Strassen's algorithm: Difference between revisions
→{{header|Wren}}: Added a version which uses Wren-matrix (retaining original as there are translations of it).
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=={{header|Wren}}==
{{libheader|Wren-fmt}}▼
Wren doesn't currently have a matrix module so I've written a rudimentary Matrix class with sufficient functionality to complete this task.
I've used the Phix entry's examples to test the Strassen algorithm implementation.
<lang ecmascript>
construct new(a) {
if (a.type != List || a.count == 0 || a[0].type != List || a[0].count == 0 || a[0][0].type != Num) {
Line 1,314 ⟶ 1,311:
e * f = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
</pre>
<br>
Since the above version was written, a Matrix module has been added and the following version uses it. The output is exactly the same as before.
<lang ecmascript>import "./matrix" for Matrix
var params = Fn.new { |r, c|
return [
[0...r, 0...c, 0, 0],
[0...r, c...2*c, 0, c],
[r...2*r, 0...c, r, 0],
[r...2*r, c...2*c, r, c]
]
}
var toQuarters = Fn.new { |m|
var r = (m.numRows/2).floor
var c = (m.numCols/2).floor
var p = params.call(r, c)
var quarters = []
for (k in 0..3) {
var q = List.filled(r, null)
for (i in p[k][0]) {
q[i - p[k][2]] = List.filled(c, 0)
for (j in p[k][1]) q[i - p[k][2]][j - p[k][3]] = m[i, j]
}
quarters.add(Matrix.new(q))
}
return quarters
}
var fromQuarters = Fn.new { |q|
var r = q[0].numRows
var c = q[0].numCols
var p = params.call(r, c)
r = r * 2
c = c * 2
var m = List.filled(r, null)
for (i in 0...c) m[i] = List.filled(c, 0)
for (k in 0..3) {
for (i in p[k][0]) {
for (j in p[k][1]) m[i][j] = q[k][i - p[k][2], j - p[k][3]]
}
}
return Matrix.new(m)
}
var strassen // recursive
strassen = Fn.new { |a, b|
if (!a.isSquare || !b.isSquare || !a.sameSize(b)) {
Fiber.abort("Matrices must be square and of equal size.")
}
if (a.numRows == 0 || (a.numRows & (a.numRows - 1)) != 0) {
Fiber.abort("Size of matrices must be a power of two.")
}
if (a.numRows == 1) return a * b
var qa = toQuarters.call(a)
var qb = toQuarters.call(b)
var p1 = strassen.call(qa[1] - qa[3], qb[2] + qb[3])
var p2 = strassen.call(qa[0] + qa[3], qb[0] + qb[3])
var p3 = strassen.call(qa[0] - qa[2], qb[0] + qb[1])
var p4 = strassen.call(qa[0] + qa[1], qb[3])
var p5 = strassen.call(qa[0], qb[1] - qb[3])
var p6 = strassen.call(qa[3], qb[2] - qb[0])
var p7 = strassen.call(qa[2] + qa[3], qb[0])
var q = List.filled(4, null)
q[0] = p1 + p2 - p4 + p6
q[1] = p4 + p5
q[2] = p6 + p7
q[3] = p2 - p3 + p5 - p7
return fromQuarters.call(q)
}
var a = Matrix.new([ [1,2], [3, 4] ])
var b = Matrix.new([ [5,6], [7, 8] ])
var c = Matrix.new([ [1, 1, 1, 1], [2, 4, 8, 16], [3, 9, 27, 81], [4, 16, 64, 256] ])
var d = Matrix.new([ [4, -3, 4/3, -1/4], [-13/3, 19/4, -7/3, 11/24],
[3/2, -2, 7/6, -1/4], [-1/6, 1/4, -1/6, 1/24] ])
var e = Matrix.new([ [1, 2, 3, 4], [5, 6, 7, 8], [9,10,11,12], [13,14,15,16] ])
var f = Matrix.new([ [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ])
System.print("Using 'normal' matrix multiplication:")
System.print(" a * b = %(a * b)")
System.print(" c * d = %((c * d).toString(6))")
System.print(" e * f = %(e * f)")
System.print("\nUsing 'Strassen' matrix multiplication:")
System.print(" a * b = %(strassen.call(a, b))")
System.print(" c * d = %(strassen.call(c, d).toString(6))")
System.print(" e * f = %(strassen.call(e, f))")</lang>
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