I was window shopping at Community Contribution of Arch Linux Fourms for totally free new application, tried to see if I can find new toy. I saw this HC, after I read and saw some examples the author posted, I decided to give it a try.
Too early? or too late?
r(t)=2-2sin(t)+sin(t)*sqrt(abs(cos(t)))/(sin(t)+1.4)
graphpeq(r(t)*cos(t),r(t)*sin(t),0,2pi,-3,3,-4,1)
If you try to define a recursion function, you will get:
fib(n)=if(n>=0,
if(n==0,0,
if(n==1,1,
fib(n-1)+fib(n-2)
)
)
)
Error : recursive definition.
Let’s trick HC!
fibr(n)=fib(n)
fib(n)=if(n>=0,
if(n==0,0,
if(n==1,1,
fibr(n-1)+fibr(n-2)
)
)
)
Some outputs:
> fib(10)==fibo(10)
1
> fib(70)
Error : too much recursion/nestedness. If you know what you are doing, you can bypass this with:
\bpn.
Argument Error : if() : at least two arguments are needed (condition, true_branch, false_branch)
> \bpn
By pass is now on.
> fib(70)
You will have to wait until only God knows how long it takes…
Note
Now, HC is allowed to define recursion function:
fib(n) = if(n<2,n,fib(n-1)+fib(n-2))
, read more. (2010-08-24)
Yes, the Fast Fourier transform!
fft(x)=for(k=0,k<length(x),k+=1,
xk=0;
for(j=0,j<length(x),j+=1,
a=x[j];
b=exp(-2pi*k*j*0i1/length(x));
xk+=a*b;
);
print(xk);
)
Example:
> x = [1,0,3i-3,4i5,5]
> fft(x)
13i2
-7.8203160070896799i3.7250338450183462
6.7264861191111235i2.6059037339171068
-8.4904181416113337i-1.3698357564173172
1.5842480295898901i-6.9611018225181358
Confirmed by result from SciPy:
>>> import scipy
>>> scipy.fft([1,0,3-3j,4+5j,5])
array([ 13.00000000+2.j , -7.82031601+3.72503385j,
6.72648612+2.60590373j, -8.49041814-1.36983576j,
1.58424803-6.96110182j])</pre>
Note: the representations of complex number are different.
Note
Here is a shorter version:
fft(x)=for(k=0,k<length(x),k+=1,
for(j=0,j<length(x),j+=1,
a=x[j];
b=exp(-2pi*k*j*0i1/length(x));
xk=if(j==0,a*b,xk+a*b);
);
y=if(k==0,[xk],join(y,[xk]));
)
(2010-08-24)
The result can be retrieved by y.
This is a great CLI program, I am going to replace SpeedCrunch. You can do some simple programming, though I found it’s still limited. (What do you expect? Signal processing using a calculator?) When I installed SpeedCrunch because I wanted one can allow me to easy input, bc is not so friendly, even I prefer CLI over GUI. Now, HC can do things I need and it’s a CLI and it’s resource-friendly. Definitely the top choice for me!
It has vector but it’s not much you can do with it at this moment, but if you just use it for 1+1, it can do much more than that. If you don’t like CLI, don’t worry, it provides GUI as well. But I didn’t try it, so no comments on that.
