Back to demo index

gnuplot demo script: bivariat.dem

autogenerated by webify.pl on Tue Jun 6 18:55:28 2017
gnuplot version gnuplot 5.2 patchlevel rc2
Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     
#
# $Id: bivariat.dem,v 1.9 2011/08/01 05:14:23 sfeam Exp $
#
# This demo is very slow and requires unusually large stack size.
# Do not attempt to run this demo under MSDOS.
#

# the function integral_f(x) approximates the integral of f(x) from 0 to x.
# integral2_f(x,y) approximates the integral from x to y.
# define f(x) to be any single variable function
#
# the integral is calculated using Simpson's rule as 
#          ( f(x-delta) + 4*f(x-delta/2) + f(x) )*delta/6
# repeated x/delta times (from x down to 0)
#
delta = 0.2
#  delta can be set to 0.025 for non-MSDOS machines
#
# integral_f(x) takes one variable, the upper limit.  0 is the lower limit.
# calculate the integral of function f(t) from 0 to x
# choose a step size no larger than delta such that an integral number of
# steps will cover the range of integration.
integral_f(x) = (x>0)?int1a(x,x/ceil(x/delta)):-int1b(x,-x/ceil(-x/delta))
int1a(x,d) = (x<=d*.1) ? 0 : (int1a(x-d,d)+(f(x-d)+4*f(x-d*.5)+f(x))*d/6.)
int1b(x,d) = (x>=-d*.1) ? 0 : (int1b(x+d,d)+(f(x+d)+4*f(x+d*.5)+f(x))*d/6.)
#
# integral2_f(x,y) takes two variables; x is the lower limit, and y the upper.
# calculate the integral of function f(t) from x to y
integral2_f(x,y) = (x<y)?int2(x,y,(y-x)/ceil((y-x)/delta)): \
                        -int2(y,x,(x-y)/ceil((x-y)/delta))
int2(x,y,d) = (x>y-d*.5) ? 0 : (int2(x+d,y,d) + (f(x)+4*f(x+d*.5)+f(x+d))*d/6.)

set autoscale
set title "approximate the integral of functions"
set samples 50
set key bottom right

f(x) = exp(-x**2)

plot [-5:5] f(x) title "f(x)=exp(-x**2)", \
  2/sqrt(pi)*integral_f(x) title "erf(x)=2/sqrt(pi)*integral_f(x)", \
  erf(x) with points


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

f(x)=cos(x)

plot [-5:5] f(x) title "f(x)=cos(x)", integral_f(x)


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

set title "approximate the integral of functions (upper and lower limits)"

f(x)=(x-2)**2-20

plot [-10:10] f(x) title "f(x)=(x-2)**2-20", integral2_f(-5,x)


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5

plot  [-10:10] f(x) title "f(x)=sin(x-1)-0.75*sin(2*x-1)+(x**2)/8-5", integral2_f(x,1)


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

#
# This definition computes the ackermann. Do not attempt to compute its
# values for non integral values. In addition, do not attempt to compute
# its beyond m = 3, unless you want to wait really long time.

ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1))

set xrange [0:3]
set yrange [0:3]

set isosamples 4
set samples 4

set title "Plot of the ackermann function"

splot ack(x, y)


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

set xrange [-5:5]
set yrange [-10:10]
set isosamples 10
set samples 100
set key top right at 4,-3
set title "Min(x,y) and Max(x,y)"

#
min(x,y) = (x < y) ? x : y
max(x,y) = (x > y) ? x : y

plot sin(x), x**2, x**3, max(sin(x), min(x**2, x**3))+0.5


Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

#
# gcd(x,y) finds the greatest common divisor of x and y,
#          using Euclid's algorithm
# as this is defined only for integers, first round to the nearest integer
gcd(x,y) = gcd1(rnd(max(x,y)),rnd(min(x,y)))
gcd1(x,y) = (y == 0) ? x : gcd1(y, x - x/y * y)
rnd(x) = int(x+0.5)

set samples 59
set xrange [1:59]
set auto
set key default

set title "Greatest Common Divisor (for integers only)"

plot gcd(x, 60) with impulses

Click here for minimal script to generate this plot


Your browser does not support the HTML 5 canvas element
          # unzoom rezoom zoom text ?
     

#
# This definition computes the sum of the first 10, 100, 1000 fourier
# coefficients of a (particular) square wave.

set title "Finite summation of 10, 100, 1000 fourier coefficients"

set samples 500
set xrange [-10:10]
set yrange [-0.4:1.2]
set key bottom right

fourier(k, x) = sin(3./2*k)/k * 2./3*cos(k*x)
sum10(x)   = 1./2 + sum [k=1:10]   fourier(k, x)
sum100(x)  = 1./2 + sum [k=1:100]  fourier(k, x)
sum1000(x) = 1./2 + sum [k=1:1000] fourier(k, x)

plot \
    sum10(x)   title "1./2 + sum [k=1:10]   sin(3./2*k)/k * 2./3*cos(k*x)", \
    sum100(x)  title "1./2 + sum [k=1:100]  sin(3./2*k)/k * 2./3*cos(k*x)", \
    sum1000(x) title "1./2 + sum [k=1:1000] sin(3./2*k)/k * 2./3*cos(k*x)"

Click here for minimal script to generate this plot