Build an identity matrix of a size known at run-time.
Anidentity matrix is a square matrix of sizen ×n,
where the diagonal elements are all1s (ones),
and all the other elements are all0s (zeroes).
F identity_matrix(size) V matrix = [[0] * size] * size L(i) 0 .< size matrix[i][i] = 1 R matrixL(row) identity_matrix(3) print(row)
[1, 0, 0][0, 1, 0][0, 0, 1]
* Identity matrix 31/03/2017INDENMAT 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 exitNN EQU 10 parameter n (90=>32K)N DC A(NN) nLL DS F n*n*4PG DC CL(NN)' ' bufferXDEC DS CL12 tempDYNA DSECTA DS F a(n,n) YREGS END INDENMAT
1000000000010000000000100000000001000000000010000000000100000000001000000000010000000000100000000001
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 ODRETURNPROC 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 ODRETURNPROC 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 screenRETURNScreenshot from Atari 8-bit computer
Get size of matrix [1-20] 131 0 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 0 1
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:
typeMatrixisarray(PositiveRange<>,PositiveRange<>)ofInteger;mat:Matrix(1..5,1..5):=(others=>(others=>0));-- then after the declarative section:foriinmat'Range(1)loopmat(i,i):=1;endloop;
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 COMMENTINT 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);SKIPFile: 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 COMMENTINT 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)#);SKIPFile: 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)
((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))
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 textend.
#include<jambo.h>MainDim(10,10)aseyes'UMatrix'Printnl'"UNIT MATRIX:\n",UMatrix'/* Classical method */Dim(10,10)aszeros(ZM)i=1Iterator(++i,#(i<=10),#(ZM[i,i]=1))Printnl'"UNIT MATRIX:\n",ZM'/* unit matrix non square*/Dim(5,8)aseyes'rareunitmatrix'Printnl'"RARE UNIT MATRIX:\n",rareunitmatrix'End
UNIT MATRIX:1,0,0,0,0,0,0,0,0,00,1,0,0,0,0,0,0,0,00,0,1,0,0,0,0,0,0,00,0,0,1,0,0,0,0,0,00,0,0,0,1,0,0,0,0,00,0,0,0,0,1,0,0,0,00,0,0,0,0,0,1,0,0,00,0,0,0,0,0,0,1,0,00,0,0,0,0,0,0,0,1,00,0,0,0,0,0,0,0,0,1UNIT MATRIX:1,0,0,0,0,0,0,0,0,00,1,0,0,0,0,0,0,0,00,0,1,0,0,0,0,0,0,00,0,0,1,0,0,0,0,0,00,0,0,0,1,0,0,0,0,00,0,0,0,0,1,0,0,0,00,0,0,0,0,0,1,0,0,00,0,0,0,0,0,0,1,0,00,0,0,0,0,0,0,0,1,00,0,0,0,0,0,0,0,0,1RARE UNIT MATRIX:1,0,0,0,0,0,0,00,1,0,0,0,0,0,00,0,1,0,0,0,0,00,0,0,1,0,0,0,00,0,0,0,1,0,0,0
Making an identity matrix in APL involves the outer product of the equality function.
For a square matrix of 3:
∘.=⍨⍳3100010001
For a function that makes an identity matrix:
ID←{∘.=⍨⍳⍵}ID51000001000001000001000001
An tacit function can be defined with one of the following equivalent lines:
ID←∘.=⍨⍳ID←⍳∘.=⍳
There is a more idomatic way however:
ID←{⍵⍵ρ1,⍵ρ0}
--------------------- IDENTITY MATRIX ------------------------ identityMatrix :: Int -> [(0|1)]onidentityMatrix(n)setxstoenumFromTo(1,n)scriptrowon|λ|(x)scriptcolon|λ|(i)ifi=xthen1else0endifend|λ|endscriptmap(col,xs)end|λ|endscriptmap(row,xs)endidentityMatrix--------------------------- TEST ---------------------------onrununlines(map(showList,¬identityMatrix(5)))endrun-------------------- GENERIC FUNCTIONS ----------------------- enumFromTo :: Int -> Int -> [Int]onenumFromTo(m,n)ifm≤nthensetlstto{}repeatwithifrommtonsetendoflsttoiendrepeatlstelse{}endifendenumFromTo-- intercalate :: String -> [String] -> Stringonintercalate(delim,xs)set{dlm,mytext item delimiters}to¬{mytext item delimiters,delim}setstoxsastextsetmytext item delimiterstodlmsendintercalate-- map :: (a -> b) -> [a] -> [b]onmap(f,xs)tellmReturn(f)setlngtolengthofxssetlstto{}repeatwithifrom1tolngsetendoflstto|λ|(itemiofxs,i,xs)endrepeatreturnlstendtellendmap-- Lift 2nd class handler function into 1st class script wrapper-- mReturn :: Handler -> ScriptonmReturn(f)ifclassoffisscriptthenfelsescriptproperty|λ|:fendscriptendifendmReturn-- showList :: [a] -> StringonshowList(xs)"["&intercalate(", ",map(mystr,xs))&"]"endshowList-- str :: a -> Stringonstr(x)xasstringendstr-- unlines :: [String] -> Stringonunlines(xs)-- A single string formed by the intercalation-- of a list of strings with the newline character.set{dlm,mytext item delimiters}to¬{mytext item delimiters,linefeed}setstoxsastextsetmytext item delimiterstodlmsendunlines
[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]
onindentityMatrix(n)setdigitsto{}setmton-1repeat(n+m)timessetendofdigitsto0endrepeatsetitemnofdigitsto1setmatrixto{}repeatwithifromnto1by-1setendofmatrixtoitemsithru(i+m)ofdigitsendrepeatreturnmatrixendindentityMatrixreturnindentityMatrix(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}}
identityM:function[n][result:array.of:@[nn]0loop0..decn'i->result\[i]\[i]:1returnresult]loop4..6'sz[printszloopidentityMsz=>printprint""]
41 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 51 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 61 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
100 INPUT "MATRIX SIZE:"; SIZE%110 GOSUB 200"IDENTITYMATRIX120 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$; : NEXT C, R170 END200 REMIDENTITYMATRIX SIZE%210 LET SIZE% = SIZE% - 1220 DIM IM(SIZE%, SIZE%)230 FOR I = 0 TO SIZE%240 LET IM(I, I) = 1 : NEXT I250 RETURN :IM
100INPUT"MATRIX SIZE:";SIZE110GOSUB200:REMIDENTITYMATRIX120FORR=0TOSIZE130FORC=0TOSIZE140S$=CHR$(13)150IFC<SIZETHENS$=""160PRINTMID$(STR$(IM(R,C)),1)S$;:REMMID$STRIPSLEADINGSPACES170NEXTC,R180END190REM *******************************200REM IDENTITYMATRIX SIZE%210SIZE=SIZE-1220DIMIM(SIZE,SIZE)230FORI=0TOSIZE240IM(I,I)=1250NEXTI260RETURN
SUBinicio(identity())FORi=LBOUND(identity,1)TOUBOUND(identity,1)FORj=LBOUND(identity,2)TOUBOUND(identity,2)LETidentity(i,j)=0NEXTjLETidentity(i,i)=1NEXTiENDSUBSUBmostrar(identity())FORi=LBOUND(identity,1)TOUBOUND(identity,1)FORj=LBOUND(identity,2)TOUBOUND(identity,2)PRINTidentity(i,j);NEXTjPRINTNEXTiENDSUBDOINPUT"Enter size of matrix ";nLOOPUNTILn>0DIMidentity(1TOn,1TOn)CALLinicio(identity())CALLmostrar(identity())
arraybase 1do input "Enter size of matrix: ", nuntil n > 0dim identity(n, n) fill 0 #we fill everything with 0# enter 1s in diagonal elementsfor i = 1 to n identity[i, i] = 1next i# print identity matrix if n < 40printif n < 40 then for i = 1 to n for j = 1 to n print identity[i, j]; next j print next ielse print "Matrix is too big to display on 80 column console"end if
Same as FreeBASIC entry.
PROGRAM"Identity matrix"VERSION"0.0000"DECLAREFUNCTIONEntry()FUNCTIONEntry()DOn=SBYTE(INLINE$("Enter size of matrix: "))LOOPUNTILn>0DIMidentity[n,n]'' all zero by default' enter 1s in diagonal elementsFORi=1TOnidentity[i,i]=1NEXTi' print identity matrix if n < 40PRINTIFn<40THENFORi=1TOnFORj=1TOnPRINTidentity[i,j];NEXTjPRINTNEXTiELSEPRINT"Matrix is too big to display on 80 column console"ENDIFENDFUNCTIONENDPROGRAM
Same as FreeBASIC entry.
repeatinput"Enter size of matrix: "nuntiln>0dimidentity(n,n)//allzerobydefault//enter1sindiagonalelementsfori=1tonidentity(i,i)=1nexti//printidentitymatrixifn<40printifn<40thenfori=1tonforj=1tonprintidentity(i,j);nextjprintnextielseprint"Matrix is too big to display on 80 column console"endif
Same as FreeBASIC entry.
(* ****** ****** *)//// How to compile://// patscc -DATS_MEMALLOC_LIBC -o idmatrix idmatrix.dats//(* ****** ****** *)//#include"share/atspre_staload.hats"//(* ****** ****** *)externfunidmatrix{n:nat}(n: size_t(n)): matrixref(int, n, n)implementidmatrix(n) =matrixref_tabulate_cloref<int> (n, n, lam(i, j) => bool2int0(i = j))(* ****** ****** *)implementmain0 () ={//val N = 5//val M = idmatrix(i2sz(N))val () = fprint_matrixref_sep (stdout_ref, M, i2sz(N), i2sz(N), " ", "\n")val () = fprint_newline (stdout_ref)//} (* end of [main0] *)msgbox%Clipboard:=I(6)returnI(n){r:="--`n",s:=" "loop%n{k:=A_index,r.="| "loop%nr.=A_index=k?"1, ":"0, "r:=RTrim(r," ,"),r.=" |`n"}loop%4*ns.=" "returnRtrim(r,"`n")"`n"s"--"}
--| 1, 0, 0, 0, 0, 0 || 0, 1, 0, 0, 0, 0 || 0, 0, 1, 0, 0, 0 || 0, 0, 0, 1, 0, 0 || 0, 0, 0, 0, 1, 0 || 0, 0, 0, 0, 0, 1 | --
# syntax: GAWK -f IDENTITY_MATRIX.AWK sizeBEGIN{size=ARGV[1]if(size!~/^[0-9]+$/){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)?1:0printf("%2d",x)# printarr[i,j]=x# build}printf("\n")}exit(0)}
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
foriin`seq$1`;doprintf'%*s\n'$1|tr' ''0'|sed"s/0/1/$i";done
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
INPUT"Enter size of matrix: "size%PROCidentitymatrix(size%,im())FORr%=0TOsize%-1FORc%=0TOsize%-1PRINTim(r%,c%),;NEXTPRINTNEXTr%ENDDEFPROCidentitymatrix(s%,RETURNm())LOCALi%DIMm(s%-1,s%-1)FORi%=0TOs%-1m(i%,i%)=1NEXTENDPROC
beads 1 program 'Identity matrix'varid : array^2 of numn = 5calc main_initloop from:1 to:n index:iloop from:1 to:n index:jid[i,j] = 1 if i == j else 0
1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
Neither very elegant nor short but it'll do
blsq ) 6 -.^^0\/r@\/'0\/.*'1+]\/{\/{rt}\/E!XX}x/+]m[sp1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1The 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
⍝ Using tableEye ← =⌜˜∘↕•Show Eye 3⍝ Using reshapeEye1 ← {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.
#include<stdlib.h>#include<stdio.h>intmain(intargc,char**argv){if(argc<2){printf("usage: identitymatrix <number of rows>\n");exit(EXIT_FAILURE);}introwsize=atoi(argv[1]);if(rowsize<0){printf("Dimensions of matrix cannot be negative\n");exit(EXIT_FAILURE);}intnumElements=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(unsignedintrow=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(unsignedintrow=0;row<rowsize;row++){for(unsignedintcolumn=0;column<rowsize;column++){printf("%d ",matrix[row][column]);}printf("\n");}}
usingSystem;usingSystem.Linq;namespaceIdentityMatrix{classProgram{staticvoidMain(string[]args){if(args.Length!=1){Console.WriteLine("Requires exactly one argument");return;}intn;if(!int.TryParse(args[0],outn)){Console.WriteLine("Requires integer parameter");return;}varidentity=Enumerable.Range(0,n).Select(i=>Enumerable.Repeat(0,n).Select((z,j)=>j==i?1:0).ToList()).ToList();foreach(varrowinidentity){foreach(vareleminrow){Console.Write(" "+elem);}Console.WriteLine();}Console.ReadKey();}}}
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
template<classT>classmatrix{public:matrix(unsignedintnSize):m_oData(nSize*nSize,0),m_nSize(nSize){}inlineT&operator()(unsignedintx,unsignedinty){returnm_oData[x+m_nSize*y];}voididentity(){intnCount=0;intnStride=m_nSize+1;std::generate(m_oData.begin(),m_oData.end(),[&](){return!(nCount++%nStride);});}inlineunsignedintsize(){returnm_nSize;}private:std::vector<T>m_oData;unsignedintm_nSize;};intmain(){intnSize;std::cout<<"Enter matrix size (N): ";std::cin>>nSize;matrix<int>oMatrix(nSize);oMatrix.identity();for(unsignedinty=0;y<oMatrix.size();y++){for(unsignedintx=0;x<oMatrix.size();x++){std::cout<<oMatrix(x,y)<<" ";}std::cout<<std::endl;}return0;}
#include<boost/numeric/ublas/matrix.hpp>intmain(){usingnamespaceboost::numeric::ublas;intnSize;std::cout<<"Enter matrix size (N): ";std::cin>>nSize;identity_matrix<int>oMatrix(nSize);for(unsignedinty=0;y<oMatrix.size2();y++){for(unsignedintx=0;x<oMatrix.size1();x++){std::cout<<oMatrix(x,y)<<" ";}std::cout<<std::endl;}return0;}
Enter matrix size (N): 51 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
fn identity-matrix n: [0:n] -> * fn i: [0:n] -> * if = i: 1 else: 05 -> identity-matrix -> * print
The (vec ) function in the following solution is with respect to vector matrices. If dealing with normal lists matrices (e.g.
'((01)(23))
, then care to remove the vec function.
(defnidentity-matrix[n](let[row(conj(repeat(decn)0)1)](vec(for[i(range1(incn))](vec(reduce conj(dropirow)(takeirow)))))))
=>(identity-matrix5)[[10000][01000][00100][00010][00001]]
The following is a more idomatic definition that utilizes infinite lists and cycling.
(defnidentity-matrix[n](taken(partitionn(decn)(cycle(conj(repeat(decn)0)1)))))
Common Lisp provides multi-dimensional arrays.
(defunmake-identity-matrix(n)(let((array(make-array(listnn):initial-element0)))(loopforibelowndo(setf(arefarrayii)1))array))
* (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))
(defunidentity-matrix(n)(loopforafrom1toncollect(loopforefrom1tonif(=ae)collect1elsecollect0)))
> (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))
BlackBox Component Builder
MODULEAlgebras;IMPORTStdLog,Strings;TYPEMatrix=POINTERTOARRAYOFARRAYOFINTEGER;PROCEDURENewIdentityMatrix(n:INTEGER):Matrix;VARm:Matrix;i:INTEGER;BEGINNEW(m,n,n);FORi:=0TOn-1DOm[i,i]:=1;END;RETURNm;ENDNewIdentityMatrix;PROCEDUREShow(m:Matrix);VARi,j:INTEGER;BEGINFORi:=0TOLEN(m,0)-1DOFORj:=0TOLEN(m,1)-1DOStdLog.Int(m[i,j]);END;StdLog.LnENDENDShow;PROCEDUREDo*;BEGINShow(NewIdentityMatrix(5));ENDDo;ENDAlgebras.
Execute: ^Q Algebras.Do
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
importstd.traits;T[][]matId(T)(insize_tn)purenothrowif(isAssignable!(T,T)){autoId=newT[][](n,n);foreach(r,row;Id){staticif(__traits(compiles,{row[]=0;})){row[]=0;// vector op doesn't work with T = BigIntrow[r]=1;}else{foreach(c;0..n)row[c]=(c==r)?1:0;}}returnId;}voidmain(){importstd.stdio,std.bigint;enumform="[%([%(%s, %)],\n %)]]";immutableid1=matId!real(5);writefln(form~"\n",id1);immutableid2=matId!BigInt(3);writefln(form~"\n",id2);// auto id3 = matId!(const int)(2); // cant't compile}
[[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]]
programIdentityMatrix;// Modified from the Pascal version{$APPTYPE CONSOLE}varmatrix:arrayofarrayofinteger;n,i,j:integer;beginwrite('Size of matrix: ');readln(n);setlength(matrix,n,n);fori:=0ton-1domatrix[i,i]:=1;fori:=0ton-1dobeginforj:=0ton-1dowrite(matrix[i,j],' ');writeln;end;end.
Size of matrix: 51 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
There are several ways in which matrices can be represented in DuckDB.In this entry, we'll focus on the representation by a table withcolumns (i,j,value).
The function defined below, I(m,n,zero) has three parameters:the first two specify the dimensions, and the `zero` allows oneto specify the type of matrix elements, which will be (1+zero)along the diagonal, and zero otherwise. This in effect allowsfor polymorphism: the one function canto be used to generate matrices for any of the many DuckDB numerical types,e.g. decimal(4,3) as in the example.
#Producean(i,j,value)tablerepresentingthematrixI(m,n)#whichistheidentitymatrixifm=ncreateorreplacefunctionI(m,n,zero)astable(withrecursivecte(i,j,ij,value)as(select1,1,(null,null),zerounionallselectif(j=n,i+1,i)asi,if(j=n,1,j+1)asj,(i,j)asij,zero+if(i=j,1,0)asvaluefromctewherei<=m)selectij[1]asi,ij[2]asj,valuefromcteoffset1);#Generatea3x3matrixwithDOUBLE(3,2)values:fromI(3,3,0.000);
┌───────┬───────┬──────────────┐│ 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 │└───────┴───────┴──────────────┘
proc idmat lng . mat[][] . len mat[][] lng for i to lng len mat[i][] lng mat[i][i] = 1 ..idmat 4 m[][]print m[][]
classAPPLICATIONinheritARGUMENTScreatemakefeature{NONE}-- Initializationmake-- Run application.localdim:INTEGER-- Dimension of the identity matrixdofromdim:=1untildim>10loopprint_matrix(identity_matrix(dim))dim:=dim+1io.new_lineendendfeature-- Accessidentity_matrix(dim:INTEGER):ARRAY2[REAL_64]requiredim>0localmatrix:ARRAY2[REAL_64]i:INTEGERdocreatematrix.make_filled(0.0,dim,dim)fromi:=1untili>dimloopmatrix.put(1.0,i,i)i:=i+1endResult:=matrixendprint_matrix(matrix:ARRAY2[REAL_64])locali,j:INTEGERdofromi:=1untili>matrix.heightloopprint("[ ")fromj:=1untilj>matrix.widthloopprint(matrix.item(i,j))print(" ")j:=j+1endprint("]%N")i:=i+1endendend
[ 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 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()) }}Enter the matrix size:31,0,00,1,00,0,1
defmoduleMatrixdodefidentity(n)doEnum.map(0..n-1,fni->forj<-0..n-1,do:(ifi==j,do:1,else:0)end)endendIO.inspectMatrix.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]]
%% 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)->caseColumnofRow->1;_->0endend).
PROGRAM IDENTITY!$DYNAMICDIM 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 FOREND PROGRAMfunction 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 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:
(SeeLAMBDA: 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)))
The formula in cell B2 below populates theB2: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 | ||||
Builds a 2D matrix with the given square size.
letidentn=Array2D.initnn(funij->ifi=jthen1else0)
ident10;;valit: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]]
USING:math.matricesprettyprint;6<identity-matrix>.
{ { 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's BASIC layer can easily manipulate square matrices of arbitrary sizes and data types in ways similar to e.g.BBC BASIC orOxygenBasic as shown elsewhere on this page. But FBSL has also anextremely 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
- m11AS SINGLE
- m12AS SINGLE
- m13AS SINGLE
- m14AS SINGLE
- m21AS SINGLE
- m22AS SINGLE
- m23AS SINGLE
- m24AS SINGLE
- m31AS SINGLE
- m32AS SINGLE
- m33AS SINGLE
- m34AS SINGLE
- m41AS SINGLE
- m42AS SINGLE
- m43AS SINGLE
- m44AS SINGLE
END TYPE
DIM mAS 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
Matrix 'm' is identity: FALSE
Matrix 'm' is identity: TRUE
Press any key to continue...
Func Identity(n)=Array id[n,n];[id]:=[1].Identity(7)[id]
[[ 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 ]]
S"fsl-util.fs"REQUIRED:build-identity( 'p n -- 'p )\ make an NxN identity matrix0DOI1+0DOIJ=IF1.0E0DUPIJ}}F!ELSE0.0E0DUPJI}}F!0.0E0DUPIJ}}F!THENLOOPLOOP;66floatmatrixa{{a{{6build-identity66a{{}}fprint
programidentitymatrixreal,dimension(:,:),allocatable::Icharacter(len=8)::fmtinteger::ms,jms=10! the desired sizeallocate(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 herewrite(*,fmt)I(:,:)deallocate(I)end programidentitymatrix
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.
ProgramIdentityIntegerNParameter(N=666)RealA(N,N)Integeri,jForAll(i=1:N,j=1:N)A(i,j)=(i/j)*(j/i)END
TheForAll 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:
DO1I=1,NDO1J=1,N1A(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 testingi = j except that the numerical values fortrue andfalse 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 deemedtrue and evenfalse. Integer arithmetic can't be relied upon across languages either, because in pl/i, integer division doesn't truncate.
' FB 1.05.0 Win64DimAsIntegernDoInput"Enter size of matrix ";nLoopUntiln>0Dimidentity(1Ton,1Ton)AsInteger'' all zero by default' enter 1s in diagonal elementsForiAsInteger=1Tonidentity(i,i)=1Next' print identity matrix if n < 40PrintIfn<40ThenForiAsInteger=1TonForjAsInteger=1TonPrintidentity(i,j);NextjPrintNextiElsePrint"Matrix is too big to display on 80 column console"EndIfPrintPrint"Press any key to quit"Sleep
Sample input/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
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}]]]Enter matrix dimension as an integer: 3┌ ┐│1 0 0││ ││0 1 0││ ││0 0 1│└ ┘
def identity( n ) = vector( n, n, \r, c -> if r == c then 1 else 0 )println( identity(3) )
((1, 0, 0), (0, 1, 0), (0, 0, 1))
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 itswebsite.
Inthis 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
include "NSLog.incl"local fn IdentityMatrix( n as NSInteger ) as CFStringRefNSInteger i, jCFMutableArrayRef tempArr = fn MutableArrayWithCapacity( n )CFMutableStringRef mutStr = fn MutableStringWithCapacity( 0 )for i = 0 to n - 1MutableArrayRemoveAllObjects( tempArr )for j = 0 to n - 1MutableArrayInsertObjectAtIndex( tempArr, @"0", j )nextMutableArrayReplaceObjectAtIndex( tempArr, @"1", i )MutableStringAppendString( mutStr, fn ArrayComponentsJoinedByString( tempArr, @" " ) )MutableStringAppendString( mutStr, @"\n" )nextend 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
3:1 0 00 1 00 0 15:1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 17:1 0 0 0 0 0 00 1 0 0 0 0 00 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 19:1 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 00 0 1 0 0 0 0 0 00 0 0 1 0 0 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 1 0 0 00 0 0 0 0 0 1 0 00 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 1
# Built-inIdentityMat(3);# One can also specify the base ringIdentityMat(3,Integersmod10);
packagemainimport("fmt""gonum.org/v1/gonum/mat")funceye(nint)*mat.Dense{m:=mat.NewDense(n,n,nil)fori:=0;i<n;i++{m.Set(i,i,1)}returnm}funcmain(){fmt.Println(mat.Formatted(eye(3)))}
⎡1 0 0⎤⎢0 1 0⎥⎣0 0 1⎦
A somewhat earlier matrix library for Go.
packagemainimport("fmt"mat"github.com/skelterjohn/go.matrix")funcmain(){fmt.Println(mat.Eye(3))}
{1, 0, 0, 0, 1, 0, 0, 0, 1}Simplest: A matrix as a slice of slices, allocated separately.
packagemainimport"fmt"funcmain(){fmt.Println(I(3))}funcI(nint)[][]float64{m:=make([][]float64,n)fori:=0;i<n;i++{a:=make([]float64,n)a[i]=1m[i]=a}returnm}
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.
packagemainimport"fmt"funcmain(){fmt.Println(I(3))}funcI(nint)[][]float64{m:=make([][]float64,n)a:=make([]float64,n*n)fori:=0;i<n;i++{a[i]=1m[i]=a[:n]a=a[n:]}returnm}
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.
packagemainimport"fmt"typematrix[]float64funcmain(){n:=3m:=I(n)// dump flat represenationfmt.Println(m)// function x turns a row and column into an index into the// flat representation.x:=func(r,cint)int{returnr*n+c}// access m by row and column.forr:=0;r<n;r++{forc:=0;c<n;c++{fmt.Print(m[x(r,c)]," ")}fmt.Println()}}funcI(nint)matrix{m:=make(matrix,n*n)// a fast way to initialize the flat representationn++fori:=0;i<len(m);i+=n{m[i]=1}returnm}
[1 0 0 0 1 0 0 0 1]1 0 0 0 1 0 0 0 1
5[ .([0]*1+ \( {.(+}*] -1% {`}%n*[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]
Solution:
defmakeIdentityMatrix={n->(0..<n).collect{i->(0..<n).collect{j->(i==j)?1:0}}}
Test:
(2..6).each{order->defiMatrix=makeIdentityMatrix(order)iMatrix.each{printlnit}println()}
[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]
matIn=[[fromEnum$i==j|i<-[1..n]]|j<-[1..n]]
And a function to show matrix pretty:
showMat::[[Int]]->StringshowMat=unlines.map(unwords.mapshow)
*Main>putStr$showMat$matId9100000000010000000001000000000100000000010000000001000000000100000000010000000001
We could alternatively bypassing the syntactic sugaring of list comprehension notation, and use a bind function directly:
idMatrix::Int->[[Int]]idMatrixn=letxs=[1..n]inxs>>=\x->[xs>>=\y->[fromEnum(x==y)]]
or reduce the number of terms a little to:
idMatrix::Int->[[Int]]idMatrixn=letxs=[1..n]in(\x->fromEnum.(x==)<$>xs)<$>xsmain::IO()main=(putStr.unlines)$unwords.fmapshow<$>idMatrix5
1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
This code works for Icon and Unicon.
linkmatrixproceduremain(argv)ifnot(integer(argv[1])>0)thenstop("Argument must be a positive integer.")matrix1:=identity_matrix(argv[1],argv[1])write_matrix(&output,matrix1)end
->im 61 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->
100 PROGRAM "Identity.bas"110 INPUT PROMPT "Enter size of matrix: ":N120 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)=0190 NEXT200 LET T(I,I)=1210 NEXT220 END DEF230 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 NEXT280 PRINT290 NEXT300 END DEF
=i.4NB. create an Identity matrix of size 41000010000100001Id=:=@i.NB. define as a verb with a user-defined nameId5NB. create an Identity matrix of size 51000001000001000001000001
publicclassPrintIdentityMatrix{publicstaticvoidmain(String[]args){intn=5;int[][]array=newint[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);}}
[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]
functionidMatrix(n){returnArray.apply(null,newArray(n)).map(function(x,i,xs){returnxs.map(function(_,k){returni===k?1:0;})});}
(()=>{// identityMatrix :: Int -> [[Int]]constidentityMatrix=n=>Array.from({length:n},(_,i)=>Array.from({length:n},(_,j)=>i!==j?0:1));// ----------------------- TEST ------------------------returnidentityMatrix(5).map(JSON.stringify).join('\n');})();
[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]
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 the definition of matrix/2 atCreate_a_two-dimensional_array_at_runtime#jq:
def identity(n): reduce range(0;n) as $i (0 | matrix(n;n); .[$i][$i] = 1);
/* Identity matrix, in Jsish */functionidentityMatrix(n){varmat=newArray(n).fill(0);for(varrinmat){mat[r]=newArray(n).fill(0);mat[r][r]=1;}returnmat;}provide('identityMatrix',1);if(Interp.conf('unitTest')){;identityMatrix(0);;identityMatrix(1);;identityMatrix(2);;identityMatrix(3);varmat=identityMatrix(4);for(varrinmat)puts(mat[r]);}/*=!EXPECTSTART!=identityMatrix(0) ==> []identityMatrix(1) ==> [ [ 1 ] ]identityMatrix(2) ==> [ [ 1, 0 ], [ 0, 1 ] ]identityMatrix(3) ==> [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ][ 1, 0, 0, 0 ][ 0, 1, 0, 0 ][ 0, 0, 1, 0 ][ 0, 0, 0, 1 ]=!EXPECTEND!=*/
promt$ jsish -u identityMatrix.jsi[PASS] identityMatrix.jsi
I is an object of type UniformScaling,representing an identity matrix of any size,boolean by default, that can be multiplied by a scalar
usingLinearAlgebraunitfloat64matrix=1.0I
UniformScaling object can be used as a function to construct a Diagonalmatrix of given size, that can be converted to a full matrix usingcollect
usingLinearAlgebradiagI3=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
usingLinearAlgebrafullI3=Matrix{Float64}(I,3,3)fullI3=Array{Float64}(I,3,3)fullI3=Array{Float64,2}(I,3,3)fullI3=zeros(3,3)+I
=4(1000010000100001)=5(1000001000001000001000001)
funmain(){print("Enter size of matrix : ")valn=readln().toInt()println()validentity=Array(n){i->IntArray(n){j->if(i==j)1else0}}// print identity matrix if n <= 40if(n<=40)for(rowinidentity)println(row.joinToString(" "))elseprintln("Matrix is too big to display on 80 column console")}
Sample input/output
Enter size of matrix : 51 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
{defidentity{lambda{:n}{A.new{S.map{{lambda{:n:i}{A.new{S.map{{lambda{:i:j}{if{=:i:j}then1else0}}:i}{S.serie0:n}}}}:n}{S.serie0:n}}}}}->identity{identity2}->[[1,0],[0,1]]{identity5}->[[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 dup iota 'A set : i.(*) A in ; [1] swap append reverse A swap reshape 'i. apply ;5 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 ]]
(defunidentity((`(,m,n))(identitymn))((m)(identitymm)))(defunidentity(mn)(lists:duplicatem(lists:duplicaten1)))
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:
>(identity3)((111)(111)(111))>(identity33)((111)(111)(111))>(identity'(33))((111)(111)(111))
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(integeriChannel,stringsName,keykId,stringsMessage){llOwnerSay("You entered "+sMessage+".");listlMatrix=[];integerx=0;integern=(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))+"]");}}}
You: 0Identity_Matrix: You entered 0.You: 1Identity_Matrix: You entered 1.Identity_Matrix: [1]You: 3Identity_Matrix: You entered 3.Identity_Matrix: [1, 0, 0]Identity_Matrix: [0, 1, 0]Identity_Matrix: [0, 0, 1]You: 5Identity_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]
functionidentity_matrix(size)localm={}fori=1,sizedom[i]={}forj=1,sizedom[i][j]=i==jand1or0endendreturnmendfunctionprint_matrix(m)fori=1,#mdoprint(table.concat(m[i]," "))endendprint_matrix(identity_matrix(5))
1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
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]
I = eye(10)
IdentityMatrix[4]
Theeye function create the identity (I) matrix, e.g.:
I=eye(10)
ident(4);/* matrix([1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]) */
/* 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)**********************************************************************/optionsreplaceformatcommentsjavacrossrefsymbolsbinaryParseArgn.Ifn=''thenn=5Say'Identity Matrix of size'n'(m[i,j] IS the Matrix)'m=int[n,n]--Allocate2Dsquarearrayatrun-timeLoopi=0Ton-1--LikeJava,arraysinNetRexxstartat0ol=''Loopj=0Ton-1m[i,j]=(i=j)ol=olm[i,j]EndSayolEnd
/* NetRexx */optionsreplaceformatcommentsjavacrossrefsymbolsnobinaryrunSample(arg)return--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~methodcreateIdMatrix(n)publicstaticDIM_='DIMENSION'm=0--Indexedstringtoholdmatrix;defaultvalueforallelementsiszerom[DIM_]=nloopi=1ton--NetRexxindexedstringsdon't have to start at zerom[i,i]=1--setthisdiagonalelementto1endireturnm--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~methoddisplayIdMatrix(m)publicstaticDIM_='DIMENSION'if\m.exists(DIM_)thensignalRuntimeException('Matrix dimension not set')n=m[DIM_]loopi=1tonol=''loopj=1Tonol=olm[i,j]endjsayolendireturn--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~methodrunSample(arg)publicstaticparseargn.ifn=''thenn=5say'Identity Matrix of size'ndisplayIdMatrix(createIdMatrix(n))return
procidentityMatrix(n:Positive):auto=result=newSeq[seq[int]](n)foriin0..<result.len:result[i]=newSeq[int](n)result[i][i]=1
def identity-matrix [n: int] { ..<$n | each {|i| ..<$n | each { $in == $i | into int } }}..5 | each { {k: $in v: (identity-matrix $in)} } | transpose -r | table -i false -e --flatten╭───┬───────┬─────────┬───────────┬─────────────┬───────────────╮│ 0 │ 1 │ 2 │ 3 │ 4 │ 5 │├───┼───────┼─────────┼───────────┼─────────────┼───────────────┤│ │ ╭───╮ │ ╭─────╮ │ ╭───────╮ │ ╭─────────╮ │ ╭───────────╮ ││ │ │ 1 │ │ │ 1 0 │ │ │ 1 0 0 │ │ │ 1 0 0 0 │ │ │ 1 0 0 0 0 │ ││ │ ╰───╯ │ │ 0 1 │ │ │ 0 1 0 │ │ │ 0 1 0 0 │ │ │ 0 1 0 0 0 │ ││ │ │ ╰─────╯ │ │ 0 0 1 │ │ │ 0 0 1 0 │ │ │ 0 0 1 0 0 │ ││ │ │ │ ╰───────╯ │ │ 0 0 0 1 │ │ │ 0 0 0 1 0 │ ││ │ │ │ │ ╰─────────╯ │ │ 0 0 0 0 1 │ ││ │ │ │ │ │ ╰───────────╯ │╰───┴───────┴─────────┴───────────┴─────────────┴───────────────╯
class IdentityMatrix { function : Matrix(n : Int) ~ Int[,] { array := Int->New[n,n]; for(row:=0; row<n; row+=1;){ for(col:=0; col<n; col+=1;){ if(row = col){ array[row, col] := 1; } else{ array[row,col] := 0; }; }; }; return array; } function : PrintMatrix(array : Int[,]) ~ Nil { sizes := array->Size(); for(row:=0; row<sizes[0]; row+=1;){ for(col:=0; col<sizes[1]; col+=1;){ value := array[row,col]; "{$value} \t"->Print(); }; '\n'->PrintLine(); }; } function : Main(args : String[]) ~ Nil { PrintMatrix(Matrix(5)); }}From the interactive loop (that we call the "toplevel"):
$ocaml#letmake_id_matrixn=letm=Array.make_matrixnn0.0infori=0topredndom.(i).(i)<-1.0done;(m);;valmake_id_matrix:int->floatarrayarray=<fun>#make_id_matrix4;;-:floatarrayarray=[|[|1.;0.;0.;0.|];[|0.;1.;0.;0.|];[|0.;0.;1.;0.|];[|0.;0.;0.;1.|]|]
another way:
#letmake_id_matrixn=Array.initn(funi->Array.initn(funj->ifi=jthen1.0else0.0));;valmake_id_matrix:int->floatarrayarray=<fun>#make_id_matrix4;;-:floatarrayarray=[|[|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.
Theeye function create the identity (I) matrix, e.g.:
I=eye(10)
(define(make-identity-matrixn)(map(lambda(i)(append(repeat0i)'(1)(repeat0(-ni1))))(iotan)))(for-eachprint(make-identity-matrix3))(for-eachprint(make-identity-matrix17))
(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 doesn't have a proper matrix class, but it does have multidimensional arrays.
say"a 3x3 identity matrix"saycallprintMatrixcreateIdentityMatrix(3)saysay"a 5x5 identity matrix"saycallprintMatrixcreateIdentityMatrix(5)::routinecreateIdentityMatrixuseargsizematrix=.array~new(size,size)loopi=1tosizeloopj=1tosizeifi==jthenmatrix[i,j]=1elsematrix[i,j]=0endjendireturnmatrix::routineprintMatrixuseargmatrixloopi=1tomatrix~dimension(1)line=""loopj=1tomatrix~dimension(2)line=linematrix[i,j]endjsaylineendi
a 3x3 identity matrix 1 0 0 0 1 0 0 0 1a 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
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 methodend classnew SquareMatrix M(8)M.SetIdentity'...del M
Built-in:
matid(9)
Custom:
matrix(9,9,i,j,i==j)
programIdentityMatrix(input,output);varmatrix:arrayofarrayofinteger;n,i,j:integer;beginwrite('Size of matrix: ');readln(n);setlength(matrix,n,n);fori:=0ton-1domatrix[i,i]:=1;fori:=0ton-1dobeginforj:=0ton-1dowrite(matrix[i,j],' ');writeln;end;end.
% ./IdentityMatrixSize of matrix: 51 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
beginvarn:=ReadInteger;varmatrix:array[,]ofinteger:=MatrGen(n,n,(i,j)->i=j?1:0);matrix.Printlnend.
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
usestrict;usewarnings;usefeature'say';subidentity_matrix{my($n)=shift()-1;map{[(0)x$_,1,(0)x($n-$_)]}0..$n}for(<456>){say"\n$_:";sayjoin' ',@$_foridentity_matrix$_;}
4:1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 5:1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 6:1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
functionidentity(integern)sequenceres=repeat(repeat(0,n),n)fori=1tondores[i][i]=1endforreturnresendfunctionppOpt({pp_Nest,1})pp(identity(3))pp(identity(5))pp(identity(7))pp(identity(9))
{{1,0,0}, {0,1,0}, {0,0,1}}{{1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0,0}, {0,0,0,1,0}, {0,0,0,0,1}}{{1,0,0,0,0,0,0}, {0,1,0,0,0,0,0}, {0,0,1,0,0,0,0}, {0,0,0,1,0,0,0}, {0,0,0,0,1,0,0}, {0,0,0,0,0,1,0}, {0,0,0,0,0,0,1}}{{1,0,0,0,0,0,0,0,0}, {0,1,0,0,0,0,0,0,0}, {0,0,1,0,0,0,0,0,0}, {0,0,0,1,0,0,0,0,0}, {0,0,0,0,1,0,0,0,0}, {0,0,0,0,0,1,0,0,0}, {0,0,0,0,0,0,1,0,0}, {0,0,0,0,0,0,0,1,0}, {0,0,0,0,0,0,0,0,1}}functionidentity($length){returnarray_map(function($key,$value){$value[$key]=1;return$value;},range(0,$length-1),array_fill(0,$length,array_fill(0,$length,0)));}functionprint_identity($identity){echoimplode(PHP_EOL,array_map(function($value){returnimplode(' ',$value);},$identity));}print_identity(identity(10));
1 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 00 0 0 0 1 0 0 0 0 00 0 0 0 0 1 0 0 0 00 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 1
(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)
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;
% 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{1dictbegin/nexchdef[11n{% [ i[exch% [ [ i11n{% [ [ i j1indexeq{1}{0}ifelse% [ [ i bexch% [ [ b i}for% [ [ b+ ipop]% [ [ b+ ]}for% [ [b+]+ ]]end}def
functionidentity($n){0..($n-1)|foreach{$row=@(0)*$n;$row[$_]=1;,$row}}functionshow($a){$a|foreach{"$_"}}$array=identity4show$array
Output:
1 0 0 00 1 0 00 0 1 00 0 0 1
$array[0][0]$array[0][1]
Output:
10
%rotates one list clockwise by one integerrotate(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 integersrotate(LoInts,LoLists,Rotated):-is_list(LoInts),maplist(rotate,LoInts,LoLists,Rotated).%helper functionappend_(Suff,Pre,List):-append([Pre],Suff,List).idmatrix(N,IdMatrix):-%make an N length list of 1s and append with N-1 0slength(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 rownumlist(0,N0,Offsets),rotate(Offsets,M,IdMatrix).main:-idmatrix(5,I),maplist(writeln,I).
?- 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 .
>ProcedureidentityMatrix(Arrayi(2),size);validonlyforsize>=0;formatsarrayi()asanidentitymatrixofsizexsizeDimi(size-1,size-1)ProtectedjForj=0Tosize-1i(j,j)=1NextEndProcedureProceduredisplayMatrix(Arraya(2))Protectedrows=ArraySize(a(),2),columns=ArraySize(a(),1)Protectedi,jFori=0TorowsForj=0TocolumnsPrint(RSet(Str(a(i,j)),3," "))NextPrintN("")NextEndProcedureIfOpenConsole()Dimi3(0,0)Dimi4(0,0)identityMatrix(i3(),3)identityMatrix(i4(),4)displayMatrix(i3())PrintN("")displayMatrix(i4())Print(#CRLF$+#CRLF$+"Press ENTER to exit"):Input()CloseConsole()EndIf
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
A simple solution, using nested lists to represent the matrix.
defidentity(size):matrix=[[0]*sizeforiinrange(size)]#matrix = [[0] * size] * size #Has a flaw. See http://stackoverflow.com/questions/240178/unexpected-feature-in-a-python-list-of-listsforiinrange(size):matrix[i][i]=1forrowsinmatrix:forelementsinrows:printelements,print""
'''Identity matrices by maps and equivalent list comprehensions'''importoperator# idMatrix :: Int -> [[Int]]defidMatrix(n):'''Identity matrix of order n, expressed as a nested map. '''eq=curry(operator.eq)xs=range(0,n)returnlist(map(lambdax:list(map(compose(int)(eq(x)),xs)),xs))# idMatrix3 :: Int -> [[Int]]defidMatrix2(n):'''Identity matrix of order n, expressed as a nested comprehension. '''xs=range(0,n)return([int(x==y)forxinxs]foryinxs)# TEST ----------------------------------------------------defmain():''' Identity matrix of dimension five, by two different routes. '''forfin[idMatrix,idMatrix2]:print('\n'+f.__name__+':','\n\n'+'\n'.join(map(str,f(5))),)# GENERIC -------------------------------------------------# compose (<<<) :: (b -> c) -> (a -> b) -> a -> cdefcompose(g):'''Right to left function composition.'''returnlambdaf:lambdax:g(f(x))# curry :: ((a, b) -> c) -> a -> b -> cdefcurry(f):'''A curried function derived from an uncurried function.'''returnlambdaa:lambdab:f(a,b)# MAIN ---if__name__=='__main__':main()
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]
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 00 1 0 00 0 1 00 0 0 1>>>A solution using the numpy library
np.mat(np.eye(size))
[ [] swap times [ 0 i^ of 1 join 0 i of join nested join ] ] is identity ( n --> [ )5 identity echo
[ [ 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 ] ]
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)}#lang racket(require math)(identity-matrix 5)
(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]])
(formerly Perl 6)
sub identity-matrix($n) { my @id; for flat ^$n X ^$n -> $i, $j { @id[$i][$j] = +($i == $j); } @id;}.say for identity-matrix(5);[1 0 0 0 0][0 1 0 0 0][0 0 1 0 0][0 0 0 1 0][0 0 0 0 1]
On the other hand, this may be clearer and/or faster:
sub identity-matrix($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[]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
[[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 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────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
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 nSay 'Identity Matrix of size' n '(m.i.j IS the Matrix)'m.=0Do 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
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.=0m.0=1000 /* the matrix' size */m.4.17.333='Walter'
size = 5im = newlist(size, size)identityMatrix(size, im)for r = 1 to size for c = 1 to size see im[r][c] next see nlnext func identityMatrix s, m m = newlist(s, s) for i = 1 to s m[i][i] = 1 next return mfunc 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:
1000001000001000001000001
Gui version
# Project : Identity Matrix# Date : 2022/16/02# Author : Gal Zsolt (~ CalmoSoft ~)# Email : <calmosoft@gmail.com>load "stdlib.ring"load "guilib.ring"size = 8C_Spacing = 1C_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 sizeLayoutButtonRow[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 = 0Output image:
3 IDN
1: [[ 1 0 0 ] [ 0 1 0 ] [ 0 0 1 ]]
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}, ""end4[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]
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]]
' formats array im() of size imsfor ims = 4 to 6print :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 "]" nextnext ims
--- 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]
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!(); }}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))[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]
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))
((1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1))
$ 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;
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
set matrix to buildIdentityMatrix(3)repeat for each item in matrixput itend repeatset matrix to buildIdentityMatrix(17)repeat for each item in matrixput itend repeatfunction buildIdentityMatrix matrixSizeset matrixList to ()repeat matrixSize timesset rowMatrixIndex to the counterset rowMatrix to ()repeat matrixSize timesif the counter equals rowMatrixIndexinsert 1 after rowMatrixelseinsert 0 after rowMatrixend ifend repeatinsert rowMatrix nested after matrixListend repeatreturn matrixListend 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)
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(' ') }}4:1 0 0 00 1 0 00 0 1 00 0 0 15:1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 16:1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1
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 J110 PRINT120 NEXT I
10
1000000000010000000000100000000001000000000010000000000100000000001000000000010000000000100000000001
(Array2D identity: (UIManager default request: 'Enter size of the matrix:') asInteger) asString
'(1 0 0 00 1 0 00 0 1 00 0 0 1 )'
function unitMatrix(n) {return map(range(n), function(k1, v1) {return map(range(n), function(k2, v2) {return v2 == v1 ? 1 : 0;});});}val eye= fn n => List.tabulate( n, fn i => List.tabulate( n, fn j=> if j=i then 1.0 else 0.0));
. mat a = I(3). mat list asymmetric a[3,3] c1 c2 c3r1 1r2 0 1r3 0 0 1
: I(3)[symmetric] 1 2 3 +-------------+ 1 | 1 | 2 | 0 1 | 3 | 0 0 1 | +-------------+
func identityMatrix(size: Int) -> [[Int]] { return (0..<size).map({i in return (0..<size).map({ $0 == i ? 1 : 0}) })}print(identityMatrix(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]]
templates identityMatrix def n: $; [1..$n -> [1..~$ -> 0, 1, $~..$n -> 0]] !end identityMatrixdef identity: 5 -> identityMatrix;$identity... -> '|$(1);$(2..last)... -> ', $;';|' -> !OUT::write
v0.5
identityMatrix templates n is $; [1..$n -> [1..~$ -> 0, 1, $~..$n -> 0]] !end identityMatrixidentity is 5 -> identityMatrix;$identity... -> '|$(1);$(2..)... -> ', $;';|' !
|1, 0, 0, 0, 0||0, 1, 0, 0, 0||0, 0, 1, 0, 0||0, 0, 0, 1, 0||0, 0, 0, 0, 1|
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::matrixproc 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 $m}Demonstrating the latter:
set m [I 5 0 1] ;# Integer 0/1 for clarity of presentationputs [$m format 2string]
1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1
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; }}IdMatrix ← ⊞=.⇡IdMatrix 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 ╯
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;}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 = IEnd Function
build_matrix(7)Sub build_matrix(n)Dim matrix()ReDim matrix(n-1,n-1)i = 0'populate the matrixFor row = 0 To n-1For col = 0 To n-1If col = i Thenmatrix(row,col) = 1Elsematrix(row,col) = 0End IfNexti = i + 1Next'display the matrixFor row = 0 To n-1For col = 0 To n-1If col < n-1 ThenWScript.StdOut.Write matrix(row,col) & " "ElseWScript.StdOut.Write matrix(row,col)End IfNextWScript.StdOut.WriteLineNextEnd Sub
1 0 0 0 0 0 00 1 0 0 0 0 00 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 1 00 0 0 0 0 0 1
Alternate version
n = 8arr = Identity(n)for i = 0 to n-1 for j = 0 to n-1 wscript.stdout.Write arr(i,j) & " " next wscript.stdout.writelinenextFunction 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 = aEnd Function1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 1
Option Explicit'------------Public Function BuildIdentityMatrix(ByVal Size As Long) As Byte()Dim i As LongDim 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 ByteDim 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 iEnd Sub'------------Sub Main() IdentityMatrixDemo 5 Debug.Print IdentityMatrixDemo 10End Sub
10000010000010000010000011000000000010000000000100000000001000000000010000000000100000000001000000000010000000000100000000001
@let { im ^(%^\@table ^(@+ =) @to) !im 4}Returns:
[[1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1]]
import "./matrix" for Matriximport "./fmt" for Fmtvar numRows = 10 // sayFmt.mprint(Matrix.identity(numRows), 2, 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 0|| 0 0 0 0 0 0 0 0 0 1|
include c:\cxpl\codes;def IntSize = 4; \number of bytes in an integerint Matrix, Size, I, J;[Text(0, "Size: "); Size:= IntIn(0);Matrix:= Reserve(Size*IntSize); \reserve memory for 2D integer arrayfor 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); ];]
Size: 51 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
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);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)
10 INPUT "Matrix size: ";size20 GO SUB 200: REM Identity matrix30 FOR r=1 TO size40 FOR c=1 TO size50 LET s$=CHR$ 1360 IF c<size THEN LET s$=" "70 PRINT i(r,c);s$;80 NEXT c90 NEXT r100 STOP 200 REM Identity matrix size220 DIM i(size,size)230 FOR i=1 TO size240 LET i(i,i)=1250 NEXT i260 RETURN