goldsectmax <- function ( f, a, b, tol = 1.0e-3, m = 100 )

#*****************************************************************************80
#
## goldsectmax seeks the maximum of a function in [a,b] by golden section.
#
#  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:
#
#    14 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.
#
{
  iter <- 0
  phi <- ( sqrt ( 5.0 ) - 1.0 ) / 2.0

  a.star <- b - phi * abs ( b - a )
  b.star <- a + phi * abs ( b - a )

  while ( tol < abs ( b - a ) )
  {
    iter <- iter + 1
    if ( m < iter )
    {
      warning ( 'goldsectmax: iteration limit exceeded.' )
      break
    }

    if ( f ( b.star ) < f ( a.star ) )
    {
      b <- b.star
      b.star <- a.star
      a.star <- b - phi * abs ( b - a )
    }
    else
    {
      a <- a.star
      a.star <- b.star
      b.star <- a + phi * abs ( b - a )
    }

  }

  value <- 0.5 * ( a + b )

  return ( value )
}