title: Curve fitting of Hyperbola and finding its parameters associated
body: <p>Assuming General formula of hyperbola to be y = 1 / (a*x + b), and we are provided with 100 data points out of which 99 points exactly fits a hyperbola and one data point is doesn't fits in it (unknown), from this information we need to find approximate values of a and b parameters for the hyperbola that will be formed from correct data points which are provided.</p>
  
  <p>The approach which I took was by using scipy.optimize.curve_fit method as              "parameters, _ = optimize.curve_fit(test, x_data ,y_data) " 
  where my "test" function was  "def test(x, a, b): return 1 / (a*x + b)" using this method provides me perfect solution is my data points are all in first quadrant but if the data is distributed in more than one quadrant then this approach fails and I get wrong values of a and b.</p>
  
  <p>Code:</p>
  
  <pre><code>import numpy as np 
  from scipy import optimize
  
  x_data = np.linspace(-5,1, num=99)
  y_data = 1 / (5 * x_data + 4) # value of original value of a = 5 &amp; b = 4 
  np.random.seed(0)
  
  # adding wrong point at 36th position
  x_data = np.insert(x_data, 36 , 7)
  y_data = np.insert(y_data, 36, 5)  
  
  def test(x, a, b):
      return 1 / (a*x + b)
  
  parameters, _ = optimize.curve_fit(test, x_data ,y_data)
  [a,b] = parameters
  
  a = 146.83956808191303
  b = 148.78257639384725
  # which is too wrong
  </code></pre>
  
  <p>Solution for above will certainly be appreciated.</p>