php – Hex, Bugs and More Physics | Emre S. Tasci

Relations…

admin — Wed, 15 Jan 2014 13:22:23 +0000

Recently, we needed to schematize the relations between the coefficients of a symmetric tensor matrix such that, beyond the tedious numerical values, the basic relations such as equivalency or (-1) times would be visible to the eye.

Consider the following 16×16 matrix:

   0.06483   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.65809   0.65809   0.60365   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.10993   0.00000   0.00000   0.37862   0.37862   0.00000   0.00000   0.00000   0.00000   0.86568   0.00000   0.00000   0.42424   0.00000   0.00000
   0.00000   0.00000   0.10993   0.00000   0.00000   0.12949   0.00000   0.00000   0.00000   0.00000   0.00000  -0.86568   0.00000   0.00000   0.42424   0.00000
   0.00000   0.00000   0.00000   0.10259   0.00000   0.00000   0.84469   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.73695
   0.00000   0.37862   0.00000   0.00000   0.01584   0.00000   0.00000   0.00000   0.00000   0.00000   0.84812   0.00000   0.00000   0.87983   0.00000   0.00000
   0.00000   0.37862   0.12949   0.00000   0.00000   0.01584   0.00000   0.00000   0.00000   0.00000   0.00000  -0.84812   0.00000   0.00000   0.87983   0.00000
   0.00000   0.00000   0.00000   0.84469   0.00000   0.00000   0.01168   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.87050
   0.65809   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.88440   0.28986   0.45572   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.65809   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.28986   0.88440   0.45572   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.60365   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.45572   0.45572   0.89801   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.86568   0.00000   0.00000   0.84812   0.00000   0.00000   0.00000   0.00000   0.00000   0.35993   0.00000   0.00000   0.19336   0.00000   0.00000
   0.00000   0.00000  -0.86568   0.00000   0.00000  -0.84812   0.00000   0.00000   0.00000   0.00000   0.00000   0.35993   0.00000   0.62239  -0.62239   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   1.18908   0.00000   0.00000   0.00000
   0.00000   0.42424   0.00000   0.00000   0.87983   0.00000   0.00000   0.00000   0.00000   0.00000   0.19336   0.62239   0.00000   0.54930   0.00000   0.00000
   0.00000   0.00000   0.42424   0.00000   0.00000   0.87983   0.00000   0.00000   0.00000   0.00000   0.00000  -0.62239   0.00000   0.00000   0.54930   0.00000
   0.00000   0.00000   0.00000   0.73695   0.00000   0.00000   0.87050   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.55094

if you really want to, you can verify that its coefficients satisfy the following properties:
Non-zero Elements:
(1,1), (1,8), (1,9), (1,10),
(2,2), (2,5), (2,6), (2,11), (2,14),
(3,3), (3,6), (3,12), (3,15),
(4,4), (4,7), (4,16),
(5,5), (5,11), (5,14),
(6,6), (6,12), (6,15),
(7,7), (7,16),
(8,8), (8,9), (8,10),
(9,9), (9,10),
(10,10),
(11,11), (11,14),
(12,12), (12,14), (12,15),
(13,13), (14,14), (15,15),
(16,16)

Equality relations:
(1,9) = (1,8)
(3,3) = (2,2)
(2,6) = (2,5)
(3,12) = -(2,11)
(3,15) = (2,14)
(6,6) = (5,5)
(6,12) = -(5,11)
(6,15) = (5,14)
(9,9) = (8,8)
(9,10) = (8,10)
(12,12) = (11,11)
(12,15) = -(12,14)
(15,15) = (14,14)

These kind of relations are sought upon tensor matrices (at least, in group theory 8), kind of postulating the imposed limits and… (have I said “relations”?). So, the sort-of-important-like thingy is to be able to spot them after evaluating some calculations in the computers.

Have you verified yet? Good! Now let’s take a look at this:

So, this is what we’ll be discussing in this post – preparation of such graphs. We’ll be using the PHP module Imagick for ImageMagick functions and objects. On Ubuntu, you can install the package from the command line as:

sudo apt-get install php5-imagick

(don’t forget to restart the http server if you’re working via a web interface instead of cli)

Before going further into the graph production, here is a description of producing a random matrix compatible with the given conditions in Octave:

Constructing a sample matrix in Octave

clear;

# Declare the matrix
T=[];

# == >> === non-zero coefficients ===== 0 =====
# I used the shorcuts and scripting of Vim to easily format the like lines..
non_zero_coeff = [];
non_zero_coeff = [non_zero_coeff; 1 1];
non_zero_coeff = [non_zero_coeff; 1 8];
non_zero_coeff = [non_zero_coeff; 1 9];
non_zero_coeff = [non_zero_coeff; 1 10];
non_zero_coeff = [non_zero_coeff; 2 2];
non_zero_coeff = [non_zero_coeff; 2 5];
non_zero_coeff = [non_zero_coeff; 2 11];
non_zero_coeff = [non_zero_coeff; 2 14];
non_zero_coeff = [non_zero_coeff; 3 3];
non_zero_coeff = [non_zero_coeff; 3 6];
non_zero_coeff = [non_zero_coeff; 3 12];
non_zero_coeff = [non_zero_coeff; 3 15];
non_zero_coeff = [non_zero_coeff; 4 4];
non_zero_coeff = [non_zero_coeff; 4 7];
non_zero_coeff = [non_zero_coeff; 3 12];
non_zero_coeff = [non_zero_coeff; 4 16];
non_zero_coeff = [non_zero_coeff; 5 5];
non_zero_coeff = [non_zero_coeff; 5 11];
non_zero_coeff = [non_zero_coeff; 1 9];
non_zero_coeff = [non_zero_coeff; 5 14];
non_zero_coeff = [non_zero_coeff; 6 6];
non_zero_coeff = [non_zero_coeff; 6 12];
non_zero_coeff = [non_zero_coeff; 1 9];
non_zero_coeff = [non_zero_coeff; 6 15];
non_zero_coeff = [non_zero_coeff; 7 7];
non_zero_coeff = [non_zero_coeff; 7 16];
non_zero_coeff = [non_zero_coeff; 8 8];
non_zero_coeff = [non_zero_coeff; 8 9];
non_zero_coeff = [non_zero_coeff; 8 10];
non_zero_coeff = [non_zero_coeff; 6 15];
non_zero_coeff = [non_zero_coeff; 9 9];
non_zero_coeff = [non_zero_coeff; 9 10];
non_zero_coeff = [non_zero_coeff; 10 10];
non_zero_coeff = [non_zero_coeff; 11 11];
non_zero_coeff = [non_zero_coeff; 11 14];
non_zero_coeff = [non_zero_coeff; 12 12];
non_zero_coeff = [non_zero_coeff; 12 14];
non_zero_coeff = [non_zero_coeff; 13 13];
non_zero_coeff = [non_zero_coeff; 14 14];
non_zero_coeff = [non_zero_coeff; 15 15];
non_zero_coeff = [non_zero_coeff; 16 16];

# Assign random values to the non-zero coefficients:
for i=1:rows(non_zero_coeff)
T(non_zero_coeff(i,1),non_zero_coeff(i,2)) = rand;
endfor
# == << === non-zero coefficients ===== 1 ===== 

# == >> === Relations ===== 0 =====
T(1,9)=T(1,8);
T(3,3)=T(2,2);
T(2,6)=T(2,5);
T(3,12)=-T(2,11);
T(3,15)=T(2,14);
T(6,6)=T(5,5);
T(6,12)=-T(5,11);
T(6,15)=T(5,14);
T(9,9)=T(8,8);
T(9,10)=T(8,10);
T(12,12)=T(11,11);
T(12,15)=-T(12,14);
T(15,15)=T(14,14);
# == << === Relations ===== 1 ===== 

# == >> === Symmetry ===== 0 =====
for i=1:rows(T)
for j=i:columns(T)
T(j,i) = T(i,j);
endfor
endfor
# == << === Symmetry ===== 1 =====

# Export the matrix to a file:
save("input.data.txt","T");

Finding out the relations between the coefficients

Doing a double loop over i=1:rows and j=i:cols, for each of the coefficients in and above the diagonal, taking one as reference (checking if abs(T(i,j))>0 and recording to an array, say “non-zero-coeff-array” if so) and then comparing it with the rest of the elements (that comes after it) with another double loop i2=i:rows and j2=j:cols. If T(i2,j2) is equal to +-T(i,j), we also note this (three values for each i2,j2 equivalency identification: i2,j2 and +/-1) in another array (say “equal-array”).

For example, according to our case the (9,9) element of the non-zero-coeff-array would be TRUE and the same element of the equal-array would be a sub-array holding the values (8,8,1).

Painting on a canvas

Once you have access to the ImageMagick library through Imagick, we can start “painting” a canvas by first defining the canvas (width, height and background color):

# Declare the object (/holder)
$image = new Imagick();

# Define the canvas (size 640x640 pixels with white background)
$image->newImage( 640, 640, new ImagickPixel( 'white' ) );

Let’s put a circle (filled, black) in the center with a radius of 30 pixels:

# Define the circle:
$circle = new ImagickDraw();
$circle->setFillColor("#000000");
$circle->circle(320,320,350,320);

# Add (/register) it to the canvas:
$image->drawImage($circle);

As for the production of the image file, we need to designate it as a PNG image and then export it to a file:
# Designate the image type as PNG:
$image->setImageFormat( "png" );

# Export (/write) it to a file "out.png":
$fp = fopen("out.png","w");
fwrite($fp,$image);
fclose($fp);


This is what you -should- get:

not bad for beginning, right? 
The circle function has 4 parameters: the (x,y) coordinates of the center and the coordinates of a point that is on the edge of the circle. Let’s draw another circle, this time an unfilled one below this filled one:

# Declare the object (/holder) 
$image = new Imagick();

 # Define the canvas (size 640x640 pixels with white background)
 $image --->newImage( 640, 640, new ImagickPixel( 'white' ) );

# Define the 1st, filled circle:
$circle = new ImagickDraw();
$circle->setFillColor("#000000");
$circle->circle(320,320,350,320);

# Add (/register) it to the canvas:
$image->drawImage($circle);

# Define the 2nd, unfilled circle:
$circle = new ImagickDraw();
$circle->setStrokeColor("#000000");
$circle->setStrokeWidth(2);
$circle->setFillColor("none");
$circle->circle(320,350,350,350);

# Add (/register) it to the canvas:
$image->drawImage($circle);

# Designate the image type as PNG:
$image->setImageFormat( "png" );

# Export (/write) it to a file "out.png":
$fp = fopen("out.png","w");
fwrite($fp,$image);
fclose($fp);


The “stroke” methods are responsible for the perimeter and the fillcolor setting to “none” ensures that we have an otherwise invisible circle.
So far, so good.. Let’s add a line that passes between the circles from (120,50) to (520,50):
# Define the line:
$line = new ImagickDraw();
$line->setStrokeColor("#000000");
$line->setStrokeWidth(2);
$line->line(120,350,520,350);
$image->drawImage($line);


Mapping the rows and cols to x and y
Suppose that we have a 16×16 matrix to be mapped onto a 640×640 canvas. We could map (i=0,j=0) to (x=0,y=0) and (i=16,j=16) to (x=640,y=640) but it wouldn’t be right:


doesn’t look right, right? And here’s the code that produced it:

# Declare the object (/holder)
$image = new Imagick(); 

# Define the canvas (size 640x640 pixels with white background) 
$image--->newImage( 640, 640, new ImagickPixel( 'white' ) );

# Define the 1st, filled circle:
$dxy = 640 / 16;
for($i=1;$i<=16;$i++)
{
for($j=1;$j<=16;$j++)
     {
         $circle = new ImagickDraw();
         $circle->setFillColor("#000000");
         $circle->circle($dxy*($j-1),$dxy*($i-1),$dxy*($j-1)+$dxy/6,$dxy*($i-1));

         # Add (/register) it to the canvas:
         $image->drawImage($circle);
     }
}

# Designate the image type as PNG:
$image->setImageFormat( "png" );

# Export (/write) it to a file "out.png":
$fp = fopen("out.png","w");
fwrite($fp,$image);
fclose($fp);

What we need to do is to shift it half of the periodicity in the x & y directions:


That’s more like it — this shift was introduced to the code by changing the coordinate parameters of the circle(s):

$circle->circle($dxy*($j-1/2),$dxy*($i-1/2),$dxy*($j-1/2)+$dxy/6,$dxy*($i-1/2));
So, depending on the value (zero/non-zero) of an element of our tensor, we can put it as a big circle (r=$dxy/6) or a small one (r=$dxy/12). In addition, if it’s negative, we can have it drawn as an unfilled one (

$circle->setStrokeColor("#000000");
$circle->setStrokeWidth(2);
$circle->setFillColor("none");


). We’re almost ready aside from the connecting the related entries!
Connecting the dots
Suppose that we’d like to connect the circles corresponding to the (i1,j1) and the (i2,j2) elements of the tensor. On the canvas, their centers will be given as ($dxy*($j1-1/2),$dxy*($i1-1/2)) and ($dxy*($j2-1/2),$dxy*($i2-1/2)) where $dxy is the conversion unit of 1 step in the row-col matrix to that of the canvas (for simplicity I assumed a square canvas which is not necessary — then we’d have a $dx=$width/$num_cols and a $dy=$height/$num_rows. Also note that the rows are associated with the height ($i <-> vertical) and the columns are with the width ($j <-> horizontal) (that’s why $j’s come before $i’s in the center equations).
So, let’s join (11,5) to (9,3): in a 640×640 canvas, (11,5) is centered at ((640/16)*(5-1/2) =  180, (640/16)*(11-1/2) = 420) and similarly (9,3) is centered at (100,340). Let’s put them on the map and connect their centers with a line:

# Declare the object (/holder)
$image = new Imagick();

# Define the canvas (size 640x640 pixels with white background)
$image->newImage( 640, 640, new ImagickPixel( 'white' ) );

$dxy = 640/16; # 40px
$radius = $dxy/6; #6.6667px

# Define the unfilled (11,5) circle:
$circle = new ImagickDraw();
$circle->setStrokeColor("#000000");
$circle->setStrokeWidth(2);
$circle->setFillColor("none");
$circle->circle(180,420,180+$radius,420);

# Add (/register) it to the canvas:
$image->drawImage($circle);

# Define the unfilled (9,3) circle:
$circle = new ImagickDraw();
$circle->setStrokeColor("#000000");
$circle->setStrokeWidth(2);
$circle->setFillColor("none");
$circle->circle(100,340,100+$radius,340);

# Add (/register) it to the canvas:
$image->drawImage($circle);

# Connect them with a line:
$line = new ImagickDraw();
$line->setStrokeColor("#000000");
$line->setStrokeWidth(2);
$line->line(180,420,100,340);
$image->drawImage($line);

# Designate the image type as PNG:
$image->setImageFormat( "png" );

# Export (/write) it to a file "out.png":
$fp = fopen("out.png","w");
fwrite($fp,$image);
fclose($fp);



Devil is in the details
By now, hopefully you’ve got the idea of how to swing things in your way. In my case, if I spent the 40% of the time doing the things I described, the remaining 60% went in adjusting the line such that it starts on the perimeter of the circle, not from the center of it, i.e.,

and this requires the determination of the angle of the line connecting our nodes. The angle of a line passing through two points (x1,y1) & (x2,y2) is given by: arctan[(y2-y1)/(x2-x1)], where the value is nothing but the A of the y=Ax+B line equation, and we need to translate the beginning and the final points of our line in this direction by an amount of a radius:
# Find the tangent of the line:
$tg = (340-420)/(100-180);
$alpha_radian = atan($tg);
$alpha_deg = $alpha_radian * 180 / M_PI;

# Connect them with a line:
$line = new ImagickDraw();
$line->setStrokeColor("#000000");
$line->setStrokeWidth(2);
$line->line(180-$radius*cos($alpha_radian),420-$radius*sin($alpha_radian),100+  $radius*cos($alpha_radian),340+$radius*sin($alpha_radian));
$image->drawImage($line);

and that’s more or less all about it!
One picture is worth a thousand words
You can have a sneak peak of the working code via here: http://144.122.31.125/cgi-bin/cryst/programs/tensor_graph/



Exploring through the paths of subgroups, collecting indexes on the way…
admin — Mon, 06 Jun 2011 14:46:23 +0000
Having a personal wiki has its pros and cons with the pros being obvious but, on the other hand, one doesn’t feel like reposting what he has already committed into the corresponding wikipedia entry (and since reposting means filtering out the sensitive information and generalizing it, it is double the effort). So this fact, more or less, explains my absence of activity in this blog for the last 1.5 years. But then, there is one negative aspect of personal wikipedia “blogging” – it’s like putting everything under the rug : you classify the data/information and then you forget that it is there. That’s when “actual” blogging (like this one) comes handy. So, sorry & welcome back..
Today, I’ll present a code that I’ve just written to parse out the compatible paths from a tree. In my case, the three is the list of subgroups with indexes that one can acquire using Bilbao Crystallographic Server’s marvelous SUBGROUPGRAPH tool. For low indexes, you can already have SUBGROUPGRAPH do this for you by specifying your supergroup G, subgroup H and the index [G:H]. For example, for G=136, H=14 and [G:H] = 8, you can have the following paths drawn:

But as I said, things can get rough when you have a high index. In that case, we can (and we will) try to parse and analyze the paths tree which is outputted by SUBGROUPGRAPH when no index is designated, e.g., for G=136, H=14:

Where you see the maximal subgroups for the involved groups and their corresponding indexes. So, to go from P4_2/mnm (#136) to P2_1/c (#14) with index 8, we can follow the path:
P4_2/mnm (#136) –[2]–> Cmmm (#65) –[2]–> Pmna (#53) –[2]–> P2_1/c (#14)
with the related indexes given in the brackets totaling to 2x2x2 = 8.
The problem I had today was to find possible paths going from G=Fd-3m (#227) to H=Cc (#9) with index [G:H] = 192.
I first parsed the subgroup list into an array with their indexes, then followed the possible paths.
                    *
 * By parsing the possible subgroup paths obtained from 
 * SUBGROUPGRAPH, finds the paths that are compatible 
 * with the given terminal super & sub groups and the 
 * designated index.
 *
 *                                              06/06/11 */

# Input Data === 0 ====================================================
$start_sup = 227;
$crit_index = 192;
$end_sub = 9;

$arr = file("data.txt"); # A sample of data.txt for the case of #227->#9
                         # is included at the end of the code.

# Input Data === 1 ====================================================

$arr_subs = Array();
$arr_labels = Array();
foreach($arr as $line)
{
    $auxarr = preg_split("/[ \t]+/",trim($line));
    #echo $auxarr[2]."\n";
    $sup = $auxarr[1];
    $suplabel = $auxarr[2];
    $arrsubs = split(";",$auxarr[3]);
    $arr_labels[$sup] = $suplabel;
    foreach($arrsubs as $subind)
    {
        $auxarr2 = Array();
        preg_match("/([0-9]+)\[([0-9]+)\]/",$subind,$auxarr2);
        #print_r($auxarr2);
        $sub = $auxarr2[1];
        $index = $auxarr2[2];
        $arr_subs[$sup][$index][] = $sub;
    }
}
#print_r($arr_subs);

# Start exploring
$start_sup = sprintf("%03d",$start_sup);
$end_sub = sprintf("%03d",$end_sub);
$arr_paths = Array();
$arr_paths[$start_sup] = 1;

findpath($start_sup);

function findpath($current_sup)
{
    global $arr_paths,$arr_subs,$crit_index,$end_sub;
    #echo "*".$current_sup."*\n";
    if(strrpos($current_sup,"-") !== FALSE)
    {
        $current_sup_last_sup = substr($current_sup,strrpos($current_sup,"-")+1);
        $current_sup_last_sup = substr($current_sup_last_sup,0,strpos($current_sup_last_sup,"["));
    }
        
    else
        $current_sup_last_sup = $current_sup;
    #echo "*".$current_sup_last_sup."*\n";
    $subindexes = array_keys($arr_subs[$current_sup_last_sup]);
    foreach($subindexes as $subindex)
    {
        $subs = $arr_subs[$current_sup_last_sup][$subindex];
        echo $subindex.": ".join(",",$subs)."\n";
        foreach($subs as $sub)
        {
            echo $current_sup."-".$sub."[".$subindex."]"."\n";
            $arr_paths[$current_sup."-".$sub."[".$subindex."]"] = $arr_paths[$current_sup] * $subindex;
            if($arr_paths[$current_sup."-".$sub."[".$subindex."]"]<$crit_index)
                findpath($current_sup."-".$sub."[".$subindex."]");
            elseif($arr_paths[$current_sup."-".$sub."[".$subindex."]"] == $crit_index && $sub == $end_sub)
                echo "\nPath Found: ".$current_sup."-".$sub."[".$subindex."]"."\n\n";
        }
    }
    #print_r($subindexes);
}
print_r($arr_paths);

/*
    data.txt:
1   227   Fd-3m   141[3];166[4];203[2];216[2]
2   220   I-43d   122[3];161[4]
3   219   F-43c   120[3];161[4];218[4]
4   218   P-43n   112[3];161[4];220[4]
5   217   I-43m   121[3];160[4];215[2];218[2]
6   216   F-43m   119[3];160[4];215[4]
7   215   P-43m   111[3];160[4];216[2];217[4];219[2]
8   203   Fd-3   070[3]
9   167   R-3c   015[3];161[2];165[3];167[4];167[5];167[7]
10   166   R-3m   012[3];160[2];164[3];166[2];166[4];166[5];166[7];167[2]
11   165   P-3c1   015[3];158[2];163[3];165[3];165[4];165[5];165[7]
12   164   P-3m1   012[3];156[2];162[3];164[2];164[3];164[4];164[5];164[7];165[2]
13   163   P-31c   015[3];159[2];163[3];163[4];163[5];163[7];165[3];167[3]
14   162   P-31m   012[3];157[2];162[2];162[3];162[4];162[5];162[7];163[2];164[3];166[3]
15   161   R3c   009[3];158[3];161[4];161[5];161[7]
16   160   R3m   008[3];156[3];160[2];160[4];160[5];160[7];161[2]
17   159   P31c   009[3];158[3];159[3];159[4];159[5];159[7];161[3]
18   158   P3c1   009[3];158[3];158[4];158[5];158[7];159[3]
19   157   P31m   008[3];156[3];157[2];157[3];157[4];157[5];157[7];159[2];160[3]
20   156   P3m1   008[3];156[2];156[3];156[4];156[5];156[7];157[3];158[2]
21   141   I41/amd   070[2];074[2];088[2];109[2];119[2];122[2];141[3];141[5];141[7];141[9]
22   122   I-42d   043[2];122[3];122[5];122[7];122[9]
23   121   I-42m   042[2];111[2];112[2];113[2];114[2];121[3];121[5];121[7];121[9]
24   120   I-4c2   045[2];116[2];117[2];120[3];120[5];120[7];120[9]
25   119   I-4m2   044[2];115[2];118[2];119[3];119[5];119[7];119[9]
26   118   P-4n2   034[2];118[3];118[5];118[7];118[9];122[2]
27   117   P-4b2   032[2];117[2];117[3];117[5];117[7];117[9];118[2]
28   116   P-4c2   027[2];112[2];114[2];116[3];116[5];116[7];116[9]
29   115   P-4m2   025[2];111[2];113[2];115[2];115[3];115[5];115[7];115[9];116[2];121[2]
30   114   P-421c   037[2];114[3];114[5];114[7];114[9]
31   113   P-421m   035[2];113[2];113[3];113[5];113[7];113[9];114[2]
32   112   P-42c   037[2];112[3];112[5];112[7];112[9];116[2];118[2]
33   111   P-42m   035[2];111[2];111[3];111[5];111[7];111[9];112[2];115[2];117[2];119[2];120[2]
34   109   I41md   043[2];044[2];109[3];109[5];109[7];109[9]
35   088   I41/a   015[2];088[3];088[5];088[7];088[9]
36   074   Imma   012[2];015[2];044[2];046[2];051[2];052[2];053[2];062[2];074[3];074[5];074[7]
37   070   Fddd   015[2];043[2];070[3];070[5];070[7]
38   064   Cmce   012[2];014[2];015[2];036[2];039[2];041[2];053[2];054[2];055[2];056[2];057[2];060[2];061[2];062[2];064[3];064[5];064[7]
39   063   Cmcm   011[2];012[2];015[2];036[2];038[2];040[2];051[2];052[2];057[2];058[2];059[2];060[2];062[2];063[3];063[5];063[7]
40   062   Pnma   011[2];014[2];026[2];031[2];033[2];062[3];062[5];062[7]
41   061   Pbca   014[2];029[2];061[3];061[5];061[7]
42   060   Pbcn   013[2];014[2];029[2];030[2];033[2];060[3];060[5];060[7]
43   059   Pmmn   011[2];013[2];025[2];031[2];056[2];059[2];059[3];059[5];059[7];062[2]
44   058   Pnnm   010[2];014[2];031[2];034[2];058[3];058[5];058[7]
45   057   Pbcm   011[2];013[2];014[2];026[2];028[2];029[2];057[2];057[3];057[5];057[7];060[2];061[2];062[2]
46   056   Pccn   013[2];014[2];027[2];033[2];056[3];056[5];056[7]
47   055   Pbam   010[2];014[2];026[2];032[2];055[2];055[3];055[5];055[7];058[2];062[2]
48   054   Pcca   013[2];014[2];027[2];029[2];032[2];052[2];054[2];054[3];054[5];054[7];056[2];060[2]
49   053   Pmna   010[2];013[2];014[2];028[2];030[2];031[2];052[2];053[2];053[3];053[5];053[7];058[2];060[2]
50   052   Pnna   013[2];014[2];030[2];033[2];034[2];052[3];052[5];052[7]
51   051   Pmma   010[2];011[2];013[2];025[2];026[2];028[2];051[2];051[3];051[5];051[7];053[2];054[2];055[2];057[2];059[2];063[2];064[2]
52   046   Ima2   008[2];009[2];026[2];028[2];030[2];033[2];046[3];046[5];046[7]
53   045   Iba2   009[2];027[2];029[2];032[2];045[3];045[5];045[7]
54   044   Imm2   008[2];025[2];031[2];034[2];044[3];044[5];044[7]
55   043   Fdd2   009[2];043[3];043[5];043[7]
56   042   Fmm2   008[2];035[2];036[2];037[2];038[2];039[2];040[2];041[2];042[3];042[5];042[7]
57   041   Aea2   007[2];009[2];029[2];030[2];032[2];033[2];041[3];041[5];041[7]
58   040   Ama2   006[2];009[2];028[2];031[2];033[2];034[2];040[3];040[5];040[7]
59   039   Aem2   007[2];008[2];026[2];027[2];028[2];029[2];039[2];039[3];039[5];039[7];041[2];045[2];046[2]
60   038   Amm2   006[2];008[2];025[2];026[2];030[2];031[2];038[2];038[3];038[5];038[7];040[2];044[2];046[2]
61   037   Ccc2   009[2];027[2];030[2];034[2];037[3];037[5];037[7]
62   036   Cmc21   008[2];009[2];026[2];029[2];031[2];033[2];036[3];036[5];036[7]
63   035   Cmm2   008[2];025[2];028[2];032[2];035[2];035[3];035[5];035[7];036[2];037[2];044[2];045[2];046[2]
64   034   Pnn2   007[2];034[3];034[5];034[7];043[2]
65   033   Pna21   007[2];033[3];033[5];033[7]
66   032   Pba2   007[2];032[2];032[3];032[5];032[7];033[2];034[2]
67   031   Pmn21   006[2];007[2];031[2];031[3];031[5];031[7];033[2]
68   030   Pnc2   007[2];030[2];030[3];030[5];030[7];034[2]
69   029   Pca21   007[2];029[2];029[3];029[5];029[7];033[2]
70   028   Pma2   006[2];007[2];028[2];028[3];028[5];028[7];029[2];030[2];031[2];032[2];040[2];041[2]
71   027   Pcc2   007[2];027[2];027[3];027[5];027[7];030[2];037[2]
72   026   Pmc21   006[2];007[2];026[2];026[3];026[5];026[7];029[2];031[2];036[2]
73   025   Pmm2   006[2];025[2];025[3];025[5];025[7];026[2];027[2];028[2];035[2];038[2];039[2];042[2]
74   015   C2/c   009[2];013[2];014[2];015[3];015[5];015[7]
75   014   P21/c   007[2];014[2];014[3];014[5];014[7]
76   013   P2/c   007[2];013[2];013[3];013[5];013[7];014[2];015[2]
77   012   C2/m   008[2];010[2];011[2];012[2];012[3];012[5];012[7];013[2];014[2];015[2]
78   011   P21/m   006[2];011[2];011[3];011[5];011[7];014[2]
79   010   P2/m   006[2];010[2];010[3];010[5];010[7];011[2];012[2];013[2]
80   008   Cm   006[2];007[2];008[2];008[3];008[5];008[7];009[2]
81   007   Pc   007[2];007[3];007[5];007[7];009[2]
82   006   Pm   006[2];006[3];006[5];006[7];007[2];008[2]
83   009   Cc   007[2];009[3];009[5];009[7]
 */

When run, the code lists all the paths with the matching ones preceded by “Path Found”, so if you grep wrt it, you’ll have, for this example:

sururi@husniya:/xxx$ php find_trpath_for_index.php |grep Path|sed "s:Path Found\: ::"
227-141[3]-070[2]-015[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-070[2]-015[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-070[2]-015[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-070[2]-043[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-012[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-012[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-010[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-011[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-012[2]-008[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-012[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-012[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-012[2]-015[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-015[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-014[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-015[2]-014[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-026[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-026[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-027[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-027[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-028[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-045[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-035[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-038[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-045[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-039[2]-046[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-036[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-037[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-040[2]-009[2]
227-141[3]-074[2]-044[2]-025[2]-042[2]-041[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-031[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-031[2]-033[2]-007[2]-009[2]
227-141[3]-074[2]-044[2]-034[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-008[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-008[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-008[2]-009[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-009[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-026[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-026[2]-036[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-029[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-031[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-026[2]-036[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-028[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-028[2]-040[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-028[2]-041[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-029[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-030[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-031[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-032[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-028[2]-041[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-030[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-030[2]-030[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-030[2]-034[2]-007[2]-009[2]
227-141[3]-074[2]-046[2]-030[2]-034[2]-043[2]-009[2]
227-141[3]-074[2]-046[2]-033[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-012[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-012[2]-015[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-010[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-051[2]-011[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-011[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-011[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-013[2]-007[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-013[2]-013[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-013[2]-013[2]-015[2]-009[2]
227-141[3]-074[2]-051[2]-013[2]-014[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-026[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-026[2]-036[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-027[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-027[2]-037[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-028[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-028[2]-040[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-028[2]-041[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-035[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-035[2]-036[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-035[2]-037[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-035[2]-045[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-035[2]-046[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-038[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-038[2]-040[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-038[2]-046[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-039[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-039[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-039[2]-041[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-039[2]-045[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-039[2]-046[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-042[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-042[2]-036[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-042[2]-037[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-042[2]-040[2]-009[2]
227-141[3]-074[2]-051[2]-025[2]-042[2]-041[2]-009[2]
227-141[3]-074[2]-051[2]-026[2]-006[2]-007[2]-009[2]
227-141[3]-074[2]-051[2]-026[2]-006[2]-008[2]-009[2]
227-141[3]-074[2]-051[2]-026[2]-007[2]-007[2]-009[2]
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227-141[3]-119[2]-115[2]-025[2]-006[2]-008[2]-009[2]
227-141[3]-119[2]-115[2]-025[2]-026[2]-007[2]-009[2]
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227-166[4]-167[2]-015[3]-013[2]-007[2]-009[2]
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227-166[4]-167[2]-015[3]-014[2]-007[2]-009[2]
227-166[4]-167[2]-161[2]-009[3]-007[2]-009[2]
227-166[4]-167[2]-161[2]-161[4]-009[3]
227-166[4]-167[2]-167[4]-015[3]-009[2]
227-166[4]-167[2]-167[4]-161[2]-009[3]
227-166[4]-166[4]-012[3]-008[2]-009[2]
227-166[4]-166[4]-012[3]-015[2]-009[2]
227-166[4]-166[4]-160[2]-008[3]-009[2]
227-166[4]-166[4]-160[2]-161[2]-009[3]
227-166[4]-166[4]-167[2]-015[3]-009[2]
227-166[4]-166[4]-167[2]-161[2]-009[3]
227-203[2]-070[3]-015[2]-009[2]-007[2]-007[2]-009[2]
227-203[2]-070[3]-015[2]-013[2]-007[2]-007[2]-009[2]
227-203[2]-070[3]-015[2]-013[2]-013[2]-007[2]-009[2]
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227-203[2]-070[3]-015[2]-014[2]-014[2]-007[2]-009[2]
227-203[2]-070[3]-043[2]-009[2]-007[2]-007[2]-009[2]
227-216[2]-119[3]-044[2]-008[2]-006[2]-007[2]-009[2]
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227-216[2]-119[3]-044[2]-031[2]-006[2]-007[2]-009[2]
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227-216[2]-215[4]-219[2]-161[4]-009[3]




Coordination Numbers
admin — Thu, 03 Sep 2009 15:31:10 +0000
Recently, we are working on liquid alloys and for our work, we need the coordination number distribution. It’s kind of a gray area when you talk about coordination number of atoms in a liquid but it’s better than nothing to understand the properties and even more. I’d like to write a log on the tools I’ve recently coded/used in order to refer to in the future if a similar situation occurs. Also, maybe there are some others conducting similar research so, the tools introduced here may be helpful to them.
Recently, while searching recent publications on liquid alloys, I’ve found a very good and resourceful article on liquid Na-K alloys by Dr. J.-F. Wax (“Molecular dynamics study of the static structure of liquid Na-K alloys”, Physica B 403 (2008) 4241-48 | doi:10.1016/j.physb.2008.09.014). In this paper, among other properties, he had also presented the partial pair distribution functions. Partial-pair distribution functions is the averaged probability that you’ll encounter an atom in r distance starting from another atom. In solid phase, due to the symmetry of the crystal structure, you have discrete values instead of a continuous distribution and everything is crystal clear but I guess that’s the price we pay dealing with liquids. 8)
Partial-pair distribution functions are very useful in the sense that they let you derive the bond-length between constituent atom species, corresponding to the first minimums of the plots. Hence, one can see the neighborhood ranges by just looking at the plots.
I’ve sent a mail to Dr. Wax explaining my research topics and my interest and asking for his research data to which he very kindly and generously replied by providing his data.
He had sent me a big file with numerous configurations (coordinates of the atoms) following each other. The first -and the simplest- task was to split the file into seperate configuration files via this bash script:

#!/bin/bash
# Script Name: split_POS4.sh
# Splits the NaK conf files compilation POS4_DAT into sepearate
# conf files.
# Emre S. Tasci 
#                                              01/09/09

linestart=2
p="p"
for (( i = 1; i <= 1000; i++ ))
do
    echo $i;
    lineend=$(expr $linestart + 2047)
    confname=$(printf "%04d" $i)
    echo -e "3\n2048" > $confname
    sed -n "$linestart,$(echo $lineend$p)" POS4_DAT >> $confname
    linestart=$(expr $lineend + 1)
    cat $confname | qhull i TO $confname.hull
done


(The compilation was of 1000 configurations, each with 2048 atoms)
As you can check in the line before the “done” closer, I’ve -proudly- used Qhull software to calculate the convex hull of each configuration. A convex hull is the -hopefully minimum- shape that covers all your system. So, for each configuration I now had 2 files: “xxxx” (where xxxx is the id/number of the configuration set) storing the coordinates (preceded by 3 and 2048, corresponding to dimension and number of atoms information for the qhull to parse & process) and “xxxx.hull” file, generated by the qhull, containing the vertices list of each facet (preceded by the total number of facets).
A facet is (in 3D) the plane formed by the vertice points. Imagine a cube, where an atom lies at each corner, 3 in the inside. So, we can say that our system consists of 11 atoms and the minimal shape that has edges selected from system’s atoms and covering the whole is a cube, with the edges being the 8 atoms at the corners. Now, add an atom floating over the face at the top. Now the convex hull that wraps our new system would no longer be a 6-faced, 8-edged cube but a 9-faced, 9-edged polygon. I need to know the convex hull geometry in order to correctly calculate the coordination number distributions (details will follow shortly).
The aforementioned two files look like:

sururi@husniya hull_calcs $ head 0001
3
2048
 0.95278770E+00 0.13334565E+02 0.13376155E+02
 0.13025256E+02 0.87618381E+00 0.20168993E+01
 0.12745038E+01 0.14068998E-01 0.22887323E+01
 0.13066590E+02 0.20788591E+01 0.58119183E+01
 0.10468218E+00 0.58523640E-01 0.64288678E+01
 0.12839412E+02 0.13117012E+02 0.79093881E+01
 0.11918105E+01 0.12163854E+02 0.10270868E+02
 0.12673985E+02 0.11642538E+02 0.10514597E+02
sururi@husniya hull_calcs $ head 0001.hull
180
568 1127 1776
1992 104 1551
956 449 1026
632 391 1026
391 632 1543
391 956 1026
966 632 1026
966 15 1039
632 966 1039


The sets of 3 numbers in the xxxx.hull file is the ids/numbers of the atoms forming the edges of the facets, i.e., they are the vertices.
To calculate the coordination number distribution, you need to pick each atom and then simply count the other atoms within the cut-off distance depending on your atom’s and the neighboring atom’s species. After you do the counting for every atom, you average the results and voilÃ ! there is your CN distribution. But here’s the catch: In order to be able to count properly, you must make sure that, your reference atom’s cutoff radii stay within your system — otherwise you’ll be undercounting. Suppose your reference atom is one of the atoms at the corners of the cube: It will (generally/approximately) lack 7/8 of the neighbouring atoms it would normally have if it was to be the center atom of the specimen/sample. Remember that we are studying a continuous liquid and trying to model the system via ensembles of samples. So we should omit these atoms which has neighborhoods outside of our systems. Since neighborhoods are defined through bond-length, we should only include the atoms with a distance to the outside of at least cut-off radii. The “outside” is defined as the region outside the convex hull and it’s designated by the facets (planes).
From the xxxx.hull file, we have the ids of the vertice atoms and their coordinates are stored in the xxxx file. To define the plane equation



we will use the three vertice points, say p1, p2 and p3. From these 3 points, we calculate the normal n as:



then, the plane equation (hence the coefficients a,b,c,d) can be derived by comparing the following equation:



Here, (x0,y0,z0) are just the coordinates of any of the vertice points. And finally, the distance D between a point p1(x1,y1,z1) and a plane (a,b,c,d) is given by:


Since vector operations are involved, I thought it’s better to do this job in Octave and wrote the following script that calculates the coefficients of the facets and then sets down to find out the points whose distances to all the facets are greater than the given cut-off radius:

sururi@husniya trunk $ cat octave_find_atoms_within.m
DummyA = 3;
%conf_index=292;

% Call from the command line like :
%   octave -q --eval "Rcut=1.65;conf_index=293;path='$(pwd)';" octave_find_atoms_within.m
% hence specifying the conf_index at the command line.

% Emre S. Tasci                     *
%
% From the positions and vertices file, calculates the plane
% equations (stored in "facet_coefficients") and then
% filters the atoms with respect to their distances to these
% facets. Writes the output to
% "hull_calcs/xxxx_insiders.txt" file
%                                              03/09/09 */

conf_index_name = num2str(sprintf("%04d",conf_index));;
%clock
clear facet_coefficients;
facet_coefficients = [];
global p v facet_coefficients
fp = fopen(strcat(path,"/hull_calcs/",conf_index_name));
k = fscanf(fp,"%d",2); % 1st is dim (=3), 2nd is number of atoms (=2048)
p = fscanf(fp,"%f",[k(1),k(2)]);
p = p';
fclose(fp);
%p = load("/tmp/del/delco");
fp = fopen(strcat(path,"/hull_calcs/",conf_index_name,".hull"));
k = fscanf(fp,"%d",1);% number of facets
v = fscanf(fp,"%d",[3,k]);
v = v';
fclose(fp);
%v = load("/tmp/del/delver");

function [a,b,c,d,e] = getPlaneCoefficients(facet_index)
    global p v
    % Get the 3 vertices
    p1 = p(v(facet_index,1)+1,:); % The +1s come from the fact 
    p2 = p(v(facet_index,2)+1,:); % that qhull enumeration begins
    p3 = p(v(facet_index,3)+1,:); % from 0 while Octave's from 1

    %printf("%d: %f %f %f %f %f %f %f %f %f\n",facet_index,p1,p2,p3);

    % Calculate the normal
    n = cross((p2-p1),(p3-p1));

    % Calculate the coefficients of the plane :
    % ax + by + cz +d = 0
    a = n(1);
    b = n(2);
    c = n(3);
    d = -(dot(n,p1));
    e = norm(n);
    if(e==0)
        printf("%f\n",p1);
        printf("%f\n",p2);
        printf("%f\n",p3);
        printf("%d\n",facet_index);
    endif
endfunction

function dist = distanceToPlane(point_index,facet_index)
    global p facet_coefficients
    k = facet_coefficients(facet_index,:);
    n = [k(1) k(2) k(3)];
    dist = abs(dot(n,p(point_index,:)) + k(4)) / k(5);
endfunction

for i = [1:size(v)(1)]
    [a,b,c,d,e] = getPlaneCoefficients(i);
    facet_coefficients = [ facet_coefficients ; [a,b,c,d,e]];
endfor

%Rcut = 1.65; % Defined from command line calling
% Find the points that are not closer than Rcut
inside_atoms = [];
for point = [1:size(p)(1)]
%for point = [1:100]
    inside=true;
    for facet = [1:size(v)(1)]
    %for facet = [1:10]
        %printf("%d - %d : %f\n",point,facet,dist);
        if (distanceToPlane(point,facet)

This script is runned within the following php code which then takes the filtered atoms and does the counting using them:

                    *
 *
 * parse_configuration_data.php
 *
 * Written in order to parse the configuation files
 * obtained from J.F. Wax in order to calculate the 
 * Coordination Number distribution. Each configuration 
 * file contain 2048 atoms' coordinates starting at the 
 * 3rd line. There is also a convex hull file generated 
 * using qhull (http://www.qhull.com) that contains the 
 * indexes (starting from 0) of the atoms that form the 
 * vertices of the convex hull. Finally there is the 
 * IP.dat file that identifies each atom (-1 for K; 1 for 
 * Na -- the second column is the relative masses).
 *
 *                                              02/09/09 */

/*
# if present, remove the previous run's results file
if(file_exists("results.txt"))
    unlink("results.txt");
 */

error_reporting(E_ALL ^ E_NOTICE);

if(!file_exists("results.txt"))
{
    $fp = fopen("results.txt","w");
    fwrite($fp,"CONF#"."\tNa".implode("\tNa",range(1,20))."\tK".implode("\tK",range(1,20))."\n");
    fclose($fp);
}

# Support for command line variable passing:
for($i=1;$i0.001)
                $arr_atoms[$passed_atom_id]["neighbour_count"] += 1;
        }
    }

    # Do the binning
    $CN_Na = Array();
    $CN_K  = Array();
    for($i=0, $size=sizeof($arr_atoms); $i<$size; $i++)
    {
        if(array_key_exists("neighbour_count",$arr_atoms[$i]))
        {
            ${"CN_".$arr_atoms[$i]['id']}[$arr_atoms[$i]["neighbour_count"]] += 1;
        }
    }

    ksort($CN_Na);
    ksort($CN_K);

    //print_r($arr_atoms);
    //print_r($CN_Na);
    //print_r($CN_K);

    # Report the results
    $filename = "results/".sprintf("%04d",$conf_index)."_results.txt";
    $fp = fopen($filename,"w");
    fwrite($fp, "### Atoms array ###\n");
    fwrite($fp,var_export($arr_atoms,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution for Na ###\n");
    fwrite($fp,var_export($CN_Na,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution for K ###\n");
    fwrite($fp,var_export($CN_K,TRUE)."\n");

    # Percentage calculation:
    $sum_Na = array_sum($CN_Na);
    $sum_K  = array_sum($CN_K);
    foreach($CN_Na as $key=>$value)
        $CN_Na[$key] = $value * 100 / $sum_Na;
    foreach($CN_K  as $key=>$value)
        $CN_K[$key]  = $value * 100 / $sum_K;
    //print_r($CN_Na);
    //print_r($CN_K);
    fwrite($fp, "\n### CN Distribution (Percentage) for Na ###\n");
    fwrite($fp,var_export($CN_Na,TRUE)."\n");
    fwrite($fp, "\n### CN Distribution (Percentage) for K ###\n");
    fwrite($fp,var_export($CN_K,TRUE)."\n");
    fclose($fp);

    # Write the summary to the results file
    $fp = fopen("results.txt","a");
    for($i=1;$i<=20;$i++)
    {
        if(!array_key_exists($i,$CN_Na))
            $CN_Na[$i] = 0;
        if(!array_key_exists($i,$CN_K))
            $CN_K[$i] = 0;
    }
    ksort($CN_Na);
    ksort($CN_K);
    fwrite($fp,sprintf("%04d",$conf_index)."\t".implode("\t",$CN_Na)."\t".implode("\t",$CN_K)."\n");
    fclose($fp);

}

function parse_types(&$arr_atoms)
{
    # Parse the types
    $i = 0;
    $fp = fopen("IP.DAT", "r");
    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $auxarr = explode(" ",$line);
        if($auxarr[0]==-1)
            $arr_atoms[$i]["id"] = "Na";
        else
            $arr_atoms[$i]["id"] = "K";
        $i++;
    }
    fclose($fp);
    array_pop($arr_atoms);
    return 0;
}

function get_vertices($conf_index)
{
    $arr_refs = Array();

    # Get the ids of the vertices of the convex hull
    $filename = "hull_calcs/".sprintf("%04d",$conf_index).".hull";
    $fp = fopen($filename, "r");

    # Bypass the first line
    $line = fgets($fp,4096);

    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $auxarr = explode(" ",$line);
        array_pop($auxarr);
        $arr_refs = array_merge($arr_refs, $auxarr);
    }
    fclose($fp);
    // $arr_refs = array_unique($arr_refs); # This doesn't lose the keys
    $arr_refs = array_keys(array_count_values($arr_refs)); # But this does.
    return $arr_refs;
}

function parse_coordinates(&$arr_atoms, $conf_index)
{
    # Parse the coordinates
    $i = 0;
    $filename = "hull_calcs/".sprintf("%04d",$conf_index);
    $fp = fopen($filename, "r");

    # Bypass the first two lines
    $line = fgets($fp,4096);
    $line = fgets($fp,4096);

    while(!feof($fp))
    {
        $line = fgets($fp,4096);
        $arr_atoms[$i]["coords"] = explode(" ",$line);
        array_shift($arr_atoms[$i]["coords"]);
        $i++;
    }
    fclose($fp);
    array_pop($arr_atoms);
    return 0;
}

function distance(&$atom1,&$atom2)
{
    # Calculate the distance between the two atoms
    $x1 = $atom1["coords"][0];
    $x2 = $atom2["coords"][0];
    $y1 = $atom1["coords"][1];
    $y2 = $atom2["coords"][1];
    $z1 = $atom1["coords"][2];
    $z2 = $atom2["coords"][2];
    return sqrt(pow($x1-$x2,2) + pow($y1-$y2,2) + pow($z1-$z2,2));
}

?>



The code above generates a “results/xxxx_results.txt” file containing all the information obtained in arrays format and also appends to “results.txt” file the relevant configuration file’s CN distribution summary. The systems can be visualized using the output generated by the following plotter.php script:

                    *
 * Parses the results/xxxx_results.txt file and generates 
 * an XYZ file such that the atoms are labeled as the 
 * vertice atoms, close-vertice atoms and inside atoms..
 *                                              02/09/09 */

# Support for command line variable passing:
for($i=1;$i system_tmp_array_dump_file');
$str=file_get_contents('system_tmp_array_dump_file');
$atom_arr=eval('return '.$str.';');
unlink('system_tmp_array_dump_file');

# Now that we have the coordinates, we itarate over the atoms to check 
# the characteristic and designate them in the XYZ file.
$fp = fopen("system_".$filename.".xyz","w");
fwrite($fp,sizeof($atom_arr)."\n");
fwrite($fp,"Generated by plotter.php\n");
for($i=0, $size=sizeof($atom_arr);$i<$size;$i++)
{
    if(!array_key_exists("in",$atom_arr[$i]))
        $atomlabel = "Mg";#Vertices
    elseif($atom_arr[$i]["in"]==TRUE)
        $atomlabel = $atom_arr[$i]["id"];#Inside atoms
    else
        $atomlabel = "O";#Close-vertice atoms
    fwrite($fp,$atomlabel."\t".implode("\t",$atom_arr[$i]["coords"]));
}
fclose($fp);
?>


which generates a “system_xxxx.xyz” file, ready to be viewed in a standard molecule viewing software. It designates the vertice atoms (of the convex hull, remember? 8)as “Mg” and the atoms close to them as “O” for easy-viewing purpose. A sample parsed file looks like this:
The filtered case of a sample Na-K system
The big orange atoms are the omitted vertice atoms; the small red ones are the atoms critically close to the facets and hence also omitted ones. You can see the purple and yellow atoms which have passed the test sitting happilly inside, with the counting done using them.. 8)



POSCAR2Cif with symmetries discovered
admin — Thu, 04 Jun 2009 08:16:57 +0000
In previous posts, I had submitted two codes:

POSCAR2Cif : that converts a given POSCAR file to CIF, so to speak, ruthlessly, i.e. just as is, without checking for symmetries or anything.
POSCAR2findsymm : another converter that takes a POSCAR file, and prepares an input file such that Harold Stokes’ findsym code from the ISOTROPY package would proceed it and deduce the symmetry information. If findsym executable is not accessible in your system (or if you run the script with the “t” flag set to on), it would just print the input to the screen and you could use it to fill the input form of the code’s web implementation, instead

Anyway, recently it occured to me to write another script that would parse the output of the POSCAR2findsymm output and use that output to construct a CIF file that contained the equivalent sites, etc.. So, ladies and gentlemen, here it is (drums roll)…
Example: Code in action

Using the same POSCAR_Pd3S file as in the POSCAR2Cif entry… Feeding it to POSCAR2findsymm and then applying findsymm2cif on it
sururi@husniya tmp $ python /code/POSCAR2findsym/POSCAR2findsym.py POSCAR_Pd3S | php /code/vaspie/findsymm2cif.php speclist=Pd,S
_cell_length_a  7.21915
_cell_length_b  5.56683
_cell_length_c  7.68685
_cell_angle_alpha       90.00000
_cell_angle_beta        90.00000
_cell_angle_gamma       90.00000
_symmetry_Int_Tables_number     40

loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
Pd01    Pd       0.75000         0.17834         0.31139
Pd02    Pd       0.75000         0.17845         0.69126
Pd03    Pd       0.50000         0.00000         0.00132
S01     S        0.75000         0.81592         0.50152

Code

#!/usr/bin/php
                               *
 *                                                        23/05/09  *

 Usage:
 f         : input file  (Default = stdin)
 o         : output file (Default = stdout)
 identical : if set (identical=1), then the output will be the 
             transformation matrix and origin shift applied to the coordinates 
             so that the given coordinates will be regained.
 speclist  : Define the name of the species, seperated by 'xx' or ',' to be used
             with neighbour listing (Default = AxxBxxCxx...)
             (Labels can also be seperated via [space] as long as speclist is given
             in quotation -- Example: ... speclist=\"Au Si\" )

 Example : php findsymmetry2cif.php f=POSCAR_RhBi4 speclist=Bi,Rh identical=1
lol;
 echo $help."\n";
 exit;
}

$input = "php://stdin";
if($_GET["f"]) $input=$_GET["f"];

$outfile = "php://stdout";
if($_GET["o"]) $outfile=$_GET["o"];

$species_type_template = Array("A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z");
if($_GET["speclist"])$species_type_template = split("xx| |,",$_GET["speclist"]);

//if(file_exists("findsymm2cif_php.tmp"))
//    unlink("findsymm2cif_php.tmp");
if($input == "php://stdin")
{
    $lol = file("php://stdin");
    $fp1 = fopen("findsymm2cif_php2.tmp","w");
    foreach($lol as $line)
        fwrite($fp1,$line);
    fclose($fp1);
    $input = "findsymm2cif_php2.tmp";
}
exec('lstart=`grep -n "Type of each atom:" '.$input.'|sed "s:^\([0-9]\+\).*:\1:gi"`;lstart=`expr $lstart + 1`;lfinish=`grep -n "Position of each atom (dimensionless coordinates)" '.$input.'|sed "s:^\([0-9]\+\).*:\1:gi"`;lfinish=`expr $lfinish - 1`;cat '.$input.' |sed -n "`echo $lstart`,`echo $lfinish`p" | sed \':a;N;$!ba;s/\n/ /g\' > findsymm2cif_php.tmp');
exec('grep "Number of atoms in unit cell:" '.$input.' -A1 | tail -n1  >> findsymm2cif_php.tmp');
exec('grep "Space Group" '.$input.' | awk \'{print $3}\'  >> findsymm2cif_php.tmp');
exec('grep "Origin at" '.$input.' | awk \'{print $3 "\t" $4 "\t" $5}\'  >> findsymm2cif_php.tmp');
exec('grep "Vectors a,b,c:" '.$input.' -A3 | tail -n3  >> findsymm2cif_php.tmp');
exec('grep "Values of a,b,c,alpha,beta,gamma:" '.$input.' -A1 | tail -n1  >> findsymm2cif_php.tmp');
exec('grep "Wyckoff" '.$input.' -A1 -n | grep "^[0-9]\+-[0-9]"| sed "s:\(^[0-9]\+\)-[0-9]\+\(.*\):\1\t\2:gi" >> findsymm2cif_php.tmp');

if($input == "findsymm2cif_php2.tmp")
{
    $input = "php://stdin";
    //unlink("findsymm2cif_php2.tmp");
}

//exec("sh findsymm2cif.sh findsymm.out",$file);

$file = file("findsymm2cif_php.tmp");
$type_atoms = split("[ \t]+",trim($file[0]));
$specie_count = Array();
$k = 0;
$specie_count[$k] = 1;
for($i=1; $i < sizeof($type_atoms); $i++)
{
    if($type_atoms[$i] != $type_atoms[$i-1])
        $k++;
    $specie_count[$k]++;
}
for($i=1; $i=1.0)
                $specie[$i][$j]-=1.0;
            while($specie[$i][$j]<0.0)
                $specie[$i][$j]+=1.0;
        }

    }
}

$fp = fopen($outfile,"w");
fwrite($fp,"_cell_length_a"."\t".$params[0]."\n");
fwrite($fp,"_cell_length_b"."\t".$params[1]."\n");
fwrite($fp,"_cell_length_c"."\t".$params[2]."\n");
fwrite($fp,"_cell_angle_alpha"."\t".$params[3]."\n");
fwrite($fp,"_cell_angle_beta"."\t".$params[4]."\n");
fwrite($fp,"_cell_angle_gamma"."\t".$params[5]."\n");
fwrite($fp,"_symmetry_Int_Tables_number"."\t".$sgno."\n\n");
fwrite($fp, "loop_\n_atom_site_label\n_atom_site_type_symbol\n_atom_site_fract_x\n_atom_site_fract_y\n_atom_site_fract_z\n");
//print_r ($specie);
$k = 0;
$specie_type = $specie[0][0];
for($i=0;$i




POSCAR2Cif
admin — Sat, 23 May 2009 16:26:12 +0000
Converts POSCAR files to CIF format. Uses Octave (latvec2par) to convert the unit cell vectors to lattice cell parameters. It is assumed (compulsory) that the atom coordinates in the POSCAR file are in fractional (direct) coordinates. 
Parameters

f         : input file  (Default = POSCAR)
o         : output file (Default = <inputfilename>.cif)
t         : if set (t=1), then the output is written to the screen
speclist  : Define the name of the species, seperated by 'xx' or ',' to be used
            with neighbour listing (Default = AxxBxxCxx...)
            (Labels can also be seperated via [space] as long as speclist is given
            in quotation -- Example: ... speclist=\"Au Si\" )

Example

sururi@husniya OUTCARs_final_structures $ cat POSCAR_Pd3S
Pd3S
   1.00000000000000
     4.7454403619558345    0.0098182468538853    0.0000000000000000
    -1.4895902658503473    4.5055989020479856    0.0000000000000000
     0.0000000000000000    0.0000000000000000    7.2191545483192190
   6   2
Direct
  0.1330548697855782  0.5102695954022698  0.2500000000000000
  0.4897304045977232  0.8669451452144267  0.7500000000000000
  0.5128136657304309  0.1302873334247993  0.2500000000000000
  0.8697126665752007  0.4871863042695738  0.7500000000000000
  0.0013210250693640  0.9986789749306360  0.0000000000000000
  0.0013210250693640  0.9986789749306360  0.5000000000000000
  0.6856021298170862  0.6825558526447357  0.2500000000000000
  0.3174442073552622  0.3143978111829124  0.7500000000000000

sururi@husniya OUTCARs_final_structures $ php POSCAR2CIF.php f=POSCAR_Pd3S t=1 speclist=Pd,S
data_
loop_
_symmetry_equiv_pos_as_xyz
x,y,z
_cell_length_a  4.745451
_cell_length_b  4.745451
_cell_length_c  7.219155
_cell_angle_alpha       90.000000
_cell_angle_beta        90.000000
_cell_angle_gamma       108.175792
loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
Pd01    Pd        0.1330548697855782  0.5102695954022698  0.2500000000000000
Pd02    Pd        0.4897304045977232  0.8669451452144267  0.7500000000000000
Pd03    Pd        0.5128136657304309  0.1302873334247993  0.2500000000000000
Pd04    Pd        0.8697126665752007  0.4871863042695738  0.7500000000000000
Pd05    Pd        0.0013210250693640  0.9986789749306360  0.0000000000000000
Pd06    Pd        0.0013210250693640  0.9986789749306360  0.5000000000000000
S01     S         0.6856021298170862  0.6825558526447357  0.2500000000000000
S02     S         0.3174442073552622  0.3143978111829124  0.7500000000000000

Code

#!/usr/bin/php
                    *
 * Script name: POSCAR2CIF.php                           *
 * Converts the specified POSCAR file to CIF format      *
 * Uses octave to convert the unit cell vectors          *
 * to lattice parameters.                                *
 *                                              23/05/09 */
 
 
//require("/code/toolbox/commandline.inc.php"); # Equivalent handling of $_GET / $_POST
# ============/code/toolbox/commandline.inc.php========================================
// Enables the same treat for command line parameters
// as those of GET parameters.
// Also sets the $first, $last ranges including the gall parameter
 
//Support for command line variable passing:
for($i=1;$i                    *
 *                                              23/05/09 *
 
 Usage:
 f         : input file  (Default = POSCAR)
 o         : output file (Default = .cif)
 t         : if set (t=1), then the output is written to the screen
 speclist  : Define the name of the species, seperated by 'xx' or ',' to be used
             with neighbour listing (Default = AxxBxxCxx...)
             (Labels can also be seperated via [space] as long as speclist is given
             in quotation -- Example: ... speclist=\"Au Si\" )
 
 Example : php POSCAR2CIF.php f=POSCAR_RhBi4 speclist=Bi,Rh
lol;
 echo $help."\n";
 exit;
}
 
 
if($_GET["file"])$inputfile = $_GET["file"];
else if($_GET["f"])$inputfile = $_GET["f"];
else $inputfile="POSCAR";
 
$outfile = $inputfile.".cif";
if($_GET["o"]) $outfile=$_GET["o"];
if($_GET["t"]) $outfile = "php://stdout";
 
$species_type_template = Array("A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z");
if($_GET["speclist"])$species_type_template = split("xx| |,",$_GET["speclist"]);
 
//echo sizeof($_GET["speclist"])."\n";
exec('sed -n "3,6p" '.$inputfile.'|awk \'{print $1"\t"$2"\t"$3}\'',$out);
$octfp = fopen("octrungetvolnpar.m","w");
 
fwrite($octfp,"kini=[\n");
for ($i=0;$i<3;$i++)
    fwrite($octfp,$out[$i]."\n");
fwrite($octfp,"];\n\n");
 
fwrite($octfp,"numatom = [".$out[3]."];\n\n");
$numatoms = split("[ \t]+",trim($out[3]));
 
// Write the octave operations
fwrite($octfp,"k1 = latvec2par (kini);totatom=sum(numatom );\n");
fwrite($octfp,"for i=1:6;printf(\"%f\\n\",k1(i));endfor;\nprintf(\"%d\\n\",totatom)\n");
 
fclose($octfp);
 
// Execute the octave file to find the lattice parameters and volume
exec('octave -q '.$thisdir.'octrungetvolnpar.m',$out3);
unlink("octrungetvolnpar.m");
//echo $out3[0]."\n";
 
/*
for ($i=0;$i




LaTeX to PNG and all that equations..
admin — Mon, 23 Mar 2009 14:32:29 +0000
After migrating this blog to a new server, I had some difficulties in writing up the equations. It was due to the fact that on this server, I wasn’t able to execute the necessary commands to parse the latex code and convert it to PNG format.
Last week, some need arouse for this and I finally coded the necessary way around to be able to convert LaTeX definitions to their PNG counterparts. Before I start to quote the necessary code and explanations, let me tell that, this method only will work if you can successfully manage to produce this conversation at your -local- computer since what the code does is to generate the image on your local computer and then copy it to the server where your blog (/or whatever you have) resides. So, make sure:

You can convert LaTeX code to PNG on your -own- computer.
You are running a httpd server so that the code can copy the output PNG file from your local computer

What the code does:

It has 3 seperate processes. Let’s designate them A, B & C.

Part A is called on the remote server. It presents a form with textbox in it where you can type the LaTeX code. The form’s target is the same file but this time on your local server, so when you submit the data —
Part B is called on your local server. Using the texvc code, an open source software that also comes packed with mediawiki, it converts the LaTeX code into a PNG image and places it under the relative math/ directory of your local server. After doing this, via the META tag ‘refresh’ it causes the page to refresh itself loading its correspondence in the remote server, hence initiating —
Part C where the generated image identified by the MD5 hashname is fetched from the local server and copied unto the relative math/ directory on the remote server. The LaTeX code that was used is also passed in the GET method and it is included in the generated code as the title of the image, so if necessary, the equation can be modified in the future.

The code is as follows:










';
    echo $html;
}
else if($_GET["file"])
{
    // COM
    $file = "math/".$_GET["file"].".png";
    if(!copy("yourlocalserver.dns.name/tex/".$file, $file)) exit( "copy failed
");
    $formula = base64_decode($_GET["formula"]);
?>

<?PHP echo $formula; ?>





";
    echo "<img src=\"/tex/".$file."\" title=\"".$formula."\">
";
}
?>


To apply this:
   1. Create a directory called ‘tex’ on both servers.

   2. Create subdir ‘math’ on both servers

   3. Create subdir ‘mathtemp’ on the local server

   4. Modify the permissions of these subdirs accordingly

   5. Place the executable ‘texvc’ in the ‘tex’ directory

   6. Place the code quoted above in the ‘tex’ directories of both servers in a file called ‘index.php’
If everything well up to this point, let’s give it a try and you shall have some output similar to this:


For an input LaTeX code of:

\sum_{n=0}^\infty\frac{x^n}{2n!}
where you can immediately see the resulting image, modify the code if there’s something wrong or copy the IMG tag and put it to your raw HTML input box in your text…



Sub-groups of space groups
admin — Thu, 03 Jul 2008 13:06:41 +0000
ISOTROPY is a highly effective program written by the guru of applications of Group Theory on Phase Transitions, Harold T. Stokes (For those who are interested in the topic, I recommend his Introduction to Isotropy Subgroups and Displacive Phase Transitions titled paper(co-authored by Dorian M. Hatch) and Structures and phase transitions in perovskites – a group-theoretical approach paper (co-authored by Christopher J. Howard).
I’m pretty new and noobie in Group Theory – it was one of the subjects I found myself always running away. Anyway, I wanted to limit my search for some specific phase transition search in the database. Say, if an A-B binary has been reported in S1 and S2 structures, I didn’t want to go all the way looking for possible transition mechanisms if S1->S2 isn’t allowed by the group theory at all!
In the meantime, I’ve begun experimenting with the ISOTROPY program, yet I’m still at the very beginning. You can find detailed information and an online version in the related website, but to give an example, suppose we’d like to know about the subgroups of spacegroup 123 (P4/mmm). We enter the following commands:
VALUE PARENT 123

SHOW PARENT

SHOW SUBGROUP

SHOW LATTICE

DISPLAY ISOTROPY
and it displays a list of which a portion is presented below:
Parent     Lattice Subgroup   Lattice

123 P4/mmm q       123 P4/mmm q

123 P4/mmm q       47 Pmmm    o

123 P4/mmm q       83 P4/m    q

123 P4/mmm q       65 Cmmm    o-b

123 P4/mmm q       10 P2/m    m

123 P4/mmm q       12 C2/m    m-b

123 P4/mmm q       2 P-1      t

123 P4/mmm q       89 P422    q

123 P4/mmm q       111 P-42m  q

123 P4/mmm q       99 P4mm    q

123 P4/mmm q       115 P-4m2  q

123 P4/mmm q       25 Pmm2    o

123 P4/mmm q       38 Amm2    o-b

123 P4/mmm q       6 Pm       m

123 P4/mmm q       123 P4/mmm q

123 P4/mmm q       127 P4/mbm q

123 P4/mmm q       127 P4/mbm q
You may have noticed that, there are some recurring lines – this is due to some other properties that we have not specifically selected for display, i.e., it would display lines only containing "123 P4/mmm" if we hadn’t specifically asked for subgroup and lattice information (in analogy with the degeneracies in QM).
I needed a table containing all the subgroups of each space-group but there were two problems:
1.  As far as I know, ISOTROPY does not accept an input file where you can pass the commands you’ve prepared via a script/macro. So, I was afraid that I would type "VALUE PARENT 1 – DISPLAY ISOTROPY – VALUE PARENT 2 – DISPLAY ISOTROPY – …" (by the way, ISOTROPY has a clever interpreter so that you can just type the first letters of commands and parameters as long as they are not dubious).
2. Again, as far as I know, you can’t direct the output to a file, meaning you have to copy the output manually and paste into a file (x230 in my case).
Luckily, it turned out that:
1. You could not supply an input file, but you could instead, paste the contents of such an input file and ISOTROPY would process it line by line.
2. Stokes had included a very useful and helpful property that all the sessions was recorded automatically in the "iso.log" file.
So, all I had to do was
1. Write a script that would produce the query to retrieve the subgroups of all 230 space-groups.
2. Paste the outcome of this script to ISOTROPY.
3. Write another script that would parse the "iso.log" file and split these reported subgroups per spacegroup (and while I’m at it, remove the duplicate lines and order the subgroups).
Maybe you won’t believe me but I am also not happy to paste lines and lines of code to this blog’s entries. I will deal it soon but in the mean time, please bear with them a little longer.. Ath the moment, I will describe the process and will include them at the end.
* build the query via query_builder.php

* feed this query to ISOTROPY

* split the space groups from the "iso.log" via split_spacegroups.php

* run sortall.php which :

    * runs the sortkillduplines.php on each of these files

    * sorts again via the sort.pl wrt to the 4th col (space number of the subgroup)

    * removes the blank lines

* And that’s it..
Here comes the codes (php+perl)
query_builder.php:





sortkillduplines:


;\nsub numerically { \$a <=> \$b; }â ".$file." > sorttemp.txt");
 else $exec = exec("perl -e âprint sort <>â ".$file." > sorttemp.txt");
 $fi = file("sorttemp.txt");
 unlink("sorttemp.txt");
 $curlinecont = "wrwerwer";
 if(!$f_seperator)
 {
     for($i=0; $iâ sorttemp2.txt");
     unlink("sorttemp2.txt");
 }
   // unlink("sortkilldup_tmp.tmp");
 ?>




split_spacegroups.php:






sortall.php:


 temp");
     $exec = exec("./sort.pl temp > temp2");
     $exec = exec("perl -pi -e \"s/^\\n//\" < temp2 > ".$filename);
 }
 unlink("temp");
 unlink("temp2");
?>

or you can directly skip all these steps and download the generated spacegroup files from here. 8)
 
Lattice values are given in Schoenflies Notation where it corresponds to (with Pearson notation):
T : triclinic (AP)

M : prmitive monoclinic (MP)

M-B : base-centered monoclinic (MC)

O : primitive orthorhombic (OP)

O-B : base-centered orthorhombic (OC)

O-V : body-centered orthorhombic (OI)

O-F : face-centered orthorhombic (OF)

Q : primitive tetragonal (TP)

Q-V : body-centered tetragonal (TI)

RH : trigonal (HR)

H : hexagonal (HP)

C : primitive cubic (CP)

C-F : face-centered cubic (CF)

C-V : body-centered cubic (CI)
Quick reference on Bravais Lattices and info on how/why they are called after Bravais but not Frankenheim..



The marriage of heaven (common elements) and hell (code writing code).
admin — Thu, 26 Jun 2008 10:57:09 +0000
So, as Blake had said, "Energy is Eternal Delight." or in other words, let’s merge the preceding two entries to write a code for a function that produces MySQL queries that will fetch the common elements involved with the given elements:
function fetch_elements($el,$order,$total)
{
    // produces the query to select the elements that have binaries with the $el
    // $order and $total are used to adjust the tab positions and designating the sets
 
    $abc = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    $tab = str_repeat("\t",($total-$order));
    $lom = <<
Now, we can call it with, for example:  

echo fetch_common_elements(Array("Ga","Fe","Gd","Y","Ti","Ge","Ce"));    
Which will output:
 SELECT *
 FROM (
         SELECT symbol_A AS symb, val1 AS valG
         FROM `dbl014`
         WHERE symbol_B = "Ce"
         GROUP BY Symbol_A
         UNION
         SELECT symbol_B AS symb, val1 AS valG
         FROM `dbl014`
         WHERE (
             symbol_A = "Ce"
             AND symbol_B != ""
         )
         GROUP BY Symbol_B
 ) AS G
 INNER JOIN (
         SELECT *
         FROM (
                 SELECT symbol_A AS symb, val1 AS valF
                 FROM `dbl014`
                 WHERE symbol_B = "Ge"
                 GROUP BY Symbol_A
                 UNION
                 SELECT symbol_B AS symb, val1 AS valF
                 FROM `dbl014`
                 WHERE (
                     symbol_A = "Ge"
                     AND symbol_B != ""
                 )
                 GROUP BY Symbol_B
         ) AS F
         INNER JOIN (
                 SELECT *
                 FROM (
                         SELECT symbol_A AS symb, val1 AS valE
                         FROM `dbl014`
                         WHERE symbol_B = "Ti"
                         GROUP BY Symbol_A
                         UNION
                         SELECT symbol_B AS symb, val1 AS valE
                         FROM `dbl014`
                         WHERE (
                             symbol_A = "Ti"
                             AND symbol_B != ""
                         )
                         GROUP BY Symbol_B
                 ) AS E
                 INNER JOIN (
                         SELECT *
                         FROM (
                                 SELECT symbol_A AS symb, val1 AS valD
                                 FROM `dbl014`
                                 WHERE symbol_B = "Y"
                                 GROUP BY Symbol_A
                                 UNION
                                 SELECT symbol_B AS symb, val1 AS valD
                                 FROM `dbl014`
                                 WHERE (
                                     symbol_A = "Y"
                                     AND symbol_B != ""
                                 )
                                 GROUP BY Symbol_B
                         ) AS D
                         INNER JOIN (
                                 SELECT *
                                 FROM (
                                         SELECT symbol_A AS symb, val1 AS valC
                                         FROM `dbl014`
                                         WHERE symbol_B = "Gd"
                                         GROUP BY Symbol_A
                                         UNION
                                         SELECT symbol_B AS symb, val1 AS valC
                                         FROM `dbl014`
                                         WHERE (
                                             symbol_A = "Gd"
                                             AND symbol_B != ""
                                         )
                                         GROUP BY Symbol_B
                                 ) AS C
                                 INNER JOIN (
                                         SELECT *
                                         FROM (
                                                 SELECT symbol_A AS symb, val1 AS valA
                                                 FROM `dbl014`
                                                 WHERE symbol_B = "Ga"
                                                 GROUP BY Symbol_A
                                                 UNION
                                                 SELECT symbol_B AS symb, val1 AS valA
                                                 FROM `dbl014`
                                                 WHERE (
                                                     symbol_A = "Ga"
                                                     AND symbol_B != ""
                                                 )
                                                 GROUP BY Symbol_B
                                         ) AS A
                                         INNER JOIN (
                                                 SELECT symbol_A AS symb, val1 AS valB
                                                 FROM `dbl014`
                                                 WHERE symbol_B = "Fe"
                                                 GROUP BY Symbol_A
                                                 UNION
                                                 SELECT symbol_B AS symb, val1 AS valB
                                                 FROM `dbl014`
                                                 WHERE (
                                                     symbol_A = "Fe"
                                                     AND symbol_B != ""
                                                 )
                                                 GROUP BY Symbol_B
                                         ) AS B
                                         USING (symb)
 
                                 ) AS D
                                 USING (symb)
 
                         ) AS E
                         USING (symb)
 
                 ) AS F
                 USING (symb)
 
         ) AS G
         USING (symb)
 
 ) AS H
 USING (symb)

and when fed to the database will yield:
 
 thank y’all.. 8)



A code to write code (as in a war to end -all- wars – 8P)
admin — Thu, 19 Jun 2008 15:03:53 +0000
Lately, I’ve been studying on the nice and efficient algorithm of Dominik Endres and he’s been very helpful in replying to my relentless mails about the algorithm and the software. Now, if you have checked the algorithm, there is a part where iteration is needed to be done over the possible bin boundary distributions. Via a smart workaround he avoids this and uses a recursive equation.
For my needs, I want to follow the brute-force approach. To requote the situation, suppose we have K=4 number of classes, let’s label these as 0,1,2,3. There are 3 different ways to group these classes into 2 (M=2-1=1) bins obeying the following rules:
* There is always at least one classification per bin.
* Bins are adjascent to each other.
* Bins can not overlap.
The number of configurations are given by the formula:
N=(K-1)! / ( (K-M-1)! M!)   (still haven’t brought back my latex renderer, sorry for that!)
 
and these 3 possible configurations for K=4, M=1 are:
|—-|—-|—-|
0            3  : Meaning, the first bin only covers the 0 class while the second bin covers 1, 2, 3.
     1       3 : Meaning, the first bin covers 0, 1 while the second bin covers 2, 3.
         2   3 : Meaning, the first bin covers 0, 1, 2 while the second bin covers 3.
 
Now, think that you are writing a code to get this values, it is easy when you pseudo-code it:


for k_0 = 0 : K-1-M
   for k_1 = k_0+1 : K-M
      …
         for k_(K-3) = k_(K-4)+1 : K-4
            for k_(K-2) = k_(K-3)+1 : K-3
               print("k_0 – k_1 – … – k_(K-2) – K-1")


            endfor
         endfor
      …
   endfor
endfor
easier said than done because the number of the k_ variables and the for loops are changing with M.
So after some trying in Octave for recursive loops with the help of the feval() function, I gave up and wrote a PHP code that writes an Octave code and it was really fun! 8)

//Support for command line variable passing:

for($i=1;$i
{

    list($var0,$val0) = explode("=",$_SERVER["argv"][$i]);

    $_GET[$var0] = $val0;

}

$K = $_GET["K"];

$M = $_GET["M"];
if(!$_GET["K"])$_GET["K"] = 10;

if(!$_GET["M"])$_GET["M"] = 2;

if(!$_GET["f"])$_GET["f"] = "lol.m";
$fp = fopen($_GET["f"],"w");

fwrite($fp, "count=0;\n");
fwrite($fp, str_repeat("\t",$m)."for k0 = 0:".($K-$M-1)."\n");
for($m=1;$m<$M;$m++)

{

    fwrite($fp, str_repeat("\t",$m)."for k".$m." = k".($m-1)."+1:".($K-$M-1+$m)."\n");

}
fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",$M)."%d\\n\",");
for($i=0;$i<$m;$i++)

    fwrite($fp, "k".$i.",");

fwrite($fp,($K-1).")\n");
fwrite($fp, str_repeat("\t",$m)."count++;\n");
for($m=$M-1;$m>=0;$m–)

{

    fwrite($fp, str_repeat("\t",$m)."endfor\n");

}
fwrite($fp,"if(count!=factorial(".$K."-1)/(factorial(".$K."-".$M."-1)*factorial(".$M.")))\n\tprintf(\"Houston, we have a problem..\");\nendif\n");
//fwrite($fp,"printf(\"count : %d\\nfactorial : %d\\n\",count,factorial(".$K."-1)/(factorial(".$K."-".$M."-1)*factorial(".$M.")));\n");
fclose($fp);
system("octave ".$_GET["f"]);

?>
Now, if you call this code with for example:
> php genfor.php K=4 M=1
it produces and runs this Octave file lol.m:
count=0;

for k0 = 0:2

    printf("%d – %d\n",k0,3)

    count++;

endfor

if(count!=factorial(4-1)/(factorial(4-1-1)*factorial(1)))

    printf("Houston, we have a problem..");

endif
which outputs:
0 – 3

1 – 3

2 – 3
And you get to keep your hands clean 8)
 
Later addition (27/6/2008) You can easily modify the code to also give you possible permutations for a set with K items and groups of M items (where ordering is not important). For example, for K=5, say {0,1,2,3,4} and M=4:
0-1-2-3

0-1-2-4

0-1-3-4

0-2-3-4

1-2-3-4
5 (=K!/(M!(K-M)!)) different sets.
The modifications we make to the code are:
* Add an optional parameter that will tell the code that, we want permutation instead of binning:
if($_GET["perm"]||$_GET["p"]||$_GET["P"])

{

    $f_perm = TRUE;

    $K+=1;

}
via the f_perm flag, we can check the type of the operation anywhere within the code. K is incremented because, previously, we were setting the end point fixed so that the last bin would always include the last point for the bins to cover all the space. But for permutationing we are not bounded by this fixication so, we have an additional freedom.
* Previously, we were just including the last point in the print() statement, we should fix this if we are permutating:
$str = "";
for($i=0;$i<$m;$i++)

    $str .= "k".$i.",";

if(!$f_perm) fwrite($fp,$str.($K-1).")\n");

else fwrite($fp, substr($str,0,-1).")\n");
The reason for instead of now writing directly to the file in the iteration we just store it in a variable (str) is to deal with the trailing comma if we are permuting, as simple as that!
and the difference between before and after the modifications is:
sururi@dutsm0175 Octave $ diff genfor.php genfor2.php

10a11,16

> if($_GET["perm"]||$_GET["p"]||$_GET["P"])

> {

>     $f_perm = TRUE;

>     $K+=1;

> }

>

21c27,30

< fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",$M)."%d\\n\",");

—

> if(!$f_perm)fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",$M)."%d\\n\",");

> else fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",($M-1))."%d\\n\",");

>

> $str = "";

24,25c33,35

<     fwrite($fp, "k".$i.",");

< fwrite($fp,($K-1).")\n");

—

>     $str .= "k".$i.",";

> if(!$f_perm) fwrite($fp,$str.($K-1).")\n");

> else fwrite($fp, substr($str,0,-1).")\n");
for the really lazy people (like myself), here is the whole deal! 8)

 //Support for command line variable passing:

for($i=1;$i
{

    list($var0,$val0) = explode("=",$_SERVER["argv"][$i]);

    $_GET[$var0] = $val0;

}



$K = $_GET["K"];

$M = $_GET["M"];

if(!$_GET["K"])$_GET["K"] = 10;

if(!$_GET["M"])$_GET["M"] = 2;

if(!$_GET["f"])$_GET["f"] = "lol.m";
if($_GET["perm"]||$_GET["p"]||$_GET["P"])

{

    $f_perm = TRUE;

    $K+=1;

}
$fp = fopen($_GET["f"],"w");

fwrite($fp, "count=0;\n");
fwrite($fp, str_repeat("\t",$m)."for k0 = 0:".($K-$M-1)."\n");
for($m=1;$m<$M;$m++)

{

    fwrite($fp, str_repeat("\t",$m)."for k".$m." = k".($m-1)."+1:".($K-$M-1+$m)."\n");

}
if(!$f_perm)fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",$M)."%d\\n\",");

else fwrite($fp, str_repeat("\t",$m)."printf(\"".str_repeat("%d – ",($M-1))."%d\\n\",");
$str = "";
for($i=0;$i<$m;$i++)

    $str .= "k".$i.",";

if(!$f_perm) fwrite($fp,$str.($K-1).")\n");

else fwrite($fp, substr($str,0,-1).")\n");
fwrite($fp, str_repeat("\t",$m)."count++;\n");
for($m=$M-1;$m>=0;$m–)

{

    fwrite($fp, str_repeat("\t",$m)."endfor\n");

}
fwrite($fp,"if(count!=factorial(".$K."-1)/(factorial(".$K."-".$M."-1)*factorial(".$M.")))\n\tprintf(\"Houston, we have a problem..\");\nendif\n");
fwrite($fp,"printf(\"count : %d\\nfactorial : %d\\n\",count,factorial(".$K."-1)/(factorial(".$K."-".$M."-1)*factorial(".$M.")));\n");
fclose($fp);
system("octave ".$_GET["f"]);

?>
After the modifications,
php genfor.php K=5 M=3 p=1
will produce
0 – 1 – 2

0 – 1 – 3

0 – 1 – 4

0 – 2 – 3

0 – 2 – 4

0 – 3 – 4

1 – 2 – 3

1 – 2 – 4

1 – 3 – 4

2 – 3 – 4



Protected: mP12, oP12, tP6
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Less is More MySQL
admin — Wed, 09 Jan 2008 09:26:33 +0000
(-Right now, I’m going to define a new category: the MySQL category!-)
Suppose that, you have a database which contains a huge number of entries about the materials (like, for instance, the Pauling Database). Let it have 163 different properties we can query about. It is optimized for queries, so, the values are enumerated and the labels for these are kept in "pauling.dblxxx" tables, which may be something like this for the "Chemical System" property:

The values are kept in "pauling.valxxx" tables:

(Where the first one is the EntryCode, the PRIMARY key that relates all the tables and the second value is the enumeration for the value. For example, 1422 for the 13. property is actually Ho-Ir 

and there is one more set of tables, the paulingv2.valxxx tables which are stored and keyed in val order, so:

if we want to find the EntryCodes corresponding to a given property, we query the paulingv2.valxxx tables
if we want to find the property that is corresponding to a given EntryCode we query the pauling.valxxx tables
if we want to "translate" the property’s enumeration, we query the pauling.dblxxx tables.

Here is the thing: Let’s say that we want the Structure Types that have an Atomic Enviroment Type (AET) of a rhombic dodecahedron , with a/b ratio 1, alpha=beta=90^o. The property numbers for these are:
Structure Type : 32

AET : 86

a/b ratio : 44

alpha : 41

beta : 42
Since the last three properties are numeric, we don’t enumerate them and the enumeration corresponding to the rhombic dodecahedron for AET is 6. So, fasten your seat belts, we are about to lift off! :
SELECT id,pauling.dbl032.val FROM pauling.dbl032 

  INNER JOIN 

  (

   SELECT DISTINCT val FROM val032

   INNER JOIN

   (

   SELECT v AS EntryCode FROM

   (

    (

     SELECT val001.val AS v FROM val001

     INNER JOIN paulingv2.val086

     USING (EntryCode)

     WHERE paulingv2.val086.val=6

    ) AS A

    INNER JOIN

    (

     (

      SELECT val001.val AS v FROM val001

      INNER JOIN paulingv2.val044

      USING (EntryCode)

      WHERE paulingv2.val044.val=1

     ) AS B

     INNER JOIN

     (

      # 41=90 && 42= 90

      (

       SELECT val001.val AS v FROM val001

       INNER JOIN paulingv2.val041

       USING (EntryCode)

       WHERE paulingv2.val041.val=90

      ) AS C

      INNER JOIN

      (

       SELECT val001.val AS v FROM val001

       INNER JOIN paulingv2.val042

       USING (EntryCode)

       WHERE paulingv2.val042.val=90

      ) AS D 

      USING (v)

     ) 

     USING (v)

    ) 

    USING (v)

   )

   ) AS G

   USING (EntryCode)

  ) 

  AS Q ON (id = Q.val) ORDER BY val;

Later addition: Assuming 86=6; we don’t really need the other constraints 44=1, 42=90, 41=90 – do we?… So it’s just the boring:
SELECT id FROM pauling.dbl032 

  INNER JOIN 

  (

   SELECT DISTINCT val FROM val032

   INNER JOIN

   (

   SELECT v AS EntryCode FROM

   (

    (

     SELECT val001.val AS v FROM val001

     INNER JOIN paulingv2.val086

     USING (EntryCode)

     WHERE paulingv2.val086.val=6

    ) AS A

   )

   ) AS G

   USING (EntryCode)

  ) 

  AS Q ON (id = Q.val) ORDER BY Q.val;



The result of this is something like this:

To be honest, it is actually something like this :

The strange symbols are the price we pay for using non-standard charsets! 
So, to tidy up, I import this  to a table with the following structure:
CREATE TABLE IF NOT EXISTS `bcc` (

  `id` smallint(5) unsigned NOT NULL default ‘0’,

  `val` varchar(254) NOT NULL default ”,

  `usagecount` smallint(5) unsigned NOT NULL default ‘0’,

  `val1` varchar(30) NOT NULL default ‘0’,

  `val2` varchar(6) default NULL,

  `val3` varchar(3) default NULL,

  `val1t` varchar(30) NOT NULL,

  `val2sp` smallint(5) unsigned NOT NULL,

  `SG` tinyint(3) unsigned NOT NULL,

  PRIMARY KEY  (`id`),

  KEY `val` (`val`),

  KEY `val1` (`val1`)

) ENGINE=MyISAM DEFAULT CHARSET=utf8;
You have already met the id and val columns. "usagecount" will be imported from the pauling.dbl013 table; val1, val2, val3 are the seperated structure type information (ie, for "CuTi,tp4,129", val1="CuTi", val2="tp4" and val3="129"); val1t is the "translated" version of val1 which is the readeable one (ie, "(Ag¡•¦§Zn¡•¥¥)©Zn" is translated as "(Ag0.56Zn0.44)8Zn"). The translation is done via the following simpe php function:
function translate_symbols($string,$f_tr2symb=true)

{

$symbol_array = array("•","¡","¢","£","¤","¥","¦","§","¨","©","ª");//subscript values

$transl_array = array(".","0","1","2","3","4","5","6","7","8","9");//subscript values
if(!$f_tr2symb)return str_replace($transl_array,$symbol_array,$string);

else return str_replace($symbol_array,$transl_array,$string);

}
"val2sp" is the sliced numeric value from the Pearson Symbol stored in the val2 column.
To tidy up:
$query = "SELECT id, val1, val2 FROM bcc";

$qresult = mysql_query($query);
while($result = mysql_fetch_array($qresult))

{

 $query2 = "UPDATE bcc SET val1t=\"".translate_symbols($result["val1"])."\", val2sp=SUBSTRING(val2,3,20) WHERE id = ".$result["id"]." LIMIT 1";

 //echo $query2."\n";

 $q2result = mysql_query($query2);

 echo mysql_error();

}
You can refer to my previous entry for slicing up the "val" column. I had already done this while constructing the pauling.dblxxx tables, so in fact the actual view of the pauling.dbl032 table is the following one

meaning, I can just import them using the id’s of my new table:
UPDATE bcc, pauling.dbl032 SET 

bcc.val = pauling.dbl032.val, 

bcc.usagecount = pauling.dbl032.usagecount,

bcc.val1 = pauling.dbl032.val1,

bcc.val2 = pauling.dbl032.val2,

bcc.val3 = pauling.dbl032.val3

WHERE bcc.id = pauling.dbl032.id
Now we have something like:

We still have some work to do. Let’s take the two structures Ni₂Al and Ni₂In. Say that we are looking for superstructures, which have the property that the "atoms occupy atomic positions according to the parent crystal structure". The AET for Ni₂Al is given as 14-b;14-b;14-b; whereas the AET for Ni₂In is given as 11-a;11-a;14-b; . We want every atom to have the parent crystal structure (14-b – the rhombic dodecahedron for bcc), so we will eliminate those ones that have other AET.
mysql_query("USE pauling");

$ids_q = mysql_query("SELECT id FROM s07pt.bcc");

while($ids = mysql_fetch_row($ids_q))

{

 $id= $ids[0];

 $query = "

 SELECT COUNT(DISTINCT val) FROM pauling.val032

 INNER JOIN

  (

         SELECT v AS EntryCode FROM

          (

                 SELECT pauling.val001.val AS v FROM pauling.val001

                 INNER JOIN paulingv2.val032

                 USING (EntryCode)

                 WHERE paulingv2.val032.val = ".$id."

          ) AS A

         INNER JOIN

          (

                 SELECT pauling.val001.val AS v FROM pauling.val001

                 INNER JOIN paulingv2.val086

                 USING (EntryCode)

                 WHERE paulingv2.val086.val != 6

          ) AS B

  USING (v)

 ) as C USING (EntryCode)";
 $query = mysql_query($query);

 $result = mysql_fetch_row($query);

 $result = mysql_result($query,0);

 $result = ($result+1)%2;

 $query = "UPDATE s07pt.bcc SET incl_theo = $result where id = $id LIMIT 1";

 $j++;

 echo $j.".\t".$query."\n";

 mysql_query($query);

}
"incl_theo" is the column which is equal to 1 if the structure in question contains no AET other than 14-b, 0 otherwise. This gives us smt. like:

 




Using LaTeX within WordPress
admin — Sun, 18 Nov 2007 20:08:24 +0000
Renderu – LaTeX parsing WordPress plugin
Adapting from Titus Barik’s “LaTeX Equations and Graphics in PHP” titled article from the Linux Journal magazine, I was able to write a plugin for WordPress that enables me to includeÂ LaTeX-type
Â $\sum\limits_{j = 1}^m {p\left( X \right)H\left( {Y|X = x_i } \right)} $
in the form of a PNG file format as :
  
$\sum\limits_{j = 1}^m {p\left( X \right)H\left( {Y|X = x_i } \right)} $
  " />
(Although there is problem with multi lined entries such as matrix)
Barik’s article explained the method for Linux, but it can easily be run on a Windows environment (as it is been running on my computer at this very moment). Just install a LaTeX distribution like MikTeX and an image manipulation package like ImageMagick and it’s ready!