#! /usr/bin/env python3
#
def ford_lstsq ( ):

#*****************************************************************************80
#
## ford_lstsq uses a least squares solver to model Ford data.
#
#  Discussion:
#
#    Least squares solver for optimal (b,m) to fit (x,y) data
#    y = b + m*x
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 October 2019
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from ford_data import ford_data

  print ( '' )
  print ( 'ford_lstsq:' )
  print ( '  Given mileage x and price y for used Fords,' )
  print ( '  seek (m,b) so that y=b+mx approximates the data.' )
  print ( '  Use least squares solver to estimate best b and m.' )
#
#  Get the (normalized) Ford data.
#
  x, y = ford_data ( )
  n = len ( x )
#
#  Create the matrix A:
#
  A = np.zeros ( [ n, 2 ] )
  A[:,0] = 1;
  A[:,1] = x;
#
#  Call least squares solver for rectangular linear system.
#  Four output quantities are returned, but we are only 
#  interested in the first one, so we put underscores to 
#  ignore the last three.
#
  bm, _, _, _ = np.linalg.lstsq ( A, y, rcond = None )

  print ( '' )
  print ( '  Estimating model parameters:' )
  print ( '  x = normalized mileage' )
  print ( '  y = normalized price' )
  print ( '  Seek relationship y = b + m * x' )
  print ( '  b = %g' % ( bm[0] ) )
  print ( '  m = %g' % ( bm[1] ) )
  e = np.sum ( ( y - bm[0] - bm[1] * x )**2 )
  print ( '  Sum-of-squares error is %g' % ( e ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'ford_lstsq:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  ford_lstsq ( )