gd <- function ( fp, x, h = 1.0e-2, tol = 1.0e-4, m = 1000 )

#*****************************************************************************80
#
## gd seeks the minimum of a multivariate function 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:
#
#    15 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
  oldx <- x
  x <- x - h * fp ( x )

  while ( tol < vecnorm ( x - oldx ) )
  {
    iter <- iter + 1
    if ( m < iter )
    {
      warning ( 'gd: iteration limit exceeded.' )
      return ( x )
    }

    oldx <- x
    x <- x - h * fp ( x )
  }

  return ( x )
}