calcmet

class IntegrwithPrec
    def initialize(f, a, b, precval, fixeps, min, max)
        @f = f;
        @a = a;
        @b = b;
        @precval = precval;
        @fixeps = fixeps;
        @min = min;
        @max = max;
    end

    def midrect(n)
        integr = 0.0;
        h = (@b - @a) / n;
        for i in 1 .. n
            integr += @f.call(@a + h * (i - 0.5));
        end
        integr * h
    end

    def trapets(n)
        integr = 0.0;
        h = (@b - @a) / n;
        for i in 1 .. (n - 1)
            integr += @f.call(@a + h * i);
        end
        (integr + (@f.call(@a) + @f.call(@b))/2) * h
    end

    def simpsons(n)
        integr = 0.0;
        h = (@b - @a) / n;

		for i in 1 .. n
			integr += 4 * @f.call(@a + h * (i - 0.5));
		end
		
		for i in 1 .. (n - 1)
			integr += 2 * @f.call(@a + h * i);
		end
			
        (integr + @f.call(@a) + @f.call(@b)) * h / 6.0
    end

    def mk(n)
        prng = Random.new;
        k = 0;
        x = 0.0;
        y = 0.0;
        for i in 0 .. (n - 1)
            x = prng.rand(@a .. @b);
            y = prng.rand(@min .. @max);
            if y < @f.call(x)
                k += 1;
            end
        end
        (@b - @a) * (@max - @min) * k / n
    end

end

class Myclass
    def midrectprec()
        funexp = Proc.new {|x| Math.exp(x)};
        calcexp = IntegrwithPrec.new(funexp, 0.0, 1.0, Math.exp(1) - 1, 0.001, 0, funexp.call(1));
        count = 2;
        $I1 = 0.0;
        $I2 = calcexp.midrect(count);
        begin
            count *= 2;
            $I1 = $I2;
            $I2 = calcexp.midrect(count);
        end until (($I1 - $I2).abs() / 3) < 0.001;
        superI = (4 * $I2 - $I1) / 3;

        print "средние прямоугольники ", count, " ", $I2, " ", superI, " ", (superI - Math.exp(1) + 1).abs(), "\n";
    end

    def trapetsprec()
    funexp = Proc.new {|x| Math.exp(x)};
    calcexp = IntegrwithPrec.new(funexp, 0.0, 1.0, Math.exp(1) - 1, 0.001, 0, funexp.call(1));
    count = 2;
    $I1 = 0.0;
    $I2 = calcexp.trapets(count);
    begin
        count *= 2;
        $I1 = $I2;
        $I2 = calcexp.trapets(count);
    end until (($I1 - $I2).abs() / 3) < 0.001;
    superI = (4 * $I2 - $I1) / 3;
    print "трапеций ", count, " ", $I2, " ", superI, " ", (superI - Math.exp(1) + 1).abs(), "\n";
    end

    def simpsonsprec()
    funexp = Proc.new {|x| Math.exp(x)};
    calcexp = IntegrwithPrec.new(funexp, 0.0, 1.0, Math.exp(1) - 1, 0.001, 0, funexp.call(1));
    count = 2;
    $I1 = 0.0;
    $I2 = calcexp.simpsons(count);
    begin
        count *= 2;
        $I1 = $I2;
        $I2 = calcexp.simpsons(count);
    end until (($I1 - $I2).abs() / 15) < 0.001;
    superI = (16 * $I2 - $I1) / 15;
    print "симпсона ", count, " ", $I2, " ", superI, " ", (superI - Math.exp(1) + 1).abs(), "\n";
    end
end

my = Myclass.new();
print "eps = 0.001\n";
print Math.exp(1) - 1, "\n";
my.midrectprec();
my.trapetsprec();
my.simpsonsprec();
funexp = Proc.new {|x| Math.exp(x)};
calcexp = IntegrwithPrec.new(funexp, 0.0, 1.0, Math.exp(1) - 1, 0.001, 0, funexp.call(1));
integr = 0.0;
integr = calcexp.mk(500);
print "монте-карло ", integr, " ", (integr - Math.exp(1) + 1).abs(), "\n";