python - gnuplot: the "sum [<var> = <start>:<end>] <expression>" strategy -


in following script, plot y(x):

enter image description here

and function u(x):

enter image description here

edit

plotting y(x) easy, having problems plot function u(x).

u(x) same function y(x), summing every step.

therefore, in order plot u(x), have tried sum [<var> = <start>:<end>] <expression> strategy. have implemented notation as:

replot sum[x=1:6] y(x) line lt -1 lw 1 lc 2 title "u(x)"

in following script:

 #   set ylabel "y" font  ", 20"  set xlabel 'x' font  ", 20"    set format y "%9.4f"  set xrange [1:6]   set yrange [0:20]  set xtics font ", 15"  set ytics font ", 15"    set key font ",17" # changes font of letters of legend   y(x) = (2*x)/(x**2)  plot y(x) line lt -1 lw 1 lc 1 title "y(x)"  replot sum[x=1:6] y(x) line lt -1 lw 1 lc 2 title "u(x)"    pause -1  set term post enh color eps  set output "y_x.eps"  replot

i not sure if sum[x=1:6] y(x) strategy indeed plotting u(x).

in order check this, can following:

we know that:

enter image description here

so, value in gnuplot u(6)? if run script, get:

enter image description here

zooming:

i see u(6) reaching value of 2.0000, , not 3.5835.

this makes me think replot sum[x=1:6] u(x) not plotting u(x_i) (second formula)

how plot u(x) ?.

enter image description here

edit 2

running replot sum[i=1:6] y(i) in script:

set ylabel "y" font  ", 20" set xlabel 'x' font  ", 20"    set format y "%9.4f"   set xrange [1:6]   set yrange [0:20]  set xtics font ", 15"  set ytics font ", 15"    set key font ",17" # changes font of letters of legend   y(x) = (2*x)/(x**2)  plot y(x) line lt -1 lw 1 lc 1 title "y(x)"    replot sum[i=1:6] y(i) line lt -1 lw 1 lc 2 title "u(x)"   pause -1  set term post enh color eps  set output "y_x.eps"  replot

produces following: u(6) = 3.000:

enter image description here

enter image description here

edit 3

using y(x) = (2.*x)/(x**2) or y(x) = (2.*x)/(x**2.), u(6) = 4.9:

enter image description here

enter image description here

edit 4

making:

n=100 replot sum[i=0:n-1] y(1. + (i+0.5)*5./n)*5./n line lt -1 lw 1 lc 5 title "sum(x)"

produces constant (cyan line) y=3.58. result of numerical approximation of summation.

enter image description here

what want achieve plot function u(x) values of x_{i}... in @ every step i, summation on previous steps performed, , new value of u generated. plot function u(x)...

in fact, plotted u(x) 6*y(x), can check if replace in script line

plot y(x) line lt -1 lw 1 lc 1 title "y(x)"

with

plot 6*y(x) line lt -1 lw 1 lc 1 title "y(x)"

that line coincide u(x).

also, note function y(x) not integrable in interval [0, 6] since behaves @ 0 1/x (in formula, obtain expression ln(0)).


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