Jump to content

Walsh matrix: Difference between revisions

Walsh matrix (view source)

Revision as of 10:51, 31 August 2023

9,734 bytes added ,  9 months ago
Added Wren
m (Add some links, clarifications)
(Added Wren)
Line 214:
| [[File:Walsh-matrix--order-5--sign-changes-sort-order--raku.svg|150px|thumb]]
|}
 
=={{header|Wren}}==
{{libheader|Wren-matrix}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascript">import "./matrix" for Matrix
import "./fmt" for Fmt
 
var walshMatrix = Fn.new { |n|
var walsh = Matrix.new(n, n, 0)
walsh[0, 0] = 1
var k = 1
while (k < n) {
for (i in 0...k) {
for (j in 0...k) {
walsh[i+k, j] = walsh[i, j]
walsh[i, j+k] = walsh[i, j]
walsh[i+k, j+k] = -walsh[i, j]
}
}
k = k + k
}
return walsh
}
 
var signChanges = Fn.new { |row|
var n = row.count
var sc = 0
for (i in 1...n) {
if (row[i-1] == -row[i]) sc = sc + 1
}
return sc
}
 
var walshCache = {} // to avoid calculating the Walsh matrix twice
 
for (order in [2, 4, 5]) {
var n = 1 << order
Fmt.print("Walsh matrix - order $d ($d x $d), natural order:", order, n, n)
var w = walshMatrix.call(n)
walshCache[order] = w
Fmt.mprint(w, 2, 0, "|", true)
System.print()
}
 
for (order in [2, 4, 5]) {
var n = 1 << order
Fmt.print("Walsh matrix - order $d ($d x $d), sequency order:", order, n, n)
var rows = walshCache[order].toList
rows.sort { |r1, r2| signChanges.call(r1) < signChanges.call(r2) }
Fmt.mprint(rows, 2, 0, "|", true)
System.print()
}</syntaxhighlight>
 
{{out}}
<pre style="height:40ex;overflow:scroll;overflow-wrap;normal;word-wrap:normal;white-space:pre;">
Walsh matrix - order 2 (4 x 4), natural order:
| 1 1 1 1|
| 1 -1 1 -1|
| 1 1 -1 -1|
| 1 -1 -1 1|
 
Walsh matrix - order 4 (16 x 16), natural order:
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1|
| 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1|
 
Walsh matrix - order 5 (32 x 32), natural order:
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1|
| 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1|
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1|
 
Walsh matrix - order 2 (4 x 4), sequency order:
| 1 1 1 1|
| 1 1 -1 -1|
| 1 -1 -1 1|
| 1 -1 1 -1|
 
Walsh matrix - order 4 (16 x 16), sequency order:
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1|
| 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1|
 
Walsh matrix - order 5 (32 x 32), sequency order:
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1|
| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1|
| 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1|
| 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1|
| 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1|
| 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1|
| 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1|
| 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1|
| 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1|
| 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1|
| 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1|
| 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1|
| 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1|
| 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1|
| 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1|
| 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1|
| 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1|
| 1 -1 1 -1 1 -1 1 -1 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>
PureFox
9,482

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/359527"
Cookies help us deliver our services. By using our services, you agree to our use of cookies.
More information