def matrices
      rows = data.size
      cols = n_classes

      # in the original implementation, these matrices are referred to
      # as `LC` and `OP`
      # * lower_class_limits (LC): optimal lower class limits
      # * variance_combinations (OP): optimal variance combinations for all classes
      lower_class_limits = *Matrix.zero(rows + 1, cols + 1)
      variance_combinations = *Matrix.zero(rows + 1, cols + 1)

      # the variance, as computed at each step in the calculation
      variance = 0

      for i in 1..cols
        lower_class_limits[1][i]    = 1
        variance_combinations[1][i] = 0
        for j in 2..rows
          variance_combinations[j][i] = Float::INFINITY
        end
      end

      for l in 2..rows
        sum         = 0 # `SZ` originally. this is the sum of the values seen thus far when calculating variance.
        sum_squares = 0 # `ZSQ` originally. the sum of squares of values seen thus far
        w           = 0 # `WT` originally. This is the number of data points considered so far.

        for m in 1..l
          lower_class_limit = l - m + 1 # `III` originally
          val = data[lower_class_limit - 1]

          # here we're estimating variance for each potential classing
          # of the data, for each potential number of classes. `w`
          # is the number of data points considered so far.
          w += 1

          # increase the current sum and sum-of-squares
          sum += val
          sum_squares += (val ** 2)

          # the variance at this point in the sequence is the difference
          # between the sum of squares and the total x 2, over the number
          # of samples.
          variance = sum_squares - (sum ** 2) / w

          i4 = lower_class_limit - 1 # `IV` originally
          if i4 != 0
            for j in 2..cols
             # if adding this element to an existing class
             # will increase its variance beyond the limit, break
             # the class at this point, setting the lower_class_limit
             # at this point.
             if variance_combinations[l][j] >= (variance + variance_combinations[i4][j - 1])
               lower_class_limits[l][j] = lower_class_limit
               variance_combinations[l][j] = variance +
                 variance_combinations[i4][j - 1]
             end
            end
          end
        end

        lower_class_limits[l][1] = 1
        variance_combinations[l][1] = variance
      end

      [lower_class_limits, variance_combinations]
    end
def matrices
      rows = data.size
      cols = n_classes

      
      
      
      
      lower_class_limits = *Matrix.zero(rows + 1, cols + 1)
      variance_combinations = *Matrix.zero(rows + 1, cols + 1)

      
      variance = 0

      for i in 1..cols
        lower_class_limits[1][i]    = 1
        variance_combinations[1][i] = 0
        for j in 2..rows
          variance_combinations[j][i] = Float::INFINITY
        end
      end

      for l in 2..rows
        sum         = 0 
        sum_squares = 0 
        w           = 0 

        for m in 1..l
          lower_class_limit = l - m + 1 
          val = data[lower_class_limit - 1]

          
          
          
          w += 1

          
          sum += val
          sum_squares += (val ** 2)

          
          
          
          variance = sum_squares - (sum ** 2) / w

          i4 = lower_class_limit - 1 
          if i4 != 0
            for j in 2..cols
             
             
             
             
             if variance_combinations[l][j] >= (variance + variance_combinations[i4][j - 1])
               lower_class_limits[l][j] = lower_class_limit
               variance_combinations[l][j] = variance +
                 variance_combinations[i4][j - 1]
             end
            end
          end
        end

        lower_class_limits[l][1] = 1
        variance_combinations[l][1] = variance
      end

      [lower_class_limits, variance_combinations]
    end
def matrices rows = data . size cols = n_classes # in the original implementation, these matrices are referred to
 # as `LC` and `OP`
 # * lower_class_limits (LC): optimal lower class limits
 # * variance_combinations (OP): optimal variance combinations for all classes
 lower_class_limits = Matrix . zero ( rows + 1 , cols + 1 ) variance_combinations = Matrix . zero ( rows + 1 , cols + 1 ) # the variance, as computed at each step in the calculation
 variance = 0 for i in 1 .. cols lower_class_limits [ 1 ] [ i ] = 1 variance_combinations [ 1 ] [ i ] = 0 for j in 2 .. rows variance_combinations [ j ] [ i ] = Float :: INFINITY end end for l in 2 .. rows sum = 0 # `SZ` originally. this is the sum of the values seen thus far when calculating variance.
 sum_squares = 0 # `ZSQ` originally. the sum of squares of values seen thus far
 w = 0 # `WT` originally. This is the number of data points considered so far.
 for m in 1 .. l lower_class_limit = l - m + 1 # `III` originally
 val = data [ lower_class_limit - 1 ] # here we're estimating variance for each potential classing
 # of the data, for each potential number of classes. `w`
 # is the number of data points considered so far.
 w += 1 # increase the current sum and sum-of-squares
 sum += val sum_squares += ( val ** 2 ) # the variance at this point in the sequence is the difference
 # between the sum of squares and the total x 2, over the number
 # of samples.
 variance = sum_squares - ( sum ** 2 ) / w i4 = lower_class_limit - 1 # `IV` originally
 if i4 != 0 for j in 2 .. cols # if adding this element to an existing class
 # will increase its variance beyond the limit, break
 # the class at this point, setting the lower_class_limit
 # at this point.
 if variance_combinations [ l ] [ j ] >= ( variance + variance_combinations [ i4 ] [ j - 1 ] ) lower_class_limits [ l ] [ j ] = lower_class_limit variance_combinations [ l ] [ j ] = variance + variance_combinations [ i4 ] [ j - 1 ] end end end end lower_class_limits [ l ] [ 1 ] = 1 variance_combinations [ l ] [ 1 ] = variance end [ lower_class_limits , variance_combinations ] end
Compute the matrices required for Jenks breaks. These matrices
 can be used for any classing of data with `classes <= n_classes`
Compute the matrices required for Jenks breaks . These matrices can be used for any classing of data with classes < = n_classes