use Benchmark qw(:all);
use application 'polytope';


#------------------------------------
# Convex hull computations with
# lrs, cdd, beneath_beyond
#------------------------------------


# Measures the time for computing the convex hull of the
# cut polytope with respect to a given graph //g// with 
# the convex hull code //ch//.
# @param String ch the convex hull code
# @param Graph g the graph from which the cut polytope is constructed
# @return TIME_OBJECT the computation time
sub time_cut_poly {
    my ($ch, $g) = @_;
    my $c = cut_polytope($g->ADJACENCY); 
    my $t;
    prefer_now $ch; my $t0=Benchmark->new; $c->FACETS;  my $t1=Benchmark->new;
    $t=timediff($t1,$t0);
    return $t;
}

# Records the average time (in //n_runs// runs) for computing the 
# convex hull of the cut polytope of a path with //n_nodes// nodes
# with the convex hull codes lrs, cdd, and beneath_beyond.
# The result is stored in a file. The path to the file can be
# specified in //fpath// (e.g. "/tmp").
# @param Int n_nodes the number of nodes of the path
# @param Int n_runs the number of runs
# @param $fpath the path to the file
sub time_path {
    my ($n_nodes, $n_runs, $fpath) = @_;
    my $date = localtime(time);
    my $g = path_graph($n_nodes);
    my $file = $fpath."/cut_poly_path_".$n_nodes."_nodes_".$n_runs."_runs.log";
    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope of a path with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") { 
    #foreach my $ch ("ppl") { 
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly($ch,$g);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average ($ch, $n_runs runs, path with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average ($ch, $n_runs runs, path with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
    }
    close OUTPUT_FILE;
}

# See subroutine time_path.
sub time_cycle {
    my ($n_nodes, $n_runs, $fpath) = @_;
    my $date = localtime(time);
    my $g = cycle_graph($n_nodes);
    my $file = $fpath."/cut_poly_cycle_".$n_nodes."_nodes_".$n_runs."_runs.log";
    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope of a cycle with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") { 
    #foreach my $ch ("ppl") { 
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly($ch,$g);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average ($ch, $n_runs runs, cycle with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average ($ch, $n_runs runs, cycle with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
    }
    close OUTPUT_FILE;
}

# See subroutine time_path.
sub time_Kn {
    my ($n_nodes, $n_runs, $fpath) = @_;
    my $date = localtime(time);
    my $g = complete($n_nodes);
    my $file = $fpath."/cut_poly_complete_".$n_nodes."_nodes_".$n_runs."_runs.log";
    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope of the complete graph with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") { 
#    foreach my $ch ("lrs","cdd") { 
#    foreach my $ch ("ppl") { 
	if($n_nodes != 7 || $ch ne "beneath_beyond"){
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly($ch,$g);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average ($ch, $n_runs runs, complete graph with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average ($ch, $n_runs runs, complete graph with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
	}
    }
    close OUTPUT_FILE;
}

#------------------------------------
# Computations up to symmetry
#------------------------------------

# Measures the time for computing the convex hull up to symmetry
# of the cut polytope with respect to a given graph //g//
# (hopefully some day with the convex hull code //ch//).
# @param String ch the convex hull code
# @param Graph g the graph from which the cut polytope is constructed
# @param GroupOfPolytope group the given subgroup of the linear symmetry group of the cut polytope
# @return TIME_OBJECT the computation time
sub time_cut_poly_sym {
    my ($ch, $g, $group) = @_;

    my $c = cut_polytope($g->ADJACENCY); 
    $c->GROUP = new group::GroupOfPolytope($group);
    my $t;
    my $rayCompMethod;
    if ($ch eq "lrs") {
	$rayCompMethod = 0; 
    } elsif ($ch eq "cdd") {
	$rayCompMethod = 1;
    } elsif ($ch eq "beneath_beyond") {
	$rayCompMethod = 2;
    } elsif ($ch eq "ppl") {
	$rayCompMethod = 3;
    } else {
	die "time_cut_poly_sym: wrong specifier for convex hull code; only lrs, cdd, or beneath_beyond are available"
    }
    my $t0=Benchmark->new;
    my ($success, $ineq, $eq) = representation_conversion_up_to_symmetry($c, $c->GROUP, 1, $rayCompMethod);
    my $t1=Benchmark->new; 
    if (!$success) {
	croak("internal sympol error");
    } 
    $t=timediff($t1,$t0);
    return $t;
}

# Records the average time (in //n_runs// runs) for computing the 
# convex hull up to symmetry of the cut polytope of a path with 
# //n_nodes// nodes (goal: with sympol+lrs, sympol+cdd).
# The result is stored in a file. The path to the file can be
# specified in //fpath// (e.g. "/tmp").
# @param Int n_nodes the number of nodes of the path
# @param Int n_runs the number of runs
# @param Bool choose_induced_syms (1) use the symmetries induced by graph symmetries 
#    or (0) the full linear symmetry group of the corresponding cut polytope    
# @param $fpath the path to the file
sub time_path_sym {
    my ($n_nodes, $n_runs, $choose_induced_syms, $fpath) = @_;
    my $date = localtime(time);
    my $g = path_graph($n_nodes);
    my $group;
    my $file; 
    my $c = cut_polytope($g->ADJACENCY); # for sym group computation

    if ($choose_induced_syms == 1) {
	my $I = new IncidenceMatrix($g->EDGES);
	my $pairs_of_gens = automorphisms($I);
	my @edge_gens = map {$_->first} @$pairs_of_gens;

	# The action on the edges of the graph induces an action on the coordinates of the cut polytope.
	my $group_on_edges = new group::GroupOfPolytope( GENERATORS=>(new Array< Array<Int> >(\@edge_gens)), DOMAIN=>$polytope::domain_OnCoords );
	$group = convert_coord_action($group_on_edges, $c->VERTICES, $polytope::domain_OnRays);
	$file = $fpath."/induced_sym_cut_poly_path_".$n_nodes."_nodes_".$n_runs."_runs.log";
    } else {
	$group = linear_symmetries($c,1);
	$file = $fpath."/sym_cut_poly_path_".$n_nodes."_nodes_".$n_runs."_runs.log";
    }

    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope up to symmetry of a path with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") {
#    foreach my $ch ("cdd") {
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== sym $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly_sym($ch,$g,$group);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average (sym $ch, $n_runs runs, path with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average (sym $ch, $n_runs runs, path with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
    }
    close OUTPUT_FILE;
}


# See subroutine time_path_sym.
sub time_cycle_sym {
    my ($n_nodes, $n_runs, $choose_induced_syms, $fpath) = @_;
    my $date = localtime(time);
    my $g = cycle_graph($n_nodes);
    my $group;
    my $file;
    my $c = cut_polytope($g->ADJACENCY); # for sym group computation
    
    if ($choose_induced_syms == 1) {
	my $I = new IncidenceMatrix($g->EDGES);
	my $pairs_of_gens = automorphisms($I);
	my @edge_gens = map {$_->first} @$pairs_of_gens;

	# The action on the edges of the graph induces an action on the coordinates of the cut polytope.
	my $group_on_edges = new group::GroupOfPolytope( GENERATORS=>(new Array< Array<Int> >(\@edge_gens)), DOMAIN=>$polytope::domain_OnCoords );
	$group = convert_coord_action($group_on_edges, $c->VERTICES, $polytope::domain_OnRays);
	$file = $fpath."/induced_sym_cut_poly_cycle_".$n_nodes."_nodes_".$n_runs."_runs.log";
    } else {
	$group = linear_symmetries($c,1);
	$file = $fpath."/sym_cut_poly_cycle_".$n_nodes."_nodes_".$n_runs."_runs.log";
    }

    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope up to symmetry of a cycle with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") {
#    foreach my $ch ("cdd") {
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== sym $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly_sym($ch,$g,$group);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average (sym $ch, $n_runs runs, cycle with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average (sym $ch, $n_runs runs, cycle with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
    }
    close OUTPUT_FILE;
}

# See subroutine time_path_sym.
sub time_Kn_sym {
    my ($n_nodes, $n_runs, $choose_induced_syms, $fpath) = @_;
    my $date = localtime(time);
    my $g = complete($n_nodes);
    my $group;
    my $file;
    my $c = cut_polytope($g->ADJACENCY); # for sym group computation
    
    if ($choose_induced_syms == 1) {
	my $I = new IncidenceMatrix($g->EDGES);
	my $pairs_of_gens = automorphisms($I);
	my @edge_gens = map {$_->first} @$pairs_of_gens;

	# The action on the edges of the graph induces an action on the coordinates of the cut polytope.
	my $group_on_edges = new group::GroupOfPolytope( GENERATORS=>(new Array< Array<Int> >(\@edge_gens)), DOMAIN=>$polytope::domain_OnCoords );
	$group = convert_coord_action($group_on_edges, $c->VERTICES, $polytope::domain_OnRays);
	$file = $fpath."/induced_sym_cut_poly_complete_".$n_nodes."_nodes_".$n_runs."_runs.log";
    } else {
	$group = linear_symmetries($c,1);
	$file = $fpath."/sym_cut_poly_complete_".$n_nodes."_nodes_".$n_runs."_runs.log";
    }

    # Open output file
    open OUTPUT_FILE, ">$file"
	or die "can't create outputfile $file: $!";
    print(OUTPUT_FILE "Date: $date\n");
    print(OUTPUT_FILE "----------------------------------------------------\n");
    print(OUTPUT_FILE "Cut polytope up to symmetry of the complete graph with ".$n_nodes." nodes:\n----------------------------------------------------\n");
    foreach my $ch ("ppl","lrs","cdd","beneath_beyond") {
#    foreach my $ch ("cdd") {
	if($n_nodes != 7 || $ch ne "beneath_beyond"){
	print(OUTPUT_FILE "\n=== $ch ===\n----------------------------------------------------\n");
	print "\n=== sym $ch ===\n";
	my $s=0; 
	foreach (0..$n_runs-1) { 
	    my $t = time_cut_poly_sym($ch,$g,$group);print timestr($t);
	    print(OUTPUT_FILE "Run ".($_+1).": ".timestr($t)."\n");
	    print timestr($t)."\n";
	    $s += $t->[1];
	} 
	print(OUTPUT_FILE "----------------------------------------------------\n");
	print(OUTPUT_FILE "Time on average (sym $ch, $n_runs runs, complete graph with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n");
	print "\nTime on average (sym $ch, $n_runs runs, complete graph with $n_nodes nodes): ". ($s*1000/$n_runs) . " milliseconds.\n\n";
	}
    }
    close OUTPUT_FILE;
}


## If you want to trigger the run commands automatically just remove the next line
return;
#------------------------------------
# Function calls
#------------------------------------
my $n_runs = 10;
my $choose_induced_syms = 1; # uses induced symmetries of graph instead of linear symmetries of cut polytope (set to 0 for linear symmetries!)

my $path = "/path/to/store/the/output/files";
foreach my $n_nodes (9,10) {
    time_path($n_nodes,$n_runs,$path);
    time_cycle($n_nodes,$n_runs,$path);
    time_path_sym($n_nodes,$n_runs,$choose_induced_syms,$path);
    time_cycle_sym($n_nodes,$n_runs,$choose_induced_syms,$path);
}

 time_Kn(6,$n_runs,$path);
 time_Kn_sym(6,$n_runs,$choose_induced_syms,$path);
 time_Kn(7,1,$path);
 time_Kn_sym(7,$n_runs,$choose_induced_syms,$path);