mirror of
https://github.com/taosdata/TDengine
synced 2026-05-24 10:09:01 +00:00
28 lines
645 B
Lua
28 lines
645 B
Lua
|
-- bisection method for solving non-linear equations
|
||
|
|
|
||
|
|
delta=1e-6 -- tolerance
|
||
|
|
|
||
|
|
function bisect(f,a,b,fa,fb)
|
||
|
|
local c=(a+b)/2
|
||
|
|
io.write(n," c=",c," a=",a," b=",b,"\n")
|
||
|
|
if c==a or c==b or math.abs(a-b)<delta then return c,b-a end
|
||
|
|
n=n+1
|
||
|
|
local fc=f(c)
|
||
|
|
if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
|
||
|
|
end
|
||
|
|
|
||
|
|
-- find root of f in the inverval [a,b]. needs f(a)*f(b)<0
|
||
|
|
function solve(f,a,b)
|
||
|
|
n=0
|
||
|
|
local z,e=bisect(f,a,b,f(a),f(b))
|
||
|
|
io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z)))
|
||
|
|
end
|
||
|
|
|
||
|
|
-- our function
|
||
|
|
function f(x)
|
||
|
|
return x*x*x-x-1
|
||
|
|
end
|
||
|
|
|
||
|
|
-- find zero in [1,2]
|
||
|
|
solve(f,1,2)
|