simionx.Integration - Numerical integration routines¶
SYNOPSIS¶
local INT = require "simionx.Integration"
-- Calculate (moment of inertia)/(mass) for sphere
-- of radius 5 via volume integration.
local mass = (4/3)*math.pi*(5)^3
print("Expecting", 10) -- equals (2/5)*(5)^2
local co = INT.montecarlo_integrate {
func = function(x,y,z, ux,uy,uz)
return (x^2 + y^2) / mass
end,
shape = INT.sphere_filled(0,0,0, 5),
min_iterations = 100000, rel_err = 0.001
}
repeat
local result, result_stdev, count, is_end = co()
print(result, result_stdev, count, is_end)
until is_end
--[[OUTPUT:
Expecting 10
1.4500000000001 0.56568542494929 2 false
10.201601740376 3.8872192893064 4 false
9.0886283261102 2.6596025108814 8 false
8.8950043916104 1.7139967190583 16 false
9.6281491592971 0.97056736497474 32 false
10.788100218533 0.67870277939624 64 false
10.066399568868 0.39300818193915 128 false
9.9114927256598 0.21441777256434 256 false
10.023885127646 0.12484348660943 512 false
10.008016691338 0.068214699144542 1024 false
10.022640402046 0.038532430498274 2048 false
9.9992880768054 0.021081642551506 4096 false
9.9958532750136 0.011474286260492 8192 false
10.001257767875 0.0061146278362448 16384 false
10.000726899752 0.0034332557814447 30709 false
9.998853501986 0.0032347632669252 32768 false
10.00004175219 0.0016990547669547 65536 false
9.9999029933063 0.00089307044213873 131072 true
--]]
--- Compute integral from 0..2PI of sin(x) dx.
print("Expecting", 2)
local co = INT.montecarlo_integrate {
func = function(x) return math.sin(x) end,
shape = INT.line(0,0,0, math.pi,0,0),
rel_err = 0.001
}
repeat
local result, result_stdev, count, is_end = co()
print(result, result_stdev, count, is_end)
until is_end
Note
See these additional sections in this topic in the offline SIMION 8.1.0 help file:- INTERFACE
SOURCE¶
D.Manura, 2007-08 (c) 2007 Scientific Instrument Services, Inc. Licensed under the terms of SIMION 8.0.
version: 20071209
