Data update

Task/Strassens-algorithm/MATLAB/strassens-algorithm.m

@@ -0,0 +1,67 @@
+clear all;close all;clc;
+
+A = [1, 2; 3, 4];
+B = [5, 6; 7, 8];
+C = [1, 1, 1, 1; 2, 4, 8, 16; 3, 9, 27, 81; 4, 16, 64, 256];
+D = [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];
+E = [1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16];
+F = eye(4);
+
+disp('Regular multiply: ');
+disp(A' * B');
+
+disp('Strassen multiply: ');
+disp(Strassen(A', B'));
+
+disp('Regular multiply: ');
+disp(C * D);
+
+disp('Strassen multiply: ');
+disp(Strassen(C, D));
+
+disp('Regular multiply: ');
+disp(E * F);
+
+disp('Strassen multiply: ');
+disp(Strassen(E, F));
+
+r = sqrt(2)/2;
+R = [r, r; -r, r];
+
+disp('Regular multiply: ');
+disp(R * R);
+
+disp('Strassen multiply: ');
+disp(Strassen(R, R));
+
+
+function C = Strassen(A, B)
+    n = size(A, 1);
+    if n == 1
+        C = A * B;
+        return
+    end
+    A11 = A(1:n/2, 1:n/2);
+    A12 = A(1:n/2, n/2+1:n);
+    A21 = A(n/2+1:n, 1:n/2);
+    A22 = A(n/2+1:n, n/2+1:n);
+    B11 = B(1:n/2, 1:n/2);
+    B12 = B(1:n/2, n/2+1:n);
+    B21 = B(n/2+1:n, 1:n/2);
+    B22 = B(n/2+1:n, n/2+1:n);
+
+    P1 = Strassen(A12 - A22, B21 + B22);
+    P2 = Strassen(A11 + A22, B11 + B22);
+    P3 = Strassen(A11 - A21, B11 + B12);
+    P4 = Strassen(A11 + A12, B22);
+    P5 = Strassen(A11, B12 - B22);
+    P6 = Strassen(A22, B21 - B11);
+    P7 = Strassen(A21 + A22, B11);
+
+    C11 = P1 + P2 - P4 + P6;
+    C12 = P4 + P5;
+    C21 = P6 + P7;
+    C22 = P2 - P3 + P5 - P7;
+
+    C = [C11 C12; C21 C22];
+end

Task/Strassens-algorithm/Scala/strassens-algorithm.scala

@@ -0,0 +1,150 @@
+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("[", ", ", "]")}"
+    )
+  }
+}