Module: Malge::LeastSquare

Defined in:
lib/malge/leastsquare.rb

Defined Under Namespace

Classes: UnableCalculationError

Class Method Summary collapse

Class Method Details

.a_exp_bx(data_pairs) ⇒ Object

Return fitted values of [a, b] in a e^bx from 2 point data_pairs;

[x0, y0], [x1, y1]

Argument ‘data_pairs’ should have two items. Raise if including the same data.

Raises:



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# File 'lib/malge/leastsquare.rb', line 74

def self.a_exp_bx(data_pairs)
  raise UnableCalculationError if data_pairs[0][1] == data_pairs[1][1]
  raise UnableCalculationError if data_pairs[0][0] == data_pairs[1][0]
  matrix = data_pairs.map { |pair| [1.0, pair[0]] }
  values = data_pairs.map { |pair| Math::log pair[1] }
  coefficients = Malge::SimultaneousEquations.cramer( matrix, values )
  coefficients[0] = Math::exp coefficients[0]
  coefficients
end

.least_square_1st_degree(data_pairs) ⇒ Object

Return values of [a_0, a_1] in y = a_0 x^0 + a_1 x^1. Argument ‘data_pairs’ should be Array of Array’s. For example,

[
  [ 1.0, 2.0],
  [ 2.0, 4.0],
  [ 3.0, 6.0],
]

Note that not [a, b] in y = ax + b.



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# File 'lib/malge/leastsquare.rb', line 19

def self.least_square_1st_degree(data_pairs)
  a = 0.0 #x^2
  #b = 0.0 #y^2
  c = 0.0 #x^1
  d = 0.0 #x*y
  e = 0.0 #y^1
  n = data_pairs.size
  data_pairs.each do |pairs|
    x = pairs[0].to_f
    y = pairs[1].to_f
    a += x**2
    #b += y**2
    c += x
    d += x*y
    e += y
  end
  a_1 = (n*d - c*e) / (n*a - c**2)
  a_0 = (a*e - c*d) / (n*a - c**2)
  [a_0, a_1]
end

.least_square_a_exp_bx(data_pairs) ⇒ Object

Return fitted values of [a, b] in a e^bx from more than two data points. Argument ‘data_pairs’ should be Array of Array’s. For example,

[
  [ 1.0, 2.0],
  [ 2.0, 4.0],
  [ 3.0, 6.0],
]



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# File 'lib/malge/leastsquare.rb', line 91

def self.least_square_a_exp_bx(data_pairs)
  data_pairs.each do |pair|
    raise UnableCalculationError if pair[1] == 0.0
  end
  data_pairs = data_pairs.map do |pair|
    [pair[0], Math::log(pair[1])]
  end
  coefficients = self.least_square_1st_degree(data_pairs)
  [Math::exp(coefficients[0]), coefficients[1]]
end

.least_square_proportional(data_pairs) ⇒ Object 



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# File 'lib/malge/leastsquare.rb', line 40

def self.least_square_proportional(data_pairs)
  a = 0.0 #x^2
  d = 0.0 #x*y
  n = data_pairs.size
  data_pairs.each do |pairs|
    x = pairs[0].to_f
    y = pairs[1].to_f
    a += x**2
    d += x*y
  end
  [d/a]
end

.variance_1st_degree(data_pairs) ⇒ Object

Return variance when fitted to y = a_0 x^0 + a_1 x^1. Argument ‘data_pairs’ should be Array of Array’s. For example,

[
  [ 1.0, 2.0],
  [ 2.0, 4.0],
  [ 3.0, 6.0],
]



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# File 'lib/malge/leastsquare.rb', line 60

def self.variance_1st_degree(data_pairs)
  coefficients = self.least_square_1st_degree(data_pairs)
  data_pairs.inject(0.0) do |sum, pair|
    x = pair[0]
    y = pair[1]
    f_x = coefficients[0] + coefficients[1] * x
    sum += (y - f_x)**2
  end
end