Численные методы(интегрирование 4 метода)

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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;
i = 1;
while (i < n)
integr += @f.call(@a + h * (i - 1)) + 4 * @f.call(@a + h * i) + @f.call(@a + h * (i + 1));
i+=2;
end
integr * h / 3.0
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";