gdls <- function ( A, b, alpha = 0.005, tol = 1.0e-6, m = 1.0e5 )

#*****************************************************************************80
#
## gdls solves a least squares problem using gradient descent.
#
#  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:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  source ( "/home/burkardt/public_html/r_src/vecnorm/vecnorm.R" ) 

  iter <- 0
  n <- ncol ( A )
  theta <- matrix ( rep ( 0, n ) )
  oldtheta <- theta + 10.0 * tol

  while ( TRUE )
  {
    iter <- iter + 1

    if ( m < iter )
    {
      warning ( 'gdls: iteration limit exceeded.' )
      return ( theta )
    }

    e <- ( A %*% theta - b )
    d <- ( t(A) %*% e )
    oldtheta <- theta
    theta <- theta - alpha * d

    if ( vecnorm ( theta - oldtheta ) < tol )
    {
      break
    }
  }

  cat ( '  number of iterations', iter, '\n' )

  return ( theta )
}