Strassen's algorithm: Difference between revisions

=={{header|Scala}}==

{{trans|Go}}

<syntaxhighlight lang="Scala">

import scala.math

object MatrixOperations {

type Matrix = Array[Array[Double]]

implicit class RichMatrix(val m: Matrix) {

def rows: Int = m.length

def cols: Int = m(0).length

def add(m2: Matrix): Matrix = {

require(

m.rows == m2.rows && m.cols == m2.cols,

"Matrices must have the same dimensions."

)

Array.tabulate(m.rows, m.cols)((i, j) => m(i)(j) + m2(i)(j))

}

def sub(m2: Matrix): Matrix = {

require(

m.rows == m2.rows && m.cols == m2.cols,

"Matrices must have the same dimensions."

)

Array.tabulate(m.rows, m.cols)((i, j) => m(i)(j) - m2(i)(j))

}

def mul(m2: Matrix): Matrix = {

require(m.cols == m2.rows, "Cannot multiply these matrices.")

Array.tabulate(m.rows, m2.cols)((i, j) =>

(0 until m.cols).map(k => m(i)(k) * m2(k)(j)).sum

)

}

def toString(p: Int): String = {

val pow = math.pow(10, p)

m.map(row =>

row

.map(value => (math.round(value * pow) / pow).toString)

.mkString("[", ", ", "]")

).mkString("[", ",\n ", "]")

}

}

def toQuarters(m: Matrix): Array[Matrix] = {

val r = m.rows / 2

val c = m.cols / 2

val p = params(r, c)

(0 until 4).map { k =>

Array.tabulate(r, c)((i, j) => m(p(k)(0) + i)(p(k)(2) + j))

}.toArray

}

def fromQuarters(q: Array[Matrix]): Matrix = {

val r = q(0).rows

val c = q(0).cols

val p = params(r, c)

Array.tabulate(r * 2, c * 2)((i, j) => q((i / r) * 2 + j / c)(i % r)(j % c))

}

def strassen(a: Matrix, b: Matrix): Matrix = {

require(

a.rows == a.cols && b.rows == b.cols && a.rows == b.rows,

"Matrices must be square and of equal size."

)

require(

a.rows != 0 && (a.rows & (a.rows - 1)) == 0,

"Size of matrices must be a power of two."

)

if (a.rows == 1) {

return a.mul(b)

}

val qa = toQuarters(a)

val qb = toQuarters(b)

val p1 = strassen(qa(1).sub(qa(3)), qb(2).add(qb(3)))

val p2 = strassen(qa(0).add(qa(3)), qb(0).add(qb(3)))

val p3 = strassen(qa(0).sub(qa(2)), qb(0).add(qb(1)))

val p4 = strassen(qa(0).add(qa(1)), qb(3))

val p5 = strassen(qa(0), qb(1).sub(qb(3)))

val p6 = strassen(qa(3), qb(2).sub(qb(0)))

val p7 = strassen(qa(2).add(qa(3)), qb(0))

val q = Array(

p1.add(p2).sub(p4).add(p6),

p4.add(p5),

p6.add(p7),

p2.sub(p3).add(p5).sub(p7)

)

fromQuarters(q)

}

private def params(r: Int, c: Int): Array[Array[Int]] = {

Array(

Array(0, r, 0, c, 0, 0),

Array(0, r, c, 2 * c, 0, c),

Array(r, 2 * r, 0, c, r, 0),

Array(r, 2 * r, c, 2 * c, r, c)

)

}

def main(args: Array[String]): Unit = {

val a: Matrix = Array(Array(1.0, 2.0), Array(3.0, 4.0))

val b: Matrix = Array(Array(5.0, 6.0), Array(7.0, 8.0))

val c: Matrix = Array(

Array(1.0, 1.0, 1.0, 1.0),

Array(2.0, 4.0, 8.0, 16.0),

Array(3.0, 9.0, 27.0, 81.0),

Array(4.0, 16.0, 64.0, 256.0)

)

val d: Matrix = Array(

Array(4.0, -3.0, 4.0 / 3.0, -1.0 / 4.0),

Array(-13.0 / 3.0, 19.0 / 4.0, -7.0 / 3.0, 11.0 / 24.0),

Array(3.0 / 2.0, -2.0, 7.0 / 6.0, -1.0 / 4.0),

Array(-1.0 / 6.0, 1.0 / 4.0, -1.0 / 6.0, 1.0 / 24.0)

)

val e: Matrix = Array(

Array(1.0, 2.0, 3.0, 4.0),

Array(5.0, 6.0, 7.0, 8.0),

Array(9.0, 10.0, 11.0, 12.0),

Array(13.0, 14.0, 15.0, 16.0)

)

val f: Matrix = Array(

Array(1.0, 0.0, 0.0, 0.0),

Array(0.0, 1.0, 0.0, 0.0),

Array(0.0, 0.0, 1.0, 0.0),

Array(0.0, 0.0, 0.0, 1.0)

)

println("Using 'normal' matrix multiplication:")

println(

s" a * b = ${a.mul(b).map(_.mkString("[", ", ", "]")).mkString("[", ", ", "]")}"

)

println(s" c * d = ${c.mul(d).toString(6)}")

println(

s" e * f = ${e.mul(f).map(_.mkString("[", ", ", "]")).mkString("[", ", ", "]")}"

)

println("\nUsing 'Strassen' matrix multiplication:")

println(

s" a * b = ${strassen(a, b).map(_.mkString("[", ", ", "]")).mkString("[", ", ", "]")}"

)

println(s" c * d = ${strassen(c, d).toString(6)}")

println(

s" e * f = ${strassen(e, f).map(_.mkString("[", ", ", "]")).mkString("[", ", ", "]")}"

)

}

}

</syntaxhighlight>

{{out}}

<pre>

Using 'normal' matrix multiplication:

a * b = [[19.0, 22.0], [43.0, 50.0]]

c * d = [[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]]

e * f = [[1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], [9.0, 10.0, 11.0, 12.0], [13.0, 14.0, 15.0, 16.0]]

Using 'Strassen' matrix multiplication:

a * b = [[19.0, 22.0], [43.0, 50.0]]

c * d = [[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]]

e * f = [[1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], [9.0, 10.0, 11.0, 12.0], [13.0, 14.0, 15.0, 16.0]]

</pre>