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Re: st: MATA all combinations / pairs of a row

 From Sebastian Eppner To statalist@hsphsun2.harvard.edu Subject Re: st: MATA all combinations / pairs of a row Date Sat, 8 Oct 2011 00:28:50 +0200

```Hi,
yes, based on the select and rowsum = 2 logic I wrote this
(unfortunately it has to use one loop... first I thought that may be
ok... in reality in really is time consuming... if there are ANY ideas
out there how to prevent the loop, i' be very grateful).

BASIC = ( 1,1,1) \ (1,1,0) \ (1,0,1) \ (0,1,1) \ (0,0,1) \ (0,1,0) \ (1,0,0)
PROPERTIES = (0,9,10) \ (0.45, 0.2, 0.35)

PROP1 = PROPERTIES[1,.]
PROP1 = diag(PROP1)
PROP1 = BASIC * PROP1

PROP2 = PROPERTIES[2,.]
PROP2 = diag(PROP2)
PROP2 = BASIC * PROP2

Now I have 3 Matrices with all the information i needed. The problem was now:

> For each row/combination in BASIC  I need to  find all PAIRS of Ones
> that are contained in the combination. For any pair, I need to
> multiply:
> PROP1 of Element1 * PROP1 of Element2  * abs(PROP2 of Element1-PROP2
> of ELEMENT2)

I calculated the latter not only for pairs, but for all rows (later i
only use the pair rows)

PAIRS =  rowmax(PROP1):*rowmin(PROP1):*(rowmax(PROP2)-rowmin(PROP2))

Then I calculate the sum of all pairs contained in the first row. see
the select() which only selects those rows that are:
- contain only elements that are also elements in row one of BASICS
(that i do by subtracting all rows from the first one, and then I look
if there is a -1 somewhere)
- contain only pairs (as Nick suggested that means the rowsum is 2)

mata: result = colsum(select(PAIRS, (rowmin(BASIC[1,.]:-BASIC):>-1):&
rowsum(BASIC):==2))

of course i need the result for all the other rows too! thats where i
cant think of anything but a loop (****jsdf)

forvalues i=2/`lastrow' {
mata: result = result \ colsum(select(PAIRS,
(rowmin(BASIC[`i',.]:-BASIC):>-1):& rowsum(BASIC):==2))
}

any suggestion would be magic.
Thanks,
Sebastian

On Thu, Oct 6, 2011 at 2:16 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> One idea only from me. Look at -select()- and think of rowsums being 2.
>
> Nick
>
> On Wed, Oct 5, 2011 at 10:08 PM, Sebastian Eppner <eppner@uni-potsdam.de> wrote:
>> Hi,
>> I have N elements. In this example N will be 3. But in my application
>> it will be usually around 7, going up to 20 in some cases…
>>
>> Each element can be either 1 or 0. My basic matrix has all 2^N, here
>> 2^3 permutations of the elements:
>>
>> BASIC = ( 1,1,1) \ (1,1,0) \ (1,0,1) \ (0,1,1) \ (0,0,1) \ (0,1,0) \
>> (1,0,0) \(0,0,0)
>>
>> The elements have 2 “properties” , PROP1 and PROP2  each, stored in 2
>> rows of another matrix, for example:
>>
>> PROPERTIES = (1.4,4.6,8.1) \ (0.2, 0.4, 0.4)
>>
>> Every row in BASIC resembles a unique combination of the elements.
>> What I want to do, is to calculate some indicators for every
>> combination, using the Properties of the elements.
>>
>> An easy example would be to calculate the total sum of PROP1 for each
>> combination. I just need to multiply the “diagonalized” first row of
>> the PROPERTIES Matrix with the BASIC Matrix and then calculate the
>> rowsum of this resulting matrix.
>>
>>
>> What I want to do now is more complex and I am really stuck. The
>> indicator I want to calculate now is the following:
>>
>> For each row/combination in BASIC  I need to  find all PAIRS of Ones
>> that are contained in the combination. For any pair, I need to
>> multiply:
>>
>> PROP1 of Element1 * PROP1 of Element2  * abs(PROP2 of Element1-PROP2
>> of ELEMENT2)
>>
>> It is the sum of all PAIRS that I need to know for every row….
>>
>>
>> Of course, not every row has PAIRS in it… all rows with only 1 One
>> have no pairs, so the result for these rows should be 0 (or missing, I
>> don’t care).
>>
>> Also, many rows (those with only 2 Ones) have only a single Pair…
>>
>> In my Example with 3 elements, only the first row sums up more than
>> one (3) Pair(s)….
>>
>>
>> I am looking for a way to solve this problem by not using loops… and
>> as much matrix algorithms as possible. Since I have a lot of BASIC
>> Matrices with more elements than 3… I guess the whole thing would be
>> very very time consuming if I started smth with loops… Maybe there is
>> no way to get rid of any loop… any idea would be very welcome (even
>> some, with a little looping).
>
> *
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>

--
Sebastian Eppner
Lehrstuhl für Vergleichende Politikwissenschaft
Wirtschafts- und Sozialwissenschaftliche Fakultät
Universität Potsdam
August-Bebel-Straße 89
14482 Potsdam
Telefon: +49-331-977-3305
eppner@uni-potsdam.de

*
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```