Differences

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--- tutorial:perl_continued [2017/07/11 08:52] – removed bullet points oroehrig
+++ tutorial:perl_continued [2017/07/26 14:44] (current) – fused with perl_intro oroehrig
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-====Using Perl within polymake====
-This is a tutorial about how to use Perl within ''polymake'', which was presented at the [[:workshop0311|polymake-Workshop]] at Darmstadt, in March 2011. A short introduction to Perl in ''polymake'' can be found at "[[tutorial:perl_intro|polymake for the Perl Newbie]]".
-===Standard data structures===
-The Perl programming language originally provides three different data structures, scalars($), arrays(@), and hashes(%). The user always has to specify the type of a variable using the appropriate symbol ''$'', ''@'', or ''%''. If you forget to do so, you will receive the following error message:
-<code>
-polytope > i=5;
-polymake:  ERROR: Unquoted string "i" may clash with future reserved word.
-</code>\\
-Here are some simple commands illustrating how to use the different data structures:
-==Scalars==
-<code>
-> $i=5;
-> $j=6;
-> $sum=$i+$j; print $sum;
-</code>
-==Arrays==
-<code>
-> @array=("a","b","c"); print scalar(@array);
-> push(@array,"d"); print "@array";
-> $first_entry=$array[0]; print $first_entry;
-> print join("\n",@array);
-> @array2=(3,1,4,2);
-> print sort(@array2);
-</code>
-==Hashes==
-<code>
-> %hash=();
-> $hash{"zero"}=0;
-> $hash{"four"}=4;
-> print keys %hash;
-> print join(", ",keys %hash);
-> print join(", ",values %hash);
-> %hash=("one",1,"two",2);
-> %hash=("one"=>1,"two"=>2);
-</code>
-==="Small objects": Data structures inherited from C++===
-In addition to the three standard data structures, the enriched version of ''Perl'' used in ''polymake'' also provides special data structures that are inherited from the ''C++''-side of ''polymake''.
-A complete list of these so-called "small objects" can be found in the [[:release_docs:latest:common.html|online documentation]] under the heading "Property types". To define a ''Perl''-variable of such a type, you initialize the variable via
-<code>
-> $my_var=new [SMALL_OBJECT]([INITIALIZATION]);
-</code>
-Note that the ''Perl''-type of the variable //my_var// is ''Scalar'', as the variable is internally treated as a reference to a ''C++''-object. You can find out the (''C++''-)type of your variable via
-<code>
-> print ref($my_var);
-</code>
-Here is a selection of three different structures that facilitate everyday work with ''polymake'':
-==Arrays==
-The small object ''Array'' can be initialized in different ways and with different template parameters:
-<code>
-> @array=("a","b","c");
-> $arr1=new Array<String>(\@array); print $arr1;
-> $arr2=new Array<Int>([3,2,5]); print $arr2;
-> $arr3=new Array<Int>(0,1,2,3); print $arr3;
-> $arr4=new Array<Int>(0..4); print $arr4;
-</code> It is also possible to convert the ''C++''-object ''Array'' into a ''Perl''-array by writing <code>
-> @arr4=@{$arr4}; print $arr2;
-</code> or simply<code>
-> @arr4=@$arr4;
-</code>
-==Sets==
-On ''C++''-side sets are stored in a balanced binary search (AVL) tree. For more information see the [[https://polymake.org/release_docs/master/PTL/classpm_1_1Set.html|PTL-documentation]]. In many cases, the small objects can be converted into ''Perl''-types in the expected way: <code>
-> $set=new Set<Int>(3,2,5); print $set;
-> print $set->size;
-> @array_from_set=@$set;
-</code>
-==Matrices==
-Here is a simple way to initialize a matrix:<code>
-> $mat=new Matrix<Rational>([[2,1,4,0,0],[3,1,5,2,1],[1,0,4,0,6]]);
-> print $mat;
-</code> You could also define it by passing a reference to an (''Perl''-)array of ''Vectors''. The single entries are interpreted as different rows: <code>
-> $row1=new Vector<Rational>([2,1,4,0,0]);
-> $row2=new Vector<Rational>([3,1,5,2,1]);
-> $row3=new Vector<Rational>([1,0,4,0,6]);
-> @matrix_rows=($row1,$row2,$row3);
-> $matrix_from_array=new Matrix<Rational>(\@matrix_rows);
-</code> You can change a single entry of a matrix in the following way (if it is not already assigned to an immutable property like ''VERTICES''!):<code>
-> $mat->row(1)->[1]=7; print $mat->row(1)->[1];
-> print $mat;
-> $mat->(1,2)=8; print $mat;
-</code> A unit matrix of a certain dimension can be defined via the user-function ''unit_matrix<COORDINATE_TYPE>(.)'': <code>
-> $unit_mat=4*unit_matrix<Rational>(3);
-> print $unit_mat;
-</code> The reason for the "strange output" is the implementation as //sparse matrix//: <code>
-> print ref($unit_mat);
-</code>However, some functions cannot deal with this special type of matrix. In this case it is necessary to transform the sparse matrix into a dense matrix first via:<code>
-> $dense=new Matrix<Rational>($unit_mat);print $dense;
-</code> or just<code>
-> $dense2=dense($unit_mat);print $dense2;
-</code> You can also work with matrices that have different types of coordinates like ''Rational'', ''Float'', or ''Int'': <code>
-> $m_rat=new Matrix<Rational>(3/5*unit_matrix<Rational>(5)); print $m_rat;
-> $m2=$mat/$m_rat; print $m2;
-> $m_int=new Matrix<Int>(unit_matrix<Rational>(5)); print $m_int;
-> $m3=$m_rat/$m_int;
-</code> The error message <code>
-polymake:  ERROR: undefined operator Matrix<Rational> / Matrix<Int> at input line 1.
-</code>indicates that you need to convert the integer matrix to a rational matrix first:<code>
-> $m3=$m_rat/(convert_to<Rational>($m_int)); print $m3;
-</code> By "/" you can add rows to a matrix, whereas "|" adds columns. By the way, this also works for ''Vector''.<code>
-> $z_vec=zero_vector<Int>($m_int->rows);
-> $extended_matrix=($z_vec|$m_int); print $extended_matrix;
-</code>
-It is also possible to nest template parameters in any way you like, e.g.
-<code>
-> $set=new Set<Int>(3,2,5);
-> $template_Ex=new Array<Set<Int>>((new Set<Int>(5,2,6)),$set); print $template_Ex; print ref($template_Ex);
-</code>
-However, if you use a template combination, you have never used before, it may take some time until you see the result. This is due to the fact that ''polymake'' compiles your new combination //on the fly//. But this is only a one-time effect, and next time you use this combination it will work without delay.
-==="Big Objects": Objects with properties===
-<code>
-> $p=new Polytope<Rational>(POINTS=>cube(4)->VERTICES);
-> $lp=new LinearProgram<Rational>(LINEAR_OBJECTIVE=>[0,1,1,1,1]);
-> $p->LP=$lp;
-> print $p->LP->MAXIMAL_VALUE;
-</code>
-===Working with Perl in polymake===
-{{:points.demo|}}
-<code>
-> open(INPUT, "< $HOME/polymake/demo/Workshop2011/points.demo");
-> $matrix=new Matrix<Rational>(<INPUT>);
-> close(INPUT);
-> print $matrix;
->
-> $p=new Polytope<Rational>(POINTS=>$matrix);
-> print $p->FACETS;
-> print $p->DIM;
-> print $p->VERTEX_SIZES;
-> ### choose "simple" vertices
-> for(my $i=0;$i<scalar(@{$p->VERTEX_SIZES});$i++){
->     if($p->VERTEX_SIZES->[$i]==$p->DIM){
-> 	print $i.": ".$p->VERTICES->row($i)."\n";
->     }
-> }
-> $s=new Set<Int>();
-> for(my $i=0;$i<scalar(@{$p->VERTEX_SIZES});$i++){
->     if($p->VERTEX_SIZES->[$i]==$p->DIM){
-> 	$s+=$i;
->     }
-> }
-> $special_points=$p->VERTICES->minor($s,All); print $special_points;
->
-> foreach(@{$s}){
->     print $p->VERTICES->row($_)."\n";
-> }
-> foreach my $index(@{$s}){
->     print $p->VERTICES->row($index)."\n";
-> }
-</code>
-===Scripts===
-[[scripting:start|Scripting]]