#*****************************************************************************80
#
## least_squares_plots: plot data, least squares line, exact formula.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    24 August 2020
#
#  Author:
#
#    John Burkardt
#
cat ( "\n" )
cat ( "least_squares_plots:\n" )
cat ( " ", version$version.string, "\n" )
cat ( "  Compare 15 data points with the least squares line\n" )
cat ( "    y = A * x + B\n" )
cat ( "  which minimizes the root-mean-square error.\n" )
cat ( "  The data is actually perturbed values of a quadratic\n" )
cat ( "  formula, which is shown for comparison:\n" )
cat ( "    y = 1/2 x^2 + 1\n" )
#
#  Read the 15 data points.
#
filename = "least_squares1_data.txt"
xy_data <- read.table ( filename, header = FALSE )
n = dim(data)[1]
#
#  Read two points on the least squares line
#
  filename = 'least_squares2_data.txt'
  xy_lsq = read.table ( filename, header = FALSE )
#
#  Read data on the exact formula.
#
  filename = 'least_squares3_data.txt'
  xy_exact = read.table ( filename, header = FALSE )
#
#  Plot three curves on one image.
#
filename = "least_squares_plots.png"
png ( filename )

plot ( xy_lsq[,1], xy_lsq[,2],
  xlab = "<--- X --->",
  ylab = "<--- Y --->",
  main = "Least squares approximation",
  col = "red",
  type = 'l',
  lwd = 4 )

lines ( xy_data[,1], xy_data[,2], type = 'p', col = "blue", pch = 16 )

lines ( xy_exact[,1], xy_exact[,2], type = 'l', col = "green", lwd = 4 )
#
#  Boy this legend() command is inadequate!
#
x = -0.5
y = 3.0
legend ( x, y, legend = c ( "red: Least squares fit",  "blue: Data", "green: Exact" ) )

grid ( )

cat ( "\n" )
cat ( "  Graphics saved as '", filename, "'\n" )
#
#  Terminate.
#
cat ( "\n" )
cat ( "least_squares_plots\n" )
cat ( "  Normal end of execution.\n" )
quit ( )