#*****************************************************************************80
#
## gdls_test tests gdls.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    20 March 2020
#
#  Author:
#
#    John Burkardt
#
cat ( date ( ), "\n" )
cat ( "\n" )
cat ( "gdls_test\n" )
cat ( " ", version$version.string, "\n" )
cat ( "  gdls solves a least squares problem using gradient descent.\n" )
cat ( "\n" )

source ( "/home/burkardt/public_html/r_src/gdls/gdls.R" )
source ( "/home/burkardt/public_html/r_src/vecnorm/vecnorm.R" )  

#
#  Define the matrix by columns...
#
A = matrix ( cbind ( 
 1.47,
 1.50,
 1.52,
 1.55,
 1.57,
 1.60,
 1.63,
 1.65,
 1.68,
 1.70,
 1.73,
 1.75,
 1.78,
 1.80,
 1.83,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0, 
 1.0 ), ncol = 2 )

b = matrix ( cbind ( 
 52.21,
 53.12,
 54.48,
 55.84,
 57.20,
 58.57,
 59.93,
 61.29,
 63.11,
 64.47,
 66.28,
 68.10,
 69.92,
 72.19,
 74.46 ), ncol = 1 )

x_exact = matrix ( cbind ( 61.272, -39.062 ), ncol = 1 )

x <- gdls ( A, b, alpha = 0.010, tol = 1.0e-7, m = 1.0e6 )
cat ( "  x       = ", x, "\n" )
cat ( "  x_exact = ", x_exact, "\n" )
cat ( "  error = ", vecnorm ( x - x_exact ), "\n" )
cat ( "\n" )
cat ( "  residual       = ", vecnorm ( b - A %*% x ), "\n" )
cat ( "  exact residual = ", vecnorm ( b - A %*% x_exact ), "\n" )
#
#  Terminate.
#
cat ( "\n" )
cat ( "gdls_test\n" )
cat ( "  Normal end of execution.\n" )
cat ( date ( ), "\n" )

quit ( )