Problem 179. Monte-Carlo integration
Write a function that estimates a d-dimensional integral to at least 1% relative precision.
- d: positive integer. The dimension of the integral.
- fun: function handle. The function accepts a row-vector of length d as an argument and returns a real scalar as a result.
- I: is the integral over fun from 0 to 1 in each direction.
1 1 1 / / / I = |dx_1 |dx_2 ...| dx_d fun([x_1,x_2,...,x_d]) / / / 0 0 0
fun = @(x) x(1)*x(2) d = 2
The result should be 0.25. An output I=0.2501 would be acceptable, because the relative deviation would be abs(0.25-0.2501)/0.25 which is smaller than 1%.
The functions in the test-suite are all positive and generally 'well behaved', i.e. not fluctuating too much. Some of the tests hav a relatively large d.
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