X-Git-Url: https://vcs.maemo.org/git/?a=blobdiff_plain;f=demo%2Fbivariat.dem;fp=demo%2Fbivariat.dem;h=aa170d79325e96b2c5b3cf718a6ab64ca8a3206f;hb=39ec1247a71f61152a4a7f502a30f06a3896c5da;hp=0000000000000000000000000000000000000000;hpb=06be459be4f5f6a7c6ff878e84f355fb2575caa8;p=gnuplot

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+#
+# $Id: bivariat.dem,v 1.8 2006/07/06 21:52:19 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
+
+pause -1 "Hit return to continue"
+
+f(x)=cos(x)
+
+plot [-5:5] f(x) title "f(x)=cos(x)", integral_f(x)
+
+pause -1 "Hit return to continue"
+
+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)
+
+pause -1 "Hit return to continue"
+
+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)
+
+pause -1 "Hit return to continue"
+
+#
+# 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)
+
+pause -1 "Hit return to continue"
+
+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
+
+pause -1 "Hit return to continue"
+
+#
+# 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
+pause -1 "Hit return to continue"
+
+reset
+