Add lua as an internal library in libs/lua

1 files changed, 27 insertions, 0 deletions

diff --git a/libs/lua/test/bisect.lua b/libs/lua/test/bisect.lua
new file mode 100644
index 0000000..f91e69b
--- /dev/null
+++ b/libs/lua/test/bisect.lua
@@ -0,0 +1,27 @@
+-- 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)