Class: Statsample::Factor::Rotation

Inherits:
Object
  • Object
show all
Includes:
DirtyMemoize
Defined in:
lib/statsample/factor/rotation.rb

Overview

Base class for rotate matrixes References:

Use Varimax, Equimax or Quartimax for desired type of rotation

Use:
a = Matrix[ [ 0.4320,  0.8129,  0.3872] 
  , [ 0.7950, -0.5416,  0.2565]  
  , [ 0.5944,  0.7234, -0.3441]  
  , [ 0.8945, -0.3921, -0.1863] ]
rotation = Statsample::Factor::Varimax(a)
rotation.iterate
p rotation.rotated
p rotation.component_transformation_matrix

Direct Known Subclasses

Equimax, Quartimax, Varimax

Constant Summary collapse

EPSILON = 
1e-15
MAX_ITERATIONS = 
25

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(matrix, opts = Hash.new) ⇒ Rotation 



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# File 'lib/statsample/factor/rotation.rb', line 31

def initialize(matrix, opts=Hash.new)
  @matrix=matrix
  @n=@matrix.row_size # Variables, p on original
  @m=@matrix.column_size # Factors, r on original
  @component_transformation_matrix=nil
  @max_iterations=MAX_ITERATIONS
  @epsilon=EPSILON
  @rotated=nil
  @h2=(@matrix.collect {|c| c**2} * Matrix.column_vector([1]*@m)).column(0).to_a
  opts.each{|k,v|
    self.send("#{k}=",v) if self.respond_to? k
  }
end

Instance Attribute Details

#component_transformation_matrix ⇒ Object (readonly)

Returns the value of attribute component_transformation_matrix.



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# File 'lib/statsample/factor/rotation.rb', line 22

def component_transformation_matrix
  @component_transformation_matrix
end

#epsilon ⇒ Object

Maximum precision



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# File 'lib/statsample/factor/rotation.rb', line 26

def epsilon
  @epsilon
end

#h2 ⇒ Object (readonly) Also known as: communalities

Returns the value of attribute h2.



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# File 'lib/statsample/factor/rotation.rb', line 22

def h2
  @h2
end

#iterations ⇒ Object (readonly)

Returns the value of attribute iterations.



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# File 'lib/statsample/factor/rotation.rb', line 22

def iterations
  @iterations
end

#max_iterations ⇒ Object

Maximum number of iterations



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# File 'lib/statsample/factor/rotation.rb', line 24

def max_iterations
  @max_iterations
end

#rotated ⇒ Object (readonly) Also known as: rotated_component_matrix

Returns the value of attribute rotated.



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# File 'lib/statsample/factor/rotation.rb', line 22

def rotated
  @rotated
end

Instance Method Details

#compute ⇒ Object 



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# File 'lib/statsample/factor/rotation.rb', line 46

def compute
  iterate
end

#iterate ⇒ Object

Start iteration



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# File 'lib/statsample/factor/rotation.rb', line 50

def iterate
  t=Matrix.identity(@m)
  b=@matrix.dup
  h=Matrix.diagonal(*@h2).collect {|c| Math::sqrt(c)}
  h_inverse=h.collect {|c| c!=0 ? 1/c : 0 }
  bh=h_inverse*b
  @not_converged=true
  @iterations=0
  while @not_converged
    break if @iterations>@max_iterations
    @iterations+=1
    #puts "Iteration #{iterations}"
    num_pairs=@m*(@m-1).quo(2)
    (0..(@m-2)).each do |i| #+ go through factor index 0:r-1-1 (begin)
      ((i+1)..(@m-1)).each do |j| #+ pair i to "rest" of factors (begin)
        
        xx = bh.column(i)
        yy = bh.column(j)
        tx = t.column(i)
        ty = t.column(j)
        
        uu = @n.times.collect {|var_i| xx[var_i]**2-yy[var_i]**2}
        vv = @n.times.collect {|var_i| 2*xx[var_i]*yy[var_i]}
        
        a  = @n.times.inject(0) {|ac,var_i| ac+ uu[var_i] }
        b  = @n.times.inject(0) {|ac,var_i| ac+ vv[var_i] }
        c  = @n.times.inject(0) {|ac,var_i| ac+ (uu[var_i]**2 - vv[var_i]**2) }
        d  = @n.times.inject(0) {|ac,var_i| ac+ (2*uu[var_i]*vv[var_i]) }
        num=x(a,b,c,d)
        den=y(a,b,c,d)
        phi=Math::atan2(num,den) / 4.0
        # puts "#{i}-#{j}: #{phi}"
        
        if(Math::sin(phi.abs) >= @epsilon)
          xx_rot=( Math::cos(phi)*xx)+(Math::sin(phi)*yy)
          yy_rot=((-Math::sin(phi))*xx)+(Math::cos(phi)*yy)
          
          
          tx_rot=( Math::cos(phi)*tx)+(Math::sin(phi)*ty)
          ty_rot=((-Math::sin(phi))*tx)+(Math::cos(phi)*ty)

          
          bh=bh.to_a

          @n.times {|row_i|
            bh[row_i][i] = xx_rot[row_i]
            bh[row_i][j] = yy_rot[row_i]
          }
          t=t.to_a
          @m.times {|row_i|
            t[row_i][i]=tx_rot[row_i]
            t[row_i][j]=ty_rot[row_i]
          }
          
          bh=Matrix.rows(bh)
          t=Matrix.rows(t)
        else
          num_pairs=num_pairs-1
          @not_converged=false if num_pairs==0
        end # if
      end #j
    end #i
  end # while
  @rotated=h*bh
  @component_transformation_matrix=t
  @rotated
end