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MathGroup Archive 2006

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Re: Re: generalized foldlist problem - part 2

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69215] Re: [mg69192] Re: [mg69138] generalized foldlist problem - part 2
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 1 Sep 2006 18:41:30 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 1 Sep 2006, at 11:41, Andrzej Kozlowski wrote:

>
> On 31 Aug 2006, at 09:38, Arkadiusz Majka wrote:
>
>> Dear All,
>>
>> Thank all of you for your help regarding my "generalized fold list
>> problem", that sounds
>>
>>>> I have two list
>>>
>>> list1=={a,b,c,d,e}
>>> list2=={3,2,5,1,6}
>>>
>>> and I want to apply a modified version of FoldList to list1 in the
>>> following way: list2 indicates that element a appears only 3 times
>>> (if
>>> space enough) beginning from the beginning of the list , element b
>>> appears 2 times, c - 5 times , etc.
>>>
>>> So the output should be
>>>
>>> GeneralizedFoldList[list1,list2]=={a,a+b,a+b+c,c+d,c+e}
>>>
>>>
>>
>> Now, I still need your help. What I want to do now, and what I have
>> problem with, is to add a constraint to the algorithm, i.e every
>> element in my GeneralizedFoldList must be less than one.
>> The following example says what to do if it is not.
>>
>> Lets take two lists
>>
>> list1=={0.9,0.8,0.7}
>> list2=={3,3,3}
>>
>> All your algorithms use PadRight (you pad 0's). So the following
>> matrix
>> is built
>>
>> {{0.9, 0.9, 0.9, 0, 0}, {0, 0.8, 0.8, 0.8, 0}, {0, 0, 0.7, 0.7, 0.7}}
>>
>> and we add elements along colums and obtain {0.9, 1.7, 2.4, 1.5, 0.7}
>>
>> The first element is less than 1 so it's ok. The second is > 1 what I
>> need to avoid. I want to avoid it by shifting the nonzero elements of
>> the second and third row of above matrix of two positions:
>> {0,0,0,0.8,0.8,0.8,0}, {0,0,0,0,0.7,0.7,0.7}.
>>
>> I go on with suming along columns and discover that everything is 
>> fine
>> until I have to add 0.8 and 0.7 what is >1. So I repeat the procedure
>> by shfting hte third row of the number of position that is needed to
>> ensure that my sum is <1.
>>
>> Finally I obtain {{0.9, 0.9, 0.9, 0, 0, 0, 0, 0,
>> 0},{0,0,0,0.8,0.8,0.8,0,0,0},{0,0,0,0,0,0,0.7,0.7,0.7}}
>> and Plus@@% is what I desire.
>>
>> Thanks in advance! I hope you will manage :)
>>
>> Arek
>>
>
>
> Here is a (not very pretty) code that should do what you want
> starting with a matrix of the above kind:
>
>
> GF[P_]:==Module[{M==P},Do[M == NestWhile[
>       Join[(PadRight[#1, Length[#1] + 1] & ) /@
>          Take[#1, s], (PadLeft[#1, Length[#1] + 1] & ) /@
>          Take[#1, s - Dimensions[#1][[1]]]] & , M,
>        !And @@ Thread[Total[#1[[All,Range[Length[
>                Flatten[Split[#1[[s]]] /. {l___,
>                    {(0)..}} :> {l}]]]]]] < 1] & ],
>     {s, Dimensions[M][[1]]}]; M]
>
>
> Let's verify that it works. First, starting with your original case:
>
>
> In[8]:==
> M=={{0.9,0.9,0.9,0,0},{0,0.8,0.8,0.8,0},{0,0,0.7,0.7,0.7}};
>
>
> In[9]:==
> GF[M]//InputForm
>
> Out[9]//InputForm==
> {{0.9, 0.9, 0.9, 0, 0, 0, 0, 0, 0},
> {0, 0, 0, 0.8, 0.8, 0.8, 0, 0, 0},
> {0, 0, 0, 0, 0, 0, 0.7, 0.7, 0.7}}
>
> Now let's change M somewhat:
>
> In[10]:==
> M=={{0.9,0.9,0.1,0,0},{0,0.1,0.8,0.3,0},{0,0,0.7,0.9,0.7}};
>
>
> In[11]:==
> GF[M]//InputForm
>
> Out[11]//InputForm==
> {{0.9, 0.9, 0.1, 0, 0, 0, 0, 0}, {0, 0, 0.1, 0.8, 0.3, 0,
>    0, 0}, {0, 0, 0, 0, 0, 0.7, 0.9, 0.7}}
>
> So you only need to combine this with your favourite code from part 1.
>
> (PS. In answering part 1 I obviously misunderstood your question, but
> I think that was mainly because I do not think your function is in
> any way a "generalisation of Fold", or even of Fold
> [Plus,element,list]. As far as I can see it does not really perform
> any kind of "folding".
>
> Andrzej Kozlowski
>


In fact I still do not fully understand your original question and, 
in particular, if the example you originally posted (and which, if 
any, of the solutions various people provided) were correct. Just in 
case, here is a "solution" to your original question, which I think 
is different from any of the ones I have seen:

GFMatrix[list1_,
     list2_] :== Normal[SparseArray[Flatten[Table[If[j =B2 i + list2
[[i]] - 1,
Rule[{i, j}, list1[[i]]], Rule[{i,
            j}, 0]], {i, Length[list2]}, {j, i, Length[list1] + i - 
1}], 1]]]

GFMatrix builds the matrix, which, I think, you need in the second 
part of the question. The code makes no use of PadLeft or PadRight. 
However, note that in your original example, the output is not the 
same as you gave as the correct one, although the output below seems 
to me to fit better your verbal description of what you wanted done:


list1=={a,b,c,d,e};
list2=={3,2,5,1,6};


GFMatrix[list1,list2]


{{a, a, a, 0, 0, 0, 0, 0, 0},
   {0, b, b, 0, 0, 0, 0, 0,
    0}, {0, 0, c, c, c, c, c,
    0, 0}, {0, 0, 0, d, 0, 0,
    0, 0, 0}, {0, 0, 0, 0, e,
    e, e, e, e}}


Total[%]


{a,a+b,a+b+c,c+d,c+e,c+e,c+e,e,e}

This is longer than the output you gave as the right solution, which 
was only a part of the above, namely {a,a+b,a+b+c,c+d,c+e}.

Andrzej Kozlowski



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