Randomizing a node-list -- long (Was: Re: Extending x

> > Then again, maybe I don't need to extend it. The two transforms I
> > would like to implement seem easy and commonplace, but are proving
> > elusive: I would like to render a node-set into rows of columns
> > without resorting to disable-output-escaping to insert the
> > modulo-column </tr><tr> break, and I'd also like to be able to
> present
> > a node-set in a new random order on each call.  If either of these
> > effects can be done directly with xsltproc, I'll be one happy
> camper.
> 
> The first one is a FAQ and you can find it in many places, just these
> days there was one at TopXML.com (sure, you don't need DOE at all,
> <tr>
> is a node, not just string). I also remember doing one at the time
> that
> combined creating a multi-column table with adding alternating
> colours
> to the rows -- could find it if this would be useful. 
> 
> For the second request -- see my article "Casting the Dice with FXSL:
> Random Number Generation Functions in XSLT" at:
> 
> http://www.topxml.com/xsl/articles/dice/default.asp

I am pleased to present a complete solution for the problem of
producing and processing randomized node-sets or node-lists (random
indices). This is a XSLT 1.0 solution and can be used immediately

The code bellow is a complete, new module of FXSL, named
randomList.xsl. It should be put in the same folder, where all other
FXSL files reside.

It imports and uses random.xsl.

The main functions/templates are:

1. randomizeList -- given a node-set and an optional seed produces a
new node-set, having nodes with the same values as the given node-set,
but ordered randomly.


2. randomMap -- given a function f, a node-set and an optional seed, it
produces a mapping of the given function f over the nodes of the
node-set, which is applied in a random order, based on the given seed.

It is efficient, because no intermediate randomized list is produced.


3. randListIndex -- given a node-set and an optional seed produces a
random index (a random permutation of the numbers from 1 to
count($node-set). This index can then be used e.g. in a xsl:for-each
loop to index randomly the elements of any node-set with the same
number of nodes.

The basic idea standing behind a list randomisation is to follow the
algorithm of producing a permutation of N elements -- that is to
produce one random number out of N in the first stage, then to produce
one random number out of the remaining N-1, etc...

Actually, a random sequence of N random numbers is produced, and its
elements are then individually scaled, so that its k-th element is in
the interval [1, N-k+1]

Bellow is the complete FXSL module:

randomList.xsl
--------------
<!--
=======================================================================
 Stylesheet: random.xsl        List Randomization Functions            

    Version: 1.0 (2002-05-03)                                          

     Author: Dimitre Novatchev                                         

     Notice: Copyright (c)2002 D.Novatchev  ALL RIGHTS RESERVED.       

             No limitation on use - except this code may not be 
             published, in whole or in part, without prior written 
             consent of the copyright owner. 
=====================================================================-->
<xsl:stylesheet version="1.0" 
 xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
 xmlns:vendor="urn:schemas-microsoft-com:xslt"
 xmlns:myIncrement="f:myIncrement" 
 xmlns:x="f:fxslRandomList.xsl"
 exclude-result-prefixes="xsl vendor myIncrement x"
>

<!--
 
========================================================================
    Imported files:                                                    

=====================================================================-->
  <xsl:import href="random.xsl"/>
  
 
  <!--
      Template: randScale                                     
      Purpose : Return an integer, scaled from [0, modulus-1] 
                to [s, t]                                     
    Parameters:                                               
     $pStart    - [optional] the start of the target interval 
     $pEnd      - [optional] the end of the target interval   
     $pN        - The number N to be scaled                   
  ============================================================-->
  
<!--
  > _randScale :: Float -> Float -> Int -> Int                     
  > randScale s t n = floor (rndScl ((t - s + 1)/dintRange ) s n)  
  >    where    dintRange = fromInt (modulus - 1)                  
                                                                   
                                                                   
  > rndScl :: Float -> Float -> Int -> Float                       
  > rndScl a b n = a * fromInt n + b                               
-->  
  <xsl:template name="_randScale" >
    <xsl:param name="arg2" select="0"/> <!--pStart-->
    <xsl:param name="arg3" select="1"/> <!--pEnd  -->
    <xsl:param name="arg1"/>            <!--pN    -->
    
    <xsl:value-of 
         select="floor( ($arg3 - $arg2 + 1) div ($modulus - 1) 
                         * $arg1 
                        + $arg2 
                       )"/>
  </xsl:template>

<!--
      Template: _dScale                                    
      Purpose : Used to prepare a random recursive index   
                for a list from a random sequence with the 
                same number of elements                    
    Parameters:                                            
     $pRandSeq  - a list of (random) numbers               
        Result: - a random recursive index                 
  =========================================================-->
  <xsl:template name="_dScale">
    <xsl:param name="pRandSeq" select="/.."/>
<!--
                                                            
    > dScale  :: [Int] -> [Int]                             
    > dScale   [] = []                                      
    > dScale (x:xs) = fstScale : (dScale xs)                
    >   where fstScale = randScale 0 (fromInt (length xs)) x
-->
    <xsl:if test="$pRandSeq">
      <el>
        <xsl:call-template name="_randScale">
          <xsl:with-param name="arg2" select="1"/> <!--s-->
          <xsl:with-param name="arg3" 
                      select="count($pRandSeq)"/> <!--end-->
          <xsl:with-param name="arg1" select="$pRandSeq[1]"/>
        </xsl:call-template>
      </el>
      
      <xsl:call-template name="_dScale">
        <xsl:with-param name="pRandSeq" 
                        select="$pRandSeq[position() > 1]"/>
      </xsl:call-template>
    </xsl:if>
  </xsl:template>
   
<!--
      Template: _randomRecursiveIndex                      
      Purpose : Used to prepare a random recursive index   
                for a list                                 
    Parameters:                                            
     $pList     - a list to be presented in a random order 
     $pSeed     - [optional] a seed for generation of the  
                  random sequence                          
        Result: - a random recursive index                 
  =========================================================-->

<!--
   > randomRecursiveIndex xs  sd 
            = dScale (take (length xs) (randomSequence sd))
-->
  <xsl:template name="_randomRecursiveIndex">
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pSeed" select="$seed"/>
    
    <xsl:variable name="vRandSequence">
      <xsl:call-template name="randomSequence">
        <xsl:with-param name="pLength" select="count($pList)"/>
        <xsl:with-param name="pSeed" select="$pSeed"/>
      </xsl:call-template>
    </xsl:variable>
    
    <xsl:call-template name="_dScale">
      <xsl:with-param name="pRandSeq" 
           select="vendor:node-set($vRandSequence)/*"/>
    </xsl:call-template>
  </xsl:template>

<!--
      Template: _permutationFromRecursiveIndex             
                                                           
      Purpose : Produce a random permutation of a list     
                based on a given random recursive index    
    Parameters:                                            
     $pList     - a list to be presented in a random order 
     $pIndex    - a list with the same length as $pList    
                  containing the random recursive index    
        Result: - a randomly permuted list                 
  =========================================================-->
  
  <xsl:template name="_permutationFromRecursiveIndex">
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pRecIndex" select="/.."/>
    
    <xsl:if test="not(count($pList) = count($pRecIndex))">
      <xsl:message terminate="yes">
       Error[permutationFromRecursiveIndex]: 
             The two lists are not the same length!
      </xsl:message>
    </xsl:if>
    
    <xsl:call-template name="_permRecIdx">
      <xsl:with-param name="pList" select="$pList"/>
      <xsl:with-param name="pRecIndex" select="$pRecIndex"/>
    </xsl:call-template>
  </xsl:template>
  
  <xsl:template name="_permRecIdx">
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pRecIndex" select="/.."/>
    
    <xsl:variable name="vIndex" 
                  select="number($pRecIndex[1])"/>
                  
    <xsl:if test="$pList">
      <el>
        <xsl:value-of 
            select="$pList[position() = $vIndex]"/>
      </el>
    
      <xsl:call-template name="_permRecIdx">
        <xsl:with-param name="pList" 
          select="$pList[position() != $vIndex]"/>
        <xsl:with-param name="pRecIndex" 
             select="$pRecIndex[position() > 1]"/>
      </xsl:call-template>
    </xsl:if>
  </xsl:template>

<!--
      Template: randomizeList                              
                                                           
      Purpose : Produce a random permutation of a list     
                based on a given seed for randomisation    
    Parameters:                                            
     $pList     - a list to be reproduced in a random order
     $pSeed     - [optional] the seed to be used           
  =========================================================-->
  
  <xsl:template name="randomizeList">
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pSeed" select="$seed"/>
    
    <xsl:variable name="vrtfRecIndex">
      <xsl:call-template name="_randomRecursiveIndex">
        <xsl:with-param name="pList" select="$pList"/>
        <xsl:with-param name="pSeed" select="$pSeed"/>
      </xsl:call-template>
    </xsl:variable>
    
    <xsl:variable name="vRecIndex" 
              select="vendor:node-set($vrtfRecIndex)/*"/>
              
    <xsl:call-template name="_permutationFromRecursiveIndex">
      <xsl:with-param name="pList" select="$pList"/>
      <xsl:with-param name="pRecIndex" select="$vRecIndex"/>
    </xsl:call-template>
  </xsl:template>

<!--
      Template: _mapFromRandIndex                          
                                                           
      Purpose : Produce a mapping of a given function      
                over a list, which will be applied randomly
                based on a given random recursive index    
    Parameters:                                            
     $pFun      - a template reference to a function       
     $pList     - a list to be processed in a random order 
     $pIndex    - a list with the same length as $pList    
                  containing the random recursive index    
        Result: - a mapping of pFun applied in random order
                  (specified by pIndex) on pList           
  =========================================================-->
  
  <xsl:template name="_mapFromRandIndex">
    <xsl:param name="pFun" select="/.."/>
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pRecIndex" select="/.."/>
    
    <xsl:if test="not(count($pList) = count($pRecIndex))">
      <xsl:message terminate="yes">
       Error[mapFromRandIndex]: 
             The two lists are not the same length!
      </xsl:message>
    </xsl:if>
    
    <xsl:call-template name="_mapRndIndex">
      <xsl:with-param name="pFun" select="$pFun"/>
      <xsl:with-param name="pList" select="$pList"/>
      <xsl:with-param name="pRecIndex" select="$pRecIndex"/>
    </xsl:call-template>
  </xsl:template>
  
  <xsl:template name="_mapRndIndex">
    <xsl:param name="pFun" select="/.."/>
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pRecIndex" select="/.."/>
    
    <xsl:variable name="vIndex" 
                  select="number($pRecIndex[1])"/>
                  
    <xsl:if test="$pList">
      <el>
        <xsl:apply-templates select="$pFun">
          <xsl:with-param name="arg1" 
           select="$pList[position() = $vIndex]"/>
        </xsl:apply-templates>
      </el>
    
      <xsl:call-template name="_mapRndIndex">
        <xsl:with-param name="pFun" select="$pFun"/>
        <xsl:with-param name="pList" 
          select="$pList[position() != $vIndex]"/>
        <xsl:with-param name="pRecIndex" 
             select="$pRecIndex[position() > 1]"/>
      </xsl:call-template>
    </xsl:if>
  </xsl:template>

<!--
      Template: randomMap                                  
                                                           
      Purpose : Produce a mapping of a given function      
                over a list, which will be applied randomly
                based on a given seed for randomization    
    Parameters:                                            
     $pFun      - a template reference to a function       
     $pList     - a list to be processed in a random order 
     $pSeed     - [optional] the seed to be used           
                   for randomization                       
  =========================================================-->
  
  <xsl:template name="randomMap">
    <xsl:param name="pFun" select="/.."/>
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pSeed" select="$seed"/>
    
    <xsl:variable name="vrtfRecIndex">
      <xsl:call-template name="_randomRecursiveIndex">
        <xsl:with-param name="pList" select="$pList"/>
        <xsl:with-param name="pSeed" select="$pSeed"/>
      </xsl:call-template>
    </xsl:variable>
    
    <xsl:variable name="vRecIndex" 
              select="vendor:node-set($vrtfRecIndex)/*"/>
              
    <xsl:call-template name="_mapFromRandIndex">
      <xsl:with-param name="pFun" select="$pFun"/>
      <xsl:with-param name="pList" select="$pList"/>
      <xsl:with-param name="pRecIndex" select="$vRecIndex"/>
    </xsl:call-template>
  </xsl:template>
 
<!--
      Template: randListIndex                              
                                                           
      Purpose : Produce a random (non-recursive)           
                index for a list                           
    Parameters:                                            
     $pList     - the list for which to                    
                  produce a random index                   
     $pSeed     - [optional] the seed to be used           
                   for randomization                       
  =========================================================-->
  
  <xsl:template name="randListIndex">
    <xsl:param name="pList" select="/.."/>
    <xsl:param name="pSeed" select="$seed"/>

    <xsl:variable name="vFunIncr" 
                  select="$x:st/myIncrement:*[1]"/>
    <xsl:variable name="vrtfNums">
      <xsl:call-template name="scanIter">
        <xsl:with-param name="arg1" select="count($pList) - 1"/>
        <xsl:with-param name="arg2" select="$vFunIncr"/>
        <xsl:with-param name="arg3" select="'1'"/>
      </xsl:call-template>
    </xsl:variable>
    
    <xsl:call-template name="randomizeList">
      <xsl:with-param name="pList" 
                      select="vendor:node-set($vrtfNums)/*"/>
      <xsl:with-param name="pSeed" select="$pSeed"/>
    </xsl:call-template>

  </xsl:template>
  
  <xsl:template match="myIncrement:*">
    <xsl:param name="arg1"/>
    
    <xsl:value-of select="$arg1 + 1"/>
  </xsl:template>
  

  <!-- *************************************************************
-->
  <!-- ********************* INTERNAL USE ONLY *********************
-->
  <!-- *************************************************************
-->
  <!-- defined constants -->
   <xsl:variable name="x:st" select="document('')/*"/>

<!--
      a template reference to an incrementing function                 

================================================================== -->
   <myIncrement:myIncrement/>

</xsl:stylesheet>

And here's a test of the functions of this module:

testListRandomizer.xslt:
-----------------------
<xsl:stylesheet version="1.0"  
 xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
 xmlns:vendor="urn:schemas-microsoft-com:xslt"
 xmlns:mySquare="f:mySquare" 
 xmlns:myDouble="f:myDouble"
 exclude-result-prefixes="xsl vendor mySquare myDouble"
 >
  
  <xsl:import href="randomList.xsl"/>
  
  <xsl:output omit-xml-declaration="yes" indent="yes"/>
   <!-- This transformation must be applied to:
        numList.xml 
     -->
  
  <mySquare:mySquare/>
  <myDouble:myDouble/>
  
  <xsl:template match="/">
  
    <xsl:variable name="vrtfRands">
      <xsl:call-template name="randomSequence">
        <xsl:with-param name="pLength" select="100"/>
      </xsl:call-template>
    </xsl:variable>
    
    Random Recursive Index (dScale (randomSequence 100)):
    
    <xsl:call-template name="_dScale">
      <xsl:with-param name="pRandSeq" 
          select="vendor:node-set($vrtfRands)/*"/>
    </xsl:call-template>
    
    Random Recursive Index 10:
    
    <xsl:variable name="vrtfRecIndex">
      <xsl:call-template name="_randomRecursiveIndex">
        <xsl:with-param name="pList" 
        select="/*/*"/>
      </xsl:call-template>
    </xsl:variable>
    
    <xsl:variable name="vRecIndex" 
              select="vendor:node-set($vrtfRecIndex)/*"/>
              
    <xsl:for-each select="$vRecIndex">
      <xsl:copy-of select="."/>

    </xsl:for-each>
    
    Randomized 10-elements list:
    <xsl:call-template name="_permutationFromRecursiveIndex">
      <xsl:with-param name="pList" select="/*/*"/>
      <xsl:with-param name="pRecIndex" select="$vRecIndex"/>
    </xsl:call-template>
    
    RandomizeList:
    <xsl:call-template name="randomizeList">
      <xsl:with-param name="pList" select="/*/*"/>
    </xsl:call-template>
    
    <xsl:variable name="vFunSquare" 
         select="document('')/*/mySquare:*[1]"/>
    
    _mapFromRandIndex (^2) [1..10] seed:
    <xsl:call-template name="_mapFromRandIndex">
      <xsl:with-param name="pFun" select="$vFunSquare"/>
      <xsl:with-param name="pList" select="/*/*"/>
      <xsl:with-param name="pRecIndex" select="$vRecIndex"/>
    </xsl:call-template>
    
    <xsl:variable name="vFunDouble" 
         select="document('')/*/myDouble:*[1]"/>
    
    randomMap (*2) [1..10] seed:
    <xsl:call-template name="randomMap">
      <xsl:with-param name="pFun" select="$vFunDouble"/>
      <xsl:with-param name="pList" select="/*/*"/>
    </xsl:call-template>
    
    randListIndex [1..10] seed:
    <xsl:call-template name="randListIndex">
      <xsl:with-param name="pList" select="/*/*"/>
    </xsl:call-template>
    
  </xsl:template>
  
  <xsl:template match="mySquare:*">
    <xsl:param name="arg1"/>
    
    <xsl:value-of select="$arg1 * $arg1"/>
  </xsl:template>

  <xsl:template match="myDouble:*">
    <xsl:param name="arg1"/>
    
    <xsl:value-of select="$arg1 + $arg1"/>
  </xsl:template>
</xsl:stylesheet>

When applied to the following source xml document:

numList.xml
-----------
<nums>
  <num>01</num>
  <num>02</num>
  <num>03</num>
  <num>04</num>
  <num>05</num>
  <num>06</num>
  <num>07</num>
  <num>08</num>
  <num>09</num>
  <num>10</num>
</nums>

the result is:


    
    Random Recursive Index (dScale (randomSequence 100)):
    
<el>27</el>
<el>90</el>
<el>14</el>
<el>78</el>
<el>65</el>
<el>13</el>
<el>27</el>
<el>85</el>
<el>75</el>
<el>33</el>
<el>31</el>
<el>26</el>
<el>9</el>
<el>40</el>
<el>31</el>
<el>80</el>
<el>19</el>
<el>44</el>
<el>52</el>
<el>7</el>
<el>8</el>
<el>73</el>
<el>55</el>
<el>16</el>
<el>68</el>
<el>20</el>
<el>29</el>
<el>4</el>
<el>3</el>
<el>30</el>
<el>51</el>
<el>41</el>
<el>14</el>
<el>32</el>
<el>66</el>
<el>4</el>
<el>19</el>
<el>51</el>
<el>48</el>
<el>59</el>
<el>30</el>
<el>1</el>
<el>49</el>
<el>57</el>
<el>14</el>
<el>53</el>
<el>13</el>
<el>10</el>
<el>10</el>
<el>38</el>
<el>13</el>
<el>37</el>
<el>13</el>
<el>36</el>
<el>22</el>
<el>7</el>
<el>28</el>
<el>25</el>
<el>28</el>
<el>7</el>
<el>29</el>
<el>3</el>
<el>34</el>
<el>28</el>
<el>7</el>
<el>13</el>
<el>14</el>
<el>5</el>
<el>32</el>
<el>25</el>
<el>25</el>
<el>24</el>
<el>8</el>
<el>26</el>
<el>23</el>
<el>14</el>
<el>11</el>
<el>18</el>
<el>15</el>
<el>6</el>
<el>5</el>
<el>6</el>
<el>9</el>
<el>4</el>
<el>8</el>
<el>14</el>
<el>12</el>
<el>12</el>
<el>5</el>
<el>2</el>
<el>5</el>
<el>1</el>
<el>4</el>
<el>1</el>
<el>4</el>
<el>4</el>
<el>1</el>
<el>2</el>
<el>1</el>
<el>1</el>
    
    Random Recursive Index 10:
    
<el>3</el>
<el>9</el>
<el>2</el>
<el>6</el>
<el>5</el>
<el>1</el>
<el>2</el>
<el>3</el>
<el>2</el>
<el>1</el>
    
    Randomized 10-elements list:
<el>03</el>
<el>10</el>
<el>02</el>
<el>08</el>
<el>07</el>
<el>01</el>
<el>05</el>
<el>09</el>
<el>06</el>
<el>04</el>
    
    RandomizeList:
<el>03</el>
<el>10</el>
<el>02</el>
<el>08</el>
<el>07</el>
<el>01</el>
<el>05</el>
<el>09</el>
<el>06</el>
<el>04</el>
    
    _mapFromRandIndex (^2) [1..10] seed:
<el>9</el>
<el>100</el>
<el>4</el>
<el>64</el>
<el>49</el>
<el>1</el>
<el>25</el>
<el>81</el>
<el>36</el>
<el>16</el>
    
    randomMap (*2) [1..10] seed:
<el>6</el>
<el>20</el>
<el>4</el>
<el>16</el>
<el>14</el>
<el>2</el>
<el>10</el>
<el>18</el>
<el>12</el>
<el>8</el>
    
    randListIndex [1..10] seed:
<el>3</el>
<el>10</el>
<el>2</el>
<el>8</el>
<el>7</el>
<el>1</el>
<el>5</el>
<el>9</el>
<el>6</el>
<el>4</el>


Cheers,
Dimitre Novatchev.






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