"SfR Fresh" - the SfR Freeware/Shareware Archive

Member "lua-5.1.4/test/bisect.lua" of archive lua-5.1.4.tar.gz:

As a special service "SfR Fresh" has tried to format the requested source page into HTML format using source code syntax highlighting with prefixed line numbers. Alternatively you can here view or download the uninterpreted source code file. That can be also achieved for any archive member file by clicking within an archive contents listing on the first character of the file(path) respectively on the according byte size field. 
    1 -- bisection method for solving non-linear equations
    2 
    3 delta=1e-6	-- tolerance
    4 
    5 function bisect(f,a,b,fa,fb)
    6  local c=(a+b)/2
    7  io.write(n," c=",c," a=",a," b=",b,"\n")
    8  if c==a or c==b or math.abs(a-b)<delta then return c,b-a end
    9  n=n+1
   10  local fc=f(c)
   11  if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
   12 end
   13 
   14 -- find root of f in the inverval [a,b]. needs f(a)*f(b)<0
   15 function solve(f,a,b)
   16  n=0
   17  local z,e=bisect(f,a,b,f(a),f(b))
   18  io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z)))
   19 end
   20 
   21 -- our function
   22 function f(x)
   23  return x*x*x-x-1
   24 end
   25 
   26 -- find zero in [1,2]
   27 solve(f,1,2)