Module: Mathpack::SLE

Defined in:
lib/mathpack/sle.rb

Constant Summary collapse

EPS = 
1e-14

Class Method Summary collapse

Class Method Details

.make_null_column(step) ⇒ Object 



32
33
34
35
36
37
38
39
40
 
# File 'lib/mathpack/sle.rb', line 32

def self.make_null_column(step)
  (step + 1).upto(@number - 1) do |i|
    alpha = -@matrix[i][step] / @matrix[step][step].to_f
    step.upto(@number - 1) do |j|
      @matrix[i][j] += @matrix[step][j] * alpha
    end
    @f[i] += @f[step] * alpha
  end
end

.solve(params) ⇒ Object 



7
8
9
10
11
12
13
14
15
16
 
# File 'lib/mathpack/sle.rb', line 7

def self.solve(params)
  type = params[:f].class
  @matrix = Marshal.load(Marshal.dump(params[:matrix])).to_a
  @f = params[:f].to_a.flatten
  fail 'Incorrect size of array or vector' unless @matrix.length == @matrix.first.length && @matrix.length == @f.length
  @number = @f.length
  @x = Array.new(@number) { |i| i + 1 }
  fail 'Matrix is singular' unless solve_direct
  type == Matrix ? Matrix.row_vector(solve_reverse) : solve_reverse
end

.solve_direct ⇒ Object 



42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
 
# File 'lib/mathpack/sle.rb', line 42

def self.solve_direct
  0.upto(@number - 1) do |i|
    maximum = 0.0
    max_line = i
    max_column = i
    i.upto(@number - 1) do |line|
      i.upto(@number - 1) do |column|
        maximum, max_line, max_column = @matrix[line][column].abs, line, column if @matrix[line][column].abs > maximum
      end
    end
    return false if maximum < EPS
    swap_lines(i, max_line) if (max_line != i)
    swap_columns(i, max_column) if (max_column != i)
    make_null_column(i)
  end
  true
end

.solve_reverse ⇒ Object 



60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
 
# File 'lib/mathpack/sle.rb', line 60

def self.solve_reverse
  result_vector = Array.new(@number)
  (@number - 1).downto(0) do |i|
    if i == (@number - 1)
      result_vector[@x[i] - 1] = @f[i] / @matrix[i][i]
    else
      sum = 0.0
      (i + 1).upto(@number - 1) do |j|
        sum += @matrix[i][j] * result_vector[@x[j] - 1]
      end
      result_vector[@x[i] - 1] = (@f[i] - sum) / @matrix[i][i]
    end
  end
  result_vector
end

.swap_columns(first_column, second_column) ⇒ Object 



25
26
27
28
29
30
 
# File 'lib/mathpack/sle.rb', line 25

def self.swap_columns(first_column, second_column)
  0.upto(@number - 1) do |i|
    @matrix[i][first_column], @matrix[i][second_column] = @matrix[i][second_column], @matrix[i][first_column]
  end
  @x[first_column], @x[second_column] = @x[second_column], @x[first_column]
end

.swap_lines(first_line, second_line) ⇒ Object 



18
19
20
21
22
23
 
# File 'lib/mathpack/sle.rb', line 18

def self.swap_lines(first_line, second_line)
  0.upto(@number - 1) do |j|
    @matrix[first_line][j], @matrix[second_line][j] = @matrix[second_line][j], @matrix[first_line][j]
  end
  @f[first_line], @f[second_line] = @f[second_line], @f[first_line]
end