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