matrix multiplication by columns

gistfile1.rb

def multiply left_matrix, right_matrix
  right_matrix_transposed = transpose right_matrix
  result = left_matrix.each.map { [] }

  right_matrix_transposed.each do |column|
    left_matrix.each_with_index do |row, row_index|
      sum = 0
      row.each_with_index do |row_value, position_index|
        sum += row_value*column[position_index]
      end
      result[row_index].push(sum)
    end
  end

  result
end

def transpose matrix
  right_matrix_transposed = matrix[0].map { [] }
  matrix.each do |row|
    row.each_with_index do |row_value, new_row|
      right_matrix_transposed[new_row].push(row_value)
    end
  end
  right_matrix_transposed
end

require 'benchmark'
require 'matrix'

Benchmark.bm do |b|
  b.report("multiply_by_columns") do
    1_000_000.times { multiply [[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[2, 4, 6], [3, 1, 2], [8, 8, 4]] }
  end

  b.report("Matrix#* Ruby 2.0") do
    a = Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    b = Matrix[[2, 4, 6], [3, 1, 2], [8, 8, 4]]
    1_000_000.times { a * b }
  end
end

Benchmark.bm do |b|
  b.report("multiply") do
    a = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [11, 22, 33]]      
    c = [[2, 4, 6, 6, 7, 7], [3, 1, 2, 6, 7, 7], [8, 8, 4, 6, 7, 7]]
    1_000_000.times { multiply a, c  }
  end

  b.report("Matrix#* Ruby 2.0") do
    a = Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9], [11, 22, 33]]
    c = Matrix[[2, 4, 6, 6, 7, 7], [3, 1, 2, 6, 7, 7], [8, 8, 4, 6, 7, 7]]
    1_000_000.times { a * c }
  end
end

# RESULTS for 1_000_000 times on 3x3*3x3
#         user     system      total        real
#mine  17.100000   0.010000  17.110000 ( 17.105483)
#ruby  20.850000   0.020000  20.870000 ( 20.873743)

# RESULTS for 1_000_000 times on 4x3*3x6
#       user     system      total        real
#mine 37.030000   0.020000  37.050000 ( 37.050012)
#ruby 54.390000   0.030000  54.420000 ( 54.431502)