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I want to find the product of the first 20 Fibonacci numbers (the fibonorial). I want implementations using While, Do, and For loops.

This is my code using Do:

Do[Sum[Print[a = a*fib[n]], {n, 1, 20}], {a, 1}]

But I can't get it working with While or For.


My fib code is as follows:

Clear[fib, x, a]
fib[1] = 1; fib[2] = 1;
fib[n_] := fib[n] = fib[n - 1] + fib[n - 2]
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Could you post the code that you had trouble with? –  jVincent Feb 15 '13 at 10:08
@ jvincent hey vincent, i actually solved it. i failed to set an initial condition. however, i am looking to improve my code, as it gives a result of every sum value, rather then just the last value which I am looking for. is there anyway to do that? \For[n = 1; a = 1, n < 21, n++, Print[a = a*fib[n]]] \a = 1; n = 1; While[n < 21, Print[a = a*fib[n]]; n++] –  julesverne Feb 15 '13 at 10:16
In the future please format the code using two ` or four indents. mathematica.stackexchange.com/faq –  Ajasja Feb 15 '13 at 10:21
You seem to be misunderstanding what Print does. It prints the results to a new line, but doesn't actually return it. If you remove Print and run either of your examples, the result will be stored in a at the end of the loop. –  jVincent Feb 15 '13 at 10:26
wow, thank you so much! –  julesverne Feb 15 '13 at 10:30
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2 Answers

up vote 3 down vote accepted

According to your specific needs, which seems to be more syntax and not performance related:

While loop:

Clear[a, n]
n = 1; a = 1;
While[n <= 20, Print[a = a*fib[n]]; n++]

For loop:

Clear[a, n]
For[n = 1; a = 1, n <= 20, n++, Print[a = a*fib[n]]]

I guess you know that there are other ways for compute Fibonacci. Roman Maeder's book, for instance, Computer Science with Mathematia or Michael Trott's Guidebook to Programming in Mathematica.

Edit: Approaches to calculate product of Fibonacci Numbers:

Times @@ Array[Fibonacci, 20]

Times @@ Fibonacci[Range@20]

a = 0; Times @@ NestWhileList[a + # &, 1, (a = #1) < Fibonacci@19 &, 2]

fibProduct[n_Integer?Positive] :=
    Module[{f1 = 1, f2 = 0, res = 1},
    Do[{f1, f2} = {f1 + f2, f1}; res *= f1, {n - 1}];

fibProduct[n_Integer?NonPositive] := Times @@ ((-1)^(n - 1) Fibonacci[Range@-n])

Edit 2: the not for the faint of heart approach:

The .tm file:

:Function:      fibProduct
:Pattern:       FibProduct[n_]
:Arguments:     { n }
:ArgumentTypes: { Integer }
:ReturnType:    Integer

The .cpp file:

#include <algorithm>
#include <iostream>
#include <numeric>
#include <iterator>
#include <vector>

using namespace std;

template<class F, class X, class S>
X foldl( F && f, X x, const S & s)
    return std::accumulate(std::begin(s), std::end(s), std::move(x), std::forward<F>(f));

unsigned long long fibProduct( int n )
    std::function<int(int)> fibonacci = [&fibonacci](int n) -> int { return (n < 2) ? 
        n : fibonacci(n - 1) + fibonacci(n - 2); };
    vector<int> vec(n);
    int i = 0;
    generate( begin(vec), end(vec), [&i, &fibonacci]() { return fibonacci(i += 1); } );

    return foldl( std::multiplies<int>(), 1, vec );


Attention: Don't use n > 10....

Edit 3: the not for the faint of memoized heart approach:

Add these includes:

#include <unordered_map>
#include <map>

Change this in .cpp file:

template <typename ReturnType, typename... Args>
std::function<ReturnType (Args...)>
memoize(ReturnType (*func) (Args...))
    auto cache = std::make_shared<std::map<std::tuple<Args...>, ReturnType>>();
    return ([=](Args... args) mutable  {
        std::tuple<Args...> t(args...);
        if (cache->find(t) == cache->end())
            (*cache)[t] = func(args...);
        return (*cache)[t];

template <typename F_ret, typename...  F_args>
std::function<F_ret (F_args...)> memoized_recursion(F_ret (*func)(F_args...))
    typedef std::function<F_ret (F_args...)> FunctionType;
    static std::unordered_map<decltype(func), FunctionType> functor_map;

    if(functor_map.find(func) == functor_map.end())
        functor_map[func] = memoize(func);

    return functor_map[func];

unsigned long fibonacci(unsigned n)
    return (n < 2) ? n :
    memoized_recursion(fibonacci)(n - 1) +
    memoized_recursion(fibonacci)(n - 2);

unsigned long long fibProduct( int n )
    vector<int> vec(n);
    int i = 0;
    generate( begin(vec), end(vec), [&i]() { return fibonacci(i += 1); } );
    return foldl( std::multiplies<int>(), 1, vec );

The rest is just proper compilation, linking and link installation in Mathematica...

Btw. you've to link explicitly against libstdc++.6.0.9.dylib (or another version number), since there is all the basic_string code etc. (MacOSX)


Has someone dealt so far, presumably yes, with big Integer issues with MathLink? Any tips for me?

Edit 4: the not for the faint of memoized heart MultiPrecision approach:

The .tm file:

:Function:      fibProductMP
:Pattern:       FibProductMP[n_]
:Arguments:     { n }
:ArgumentTypes: { Integer }
:ReturnType:    Manual

The .cpp file:

Add this include:

#include <boost/multiprecision/integer.hpp>

Maybe, if you'd like to avoid long namespace names:

using boost::multiprecision::cpp_int;

template<typename T>
inline T Identity(const std::multiplies<T>&) { return T(1); }

void fibProductMP( int n )
    vector<int> vec(n);
    int i = 0;
    generate( begin(vec), end(vec), [&i]() { return fibonacci(i += 1); } );
    cpp_int result = foldl( std::multiplies<cpp_int>(), Identity<cpp_int
        (multiplies<cpp_int>()), vec );
    MLPutString(stdlink, result.str().c_str() );

Mathematica side:

link = Install["wherever the binary is", LinkMode -> Launch];


(* 607373569868916007005878071331449502263924414704952629297115029592606\
    043656028160000000 *)

What we've achieved is a multiprecision FibProduct function which is cool, decent C++11 code, exception safe and memoized. Now I'd be tempted to say victory!

P.S.: My life wouldn't be what it is, if there would not still exist one caveat. I return the result as a const char*; so a ToExpression is needed to reuse the result for further calculations.

Just can't get enough (until 47 ;) ... Gosh...could solve that as well, but I've to say, enough is enough :)

FibProductMP[#] & /@ Range[47] // TableForm

enter image description here

That was real fun...

Thank you.

share|improve this answer
Yes, it seemed as i didn't specify a value of a, in which it was not computing my loops correctly for While or For. Thank you very much for the prompt response! –  julesverne Feb 15 '13 at 10:43
I credit you with reviving my interest in C++! I abandoned it years ago when I got tired of spending a whole day updating dependencies every time I wanted to do 5 minutes worth of coding, but your code above just plain works (up to n = 40 at least!). –  Reb.Cabin Feb 15 '13 at 17:15
Thank you :) With C++11 out, C++ feels like a whole new language. Id didn't wanted to exaggerate things, but normally I'd leave out the "1" for foldl and insert: template<typename T> inline T Identity(const std::multiplies<T>&) {return T(1);} foldl(std::multiplies<int>(), Identity<int>(std::multiplies), vec ); That would be, mathematically, clearer. –  Stefan Feb 15 '13 at 17:51
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For/Do/While Loops are generally to be avoided in Mathematica.

Instead this can be solved with a single line

Times @@ (fib /@ Range[20])

Range just generates a list of numbers from 1 to 20. The /@ is short for Map, which applies fib to every element of the list. The @@ is short for Apply, which gives you Times[...] instead of List[...].

share|improve this answer
One might also use Fibonacci[n] (especially if you're lazy as I am...) –  Pinguin Dirk Feb 15 '13 at 10:44
Being lazy and loop averse too, I would suggest Times @@ Round[GoldenRatio^Range[20]/Sqrt[5]] –  KennyColnago Feb 16 '13 at 0:38
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