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Annotation of OpenXM_contrib/gnuplot/demo/bivariat.dem, Revision 1.1.1.1

1.1       maekawa     1: #
                      2: # $Id: bivariat.dem,v 1.2 1993/09/27 17:11:14 alex Exp $
                      3: #
                      4: # This demo is very slow and requires unusually large stack size.
                      5: # Do not attempt to run this demo under MSDOS.
                      6: #
                      7:
                      8: # the function integral_f(x) approximates the integral of f(x) from 0 to x.
                      9: # integral2_f(x,y) approximates the integral from x to y.
                     10: # define f(x) to be any single variable function
                     11: #
                     12: # the integral is calculated as the sum of f(x_n)*delta
                     13: #   do this x/delta times (from x down to 0)
                     14: #
                     15: f(x) = exp(-x**2)
                     16: delta = 0.2
                     17: #  delta can be set to 0.025 for non-MSDOS machines
                     18: #
                     19: # integral_f(x) takes one variable, the upper limit.  0 is the lower limit.
                     20: # calculate the integral of function f(t) from 0 to x
                     21: integral_f(x) = (x>0)?integral1a(x):-integral1b(x)
                     22: integral1a(x) = (x<=0)?0:(integral1a(x-delta)+delta*f(x))
                     23: integral1b(x) = (x>=0)?0:(integral1b(x+delta)+delta*f(x))
                     24: #
                     25: # integral2_f(x,y) takes two variables; x is the lower limit, and y the upper.
                     26: # claculate the integral of function f(t) from x to y
                     27: integral2_f(x,y) = (x<y)?integral2(x,y):-integral2(y,x)
                     28: integral2(x,y) = (x>y)?0:(integral2(x+delta,y)+delta*f(x))
                     29:
                     30: set autoscale
                     31: set title "approximate the integral of functions"
                     32: set samples 50
                     33:
                     34: 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)"
                     35:
                     36: pause -1 "Hit return to continue"
                     37:
                     38: f(x)=sin(x)
                     39:
                     40: plot [-5:5] f(x) title "f(x)=sin(x)", integral_f(x)
                     41:
                     42: pause -1 "Hit return to continue"
                     43:
                     44: set title "approximate the integral of functions (upper and lower limits)"
                     45:
                     46: f(x)=(x-2)**2-20
                     47:
                     48: plot [-10:10] f(x) title "f(x)=(x-2)**2-20", integral2_f(-5,x)
                     49:
                     50: pause -1 "Hit return to continue"
                     51:
                     52: f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5
                     53:
                     54: 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)
                     55:
                     56: pause -1 "Hit return to continue"
                     57:
                     58: #
                     59: # This definition computes the ackermann. Do not attempt to compute its
                     60: # values for non integral values. In addition, do not attempt to compute
                     61: # its beyond m = 3, unless you want to wait really long time.
                     62:
                     63: ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1))
                     64:
                     65: set xrange [0:3]
                     66: set yrange [0:3]
                     67:
                     68: set isosamples 4
                     69: set samples 4
                     70:
                     71: set title "Plot of the ackermann function"
                     72:
                     73: splot ack(x, y)
                     74:
                     75: pause -1 "Hit return to continue"
                     76:
                     77: set xrange [-5:5]
                     78: set yrange [-10:10]
                     79: set isosamples 10
                     80: set samples 100
                     81: set key 4,-3
                     82: set title "Min(x,y) and Max(x,y)"
                     83:
                     84: #
                     85: min(x,y) = (x < y) ? x : y
                     86: max(x,y) = (x > y) ? x : y
                     87:
                     88: plot sin(x), x**2, x**3, max(sin(x), min(x**2, x**3))+0.5
                     89:
                     90: pause -1 "Hit return to continue"
                     91:
                     92: #
                     93: # gcd(x,y) finds the greatest common divisor of x and y,
                     94: #          using Euclid's algorithm
                     95: # as this is defined only for integers, first round to the nearest integer
                     96: gcd(x,y) = gcd1(rnd(max(x,y)),rnd(min(x,y)))
                     97: gcd1(x,y) = (y == 0) ? x : gcd1(y, x - x/y * y)
                     98: rnd(x) = int(x+0.5)
                     99:
                    100: set samples 59
                    101: set xrange [1:59]
                    102: set auto
                    103: set key
                    104:
                    105: set title "Greatest Common Divisor (for integers only)"
                    106:
                    107: plot gcd(x, 60)
                    108: pause -1 "Hit return to continue"
                    109:
                    110: set xrange [-10:10]
                    111: set yrange [-10:10]
                    112: set auto
                    113: set isosamples 10
                    114: set samples 100
                    115: set title ""
                    116: