#  midpoint_input.txt
#
#  Discussion:
#
#    Suggest how the midpoint quadrature rule works.
#
#    Consider the function poly(x) = (x+1)*(x-1)*(x-1)*(4-x) over [0,4].
#    Approximate it by rectangles whose heights are the midpoints of 10, 20 or 40 intervals.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 October 2013
#
#  Author:
#
#    John Burkardt
#
set term png
set output "midpoint10.png"
set grid
#
#  Define a thick cyan line to be used for the plot of poly(x):
#
set style line 1 lw 4 linecolor rgb "black"
#
#  Setting the fill to solid means the "boxes" will be filled in when
#  we draw them.
#
set style fill solid
#
#  Plot poly(x) with linestyle 1 versus 10 rectangles.
#
set output "midpoint10.png"
set title "Midpoint Quadrature Rule with 10 Intervals"
set timestamp
plot [x=0:4] (x+1)*(x-1)*(x-1)*(4-x) ls 1, "poly10.txt" using 1:2:(0.37) with boxes
#
#  Plot poly(x) with linestyle 1 versus 20 rectangles.
#
set output "midpoint20.png"
set title "Midpoint Quadrature Rule with 20 Intervals"
set timestamp
plot [x=0:4] (x+1)*(x-1)*(x-1)*(4-x) ls 1, "poly20.txt" using 1:2:(0.18) with boxes
#
#  Plot poly(x) with linestyle 1, versus 40 rectangles.
#
set output "midpoint40.png"
set title "Midpoint Quadrature Rule with 40 Intervals"
set timestamp
plot [x=0:4] (x+1)*(x-1)*(x-1)*(4-x) ls 1, "poly40.txt" using 1:2:(0.08) with boxes
#
#  Terminate.
#
quit