lua/test/bisect.lua

   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)