FOR J=LBOUND(T,2) TO UBOUND(T,2) 260 PRINT T(I,J); 270 NEXT 280 PRINT 290 NEXT 300 END DEF</lang>
J
<lang j> = i. 4 NB. create an Identity matrix of size 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
makeI=: =@i. NB. define as a verb with a user-defined name makeI 5 NB. create an 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</lang>
Java
<lang Java>public class PrintIdentityMatrix {
public static void main(String[] args) {
int n = 5;
int[][] array = new int[n][n];
IntStream.range(0, n).forEach(i -> array[i][i] = 1);
Arrays.stream(array)
.map((int[] a) -> Arrays.toString(a))
.forEach(System.out::println);
}
}</lang>
- 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]
JavaScript
ES5
<lang Javascript>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;
})
});
}</lang>
ES6
<lang JavaScript>(() => {
// identityMatrix :: Int -> Int const identityMatrix = n => Array.from({ length: n }, (_, i) => Array.from({ length: n }, (_, j) => i !== j ? 0 : 1));
// ----------------------- TEST ------------------------
return identityMatrix(5)
.map(JSON.stringify)
.join('\n');
})();</lang>
- 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]
jq
Construction
<lang jq>def identity(n):
[range(0;n) | 0] as $row | reduce range(0;n) as $i ([]; . + [ $row | .[$i] = 1 ] );</lang>
Example: <lang jq>identity(4)</lang>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: <lang jq>def identity(n):
reduce range(0;n) as $i (0 | matrix(n;n); .[$i][$i] = 1);
</lang>
Jsish
<lang javascript>/* Identity matrix, in Jsish */ function identityMatrix(n) {
var mat = new Array(n).fill(0);
for (var r in mat) {
mat[r] = new Array(n).fill(0);
mat[r][r] = 1;
}
return mat;
}
provide('identityMatrix', 1);
if (Interp.conf('unitTest')) {
- identityMatrix(0);
- identityMatrix(1);
- identityMatrix(2);
- identityMatrix(3);
var mat = identityMatrix(4); for (var r in mat) puts(mat[r]);
}
/*
!EXPECTSTART!
identityMatrix(0) ==> [] identityMatrix(1) ==> [ [ 1 ] ] identityMatrix(2) ==> [ [ 1, 0 ], [ 0, 1 ] ] identityMatrix(3) ==> [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] [ 1, 0, 0, 0 ] [ 0, 1, 0, 0 ] [ 0, 0, 1, 0 ] [ 0, 0, 0, 1 ]
!EXPECTEND!
- /</lang>
- Output:
promt$ jsish -u identityMatrix.jsi [PASS] identityMatrix.jsi
Julia
I is an object of type UniformScaling, representing an identity matrix of any size, boolean by default, that can be multiplied by a scalar <lang Julia>using LinearAlgebra unitfloat64matrix = 1.0I</lang>
UniformScaling object can be used as a function to construct a Diagonal matrix of given size, that can be converted to a full matrix using collect <lang Julia>using LinearAlgebra diagI3 = 1.0I(3) fullI3 = collect(diagI3)</lang>
The function I(3) is not defined in Julia-1.0.5. Other ways to construct a full matrix of given size are
<lang Julia>using LinearAlgebra fullI3 = Matrix{Float64}(I, 3, 3) fullI3 = Array{Float64}(I, 3, 3) fullI3 = Array{Float64,2}(I, 3, 3) fullI3 = zeros(3,3) + I</lang>
K
<lang 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)
</lang>
Kotlin
<lang scala>// 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")
}</lang> 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
Lambdatalk
<lang scheme> {def identity
{lambda {:n}
{A.new {S.map {{lambda {:n :i}
{A.new {S.map {{lambda {:i :j}
{if {= :i :j} then 1 else 0} } :i}
{S.serie 0 :n}}}} :n}
{S.serie 0 :n}} }}}
-> identity
{identity 2} -> [[1,0],[0,1]]
{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]] </lang>
Lang5
<lang lang5>: identity-matrix
dup iota 'A set
: i.(*) A in ; [1] swap append reverse A swap reshape 'i. apply ;
5 identity-matrix .</lang>
- 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
<lang lisp> (defun identity
((`(,m ,n)) (identity m n)) ((m) (identity m m)))
(defun identity (m n)
(lists:duplicate m (lists:duplicate n 1)))
</lang>
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:
<lang lisp> > (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))
</lang>
LSL
To test it yourself; rez a box on the ground, and add the following as a New Script. <lang LSL>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))+"]"); } } }</lang>
- 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
<lang 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))</lang>
- 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: <lang Maple> > LinearAlgebra:-IdentityMatrix( 4 );
[1 0 0 0]
[ ]
[0 1 0 0]
[ ]
[0 0 1 0]
[ ]
[0 0 0 1]
</lang> Here, for instance, is another, in which the entries are (4-byte) floats. <lang Maple> > Matrix( 4, shape = scalar[1], datatype = float[4] );
[1. 0. 0. 0.]
[ ]
[0. 1. 0. 0.]
[ ]
[0. 0. 1. 0.]
[ ]
[0. 0. 0. 1.]
</lang> Yet another, with 2-byte integer entries: <lang Maple> > Matrix( 4, shape = identity, datatype = integer[ 2 ] );
[1 0 0 0]
[ ]
[0 1 0 0]
[ ]
[0 0 1 0]
[ ]
[0 0 0 1]
</lang>
MathCortex
<lang MathCortex>I = eye(10)</lang>
Mathematica / Wolfram Language
<lang Mathematica>IdentityMatrix[4]</lang>
MATLAB / Octave
The eye function create the identity (I) matrix, e.g.:
<lang MATLAB>I = eye(10)</lang>
Maxima
<lang maxima>ident(4); /* matrix([1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]) */</lang>
NetRexx
Using int Array
<lang NetRexx>/* 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
</lang>
Using Indexed String
<lang NetRexx>/* 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
</lang>
Nim
<lang nim>proc identityMatrix(n: Positive): auto =
result = newSeq[seq[int]](n) for i in 0 ..< result.len: result[i] = newSeq[int](n) result[i][i] = 1</lang>
Objeck
<lang 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];
"{$value} \t"->Print();
};
'\n'->PrintLine();
};
}
function : Main(args : String[]) ~ Nil {
PrintMatrix(Matrix(5));
}
} </lang>
OCaml
From the interactive loop (that we call the "toplevel"):
<lang ocaml>$ 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.|] |]</lang>
another way:
<lang ocaml># 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.|] |]</lang>
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.:
<lang octave>I = eye(10)</lang>
Ol
<lang scheme> (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))</lang>
- 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. <lang ooRexx> 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
</lang>
- 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
<lang 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 </lang>
PARI/GP
Built-in: <lang parigp>matid(9)</lang>
Custom: <lang parigp>matrix(9,9,i,j,i==j)</lang>
Pascal
<lang 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.</lang>
- 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
<lang 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";
} </lang>
- 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
<lang 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);}, $identity)); } print_identity(identity(10)); </lang>
- Output:
1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
PicoLisp
<lang PicoLisp>(de identity (Size)
(let L (need Size (1) 0)
(make
(do Size
(link (copy (rot L))) ) ) ) )</lang>
Test: <lang PicoLisp>: (identity 3) -> ((1 0 0) (0 1 0) (0 0 1))
- (mapc println (identity 5))
(1 0 0 0 0) (0 1 0 0 0) (0 0 1 0 0) (0 0 0 1 0) (0 0 0 0 1)</lang>
PL/I
<lang PL/I> identity: procedure (A, n);
declare A(n,n) fixed controlled; declare (i,n) fixed binary; allocate A; A = 0; do i = 1 to n; A(i,i) = 1; end;
end identity; </lang>
PostScript
<lang PostScript> % n ident [identity-matrix] % create an identity matrix of dimension n*n. % Uses a local dictionary for its one parameter, perhaps overkill. % Constructs arrays of arrays of integers using [], for loops, and stack manipulation. /ident { 1 dict begin /n exch def
[
1 1 n { % [ i
[ exch % [ [ i
1 1 n { % [ [ i j
1 index eq { 1 }{ 0 } ifelse % [ [ i b
exch % [ [ b i
} for % [ [ b+ i
pop ] % [ [ b+ ]
} for % [ [b+]+ ]
]
end } def </lang>
PowerShell
<lang PowerShell> function identity($n) {
0..($n-1) | foreach{$row = @(0) * $n; $row[$_] = 1; ,$row}
} function show($a) { $a | foreach{ "$_"} } $array = identity 4 show $array </lang> Output:
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
<lang PowerShell> $array[0][0] $array[0][1] </lang> Output:
1 0
Prolog
<lang Prolog>%rotates one list clockwise by one integer rotate(Int,List,Rotated) :- integer(Int), length(Suff,Int), append(Pre,Suff,List), append(Suff,Pre,Rotated). %rotates a list of lists by a list of integers rotate(LoInts,LoLists,Rotated) :- is_list(LoInts), maplist(rotate,LoInts,LoLists,Rotated).
%helper function append_(Suff,Pre,List) :- append([Pre],Suff,List). idmatrix(N,IdMatrix):- %make an N length list of 1s and append with N-1 0s length(Ones,N), maplist(=(1),Ones), succ(N0,N), length(Zeros,N0), maplist(=(0),Zeros), maplist(append_(Zeros),Ones,M), %create the offsets at rotate each row numlist(0,N0,Offsets), rotate(Offsets,M,IdMatrix).
main :- idmatrix(5,I), maplist(writeln,I). </lang>
- Output:
?- main. [1,0,0,0,0] [0,1,0,0,0] [0,0,1,0,0] [0,0,0,1,0] [0,0,0,0,1] true .
PureBasic
<lang purebasic>>Procedure identityMatrix(Array i(2), size) ;valid only for size >= 0
;formats array i() as an identity matrix of size x size Dim i(size - 1, size - 1)
Protected j For j = 0 To size - 1 i(j, j) = 1 Next
EndProcedure
Procedure displayMatrix(Array a(2))
Protected rows = ArraySize(a(), 2), columns = ArraySize(a(), 1)
Protected i, j
For i = 0 To rows
For j = 0 To columns
Print(RSet(Str(a(i, j)), 3, " "))
Next
PrintN("")
Next
EndProcedure
If OpenConsole()
Dim i3(0, 0)
Dim i4(0, 0)
identityMatrix(i3(), 3)
identityMatrix(i4(), 4)
displayMatrix(i3())
PrintN("")
displayMatrix(i4())
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf</lang>
- 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. <lang python>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 ""</lang>
Nested maps and comprehensions
<lang python>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()</lang>
- 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. <lang python>>>> 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 >>> </lang>
Numpy
A solution using the numpy library <lang python> np.mat(np.eye(size)) </lang>
Quackery
<lang quackery>[ [] swap times
[ 0 i^ of 1 join 0 i of
join nested join ] ] is identity ( n --> [ )
5 identity echo</lang>
- 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 ] ]
R
When passed a single scalar argument, diag produces an identity matrix of size given by the scalar. For example:
<lang rsplus>diag(3)</lang>
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 <lang rsplus>Identity_matrix=function(size){
x=matrix(0,size,size)
for (i in 1:size) {
x[i,i]=1
}
return(x)
}</lang>
Racket
<lang racket>
- lang racket
(require math) (identity-matrix 5) </lang>
- 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)
<lang perl6>sub identity-matrix($n) {
my @id;
for flat ^$n X ^$n -> $i, $j {
@id[$i][$j] = +($i == $j);
}
@id;
}
.say for identity-matrix(5);</lang>
- Output:
[1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1]
On the other hand, this may be clearer and/or faster: <lang perl6>sub identity-matrix($n) {
my @id = [0 xx $n] xx $n; @id[$_][$_] = 1 for ^$n; @id;
}</lang>
Here is yet an other way to do it: <lang perl6>sub identity-matrix($n) {
[1, |(0 xx $n-1)], *.rotate(-1) ... *[*-1]
}</lang>
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. <lang rexx>/*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</lang>
- 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?! <lang rexx> /* 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=olformat(m.i.j,2) /* or ol=ol (i=j) */ End Say ol End
</lang>
- 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: <lang rexx> m.=0 m.0=1000 /* the matrix' size */ m.4.17.333='Walter' </lang>
Ring
<lang 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
</lang> Output:
10000 01000 00100 00010 00001
Gui version
<lang ring>
- Project : Identity Matrix
- Date : 2022/16/02
- Author : Gal Zsolt (~ CalmoSoft ~)
- Email : <calmosoft@gmail.com>
load "stdlib.ring" load "guilib.ring"
size = 8 C_Spacing = 1
C_ButtonBlueStyle = 'border-radius:6px;color:black; background-color: blue' C_ButtonOrangeStyle = 'border-radius:6px;color:black; background-color: orange'
Button = newlist(size,size) LayoutButtonRow = list(size)
app = new qApp {
win = new qWidget() {
setWindowTitle('Identity Matrix') move(500,100) reSize(600,600) winheight = win.height() fontSize = 18 + (winheight / 100)
LayoutButtonMain = new QVBoxLayout()
LayoutButtonMain.setSpacing(C_Spacing) LayoutButtonMain.setContentsmargins(0,0,0,0)
for Row = 1 to size LayoutButtonRow[Row] = new QHBoxLayout() { setSpacing(C_Spacing) setContentsmargins(0,0,0,0) }
for Col = 1 to size
Button[Row][Col] = new QPushButton(win) {
setSizePolicy(1,1)
}
LayoutButtonRow[Row].AddWidget(Button[Row][Col]) next LayoutButtonMain.AddLayout(LayoutButtonRow[Row]) next
LayoutDataRow1 = new QHBoxLayout() { setSpacing(C_Spacing) setContentsMargins(0,0,0,0) }
LayoutButtonMain.AddLayout(LayoutDataRow1)
setLayout(LayoutButtonMain)
show()
}
pBegin()
exec()
}
func pBegin()
for Row = 1 to size
for Col = 1 to size
if Row = Col
Button[Row][Col].setStyleSheet(C_ButtonOrangeStyle)
Button[Row][Col].settext("1")
else
Button[Row][Col].setStyleSheet(C_ButtonBlueStyle)
Button[Row][Col].settext("0")
ok
next
next
score = 0
</lang>
Ruby
Using Array
<lang ruby>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</lang>
- 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
<lang ruby> 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]]
</lang>
Run BASIC
<lang runbasic>' 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</lang>
- 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.
<lang rust> 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!();
}
} </lang>
Scala
<lang 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))</lang>
- 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: <lang scheme> (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 '())))
</lang> Test program: <lang scheme> (display (identity 4)) </lang>
- Output:
((1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1))
Seed7
<lang 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;</lang>
- 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
<lang 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 </lang> 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
<lang ruby>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(' ')
}
}</lang>
- 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. <lang zxbasic> 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</lang>
- Input:
10
- Output:
1000000000 0100000000 0010000000 0001000000 0000100000 0000010000 0000001000 0000000100 0000000010 0000000001
Smalltalk
<lang smalltalk>(Array2D identity: (UIManager default request: 'Enter size of the matrix:') asInteger) asString</lang>
- Output:
'(1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )'
Sparkling
<lang sparkling>function unitMatrix(n) { return map(range(n), function(k1, v1) { return map(range(n), function(k2, v2) { return v2 == v1 ? 1 : 0; }); }); }</lang>
Standard ML
<lang 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));</lang>
Stata
Stata matrix
<lang stata>. mat a = I(3) . mat list a
symmetric a[3,3]
c1 c2 c3
r1 1 r2 0 1 r3 0 0 1</lang>
Mata
<lang stata>: I(3) [symmetric]
1 2 3 +-------------+ 1 | 1 | 2 | 0 1 | 3 | 0 0 1 | +-------------+</lang>
Swift
<lang swift>func identityMatrix(size: Int) -> Int {
return (0..<size).map({i in
return (0..<size).map({ $0 == i ? 1 : 0})
})
}
print(identityMatrix(size: 5))</lang>
- 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
<lang tailspin> templates identityMatrix
def n: $; [1..$n -> [1..~$ -> 0, 1, $~..$n -> 0]] !
end identityMatrix
def identity: 5 -> identityMatrix; $identity... -> '|$(1);$(2..last)... -> ', $;';| ' -> !OUT::write </lang>
- 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: <lang tcl>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
}</lang> Or alternatively with the help of the tcllib package for rectangular data structures:
<lang tcl>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 $m
}</lang> Demonstrating the latter: <lang tcl>set m [I 5 0 1] ;# Integer 0/1 for clarity of presentation puts [$m format 2string]</lang>
- 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
<lang 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;
}
} </lang>
Vala
<lang 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; }</lang>
VBA
<lang vb>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</lang>
VBScript
<lang vb> 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 </lang>
- 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
<lang vbscript> 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 </lang>
- 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
<lang vb>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 </lang>
- Output:
10000 01000 00100 00010 00001 1000000000 0100000000 0010000000 0001000000 0000100000 0000010000 0000001000 0000000100 0000000010 0000000001
Wortel
<lang wortel>@let {
im ^(%^\@table ^(@+ =) @to)
!im 4
}</lang> Returns:
[[1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1]]
Wren
<lang ecmascript>import "/matrix" for Matrix import "/fmt" for Fmt
var numRows = 10 // say Fmt.mprint(Matrix.identity(numRows), 2, 0)</lang>
- 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|
XPL0
<lang 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);
];
]</lang>
- 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: <lang zkl>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);</lang>
- 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
<lang zxbasic>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</lang>