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Ruby Implementation of Riemann Sum (left and right solution)
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# https://en.wikipedia.org/wiki/Riemann_sum | |
class RiemannSum | |
def initialize(f, v_start, v_end, n_step) | |
@f = f | |
@v_start = v_start | |
@v_end = v_end | |
@n_step = n_step | |
@step_size = (v_end - v_start) / (n_step * 1.0) | |
end | |
def solve_left | |
sum = 0 | |
s, e = @v_start, @v_end | |
@n_step.times do | |
sum += @f.call(s) * @step_size | |
s = [s + @step_size, e].min | |
end | |
sum | |
end | |
def solve_right | |
sum = 0 | |
s = @v_start + @step_size | |
e = @v_end | |
@n_step.times do | |
sum += @f.call(s) * @step_size | |
s = [s + @step_size, e].min | |
end | |
sum | |
end | |
end | |
# \displaystyle\int_{3}^{10} \left( -10x^{2}+3x+6\right) dx | |
f = ->(x) { -10*(x**2) + 3*x + 6 } | |
r = RiemannSum.new(f, 3, 10, 2) | |
=> #<RiemannSum:0x00000001f63e88 @f=#<Proc:0x00000001f75e58@(irb):2 (lambda)>, @v_start=3, @v_end=10, @n_step=2, @step_size=3.5> | |
r.solve_left | |
# => -1652.0 | |
r.solve_right | |
# => -4763.5 |
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