Identity matrix
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
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).
- Related tasks
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)
- 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
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
- Output:
1000000000 0100000000 0010000000 0001000000 0000100000 0000010000 0000001000 0000000100 0000000010 0000000001
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
- 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.
-- 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);
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
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 -*- #
PR READ "prelude/vector_base.a68" PR;
PR READ "prelude/matrix_base.a68" PR;
PR READ "prelude/matrix_ident.a68" PR;
SKIP
File: test/matrix_ident.a68
#!/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)
- 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.
Amazing Hopper
#include <jambo.h>
Main
Dim( 10,10 ) as eyes 'UMatrix'
Printnl ' "UNIT MATRIX:\n", UMatrix '
/* Classical method */
Dim (10,10) as zeros (ZM)
i=1
Iterator ( ++i, #(i<=10), #( ZM[i,i]=1 ) )
Printnl ' "UNIT MATRIX:\n", ZM '
/* unit matrix non square*/
Dim ( 5,8 ) as eyes 'rare unit matrix'
Printnl ' "RARE UNIT MATRIX:\n", rare unit matrix '
End
- Output:
UNIT MATRIX: 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 UNIT MATRIX: 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 RARE UNIT MATRIX: 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
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]
Simple alternative
on indentityMatrix(n)
set digits to {}
set m to n - 1
repeat (n + m) times
set end of digits to 0
end repeat
set item n of digits to 1
set matrix to {}
repeat with i from n to 1 by -1
set end of matrix to items i thru (i + m) of digits
end repeat
return matrix
end indentityMatrix
return indentityMatrix(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}}
Arturo
identityM: function [n][
result: array.of: @[n n] 0
loop 0..dec n 'i -> result\[i]\[i]: 1
return result
]
loop 4..6 'sz [
print sz
loop identityM sz => print
print ""
]
- 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
BASIC
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$; : NEXT C, R
170 END
200 REMIDENTITYMATRIX SIZE%
210 LET SIZE% = SIZE% - 1
220 DIM IM(SIZE%, SIZE%)
230 FOR I = 0 TO SIZE%
240 LET IM(I, I) = 1 : NEXT I
250 RETURN :IM
Commodore BASIC
100 INPUT "MATRIX SIZE:"; SIZE
110 GOSUB 200: REM IDENTITYMATRIX
120 FOR R = 0 TO SIZE
130 FOR C = 0 TO SIZE
140 S$ = CHR$(13)
150 IF C < SIZE THEN S$ = ""
160 PRINT MID$(STR$(IM(R, C)),1)S$;:REM MID$ STRIPS LEADING SPACES
170 NEXT C, R
180 END
190 REM *******************************
200 REM IDENTITYMATRIX SIZE%
210 SIZE = SIZE - 1
220 DIM IM(SIZE, SIZE)
230 FOR I = 0 TO SIZE
240 IM(I, I) = 1
250 NEXT I
260 RETURN
QBasic
SUB inicio(identity())
FOR i = LBOUND(identity,1) TO UBOUND(identity,1)
FOR j = LBOUND(identity,2) TO UBOUND(identity,2)
LET identity(i,j) = 0
NEXT j
LET identity(i,i) = 1
NEXT i
END SUB
SUB mostrar(identity())
FOR i = LBOUND(identity,1) TO UBOUND(identity,1)
FOR j = LBOUND(identity,2) TO UBOUND(identity,2)
PRINT identity(i,j);
NEXT j
PRINT
NEXT i
END SUB
DO
INPUT "Enter size of matrix "; n
LOOP UNTIL n > 0
DIM identity(1 TO n, 1 TO n)
CALL inicio(identity())
CALL mostrar(identity())
BASIC256
arraybase 1
do
input "Enter size of matrix: ", n
until n > 0
dim identity(n, n) fill 0 #we fill everything with 0
# enter 1s in diagonal elements
for i = 1 to n
identity[i, i] = 1
next i
# print identity matrix if n < 40
print
if n < 40 then
for i = 1 to n
for j = 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
- Output:
Same as FreeBASIC entry.
XBasic
PROGRAM "Identity matrix"
VERSION "0.0000"
DECLARE FUNCTION Entry ()
FUNCTION Entry ()
DO
n = SBYTE(INLINE$("Enter size of matrix: "))
LOOP UNTIL n > 0
DIM identity[n, n] '' all zero by default
' enter 1s in diagonal elements
FOR i = 1 TO n
identity[i, i] = 1
NEXT i
' print identity matrix if n < 40
PRINT
IF n < 40 THEN
FOR i = 1 TO n
FOR j = 1 TO n
PRINT identity[i, j];
NEXT j
PRINT
NEXT i
ELSE
PRINT "Matrix is too big to display on 80 column console"
END IF
END FUNCTION
END PROGRAM
- Output:
Same as FreeBASIC entry.
Yabasic
repeat
input "Enter size of matrix: " n
until n > 0
dim identity(n, n) // all zero by default
// enter 1s in diagonal elements
for i = 1 to n
identity(i, i) = 1
next i
// print identity matrix if n < 40
print
if n < 40 then
for i = 1 to n
for j = 1 to n
print identity(i, j);
next j
print
next i
else
print "Matrix is too big to display on 80 column console"
end if
- Output:
Same as FreeBASIC entry.
ATS
(* ****** ****** *)
//
// How to compile:
//
// patscc -DATS_MEMALLOC_LIBC -o idmatrix idmatrix.dats
//
(* ****** ****** *)
//
#include
"share/atspre_staload.hats"
//
(* ****** ****** *)
extern
fun
idmatrix{n:nat}(n: size_t(n)): matrixref(int, n, n)
implement
idmatrix(n) =
matrixref_tabulate_cloref<int> (n, n, lam(i, j) => bool2int0(i = j))
(* ****** ****** *)
implement
main0 () =
{
//
val N = 5
//
val M = idmatrix(i2sz(N))
val () = fprint_matrixref_sep (stdout_ref, M, i2sz(N), i2sz(N), " ", "\n")
val () = fprint_newline (stdout_ref)
//
} (* end of [main0] *)
AutoHotkey
msgbox % Clipboard := I(6)
return
I(n){
r := "--`n" , s := " "
loop % n
{
k := A_index , r .= "| "
loop % n
r .= A_index=k ? "1, " : "0, "
r := RTrim(r, " ,") , r .= " |`n"
}
loop % 4*n
s .= " "
return Rtrim(r,"`n") "`n" s "--"
}
- Output:
-- | 1, 0, 0, 0, 0, 0 | | 0, 1, 0, 0, 0, 0 | | 0, 0, 1, 0, 0, 0 | | 0, 0, 0, 1, 0, 0 | | 0, 0, 0, 0, 1, 0 | | 0, 0, 0, 0, 0, 1 | --
AWK
# syntax: GAWK -f IDENTITY_MATRIX.AWK size
BEGIN {
size = ARGV[1]
if (size !~ /^[0-9]+$/) {
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
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
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
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
- 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
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
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#a?dr@{(D!)\/1\/^^bx\/[+}m[e!
Shorter alternative:
blsq ) 6 ^^^^10\/**XXcy\/co.+sp
BQN
⍝ Using table
Eye ← =⌜˜∘↕
•Show Eye 3
⍝ Using reshape
Eye1 ← {𝕩‿𝕩⥊1∾𝕩⥊0}
Eye1 5
┌─
╵ 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
┘
Eye
generates an identity matrix using a table of equality for [0,n).
Eye1
reshapes a boolean vector to generate the matrix.
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");
}
}
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();
}
Console.ReadKey();
}
}
}
- 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++
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;
}
#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
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
DuckDB
There are several ways in which matrices can be represented in DuckDB. In this entry, we'll focus on the representation by a table with columns (i,j,value).
The function defined below, I(m,n,zero) has three parameters: the first two specify the dimensions, and the `zero` allows one to specify the type of matrix elements, which will be (1+zero) along the diagonal, and zero otherwise. This in effect allows for polymorphism: the one function can to be used to generate matrices for any of the many DuckDB numerical types, e.g. decimal(4,3) as in the example.
# Produce an (i,j,value) table representing the matrix I(m,n)
# which is the identity matrix if m = n
create or replace function I(m,n,zero) as table (
with recursive cte(i,j,ij,value) as (
select 1, 1, (null,null), zero
union all
select if(j=n, i+1, i) as i,
if(j=n, 1, j+1) as j,
(i, j) as ij,
zero + if(i=j, 1, 0) as value
from cte
where i <= m
)
select ij[1] as i, ij[2] as j, value
from cte
offset 1
);
# Generate a 3x3 matrix with DOUBLE(3,2) values:
from I(3, 3, 0.000);
- Output:
┌───────┬───────┬──────────────┐ │ i │ j │ value │ │ int32 │ int32 │ decimal(4,3) │ ├───────┼───────┼──────────────┤ │ 1 │ 1 │ 1.000 │ │ 1 │ 2 │ 0.000 │ │ 1 │ 3 │ 0.000 │ │ 2 │ 1 │ 0.000 │ │ 2 │ 2 │ 1.000 │ │ 2 │ 3 │ 0.000 │ │ 3 │ 1 │ 0.000 │ │ 3 │ 2 │ 0.000 │ │ 3 │ 3 │ 1.000 │ └───────┴───────┴──────────────┘
EasyLang
proc idmat lng . mat[][] .
len mat[][] lng
for i to lng
len mat[i][] lng
mat[i][i] = 1
.
.
idmat 4 m[][]
print m[][]
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 6.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)
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)
IDMATRIX
=LAMBDA(n,
LET(
ixs, SEQUENCE(n, n, 0, 1),
x, MOD(ixs, n),
y, QUOTIENT(ixs, n),
IF(x = y,
1,
0
)
)
)
- 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.
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
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...
Fermat
Func Identity(n)=Array id[n,n];[id]:=[1].
Identity(7)
[id]
- 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
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
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, and shows how to nicely format it using built-in routines.
n = parseInt[input["Enter matrix dimension as an integer: "]]
println[formatMatrix[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. 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.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
Test cases
FutureBasic
include "NSLog.incl"
local fn IdentityMatrix( n as NSInteger ) as CFStringRef
NSInteger i, j
CFMutableArrayRef tempArr = fn MutableArrayWithCapacity( n )
CFMutableStringRef mutStr = fn MutableStringWithCapacity( 0 )
for i = 0 to n - 1
MutableArrayRemoveAllObjects( tempArr )
for j = 0 to n - 1
MutableArrayInsertObjectAtIndex( tempArr, @"0", j )
next
MutableArrayReplaceObjectAtIndex( tempArr, @"1", i )
MutableStringAppendString( mutStr, fn ArrayComponentsJoinedByString( tempArr, @" " ) )
MutableStringAppendString( mutStr, @"\n" )
next
end fn = fn StringWithString( mutStr )
NSLog( @"3:\n%@", fn IdentityMatrix( 3 ) )
NSLog( @"5:\n%@", fn IdentityMatrix( 5 ) )
NSLog( @"7:\n%@", fn IdentityMatrix( 7 ) )
NSLog( @"9:\n%@", fn IdentityMatrix( 9 ) )
HandleEvents
- Output:
3: 1 0 0 0 1 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 7: 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 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
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]
Haskell
matI n = [ [fromEnum $ i == j | i <- [1..n]] | j <- [1..n]]
And a function to show matrix pretty:
showMat :: [[Int]] -> String
showMat = unlines . map (unwords . map show)
*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
We could alternatively bypassing the syntactic sugaring of list comprehension notation, and use a bind function directly:
idMatrix :: Int -> [[Int]]
idMatrix n =
let xs = [1 .. n]
in xs >>= \x -> [xs >>= \y -> [fromEnum (x == y)]]
or reduce the number of terms a little to:
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
- 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.
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
- 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
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
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
Id=: =@i. NB. define as a verb with a user-defined name
Id 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
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);
}
}
- 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
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;
})
});
}
ES6
(() => {
// 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');
})();
- 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
def identity(n):
[range(0;n) | 0] as $row
| 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
I is an object of type UniformScaling, representing an identity matrix of any size, boolean by default, that can be multiplied by a scalar
using LinearAlgebra
unitfloat64matrix = 1.0I
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
using LinearAlgebra
diagI3 = 1.0I(3)
fullI3 = collect(diagI3)
The function I(3) is not defined in Julia-1.0.5. Other ways to construct a full matrix of given size are
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
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
fun main() {
print("Enter size of matrix : ")
val n = readln().toInt()
println()
val identity = Array(n) { i ->
IntArray(n) { j ->
if (i == j) 1 else 0
}
}
// print identity matrix if n <= 40
if (n <= 40)
for (row in identity) println(row.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
Lambdatalk
{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]]
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
/* 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: Positive): auto =
result = newSeq[seq[int]](n)
for i in 0 ..< result.len:
result[i] = newSeq[int](n)
result[i][i] = 1
Nu
def identity-matrix [n: int] {
..<$n | each {|i| ..<$n | each { $in == $i | into int } }
}
..5 | each { {k: $in v: (identity-matrix $in)} } | transpose -r | table -i false -e --flatten
- Output:
╭───┬───────┬─────────┬───────────┬─────────────┬───────────────╮ │ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │ ├───┼───────┼─────────┼───────────┼─────────────┼───────────────┤ │ │ ╭───╮ │ ╭─────╮ │ ╭───────╮ │ ╭─────────╮ │ ╭───────────╮ │ │ │ │ 1 │ │ │ 1 0 │ │ │ 1 0 0 │ │ │ 1 0 0 0 │ │ │ 1 0 0 0 0 │ │ │ │ ╰───╯ │ │ 0 1 │ │ │ 0 1 0 │ │ │ 0 1 0 0 │ │ │ 0 1 0 0 0 │ │ │ │ │ ╰─────╯ │ │ 0 0 1 │ │ │ 0 0 1 0 │ │ │ 0 0 1 0 0 │ │ │ │ │ │ ╰───────╯ │ │ 0 0 0 1 │ │ │ 0 0 0 1 0 │ │ │ │ │ │ │ ╰─────────╯ │ │ 0 0 0 0 1 │ │ │ │ │ │ │ │ ╰───────────╯ │ ╰───┴───────┴─────────┴───────────┴─────────────┴───────────────╯
Objeck
class IdentityMatrix {
function : Matrix(n : Int) ~ Int[,] {
array := Int->New[n,n];
for(row:=0; row<n; row+=1;){
for(col:=0; col<n; col+=1;){
if(row = col){
array[row, col] := 1;
}
else{
array[row,col] := 0;
};
};
};
return array;
}
function : PrintMatrix(array : Int[,]) ~ Nil {
sizes := array->Size();
for(row:=0; row<sizes[0]; row+=1;){
for(col:=0; col<sizes[1]; col+=1;){
value := array[row,col];
"{$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
PascalABC.NET
begin
var n := ReadInteger;
var matrix: array [,] of integer := MatrGen(n,n,(i,j) -> i = j ? 1 : 0);
matrix.Println
end.
- Output:
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
use strict;
use warnings;
use feature 'say';
sub identity_matrix {
my($n) = shift() - 1;
map { [ (0) x $_, 1, (0) x ($n - $_) ] } 0..$n
}
for (<4 5 6>) {
say "\n$_:";
say join ' ', @$_ for identity_matrix $_;
}
- Output:
4: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 5: 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 6: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
Phix
function identity(integer n) sequence res = repeat(repeat(0,n),n) for i=1 to n do res[i][i] = 1 end for return res end function ppOpt({pp_Nest,1}) pp(identity(3)) pp(identity(5)) pp(identity(7)) pp(identity(9))
- Output:
{{1,0,0}, {0,1,0}, {0,0,1}}
{{1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0,0}, {0,0,0,1,0}, {0,0,0,0,1}}
{{1,0,0,0,0,0,0}, {0,1,0,0,0,0,0}, {0,0,1,0,0,0,0}, {0,0,0,1,0,0,0}, {0,0,0,0,1,0,0}, {0,0,0,0,0,1,0}, {0,0,0,0,0,0,1}}
{{1,0,0,0,0,0,0,0,0}, {0,1,0,0,0,0,0,0,0}, {0,0,1,0,0,0,0,0,0}, {0,0,0,1,0,0,0,0,0}, {0,0,0,0,1,0,0,0,0}, {0,0,0,0,0,1,0,0,0}, {0,0,0,0,0,0,1,0,0}, {0,0,0,0,0,0,0,1,0}, {0,0,0,0,0,0,0,0,1}}
PHP
function identity($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]
$array[0][1]
Output:
1 0
Prolog
%rotates one list clockwise by one integer
rotate(Int,List,Rotated) :-
integer(Int),
length(Suff,Int),
append(Pre,Suff,List),
append(Suff,Pre,Rotated).
%rotates a list of lists by a list of integers
rotate(LoInts,LoLists,Rotated) :-
is_list(LoInts),
maplist(rotate,LoInts,LoLists,Rotated).
%helper function
append_(Suff,Pre,List) :-
append([Pre],Suff,List).
idmatrix(N,IdMatrix):-
%make an N length list of 1s and append with N-1 0s
length(Ones,N),
maplist(=(1),Ones),
succ(N0,N),
length(Zeros,N0),
maplist(=(0),Zeros),
maplist(append_(Zeros),Ones,M),
%create the offsets at rotate each row
numlist(0,N0,Offsets),
rotate(Offsets,M,IdMatrix).
main :-
idmatrix(5,I),
maplist(writeln,I).
- Output:
?- main. [1,0,0,0,0] [0,1,0,0,0] [0,0,1,0,0] [0,0,0,1,0] [0,0,0,0,1] true .
PureBasic
>Procedure identityMatrix(Array i(2), size) ;valid only for size >= 0
;formats array i() as an identity matrix of size x size
Dim i(size - 1, size - 1)
Protected j
For j = 0 To size - 1
i(j, j) = 1
Next
EndProcedure
Procedure displayMatrix(Array a(2))
Protected rows = ArraySize(a(), 2), columns = ArraySize(a(), 1)
Protected i, j
For i = 0 To rows
For j = 0 To columns
Print(RSet(Str(a(i, j)), 3, " "))
Next
PrintN("")
Next
EndProcedure
If OpenConsole()
Dim i3(0, 0)
Dim i4(0, 0)
identityMatrix(i3(), 3)
identityMatrix(i4(), 4)
displayMatrix(i3())
PrintN("")
displayMatrix(i4())
Print(#CRLF$ + #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
'''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))
Quackery
[ [] swap times
[ 0 i^ of 1 join 0 i of
join nested join ] ] is identity ( n --> [ )
5 identity echo
- 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:
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)
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]
}
Red
Red[]
identity-matrix: function [size][
matrix: copy []
repeat i size [
append/only matrix append/dup copy [] 0 size
matrix/:i/:i: 1
]
matrix
]
probe 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]]
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
Gui version
# 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
Output image:
RPL
- Input:
3 IDN
- Output:
1: [[ 1 0 0 ] [ 0 1 0 ] [ 0 0 1 ]]
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
require 'matrix'
p 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
(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
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 -> [1..~$ -> 0, 1, $~..$n -> 0]] !
end identityMatrix
def identity: 5 -> identityMatrix;
$identity... -> '|$(1);$(2..last)... -> ', $;';|
' -> !OUT::write
v0.5
identityMatrix templates
n is $;
[1..$n -> [1..~$ -> 0, 1, $~..$n -> 0]] !
end identityMatrix
identity is 5 -> identityMatrix;
$identity... -> '|$(1);$(2..)... -> ', $;';|
' !
- 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:
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;
}
}
Uiua
IdMatrix ← ⊞=.⇡
IdMatrix 7
- 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 ╯
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
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]]
Wren
import "./matrix" for Matrix
import "./fmt" for Fmt
var numRows = 10 // say
Fmt.mprint(Matrix.identity(numRows), 2, 0)
- 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
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
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
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