How to plot a function of functions

Question

I would like to get a plot like this

which is generated in Gnuplot but plotting from a file.

The Gnuplot scrip that contains all the functions is the following:

set encoding iso_8859_1
set key right top font "Helvetica,17"
set ylabel "Received power, P_t (dBm)" font "Helvetica,18"
set xlabel "Separation distance, r (m)" font "Helvetica,18"
set xtics font "Helvetica,16"
set ytics font "Helvetica,16"
set size 1, 1.2
set terminal postscript color eps enhanced
set grid xtics ytics
set key spacing 1.5
set key box linestyle 1 width 3
set logscale x
set grid xtics mxtics
set output "link-up-test.eps"
h1=1.85
h2=0.5
r(x) = sqrt((h1 - h2)**2 + x**2 )
lmb = 300/865.7
H(x) = sqrt( 1- (4*h1*h2)/(x**2 + (h1 + h2)**2 ) )
theta(x) = 2*pi/lmb*( sqrt((h1 + h2)**2+x**2 ) - sqrt((h1 - h2)**2+ x**2) )
q_e(x) = H(x)**2*(sin(theta(x)))**2 + (1 - H(x)*cos(theta(x)))**2
P_x_G = 4
sigma = 1.94
invsqrt2pi = 0.398942280401433
normal(x,mu,sigma)=sigma<=0?1/0:invsqrt2pi/sigma*exp(-0.5*((x-mu)/sigma)**2)
rnd(x) = 10**(-normal(x,0,sigma)/10)
pot_t(x) = 10*log10( 1000*(P_x_G*1.622*((300/lmb)**2) *0.5*1) / (((4*pi*r(x))**2) *1.2*1)*q_e(x)*rnd(x) )
plot [1:12][] pot_t(x) t "up"  w lines ls 1

With this script, I get the following plot

which is has similar form but it does not have the randomness os the function rnd(x) and it does not have the same levels in the y-axis.

I am missing something but I have checked several times the functions several times. I would like to know why is not the same figure.

Regards

pablo pablo · Accepted Answer · 2018-05-09T21:53:57

I would like to give my solution to this question. I have used the Box-Muller method to generate Gaussian samples.

h1=1.85
h2=0.5
r(x) = sqrt((h1 - h2)**2 + x**2 )
lmb = 300/865.7
H(x) = sqrt( 1- (4*h1*h2)/(x**2 + (h1 + h2)**2 ) )
theta(x) = 2*pi/lmb*( sqrt((h1 + h2)**2+x**2 ) - sqrt((h1 - h2)**2 + x**2) )
q_e(x) = H(x)**2*(sin(theta(x)))**2 + (1 - H(x)*cos(theta(x)))**2
P_G = 4

sigma = 1.94


normal(x,mu,sigma) = sqrt(-2.0 * log(rand(0))) * cos(2*pi * rand(0)) * sigma + mu
rnd(x) = 10**(-normal(x,0,sigma)/10)

pot_t(x) = 10*log10( 1000*(P_G*1.622*((lmb)**2) *0.5*1) / (((4*pi*r(x))**2) *1.2*1)*q_e(x)*rnd(x) )
set samples 1000
plot [1:12][] pot_t(x) t "up"  w lines ls 1

Which creates this plot:

The samples are generated with the function normal(x, mu, sigma). There is only an issue with this solution When I plot with set logscale x the plot of points should be denser when the x-axis are more concentrated (see first plot above), but it seems that Gnuplot first makes the logscale of the x-axis and after that takes equidistant samples in figure dealing the log scale as a linear scale. I would appreciate if anyone could answer this or improve the solution.

Regards

How to plot a function of functions

2 Answers