Walsh matrix: Difference between revisions
Content deleted Content added
Thundergnat (talk | contribs) m Promote to full task. Over a year as a draft, multiple implementations, little controversy. |
|||
(7 intermediate revisions by 3 users not shown) | |||
Line 1:
{{
{{Wikipedia|Walsh matrix}}
Line 50:
;* [[Kronecker product|Related task: Kronecker product]]
=={{header|Ada}}==
This solution demonstrates Ada enumerations for matrix values, for how to display the matrix (with numbers or as "red" (`#`) and green (`_`), and as array indices. It also illustrates usage of a default value of a procedure parameter.
<syntaxhighlight lang="ada">
pragma Ada_2022;
with Ada.Containers.Generic_Array_Sort;
with Ada.Text_IO;
procedure Walsh_Matrices is
package IO renames Ada.Text_IO;
-- SECTION
-- Definition of a Walsh Matrix
type Walsh_Value is (Red, Green);
Opposite : constant array (Walsh_Value) of Walsh_Value :=
[Red => Green, Green => Red];
type Walsh_Matrix is
array (Positive range <>, Positive range <>) of Walsh_Value;
-- SECTION
-- Sorting the matrix
-- In order to avail ourselves of Ada's standard library,
-- we define an auxiliary data
-- that records the number of sign changes in a given row.
-- We sort an array of **that** structure, then
-- use that to sort the matrix.
type Sort_Data_Record is record
Row : Positive;
Sign_Changes : Natural;
end record;
type Sort_Data_Array is array (Positive range <>) of Sort_Data_Record;
function "<" (Left, Right : Sort_Data_Record) return Boolean is
(Left.Sign_Changes < Right.Sign_Changes);
procedure Sort_By_Sequency is new Ada.Containers.Generic_Array_Sort
(Index_Type => Positive, Element_Type => Sort_Data_Record,
Array_Type => Sort_Data_Array);
function Number_Of_Sign_Changes
(Matrix : Walsh_Matrix; Row : Positive) return Natural
is
Result : Natural := 0;
begin
for Col in 2 .. Matrix'Last (2) loop
Result :=
@ + (if Matrix (Row, Col) = Matrix (Row, Col - 1) then 0 else 1);
end loop;
return Result;
end Number_Of_Sign_Changes;
procedure Sort_Matrix_By_Sequency (Matrix : in out Walsh_Matrix) is
Sort_Data : Sort_Data_Array (Matrix'Range (1)) :=
[for Ith in Matrix'Range (1) =>
(Row => Ith,
Sign_Changes => Number_Of_Sign_Changes (Matrix, Ith))];
Temp : Walsh_Matrix (Matrix'Range (1), Matrix'Range (2));
begin
Sort_By_Sequency (Sort_Data);
for Row in Matrix'Range (1) loop
for Col in Matrix'Range (2) loop
Temp (Row, Col) := Matrix (Sort_Data (Row).Row, Col);
end loop;
end loop;
Matrix := Temp;
end Sort_Matrix_By_Sequency;
-- SECTION
-- Displaying a Walsh Matrix
type Display is (Number, Color);
-- for the colors we imitate the Algol implementation
Output : constant array (Walsh_Value, Display) of String (1 .. 2) :=
[Red => [Number => "-1", Color => " #"],
Green => [Number => " 1", Color => " _"]];
procedure Put (W : Walsh_Matrix; Kind : Display := Number) is
begin
for Row in W'Range (1) loop
IO.Put ("( ");
for Col in W'Range (2) loop
IO.Put (Output (W (Row, Col), Kind) & " ");
end loop;
IO.Put_Line (" )");
end loop;
end Put;
-- SECTION
-- Creating a Walsh Matrix
procedure Fill (W : in out Walsh_Matrix; Row, Col, Dim : Positive) is
-- recursively fills a 2^Dim square submatrix of W,
-- starting from the given row and column
begin
if Dim = 1 then
W (Row, Col) := Green;
W (Row, Col + 1) := Green;
W (Row + 1, Col) := Green;
W (Row + 1, Col + 1) := Red;
else
Fill (W, Row, Col, Dim - 1);
Fill (W, Row, Col + 2**(Dim - 1), Dim - 1);
Fill (W, Row + 2**(Dim - 1), Col, Dim - 1);
Fill (W, Row + 2**(Dim - 1), Col + 2**(Dim - 1), Dim - 1);
for R in Row + 2**(Dim - 1) .. Row + 2**Dim - 1 loop
for C in Col + 2**(Dim - 1) .. Col + 2**Dim - 1 loop
W (R, C) := Opposite (@);
end loop;
end loop;
end if;
end Fill;
function New_Matrix (Dimension : Positive) return Walsh_Matrix is
Result : Walsh_Matrix (1 .. 2**Dimension, 1 .. 2**Dimension);
begin
Fill (Result, Result'First (1), Result'First (2), Dimension);
return Result;
end New_Matrix;
-- SECTION
-- a few values
W_1 : Walsh_Matrix := New_Matrix (1);
W_2 : Walsh_Matrix := New_Matrix (2);
W_5 : Walsh_Matrix := New_Matrix (5);
begin
Put (W_1, Color);
IO.New_Line;
Sort_Matrix_By_Sequency (W_1);
Put (W_1, Color);
IO.New_Line;
Put (W_2, Color);
IO.New_Line;
Sort_Matrix_By_Sequency (W_2);
Put (W_2, Color);
IO.New_Line;
Put (W_5, Color);
IO.New_Line;
Put (W_5);
IO.New_Line;
Sort_Matrix_By_Sequency (W_5);
Put (W_5, Color);
IO.New_Line;
end Walsh_Matrices;
</syntaxhighlight>
{{out}}
<pre>
( _ _ )
( _ # )
( _ _ )
( _ # )
( _ _ _ _ )
( _ # _ # )
( _ _ # # )
( _ # # _ )
( _ _ _ _ )
( _ _ # # )
( _ # # _ )
( _ # _ # )
( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ )
( _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # )
( _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # )
( _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ )
( _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # )
( _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ )
( _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ )
( _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # )
( _ _ _ _ _ _ _ _ # # # # # # # # _ _ _ _ _ _ _ _ # # # # # # # # )
( _ # _ # _ # _ # # _ # _ # _ # _ _ # _ # _ # _ # # _ # _ # _ # _ )
( _ _ # # _ _ # # # # _ _ # # _ _ _ _ # # _ _ # # # # _ _ # # _ _ )
( _ # # _ _ # # _ # _ _ # # _ _ # _ # # _ _ # # _ # _ _ # # _ _ # )
( _ _ _ _ # # # # # # # # _ _ _ _ _ _ _ _ # # # # # # # # _ _ _ _ )
( _ # _ # # _ # _ # _ # _ _ # _ # _ # _ # # _ # _ # _ # _ _ # _ # )
( _ _ # # # # _ _ # # _ _ _ _ # # _ _ # # # # _ _ # # _ _ _ _ # # )
( _ # # _ # _ _ # # _ _ # _ # # _ _ # # _ # _ _ # # _ _ # _ # # _ )
( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ # # # # # # # # # # # # # # # # )
( _ # _ # _ # _ # _ # _ # _ # _ # # _ # _ # _ # _ # _ # _ # _ # _ )
( _ _ # # _ _ # # _ _ # # _ _ # # # # _ _ # # _ _ # # _ _ # # _ _ )
( _ # # _ _ # # _ _ # # _ _ # # _ # _ _ # # _ _ # # _ _ # # _ _ # )
( _ _ _ _ # # # # _ _ _ _ # # # # # # # # _ _ _ _ # # # # _ _ _ _ )
( _ # _ # # _ # _ _ # _ # # _ # _ # _ # _ _ # _ # # _ # _ _ # _ # )
( _ _ # # # # _ _ _ _ # # # # _ _ # # _ _ _ _ # # # # _ _ _ _ # # )
( _ # # _ # _ _ # _ # # _ # _ _ # # _ _ # _ # # _ # _ _ # _ # # _ )
( _ _ _ _ _ _ _ _ # # # # # # # # # # # # # # # # _ _ _ _ _ _ _ _ )
( _ # _ # _ # _ # # _ # _ # _ # _ # _ # _ # _ # _ _ # _ # _ # _ # )
( _ _ # # _ _ # # # # _ _ # # _ _ # # _ _ # # _ _ _ _ # # _ _ # # )
( _ # # _ _ # # _ # _ _ # # _ _ # # _ _ # # _ _ # _ # # _ _ # # _ )
( _ _ _ _ # # # # # # # # _ _ _ _ # # # # _ _ _ _ _ _ _ _ # # # # )
( _ # _ # # _ # _ # _ # _ _ # _ # # _ # _ _ # _ # _ # _ # # _ # _ )
( _ _ # # # # _ _ # # _ _ _ _ # # # # _ _ _ _ # # _ _ # # # # _ _ )
( _ # # _ # _ _ # # _ _ # _ # # _ # _ _ # _ # # _ _ # # _ # _ _ # )
( 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 )
( 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 )
( 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 )
( 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 )
( 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 )
( 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 )
( 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 )
( 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 )
( 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 )
( 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 )
( 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 )
( 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 )
( 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 )
( 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 )
( 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 )
( 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 )
( 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 )
( 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 )
( 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 )
( 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 )
( 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 )
( 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 )
( 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 )
( 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 )
( 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 )
( 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 )
( 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 )
( 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 )
( 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 )
( 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 )
( 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 )
( 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 )
( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ )
( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ # # # # # # # # # # # # # # # # )
( _ _ _ _ _ _ _ _ # # # # # # # # # # # # # # # # _ _ _ _ _ _ _ _ )
( _ _ _ _ _ _ _ _ # # # # # # # # _ _ _ _ _ _ _ _ # # # # # # # # )
( _ _ _ _ # # # # # # # # _ _ _ _ _ _ _ _ # # # # # # # # _ _ _ _ )
( _ _ _ _ # # # # # # # # _ _ _ _ # # # # _ _ _ _ _ _ _ _ # # # # )
( _ _ _ _ # # # # _ _ _ _ # # # # # # # # _ _ _ _ # # # # _ _ _ _ )
( _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # )
( _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ _ _ # # # # _ _ )
( _ _ # # # # _ _ _ _ # # # # _ _ # # _ _ _ _ # # # # _ _ _ _ # # )
( _ _ # # # # _ _ # # _ _ _ _ # # # # _ _ _ _ # # _ _ # # # # _ _ )
( _ _ # # # # _ _ # # _ _ _ _ # # _ _ # # # # _ _ # # _ _ _ _ # # )
( _ _ # # _ _ # # # # _ _ # # _ _ _ _ # # _ _ # # # # _ _ # # _ _ )
( _ _ # # _ _ # # # # _ _ # # _ _ # # _ _ # # _ _ _ _ # # _ _ # # )
( _ _ # # _ _ # # _ _ # # _ _ # # # # _ _ # # _ _ # # _ _ # # _ _ )
( _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # )
( _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ _ # # _ )
( _ # # _ _ # # _ _ # # _ _ # # _ # _ _ # # _ _ # # _ _ # # _ _ # )
( _ # # _ _ # # _ # _ _ # # _ _ # # _ _ # # _ _ # _ # # _ _ # # _ )
( _ # # _ _ # # _ # _ _ # # _ _ # _ # # _ _ # # _ # _ _ # # _ _ # )
( _ # # _ # _ _ # # _ _ # _ # # _ _ # # _ # _ _ # # _ _ # _ # # _ )
( _ # # _ # _ _ # # _ _ # _ # # _ # _ _ # _ # # _ _ # # _ # _ _ # )
( _ # # _ # _ _ # _ # # _ # _ _ # # _ _ # _ # # _ # _ _ # _ # # _ )
( _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # )
( _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ _ # _ # # _ # _ )
( _ # _ # # _ # _ _ # _ # # _ # _ # _ # _ _ # _ # # _ # _ _ # _ # )
( _ # _ # # _ # _ # _ # _ _ # _ # # _ # _ _ # _ # _ # _ # # _ # _ )
( _ # _ # # _ # _ # _ # _ _ # _ # _ # _ # # _ # _ # _ # _ _ # _ # )
( _ # _ # _ # _ # # _ # _ # _ # _ _ # _ # _ # _ # # _ # _ # _ # _ )
( _ # _ # _ # _ # # _ # _ # _ # _ # _ # _ # _ # _ _ # _ # _ # _ # )
( _ # _ # _ # _ # _ # _ # _ # _ # # _ # _ # _ # _ # _ # _ # _ # _ )
( _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # _ # )
</pre>
=={{header|ALGOL 68}}==
Line 798 ⟶ 1,072:
'''Works with jaq, the Rust implementation of jq'''
This entry uses a non-recursive method for creating Walsh matrices, but the `kprod` definition
at [[Kronecker_product#jq]] could also be used as follows:
<syntaxhighlight lang="jq">
## Generate a Walsh matrix of size 2^$n for $n >= 1
def walsh:
. as $n
| [[1, 1], [1, -1]] as $w2
| if $n < 2 then $w2 else kprod($w2; $n - 1 | walsh) end;
</syntaxhighlight>
<syntaxhighlight lang="jq">
## Generic matrix functions
Line 829 ⟶ 1,113:
| reduce range(0; .[$i]|length) as $j ("|"; . + ($in[$i][$j]|lpad($w)))
| . + " |" ;
def cprint:
. as $in
| range(0; length) as $i
| reduce range(0; .[$i]|length) as $j (""; . + ($in[$i][$j]));
def color: if . == 1 then "🟥" else "🟩" end;
</syntaxhighlight>
'''Walsh matrices'''
Line 838 ⟶ 1,129:
| .k = 1
| until (.k >= $n;
| .walsh[$i+$k][$j] = $wij
| .walsh[$i][$j+$k] = $wij
| .walsh[$i+$k][$j+$k] = -$wij ))
| .k += .k )
| .walsh ;
Line 863 ⟶ 1,154:
"";
def task3:
5 as $order
| pow(2; $order)
| "Walsh matrix - order \($order) (\(.) x \(.)), natural order:",
(walshMatrix | map(map(color)) | cprint),
"";
def task4:
5 as $order
| pow(2; $order)
| "Walsh matrix - order \($order) (\(.) x \(.)), sequency order:",
(walshMatrix | sort_by( signChanges ) | map(map(color)) | cprint),
"";
task1, task2, task3, task4
</syntaxhighlight>
{{output}}
The output for the last two tasks is as follows:
<pre>
Walsh matrix - order 5 (32 x 32), natural order:
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩
🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩
🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥
🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩
🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥
🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥
🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩
🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥
🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥
🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩
🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥
🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩
🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩
🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩
🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥
🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥
🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩
🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥
🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩
🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩
🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥
🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥
🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩
🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩
🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥
🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩
🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥
🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥
🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩
Walsh matrix - order 5 (32 x 32), sequency order:
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥
🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥
🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩
🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥
🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩
🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥
🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩
🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥
🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩
🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥
🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟥🟥🟩🟩
🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥
🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩
🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥
🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩
🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥
🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩
🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥
🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟥🟩🟩🟥🟩🟥🟥🟩
🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥
🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩
🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥
🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩
🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥
🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩
🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥
🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟥🟩🟥🟩🟥🟩🟥🟩
🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥
🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩🟥🟩
</pre>
=={{header|Julia}}==
Line 1,400 ⟶ 1,775:
===Wren-cli===
Text mode version.
<syntaxhighlight lang="
import "./fmt" for Fmt
Line 1,572 ⟶ 1,947:
{{libheader|Wren-polygon}}
Image mode version.
<syntaxhighlight lang="
import "input" for Keyboard
import "graphics" for Canvas, Color
|