Data update

Task/Strassens-algorithm/Ruby/strassens-algorithm.rb

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+class Shape < Struct.new(:rows, :cols)
+end
+
+class Matrix
+  attr_reader :data
+
+  def initialize(data = [])
+    @data = data
+  end
+
+  def self.block(blocks)
+    m = []
+    # blocks is an array of arrays of Matrix objects
+    # Process horizontal blocks row by row
+    top_blocks = blocks[0]  # [c11, c12]
+    bottom_blocks = blocks[1]  # [c21, c22]
+
+    # Combine top blocks horizontally
+    top_rows = []
+    (0...top_blocks[0].rows).each do |i|
+      row = []
+      top_blocks.each { |block| row.concat(block.data[i]) }
+      top_rows << row
+    end
+
+    # Combine bottom blocks horizontally
+    bottom_rows = []
+    (0...bottom_blocks[0].rows).each do |i|
+      row = []
+      bottom_blocks.each { |block| row.concat(block.data[i]) }
+      bottom_rows << row
+    end
+
+    # Combine all rows vertically
+    m = top_rows + bottom_rows
+    Matrix.new(m)
+  end
+
+  def dot(b)
+    raise "Matrix dimensions don't match" unless self.cols == b.rows
+
+    result = []
+    @data.each do |row|
+      new_row = []
+      b.cols.times do |c|
+        col = b.data.map { |r| r[c] }
+        new_row << row.zip(col).map { |x, y| x * y }.sum
+      end
+      result << new_row
+    end
+    Matrix.new(result)
+  end
+
+  def *(b)
+    dot(b)
+  end
+
+  def +(b)
+    raise "Matrix dimensions don't match" unless self.shape == b.shape
+
+    rows, cols = self.rows, self.cols
+    result = []
+    rows.times do |i|
+      new_row = []
+      cols.times do |j|
+        new_row << @data[i][j] + b.data[i][j]
+      end
+      result << new_row
+    end
+    Matrix.new(result)
+  end
+
+  def -(b)
+    raise "Matrix dimensions don't match" unless self.shape == b.shape
+
+    rows, cols = self.rows, self.cols
+    result = []
+    rows.times do |i|
+      new_row = []
+      cols.times do |j|
+        new_row << @data[i][j] - b.data[i][j]
+      end
+      result << new_row
+    end
+    Matrix.new(result)
+  end
+
+  def strassen(b)
+    rows, cols = self.rows, self.cols
+
+    raise "Matrices must be square" unless rows == cols
+    raise "Matrices must be the same shape" unless self.shape == b.shape
+    raise "Shape must be a power of 2" unless rows > 0 && (rows & (rows - 1)) == 0
+
+    if rows == 1
+      return self.dot(b)
+    end
+
+    p = rows / 2
+
+    a11 = Matrix.new(@data[0...p].map { |row| row[0...p] })
+    a12 = Matrix.new(@data[0...p].map { |row| row[p..-1] })
+    a21 = Matrix.new(@data[p..-1].map { |row| row[0...p] })
+    a22 = Matrix.new(@data[p..-1].map { |row| row[p..-1] })
+
+    b11 = Matrix.new(b.data[0...p].map { |row| row[0...p] })
+    b12 = Matrix.new(b.data[0...p].map { |row| row[p..-1] })
+    b21 = Matrix.new(b.data[p..-1].map { |row| row[0...p] })
+    b22 = Matrix.new(b.data[p..-1].map { |row| row[p..-1] })
+
+    m1 = (a11 + a22).strassen(b11 + b22)
+    m2 = (a21 + a22).strassen(b11)
+    m3 = a11.strassen(b12 - b22)
+    m4 = a22.strassen(b21 - b11)
+    m5 = (a11 + a12).strassen(b22)
+    m6 = (a21 - a11).strassen(b11 + b12)
+    m7 = (a12 - a22).strassen(b21 + b22)
+
+    c11 = m1 + m4 - m5 + m7
+    c12 = m3 + m5
+    c21 = m2 + m4
+    c22 = m1 - m2 + m3 + m6
+
+    Matrix.block([[c11, c12], [c21, c22]])
+  end
+
+  def round(ndigits = nil)
+    rounded_data = @data.map do |row|
+      row.map do |element|
+        if ndigits
+          (element * (10 ** ndigits)).round / (10.0 ** ndigits)
+        else
+          element.round
+        end
+      end
+    end
+    Matrix.new(rounded_data)
+  end
+
+  def shape
+    cols = @data.empty? ? 0 : @data[0].length
+    Shape.new(@data.length, cols)
+  end
+
+  def rows
+    @data.length
+  end
+
+  def cols
+    @data.empty? ? 0 : @data[0].length
+  end
+
+  def to_s
+    @data.inspect
+  end
+
+  def inspect
+    @data.inspect
+  end
+end
+
+def examples
+  a = Matrix.new([
+    [1, 2],
+    [3, 4]
+  ])
+
+  b = Matrix.new([
+    [5, 6],
+    [7, 8]
+  ])
+
+  c = Matrix.new([
+    [1, 1, 1, 1],
+    [2, 4, 8, 16],
+    [3, 9, 27, 81],
+    [4, 16, 64, 256]
+  ])
+
+  d = Matrix.new([
+    [4, -3, 4.0/3, -1.0/4],
+    [-13.0/3, 19.0/4, -7.0/3, 11.0/24],
+    [3.0/2, -2, 7.0/6, -1.0/4],
+    [-1.0/6, 1.0/4, -1.0/6, 1.0/24]
+  ])
+
+  e = Matrix.new([
+    [1, 2, 3, 4],
+    [5, 6, 7, 8],
+    [9, 10, 11, 12],
+    [13, 14, 15, 16]
+  ])
+
+  f = Matrix.new([
+    [1, 0, 0, 0],
+    [0, 1, 0, 0],
+    [0, 0, 1, 0],
+    [0, 0, 0, 1]
+  ])
+
+  puts "Naive matrix multiplication:"
+  puts "  a * b = #{a * b}"
+  puts "  c * d = #{(c * d).round}"
+  puts "  e * f = #{e * f}"
+
+  puts "Strassen's matrix multiplication:"
+  puts "  a * b = #{a.strassen(b)}"
+  puts "  c * d = #{c.strassen(d).round}"
+  puts "  e * f = #{e.strassen(f)}"
+end
+
+if __FILE__ == $0
+  examples
+end