Fri, 19 Nov 2010 03:37:51 +0000
Implement OP_ADD, OP_SUB, OP_LT
57 | 1 | -- bisect.lua |
2 | -- bisection method for solving non-linear equations | |
3 | ||
4 | delta=1e-6 -- tolerance | |
5 | ||
6 | function bisect(f,a,b,fa,fb) | |
7 | local c=(a+b)/2 | |
8 | io.write(n," c=",c," a=",a," b=",b,"\n") | |
9 | if c==a or c==b or math.abs(a-b)<delta then return c,b-a end | |
10 | n=n+1 | |
11 | local fc=f(c) | |
12 | if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end | |
13 | end | |
14 | ||
15 | -- find root of f in the inverval [a,b]. needs f(a)*f(b)<0 | |
16 | function solve(f,a,b) | |
17 | n=0 | |
18 | local z,e=bisect(f,a,b,f(a),f(b)) | |
19 | io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z))) | |
20 | end | |
21 | ||
22 | -- our function | |
23 | function f(x) | |
24 | return x*x*x-x-1 | |
25 | end | |
26 | ||
27 | -- find zero in [1,2] | |
28 | solve(f,1,2) | |
29 |