finalized tophat fft program

scripts/templates/tophat_freqdomain.gp

@@ -1,6 +1,6 @@
 set terminal pdf
 set termopt enhanced
-set output "pres/img/tophat_freqdomain.pdf"
+set output "tophat_freqdomain.pdf"
 
 set xrange [0.005:0.620]
 set logscale x
@@ -8,7 +8,7 @@ set xlabel "Temporal Frequency [days^{-1}]" font "Times,24"
 set xtics font 'Times,16'
 set mxtics
 
-set yrange [-11:11]
+set yrange [-30:30]
 set ylabel "Time Delay [days]" font "Times,24"
 set ytics font 'Times,16'
 set mytics
@@ -17,6 +17,6 @@ set mytics
 unset key
 
 
-plot "analyses/tables/tophat_fft1.tab" using 1:(-1*$2) with lines lc rgb "red", \
+plot "analyses/tables/tophat_fft1.tab" using 1:2 with lines lc rgb "red", \
-    "analyses/tables/tophat_fft2.tab" using 1:(-1*$2) with lines lc rgb "green", \
+    "analyses/tables/tophat_fft2.tab" using 1:2 with lines lc rgb "green", \
-    "analyses/tables/tophat_fft3.tab" using 1:(-1*$2) with lines lc rgb "blue"
+    "analyses/tables/tophat_fft3.tab" using 1:2 with lines lc rgb "blue"

scripts/templates/tophat_timedomain.gp

@@ -1,7 +1,7 @@
 set terminal pdf
-set output "pres/img/tophat_timedomain.pdf"
+set output "tophat_timedomain.pdf"
 
-set xrange [0:25]
+set xrange [0:35]
 set xlabel "Time [days]" font "Times,24"
 set xtics font 'Times,16'
 set mxtics

scripts/tophat_fft.pl

@@ -6,55 +6,66 @@ use PDL;
 use PDL::FFT;
 use PDL::IO::Misc;
 
-my $twoPI = 2*3.1415926539;
+my $_2π = 2*3.1415926539;
 
 # space parameters
-our $xres=.001;
+our $xres= 0.1;
 our $xmin = 0;
-our $xmax = 250;
+our $xmax = 2500;
-our $xbins = ($xmax-$xmin)/$xres;
+our $xbins = ($xmax-$xmin)/$xres + 1;
+
+say "Using $xbins bins";
 
 # tophat parameters
-my $μ1=15;
+my $μ1=7;
 my $Δ1=5; # full width
-my $μ2=15;
-my $Δ2=5; # full width
-my $μ3=15;
-my $Δ3=5; # full width
 
-say "Creating $xbins bins";
+my @tophat_list = ([$μ1,$Δ1],[28,8],[15,11]);
 
-# Complex Number z(x) = u(x) + iv(x)
+our $tophat_count = 0;
-my @th_list=tophat($μ1,$Δ1);
+foreach my $pars (@tophat_list) {
-my $u = pdl(@th_list);
+    $tophat_count++;
-my $v = zeroes($u);
 
+    # Capture tophat into piddle
+    # Complex Number z(x) = u(x) + iv(x)
+    my @tophat=tophat(@$pars[0],@$pars[1]);
+    my $u = pdl(@tophat);
+    my $v = zeroes($u);
 
-foreach (('1','2','3')) {
+    $x_coords = $u->xlinvals($xmin,$xmax);
 
-    # Output time-domain tophat
+    # Output x-domain tophat
-    open $tophattab, '>', "analyses/tables/tophat${$_}.tab";
+    wcols $x_coords,$u,"analyses/tables/tophat${tophat_count}.tab";
-    for ($i=0; $i < $xbins; $i++) {
-        my $x_coord = ($xmax-$xmin)*($i/$xbins) + $xmin;
-        say $tophattab "$x_coord $th_list[$i]";
-    }
-    close $tophattab;
 
-    # Transform z(x) to Z(1/x) = U(1/x) + iV(1/x)
+    # Transform z(x) to Z(x⁻¹) = U(x⁻¹) + iV(x⁻¹)
     my $U = $u;
     my $V = $v;
     fft($U,$V);
+
     # Determine frequency coordinates
     my $num_elements = nelem($U);
     say "Found $num_elements elements.";
-    $f = $U->xlinvals(-($num_elements/2-1)/$num_elements/$xres,1/2/$xres)->rotate(-($num_elements/2 -1));
 
-    say "$f[1]";
+    if ($num_elements % 2 == 0) {
+        # even number of bins
+        $f = $U->xlinvals(
+                -(${num_elements}/2-1)/${num_elements}/${xres}, 1/2/${xres}
+                )->rotate(-(${num_elements}/2 -1));
+    }
+    else {
+        #odd number of bins
+        $f = $U->xlinvals(
+                    -(${num_elements}/2-0.5)/${num_elements}/${xres},
+                        (${num_elements}/2-0.5)/${num_elements}/${xres}
+                    )->rotate(-(${num_elements}-1)/2);
+    }
 
+
+    # Calculate x offset
     my $φdiff = atan2($V,$U);
-    my $timelag = $φdiff/($twoPI*$f);
+    my $offset = $φdiff/($_2π*$f);
 
-    wcols $f,$timelag,"analyses/tables/tophat_fft${$_}.tab";
+    wcols $f,$offset,"analyses/tables/tophat_fft${tophat_count}.tab";
 
 }
 
@@ -62,10 +73,9 @@ sub tophat {
     (my $mean,my $width) = @_;
     my $halfwidth = $width/2;
     my @vals = ();
-    for ($i=0; $i < $xbins; $i++) {
+    for (my $x_coord = $xmin; $x_coord <= $xmax; $x_coord += $xres) {
-        my $x_coord = ($xmax-$xmin)*($i/$xbins) + $xmin;
+        push @vals, ($x_coord >= ($mean - $halfwidth) &&
-        if ($x_coord >= ($mean - $halfwidth ) && $x_coord <= ($mean + $halfwidth)) { push @vals, 1/$width; }
+                    $x_coord <= ($mean + $halfwidth)) ? 1/$width : 0;
-        else { push @vals, 0; }
     }
     return @vals;
 }