#! /usr/bin/env python
#
def lstsq_solve_test ( ):

#*****************************************************************************80
#
## LSTSQ_SOLVE_TEST tests the NUMPY LINALG LSTSQ operator.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 August 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_norm import r8vec_norm
  from test_ls import p00_a
  from test_ls import p00_b
  from test_ls import p00_m
  from test_ls import p00_n
  from test_ls import p00_prob_num
  from test_ls import p00_x

  print ( '' )
  print ( 'LSTSQ_SOLVE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  NUMPY LINALG\'s LSTSQ function x=np.linalg.lstsq(A,b)\n' )
  print ( '  solves a linear system A*x = b in the least squares sense.' )
  print ( '  Compare a tabulated solution X1 to the LSTSQ result X2.' )

  prob_num = p00_prob_num ( )

  print ( '' )
  print ( '  Number of problems = %d' % ( prob_num ) )
  print ( '' )
  print ( '  Index     M     N          ||B||   ||X1 - X2||' ),
  print ( '        ||X1||        ||X2||         ||R1||        ||R2||' )
  print ( '' )

  for prob in range ( 1, prob_num + 1 ):
#
#  Get problem size.
#
    m = p00_m ( prob )
    n = p00_n ( prob )
#
#  Retrieve problem data.
#
    a = p00_a ( prob, m, n )
    b = p00_b ( prob, m )
    x1 = p00_x ( prob, n )

    b_norm = r8vec_norm ( m, b )
    x1_norm = r8vec_norm ( n, x1 )
    r1 = np.dot ( a, x1 ) - b
    r1_norm = r8vec_norm ( m, r1 )
#
#  Use NUMPY's LINALG.LSTSQ on the problem.
#
    x2, r, rank, s = np.linalg.lstsq ( a, b, rcond = None )

    x2_norm = r8vec_norm ( n, x2 )
    r2 = np.dot ( a, x2 ) - b
    r2_norm = r8vec_norm ( m, r2 )
#
#  Compare tabulated and computed solutions.
#
    x_diff_norm = r8vec_norm ( n, x1 - x2 )
#
#  Report results for this problem.
#
    print ( '  %5d  %4d  %4d' % ( prob, m, n ), end = '' )
    print ( '  %12.4g  %12.4g' % ( b_norm, x_diff_norm ), end = '' )
    print ( '  %12.4g  %12.4g' % ( x1_norm, x2_norm ), end = '' )
    print ( '  %12.4g  %12.4g' % ( r1_norm, r2_norm ), end = '' )
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'LSTSQ_SOLVE_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  lstsq_solve_test ( )
  timestamp ( )