Matrix with two diagonals

Matrix with two diagonals is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Draw a square matrix which has 1's on both diagonals but 0's elsewhere.
If you can please use GUI

Ada

<lang Ada>with Ada.Text_Io; use Ada.Text_Io; with Ada.Command_Line;

procedure Matrix_With_Diagonals is

  type Matrix_Type is array (Positive range <>, Positive range <>) of Character;

  function Matrix_X (Length : Natural) return Matrix_Type is
  begin
     return M : Matrix_Type (1 .. Length, 1 .. Length) do
        for Row in M'Range (1) loop
           for Col in M'Range (2) loop
              M (Row, Col) := (if
                                 Row = Col or else
                                 Row = M'Last (2) - (Col - M'First (1))
                               then '1' else '0');
           end loop;
        end loop;
     end return;
  end Matrix_X;

  procedure Put (M : Matrix_Type) is
  begin
     for Row in M'Range (1) loop
        for Col in M'Range (2) loop
           Put (' ');
           Put (M (Row, Col));
        end loop;
        New_Line;
     end loop;
  end Put;

begin

  Put (Matrix_X (Length => Natural'Value (Ada.Command_Line.Argument (1))));

exception

  when others =>
     Put_Line ("Usage: ./matrix_with_diagonals <side-length>");

end Matrix_With_Diagonals;</lang>

ALGOL 68

<lang algol68>BEGIN # draw a matrix with 1s on the diagonals and 0s elsewhere #

   # draws a matrix with height and width = n with 1s on the diagonals #
   PROC draw 2 diagonals = ( INT n )VOID:
        BEGIN
           INT l pos := 1;
           INT r pos := n;
           FOR i TO n DO
               FOR j TO n DO
                   print( ( " ", whole( ABS ( j = l pos OR j = rpos ), 0 ) ) )
               OD;
               print( ( newline ) );
               l pos +:= 1;
               r pos -:= 1
           OD
        END # draw 2 diagonals # ;
   # test the draw 2 diagonals procedure #
   draw 2 diagonals( 10 );
   print( ( newline ) );
   draw 2 diagonals( 11 )

END</lang>

Output:

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

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

APL

Works with: Dyalog APL

<lang apl>twoDiagonals ← (⌽∨⊢)∘.=⍨∘⍳ twoDiagonals¨ 10 11</lang>

Output:

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

AppleScript

Procedural

<lang applescript>on twoDiagonalMatrix(n)

   if (n < 2) then error "twoDiagonalMatrix() handler: parameter must be > 1."
   
   set digits to {}
   set oddness to n mod 2
   repeat (n - 1 + oddness) times
       set end of digits to 0
   end repeat
   set m to n div 2 + oddness -- Middle index of digit source list.
   set item m of digits to 1
   
   set matrix to {}
   set leftLen to m - 1 -- Length of left end of each row - 1.
   set rightLen to leftLen - oddness -- Length of right end ditto.
   -- Assemble the first m rows from the relevant sections of 'digits'.
   repeat with i from m to 1 by -1
       set end of matrix to items i thru (i + leftLen) of digits & items -(i + rightLen) thru -i of digits
   end repeat
   
   -- The remaining rows are the reverse of these, not repeating the mth where n is odd.
   return matrix & reverse of items 1 thru (m - oddness) of matrix

end twoDiagonalMatrix

-- Task code. on matrixToText(matrix, separator)

   copy matrix to matrix
   set astid to AppleScript's text item delimiters
   set AppleScript's text item delimiters to separator
   repeat with thisLine in matrix
       set thisLine's contents to thisLine as text
   end repeat
   set AppleScript's text item delimiters to linefeed
   set matrix to matrix as text
   set AppleScript's text item delimiters to astid
   return matrix

end matrixToText

return linefeed & matrixToText(twoDiagonalMatrix(7), space) & ¬

   (linefeed & linefeed & matrixToText(twoDiagonalMatrix(8), space))</lang>

Output:

<lang applescript>" 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1

1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1"</lang>

Functional

<lang applescript>---------------- MATRIX WITH TWO DIAGONALS ---------------

-- bothDiagonals :: Int -> Int on bothDiagonals(n)

   -- A square matrix of dimension n with ones
   -- along both diagonals, and zeros elsewhere.
   script idOrReflection
       on |λ|(x, y)
           ({y, 1 + n - y} contains x) as integer
       end |λ|
   end script
   
   matrix(n, n, idOrReflection)

end bothDiagonals

---

TEST -------------------------

on run

   -- Two diagonal matrices of dimensions 7 and 8
   
   unlines(map(compose(showMatrix, bothDiagonals), ¬
       {7, 8}))

end run

---

GENERIC ------------------------

-- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c on compose(f, g)

   script
       property mf : mReturn(f)
       property mg : mReturn(g)
       on |λ|(x)
           mf's |λ|(mg's |λ|(x))
       end |λ|
   end script

end compose

-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)

   if m ≤ n then
       set xs to {}
       repeat with i from m to n
           set end of xs to i
       end repeat
       xs
   else
       {}
   end if

end enumFromTo

-- matrix :: Int -> Int -> ((Int, Int) -> a) -> a on matrix(nRows, nCols, f)

   -- A matrix of a given number of columns and rows,
   -- in which each value is a given function of its
   -- (zero-based) column and row indices.
   script go
       property g : mReturn(f)'s |λ|
       on |λ|(iRow)
           set xs to {}
           repeat with iCol from 1 to nCols
               set end of xs to g(iRow, iCol)
           end repeat
           xs
       end |λ|
   end script
   
   map(go, enumFromTo(1, nRows))

end matrix

-- map :: (a -> b) -> [a] -> [b] on map(f, xs)

   -- The list obtained by applying f
   -- to each element of 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

-- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)

   -- 2nd class handler function lifted into 1st class script wrapper. 
   if script is class of f then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn

-- showMatrix :: a -> String on showMatrix(rows)

   -- String representation of a matrix.
   script
       on |λ|(cells)
           unwords(map(my str, cells))
       end |λ|
   end script
   
   unlines(map(result, rows)) & linefeed

end showMatrix

-- 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

-- unwords :: [String] -> String on unwords(xs)

   set {dlm, my text item delimiters} to ¬
       {my text item delimiters, space}
   set s to xs as text
   set my text item delimiters to dlm
   return s

end unwords</lang>

Output:

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

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

AWK

<lang AWK>

1. syntax: GAWK -f MATRIX_WITH_TWO_DIAGONALS.AWK

BEGIN {

   for (n=6; n<=7; n++) {
     for (i=1; i<=n; i++) {
       for (j=1; j<=n; j++) {
         tmp = (i==j || i+j==n+1) ? 1 : 0
         printf("%2d",tmp)
       }
       printf("\n")
     }
     print("")
   }
   exit(0)

} </lang>

Output:

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

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

Basic

<lang qbasic>100 REM 110 REM DIAGONAL-DIAGONAL MATRIX 120 REM 130 LET N = 7 140 DIM A(N,N) 150 FOR I=1 TO N 150 FOR J=1 TO N 160 LET A(I,J) = 0 170 NEXT J 180 LET J1 = I 190 LET J2 = N - I + 1 200 LET A(I,J1) = 1 210 LET A(I,J2) = 1 220 NEXT I 230 REM 240 FOR I=1 TO N 250 FOR J=1 TO N 260 PRINT " ";A(I,J); 270 NEXT J 280 PRINT 290 NEXT I 300 END </lang>

Output:

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

BCPL

<lang bcpl>get "libhdr"

let diagonals(size) be

   for y = 1 to size
       for x = 1 to size
           do writef("%C%C", 
               x=y | size-x=y-1 -> '1', '0',
               x=size -> '*N', ' ')
 

let start() be $( diagonals(9)

   wrch('*N')
   diagonals(10)

$)</lang>

Output:

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

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

C

Translation of: Wren

<lang c>#include <stdio.h>

void specialMatrix(unsigned int n) {

   int i, j;
   for (i = 0; i < n; ++i) {
       for (j = 0; j < n; ++j) {
           if (i == j || i + j == n - 1) {
               printf("%d ", 1);
           } else {
               printf("%d ", 0);
           }
       }
       printf("\n");
   }

}

int main() {

   specialMatrix(10); // even n
   printf("\n");
   specialMatrix(11); // odd n
   return 0;

}</lang>

Output:

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

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

C++

<lang cpp>#include <concepts>

1. include <iostream>

// Print each element of a matrix according to a predicate. It // will print a '1' if the predicate function is true, otherwise '0'. void PrintMatrix(std::predicate<int, int, int> auto f, int size) {

 for(int y = 0; y < size; y++)
 {
   for(int x = 0; x < size; x++)
   {
     std::cout << " " << f(x, y, size);
   }
   std::cout << "\n";
 }
 std::cout << "\n";

}

int main() {

 // a lambda to create diagonals
 auto diagonals = [](int x, int y, int size)
 {
   return x == y || ((size - x - 1) == y);
 };
 
 PrintMatrix(diagonals, 8);
 PrintMatrix(diagonals, 9);

}

</lang>

Output:

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

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

CLU

<lang clu>matrix = array[array[int]]

diagonals = proc (size: int) returns (matrix)

   mat: matrix := matrix$new()
   for y: int in int$from_to(1, size) do
       line: array[int] := array[int]$new()
       for x: int in int$from_to(1, size) do
           n: int
           if x=y cor size-x=y-1 
               then n := 1
               else n := 0
           end
           array[int]$addh(line, n)
       end
       matrix$addh(mat, line)
   end
   return(mat)

end diagonals

print_matrix = proc (s: stream, mat: matrix)

   for line: array[int] in matrix$elements(mat) do
       for elem: int in array[int]$elements(line) do   
           stream$puts(s, " " || int$unparse(elem))
       end
       stream$putl(s, "")
   end

end print_matrix

start_up = proc ()

   po: stream := stream$primary_output()
   print_matrix(po, diagonals(9))
   stream$putl(po, "")
   print_matrix(po, diagonals(10))

end start_up</lang>

Output:

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

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

Draco

<lang draco>proc setDiagonals([*,*] byte matrix) void:

   word x, y, width, height;
   width := dim(matrix, 1);
   height := dim(matrix, 2);
   for x from 0 upto width-1 do
       for y from 0 upto height-1 do
           matrix[x,y] :=
               if x = y or width - x - 1 = y
                   then 1
                   else 0
               fi
       od
   od

corp

proc printMatrix([*,*] byte matrix) void:

   word x, y, width, height;
   width := dim(matrix, 1);
   height := dim(matrix, 2);
   for y from 0 upto height-1 do
       for x from 0 upto width-1 do
           write(' ', matrix[x,y]:1)
       od;
       writeln()
   od

corp

proc main() void:

   [9,9] byte m_odd;
   [10,10] byte m_even;
   
   setDiagonals(m_odd);
   printMatrix(m_odd);
   writeln();
   
   setDiagonals(m_even);
   printMatrix(m_even)

corp</lang>

Output:

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

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

Excel

LAMBDA

Excel can lift functions over scalar values to functions over two-dimensional arrays.

Here we bind the name TwoDiagonalMatrix to a lambda expression in the Name Manager of the Excel WorkBook:

(See LAMBDA: The ultimate Excel worksheet function)

Works with: Office 365 betas 2021

<lang lisp>TwoDiagonalMatrix =LAMBDA(n,

   LET(
       ixs, SEQUENCE(n, n, 0, 1),
       x, MOD(ixs, n),
       y, QUOTIENT(ixs, n),
       
       IF(x = y,
           1,
           IF(x = (n - y) - 1, 1, 0)
       )
   )

)</lang>

Output:

The formulae in cells A2 and B2 populate the whole of each adjacent matrix.

	fx	=TwoDiagonalMatrix(A2)
	A	B	C	D	E	F	G	H	I
1	N	Matrix
2	7	1	0	0	0	0	0	1
3		0	1	0	0	0	1	0
4		0	0	1	0	1	0	0
5		0	0	0	1	0	0	0
6		0	0	1	0	1	0	0
7		0	1	0	0	0	1	0
8		1	0	0	0	0	0	1
9
10	8	1	0	0	0	0	0	0	1
11		0	1	0	0	0	0	1	0
12		0	0	1	0	0	1	0	0
13		0	0	0	1	1	0	0	0
14		0	0	0	1	1	0	0	0
15		0	0	1	0	0	1	0	0
16		0	1	0	0	0	0	1	0
17		1	0	0	0	0	0	0	1

Recent builds of Excel have also introduced a MAKEARRAY function, which takes a lambda expression as an argument.

Binding the name bothDiagonalMatrix in the Excel Name Manager: <lang lisp>bothDiagonalMatrix =LAMBDA(n,

   MAKEARRAY(
       n, n, 
       LAMBDA(
           x, y, 
           INT(OR(
               x = y, 
               x = (1 + n - y)
           ))
       )
   )

)</lang>

Output:

	fx	=bothDiagonalMatrix(A2)
	A	B	C	D	E	F	G	H	I
1	N	Matrix
2	7	1	0	0	0	0	0	1
3		0	1	0	0	0	1	0
4		0	0	1	0	1	0	0
5		0	0	0	1	0	0	0
6		0	0	1	0	1	0	0
7		0	1	0	0	0	1	0
8		1	0	0	0	0	0	1
9
10	8	1	0	0	0	0	0	0	1
11		0	1	0	0	0	0	1	0
12		0	0	1	0	0	1	0	0
13		0	0	0	1	1	0	0	0
14		0	0	0	1	1	0	0	0
15		0	0	1	0	0	1	0	0
16		0	1	0	0	0	0	1	0
17		1	0	0	0	0	0	0	1

F#

<lang fsharp> // Matrix with two diagonals. Nigel Galloway: February 17th., 2022 let m11 m=Array2D.init m m (fun n g->if n=g || n+g=m-1 then 1 else 0) printfn "%A\n\n%A" (m11 5) (m11 6) </lang>

Output:

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

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

Factor

Works with: Factor version 0.99 2021-06-02

<lang factor>USING: io kernel math math.matrices prettyprint ;

<x-matrix> ( n -- matrix )

   dup dup 1 - '[ 2dup = -rot + _ = or 1 0 ? ] <matrix-by-indices> ;

6 <x-matrix> simple-table. nl 7 <x-matrix> simple-table.</lang>

Output:

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

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

FreeBASIC

Text based

<lang freebasic>Sub twoDiagonalMatrix(n As Integer)

   For i As Integer = 1 To n
       For j As Integer = 1 To n
           Print Iif((i = j) Or (i + j = n + 1), "1 ", "0 ");
       Next j
       Print
   Next i

End Sub

twoDiagonalMatrix(6) Print twoDiagonalMatrix(7) Sleep</lang>

Output:

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

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

Graphical

<lang freebasic>Dim As Integer n = 8, size = 60 * n + 70 Screenres size, size, 24 Cls Windowtitle "Matrix with two diagonals"

Dim As Integer beige = Rgb(245, 245, 220), brown = Rgb(171, 82, 54)

For x As Integer = 0 To n

   For y As Integer = 0 To n
       Dim As Integer cx = x*60 + 10
       Dim As Integer cy = y*60 + 10
       'If (x + y) Mod 2 = 0 Then
       If (x = y) Or (x + y = n) Then
           Line (cx,cy) - (cx+50, cy+50), brown, BF
           Draw String (cx + 20, cy + 20), "1", beige
       Else
           Line (cx,cy) - (cx+50, cy+50), beige, BF
       End If
   Next y

Next x Bsave "twoDiagonalMatrix.bmp",0 Sleep</lang>

Output:

https://www.dropbox.com/s/ph9r28gpkp8ao8n/twoDiagonalMatrix.bmp?dl=0

Fortran

Free form

Works with: Fortran 95

Fortran stores data in columns. Therefore, it should be checked whether instead of filling the matrix row by row (as below) it would be better to do it column by column. The profit would be cache hit optimization, better communication between CPU and RAM. Fortran allows you to zero the entire array, such as the a array below, simply by substituting a = 0. Unfortunately, an array 100x100 (that is, the choosen maximum size) would be filled with zeros even if, as in the example, we would need a much smaller array. You can also eliminate the variables j1 and j2 by replacing them with i and n - i + 1 respectively, but the source code would be slightly less readable. <lang Fortran>program prog

   dimension a(100, 100)

   n = 7

   j1 = 1
   j2 = n
   do i = 1, n
       do j = 1, n
           a(i, j) = 0.
       end do
       a(i, j1) = 1
       a(i, j2) = 1
       j1 = j1 + 1
       j2 = j2 - 1
   end do

   do i = 1, n
       print *, (a(i, j), j=1,n)
   end do

end </lang>

Output:

   1.00000000       0.00000000E+00   0.00000000E+00   0.00000000E+00   0.00000000E+00   0.00000000E+00   1.00000000    
   0.00000000E+00   1.00000000       0.00000000E+00   0.00000000E+00   0.00000000E+00   1.00000000       0.00000000E+00
   0.00000000E+00   0.00000000E+00   1.00000000       0.00000000E+00   1.00000000       0.00000000E+00   0.00000000E+00
   0.00000000E+00   0.00000000E+00   0.00000000E+00   1.00000000       0.00000000E+00   0.00000000E+00   0.00000000E+00
   0.00000000E+00   0.00000000E+00   1.00000000       0.00000000E+00   1.00000000       0.00000000E+00   0.00000000E+00
   0.00000000E+00   1.00000000       0.00000000E+00   0.00000000E+00   0.00000000E+00   1.00000000       0.00000000E+00
   1.00000000       0.00000000E+00   0.00000000E+00   0.00000000E+00   0.00000000E+00   0.00000000E+00   1.00000000      

Fixed form

Works with: Fortran 77

Fortran is the oldest high-level programming language. It is constantly evolving and unfortunately there are no longer (or at least I do not have) computers on which to test whether the program works in the old Fortran IV or an even older dialect. The example below should be in Fortran IV, but unfortunately it was tested with a modern Fortran 2018 compiler, so even in legacy mode it is not Fortran IV but Fortran 77. However, it seems that it should work on CDC6000 mainframe ... if someone obviously has CDC6000. <lang fortran>C DIAGONAL-DIAGONAL MATRIX IN FORTRAN 77

      PROGRAM PROG

      DIMENSION A(100, 100)

      N = 7

      A = 0.
      DO 10 I = 1, N
      A(I, I) = 1.
 10   A(I, N - I + 1) = 1.

      DO 20 I = 1, N
 20   PRINT *, (A(I, J), J=1,N)

      END</lang>

Go

Translation of: Wren

<lang go>package main

import "fmt"

func specialMatrix(n uint) {

   for i := uint(0); i < n; i++ {
       for j := uint(0); j < n; j++ {
           if i == j || i+j == n-1 {
               fmt.Printf("%d ", 1)
           } else {
               fmt.Printf("%d ", 0)
           }
       }
       fmt.Println()
   }

}

func main() {

   specialMatrix(8) // even n
   fmt.Println()
   specialMatrix(9) // odd n

}</lang>

Output:

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

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

Haskell

<lang haskell>---------------- MATRIX WITH TWO DIAGONALS ---------------

twoDiagonalMatrix :: Int -> Int twoDiagonalMatrix n = flip (fmap . go) xs <$> xs

 where
   xs = [1 .. n]
   go x y
     | y == x = 1
     | y == succ (subtract x n) = 1
     | otherwise = 0

---

TEST -------------------------

main :: IO () main =

 mapM_ putStrLn $
   unlines . fmap (((' ' :) . show) =<<)
     . twoDiagonalMatrix
     <$> [7, 8]</lang>

Or, in the form of a list comprehension: <lang haskell>-------------- MATRIX WITH TWO DIAGONALS ---------------

twoDiagonalMatrix :: Int -> Int twoDiagonalMatrix n =

 let xs = [1 .. n]
  in [ [ fromEnum $ x `elem` [y, succ (n - y)]
         | x <- xs
       ]
       | y <- xs
     ]

---

TEST -------------------------

main :: IO () main =

 mapM_ putStrLn $
   unlines . fmap (((' ' :) . show) =<<)
     . twoDiagonalMatrix
     <$> [7, 8]</lang>

Output:

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

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

and in terms of the Data.Matrix library: <lang haskell>import Data.Matrix

twoDiagonals :: Int -> Matrix Int twoDiagonals n =

 matrix
   n
   n
   (\(a, b) -> fromEnum $ a `elem` [b, succ (n - b)])

main :: IO () main =

 mapM_ print $ twoDiagonals <$> [7, 8]</lang>

Output:

┌               ┐
│ 1 0 0 0 0 0 1 │
│ 0 1 0 0 0 1 0 │
│ 0 0 1 0 1 0 0 │
│ 0 0 0 1 0 0 0 │
│ 0 0 1 0 1 0 0 │
│ 0 1 0 0 0 1 0 │
│ 1 0 0 0 0 0 1 │
└               ┘
┌                 ┐
│ 1 0 0 0 0 0 0 1 │
│ 0 1 0 0 0 0 1 0 │
│ 0 0 1 0 0 1 0 0 │
│ 0 0 0 1 1 0 0 0 │
│ 0 0 0 1 1 0 0 0 │
│ 0 0 1 0 0 1 0 0 │
│ 0 1 0 0 0 0 1 0 │
│ 1 0 0 0 0 0 0 1 │
└                 ┘

J

Implementation:

<lang J>task=: Template:(+.</lang>

In other words, generate an order n identity matrix, flip it and (treating it as a bit matrix) OR the two matrices.

Some examples:

<lang J> task 2 1 1 1 1

  task 3

1 0 1 0 1 0 1 0 1

  task 4

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

  task 5

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

  task 6

1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1</lang>

Java

The "Java philosophy" is the object-oriented paradigm. The example solution given below is therefore somewhat incomplete. We should first declare the matrix as an interface (or abstract class), then create a whole hierarchy of subclasses where DiagonalDiagonalMatrix would be a subclass of SquareMatrix or something like that. Of course, it's a gigantic job, but as a result we would have a library competing with Matlab / Octave etc., compliant with SOLID principles. <lang java>package example.diagdiag;

public class Program {

   public static void main(String[] args) {
       DiagonalDiagonalMatrix A = new DiagonalDiagonalMatrix(7);
       System.out.println(A);
   }

}

class DiagonalDiagonalMatrix {

   final int n;
   private double[][] a = null;

   public Matrix(int n) {
       this.n = n;
   }

   public double get(int i, int j) {
       if (a == null) {
           return (i == j || i == n - j + 1) ? 1.0 : 0.0;
       } else {
           return a[i - 1][j - 1];
       }
   }

// Not necessary for the task: a lazy creation of the dense matrix. // // public void put(int i, int j, double value) { // if (a == null) { // a = new double[n][n]; // for (int p = 1; p <= n; i++) { // for (int q = 1; q <= n; j++) { // a[p - 1][q - 1] = get(p, q); // } // } // } // a[i - 1][j - 1] = value; // }

   @Override
   public String toString() {
       StringBuilder sb = new StringBuilder();
       for (int i = 1; i <= n; i++) {
           for (int j = 1; j <= n; j++) {
               sb.append('\t');
               sb.append(get(i, j));
           }
           sb.append('\n');
       }
       return sb.toString();
   }

}</lang>

Output:

	1.0	0.0	0.0	0.0	0.0	0.0	1.0
	0.0	1.0	0.0	0.0	0.0	1.0	0.0
	0.0	0.0	1.0	0.0	1.0	0.0	0.0
	0.0	0.0	0.0	1.0	0.0	0.0	0.0
	0.0	0.0	1.0	0.0	1.0	0.0	0.0
	0.0	1.0	0.0	0.0	0.0	1.0	0.0
	1.0	0.0	0.0	0.0	0.0	0.0	1.0

JavaScript

<lang javascript>(() => {

   "use strict";

   // ------------ MATRIX WITH TWO DIAGONALS ------------

   // doubleDiagonal :: Int -> Int
   const doubleDiagonal = n => {
       // A square matrix of dimension n with ones
       // along both diagonals, and zeros elsewhere.
       const xs = enumFromTo(1)(n);

       return xs.map(
           y => xs.map(
               x => Number(
                   [y, 1 + n - y].includes(x)
               )
           )
       );
   };

   // ---------------------- TEST -----------------------
   const main = () => [7, 8].map(
       n => showMatrix(
           doubleDiagonal(n)
       )
   ).join("\n\n");

   // --------------------- GENERIC ---------------------

   // enumFromTo :: Int -> Int -> [Int]
   const enumFromTo = m =>
       n => Array.from({
           length: 1 + n - m
       }, (_, i) => m + i);

   // showMatrix :: a -> String
   const showMatrix = rows =>
       // String representation of a matrix.
       rows.map(
           row => row.map(String).join(" ")
       ).join("\n");

   // MAIN --
   return main();

})();</lang>

Or, in terms of a more general matrix function: <lang javascript>(() => {

   "use strict";

   // ------------ MATRIX WITH TWO DIAGONALS ------------

   // bothDiagonals :: Int -> Int
   const bothDiagonals = n =>
       matrix(n)(n)(
           y => x => Number(
               [y, (n - y) - 1].includes(x)
           )
       );

   // ---------------------- TEST -----------------------
   const main = () => [7, 8].map(
       compose(
           showMatrix,
           bothDiagonals
       )
   ).join("\n\n");

   // --------------------- GENERIC ---------------------

   // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
   const compose = (...fs) =>
       // A function defined by the right-to-left
       // composition of all the functions in fs.
       fs.reduce(
           (f, g) => x => f(g(x)),
           x => x
       );

   // matrix Int -> Int -> (Int -> Int -> a) -> a
   const matrix = nRows => nCols =>
       // A matrix of a given number of columns and rows,
       // in which each value is a given function of its
       // (zero-based) column and row indices.
       f => Array.from({
           length: nRows
       }, (_, iRow) => Array.from({
           length: nCols
       }, (__, iCol) => f(iRow)(iCol)));

   // showMatrix :: a -> String
   const showMatrix = rows =>
       // String representation of a matrix.
       rows.map(
           row => row.map(String).join(" ")
       ).join("\n");

   // MAIN ---
   return main();

})();</lang>

Output:

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

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

jq

Works with: jq

Works with gojq, the Go implementation of jq <lang jq>def bidiagonal_matrix:

 . as $n
 | [range(0; $n) | 0] as $z
 | reduce range(0; $n) as $i ([];
     . + [$z | .[$i] = 1 | .[$n-$i-1] = 1] );

def display:

 map(join(" ")) | join("\n");</lang>

Example <lang jq>9|bidiagonal_matrix|display</lang>

Output:

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

Julia

<lang julia> julia> twodiagonalmat(n) = [Int(i == j || i == n - j + 1) for j in 1:n, i in 1:n] twodiagonalmat (generic function with 1 method)

julia> twodiagonalmat(1) 1×1 Matrix{Int64}:

1

julia> twodiagonalmat(2) 2×2 Matrix{Int64}:

1  1
1  1

julia> twodiagonalmat(3) 3×3 Matrix{Int64}:

1  0  1
0  1  0
1  0  1

julia> twodiagonalmat(4) 4×4 Matrix{Int64}:

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

julia> twodiagonalmat(5) 5×5 Matrix{Int64}:

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

</lang>

Sparse matrix version

<lang julia>julia> using LinearAlgebra

julia> twodiagonalsparse(n) = I(n) .| rotl90(I(n)) twodiagonalsparse (generic function with 1 method)

julia> twodiagonalsparse(7) 7×7 SparseArrays.SparseMatrixCSC{Bool, Int64} with 13 stored entries:

1  ⋅  ⋅  ⋅  ⋅  ⋅  1
⋅  1  ⋅  ⋅  ⋅  1  ⋅
⋅  ⋅  1  ⋅  1  ⋅  ⋅
⋅  ⋅  ⋅  1  ⋅  ⋅  ⋅
⋅  ⋅  1  ⋅  1  ⋅  ⋅
⋅  1  ⋅  ⋅  ⋅  1  ⋅
1  ⋅  ⋅  ⋅  ⋅  ⋅  1

julia> twodiagonalsparse(8) 8×8 SparseArrays.SparseMatrixCSC{Bool, Int64} with 16 stored entries:

1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1
⋅  1  ⋅  ⋅  ⋅  ⋅  1  ⋅
⋅  ⋅  1  ⋅  ⋅  1  ⋅  ⋅
⋅  ⋅  ⋅  1  1  ⋅  ⋅  ⋅
⋅  ⋅  ⋅  1  1  ⋅  ⋅  ⋅
⋅  ⋅  1  ⋅  ⋅  1  ⋅  ⋅
⋅  1  ⋅  ⋅  ⋅  ⋅  1  ⋅
1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1

</lang>

Matlab

<lang Matlab>function A = diagdiag(N, sparse) % Create an diagonal-diagonal square matrix. % % Parameters: % % N -- number of rows (columns); % sparse -- should be true to create a sparse matrix, % default false (dense matrix). % % Return: % % A matrix where all elements A(i, j) are zero except % elements on the diagonal or on the back-diagonal. % The diagonal (and back-diagonal) elements are equal 1.

   if nargin < 2
       sparse = false;
   end        
   
   if sparse
       A = speye(N);
   else
       A = eye(N);
   end
   
   A = fliplr(A);
   A(1:N+1:end) = 1;

end</lang>

Output:

>> diagdiag(7)

ans =

  Columns 1 through 7

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

>> diagdiag(7, true)

ans =

   (1,1)        1
   (7,1)        1
   (2,2)        1
   (6,2)        1
   (3,3)        1
   (5,3)        1
   (4,4)        1
   (3,5)        1
   (5,5)        1
   (2,6)        1
   (6,6)        1
   (1,7)        1
   (7,7)        1

Pascal

<lang pascal>program bidiagonal; const N = 7; type

   index = 1..N;

var

   a : array[index, index] of real;
   i, j, j1, j2 : index;

begin

   for i := 1 to N do
   begin
       for j := 1 to N do
           a[i, j] := 0.0;
       j1 := i;
       j2 := N - i + 1;
       a[i, j1] := 1.0;
       a[i, j2] := 1.0;
   end;
   
   for i := 1 to N do
   begin
       for j := 1 to N do
           write(a[i, j]:2:0);
       writeln();
   end

end. </lang>

Output:

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

Perl

Strings

<lang perl>#!/usr/bin/perl

use strict; #https://rosettacode.org/wiki/Matrix_with_two_diagonals use warnings;

print diagonal($_), "\n" for 10, 11;

sub diagonal

 {
 my $n =  shift() - 1;
 local $_ = 1 . 0 x ($n - 1) . 2 . "\n" . (0 . 0 x $n . "\n") x $n;
 1 while s/(?<=1...{$n})0/1/s or s/(?<=2.{$n})[01]/2/s;
 return tr/2/1/r =~ s/\B/ /gr;
 }</lang>

Output:

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

Numbers

<lang perl>use strict; use warnings; use feature 'say';

sub dual_diagonal {

   my($n) = shift() - 1;
   my @m;
   for (0..$n) {
       my @rr = reverse my @r = ( (0) x $_, 1, (0) x ($n-$_) );
       push @m, [ map { $r[$_] or $rr[$_] } 0..$n ]
   }
   @m

}

say join ' ', @$_ for dual_diagonal(4); say ; say join ' ', @$_ for dual_diagonal(5); </lang>

Output:

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

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

Phix

numbers

Tee hee, pick the bones out of this one. Lovely.

with javascript_semantics
for n=6 to 7 do
    pp(apply(true,reinstate,{repeat(repeat(0,n),n),apply(true,sq_mul,{tagset(n),{{1,-1}}}),{{1,1}}}),{pp_Nest,1})
end for

Output:

{{1,0,0,0,0,1},
 {0,1,0,0,1,0},
 {0,0,1,1,0,0},
 {0,0,1,1,0,0},
 {0,1,0,0,1,0},
 {1,0,0,0,0,1}}
{{1,0,0,0,0,0,1},
 {0,1,0,0,0,1,0},
 {0,0,1,0,1,0,0},
 {0,0,0,1,0,0,0},
 {0,0,1,0,1,0,0},
 {0,1,0,0,0,1,0},
 {1,0,0,0,0,0,1}}

Slightly saner, shows sackly same stuff:

with javascript_semantics
for n=6 to 7 do
    sequence s = repeat(repeat(0,n),n)
    for i=1 to n do
        s[i][i] = 1
        s[i][-i] = 1
    end for
    pp(s,{pp_Nest,1})
end for

strings

with javascript_semantics
for n=6 to 7 do
    sequence s = repeat(join(repeat('0',n),' '),n)
    for i=1 to n do
        integer j = 2*i-1
        s[i][j] = '1'
        s[i][-j] = '1'
    end for
    printf(1,"%s\n\n",{join(s,"\n")})
end for

Output:

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

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

GUI/online

Library: Phix/pGUI

Library: Phix/online

Based on 2048#Phix, and uses the same colour and font choices. You can run this online here.

with javascript_semantics
include pGUI.e

constant TITLE = "Strange Identity Matrices",
         HELPTXT = """
Press F1 to see this help text.
Press +/- to increase or decrease the matrix size
Press 'M' for a mosaic pattern
Press 'O' for outer or four sides of a square
Press 'X' for two diagonals
The window can be fully resized
(MINSIZE does not yet work in a browser)
"""

function help()
    IupMessage(TITLE,HELPTXT,bWrap:=false)
    return IUP_DEFAULT
end function

Ihandle canvas, dlg
cdCanvas cddbuffer, cdcanvas

sequence board
integer n = 5,
        mtype = 'X' -- (two diags) or 'O'uter or 'M'osaic

function mosaic()
    for y=1 to n do
        for x=1+odd(n+y) to n by 2 do
            board[y][x] = "1"
        end for
    end for
    return "mosaic"
end function

function outer()
    for y=1 to n do
        integer step = iff(y=1 or y=n?1:n-1)
        for x=1 to n by step do
            board[y][x] = "1"
        end for
    end for
    return "four sides"
end function

function diag()
    for i=1 to n do
        board[i][i] = "1"
        board[i][-i] = "1"
    end for
    return "two diagonals"
end function

function redraw_cb(Ihandle /*ih*/)
    integer {dw,dh} = IupGetIntInt(canvas, "DRAWSIZE"),
            ms = n*5+5,                 -- margin space
            mx = min(dw,dh)-ms,         -- max size
            ts = floor(mx/n),           -- max tile size
            th = floor(ts/2),           -- for text posn
            os = ts*n+ms,               -- overall size
            ox = floor((dw-os)/2),      -- top right x
            oy = floor((dh-os)/2),      -- top right y
            font_size = floor((ts+10)/2)

    board = repeat(repeat("0",n),n)
    string title
    switch mtype do
        case 'M': title = mosaic()
        case 'O': title = outer()
        case 'X': title = diag()
    end switch
    IupSetStrAttribute(dlg,"TITLE","%s (%dx%d, %s)",{TITLE,n,n,title})

    cdCanvasActivate(cddbuffer)
    cdCanvasSetBackground(cddbuffer, #FAF8EF)
    cdCanvasClear(cddbuffer)
    cdCanvasSetForeground(cddbuffer, #BBADA0)
    cdCanvasRoundedBox(cddbuffer, ox, ox+os, oy, oy+os, 10, 10)
    cdCanvasFont(cddbuffer, "Calibri", CD_BOLD, font_size)

    integer tx = ox+5
    for y=1 to n do
        integer ty = oy+5
        for x=1 to n do
            string bxy = board[x][y]
            cdCanvasSetForeground(cddbuffer, #EEE4DA)
            cdCanvasRoundedBox(cddbuffer, tx, tx+ts-2, ty, ty+ts-2, 5, 5)
            cdCanvasSetForeground(cddbuffer, #776E65)
            cdCanvasText(cddbuffer, tx+th, ty+th, bxy) 
            ty += ts+5
        end for
        tx += ts+5
    end for

    cdCanvasFlush(cddbuffer)
    return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
    cdcanvas = cdCreateCanvas(CD_IUP, ih)
    cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
    cdCanvasSetTextAlignment(cddbuffer, CD_CENTER) 
    return IUP_DEFAULT
end function

function key_cb(Ihandle /*ih*/, atom c)
    if c=K_ESC then return IUP_CLOSE end if
    if c=K_F1 then return help() end if
    if c='+' then n += 1 end if
    if c='-' then n -= (n>1) end if
    c = upper(c)
    if find(c,"MOX") then mtype = c end if
    IupUpdate(canvas)
    return IUP_CONTINUE
end function

IupOpen()
canvas = IupCanvas("RASTERSIZE=532x532")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas,"MINSIZE=440x450")
IupSetCallback(dlg, "K_ANY", Icallback("key_cb"))
IupSetAttributeHandle(NULL,"PARENTDIALOG",dlg)
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
if platform()!=JS then
    IupMainLoop()
    IupClose()
end if

PHP

<lang php><?php

$n = 9; // the number of rows

for ($i = 1; $i <= $n; $i++) {

   for ($j = 1; $j <= $n; $j++) {
       echo ($i == $j || $i == $n - $j + 1) ? ' 1' : ' 0';
   }
   echo "\n";

} </lang>

Output:

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

Python

Pure Python

<lang python>Matrix with two diagonals

1. twoDiagonalMatrix :: Int -> Int

def twoDiagonalMatrix(n):

   A square matrix of dimension n with ones
      along both diagonals, and zeros elsewhere.
   
   return matrix(
       n, n, lambda row, col: int(
           row in (col, 1 + (n - col))
       )
   )

1. ------------------------- TEST -------------------------
2. main :: IO ()

def main():

   Matrices of dimension 7 and 8
   for n in [7, 8]:
       print(
           showMatrix(
               twoDiagonalMatrix(n)
           ) + '\n'
       )

1. ----------------------- GENERIC ------------------------

1. matrix :: Int -> Int -> ((Int, Int) -> a) -> a

def matrix(nRows, nCols, f):

   A matrix of a given number of columns and rows,
      in which each value is a given function over the
      tuple of its (one-based) row and column indices.
   
   return [
       [f(y, x) for x in range(1, 1 + nCols)]
       for y in range(1, 1 + nRows)
   ]

1. showMatrix :: Int -> String

def showMatrix(rows):

   String representation of a matrix
   return '\n'.join([
       ' '.join([str(x) for x in y]) for y in rows
   ])

1. MAIN ---

if __name__ == '__main__':

   main()</lang>

Output:

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

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

NumPy

Library: numpy

<lang Python>import numpy as np

def diagdiag(n):

   """
   Create a diagonal-diagonal matrix

   Args:
       n (int): number of rows.

   Returns:
       a (numpy matrix): double diagonal matrix.

   """
   d = np.eye(n)
   a = d + np.fliplr(d)
   if n % 2:
       k = (n - 1) // 2
       a[k, k] = 1
   return a

print(diagdiag(7))</lang>

Output:

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

Raku

<lang perl6>sub dual-diagonal($n) { ([1, |(0 xx $n-1)], *.rotate(-1) … *[*-1]).map: { [$_ Z|| .reverse] } }

.say for dual-diagonal(6); say ; .say for dual-diagonal(7);</lang>

Output:

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

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

Red

<lang rebol>Red[]

x-matrix: function [size][

   repeat i size [
       repeat j size [
           prin either any [i = j i + j = (size + 1)] [1] [0]
           prin sp
       ]
       prin newline
   ]

]

x-matrix 6 prin newline x-matrix 7</lang>

Output:

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

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

Ring

<lang ring>

1. Project : Identity Matrix
2. Date  : 2022/16/02
3. Author  : Gal Zsolt (~ CalmoSoft ~)
4. 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 or Row + Col = 9
               Button[Row][Col].setStyleSheet(C_ButtonOrangeStyle)
               Button[Row][Col].settext("1")
            else
               Button[Row][Col].setStyleSheet(C_ButtonBlueStyle)
               Button[Row][Col].settext("0")
            ok

next

    next
    score = 0

</lang> Outpu image:
Special identity matrix with two diagonals

Wren

A terminal based solution as I don't like asking people to view external images. <lang ecmascript>var specialMatrix = Fn.new { |n|

   for (i in 0...n) {
       for (j in 0...n) {
           System.write((i == j || i + j == n - 1) ? "1 " : "0 ")
       }
       System.print()
   }

}

specialMatrix.call(6) // even n System.print() specialMatrix.call(7) // odd n</lang>

Output:

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

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

XPL0

<lang XPL0>proc DrawMat(S); int S, I, J; [for I:= 0 to S-1 do

   [for J:= 0 to S-1 do
       Text(0, if J=I or J=S-1-I then "1 " else "0 ");
   CrLf(0);
   ];

]; [DrawMat(6); CrLf(0);

DrawMat(7);  CrLf(0);

]</lang>

Output:

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

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