September Morn Update

Task/Deconvolution-1D/Perl/deconvolution-1d.pl

@@ -0,0 +1,66 @@
+use Math::Cartesian::Product;
+
+sub deconvolve {
+    our @g; local *g = shift;
+    our @f; local *f = shift;
+    my(@m,@d);
+
+    my $h = 1 + @g - @f;
+    push @m, [(0) x $h, $g[$_]] for 0..$#g;
+    for my $j (0..$h-1) {
+        for my $k (0..$#f) {
+            $m[$j + $k][$j] = $f[$k]
+        }
+    }
+    rref(\@m);
+    push @d, @{ $m[$_] }[$h] for 0..$h-1;
+    @d;
+}
+
+sub convolve {
+    our @f; local *f = shift;
+    our @h; local *h = shift;
+    my @i;
+    for my $x (cartesian {@_} [0..$#f], [0..$#h]) {
+        push @i, @$x[0]+@$x[1];
+    }
+    my $cnt = 0;
+    my @g = (0) x (@f + @h - 1);
+    for my $x (cartesian {@_} [@f], [@h]) {
+        $g[$i[$cnt++]] += @$x[0]*@$x[1];
+    }
+    @g;
+}
+
+sub rref {
+  our @m; local *m = shift;
+  @m or return;
+  my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
+
+  foreach my $r (0 .. $rows - 1) {
+     $lead < $cols or return;
+      my $i = $r;
+
+      until ($m[$i][$lead])
+         {++$i == $rows or next;
+          $i = $r;
+          ++$lead == $cols and return;}
+
+      @m[$i, $r] = @m[$r, $i];
+      my $lv = $m[$r][$lead];
+      $_ /= $lv foreach @{ $m[$r] };
+
+      my @mr = @{ $m[$r] };
+      foreach my $i (0 .. $rows - 1)
+         {$i == $r and next;
+          ($lv, my $n) = ($m[$i][$lead], -1);
+          $_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
+
+      ++$lead;}
+}
+
+my @h = qw<-8 -9 -3 -1 -6 7>;
+my @f = qw<-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1>;
+print '  conv(f,h) = g = ' . join(' ', my @g = convolve(\@f, \@h)) . "\n";
+print 'deconv(g,f) = h = ' . join(' ', deconvolve(\@g, \@f)) . "\n";
+print 'deconv(g,h) = f = ' . join(' ', deconvolve(\@g, \@h)) . "\n";

Task/Deconvolution-1D/Python/deconvolution-1d-2.py

@@ -0,0 +1,38 @@
+import numpy
+
+h = [-8,-9,-3,-1,-6,7]
+f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
+g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
+
+# https://stackoverflow.com/questions/14267555/find-the-smallest-power-of-2-greater-than-n-in-python
+
+def shift_bit_length(x):
+    return 1<<(x-1).bit_length()
+
+def conv(a, b):
+    p = len(a)
+    q = len(b)
+    n = p + q - 1
+    r = shift_bit_length(n)
+    y = numpy.fft.ifft(numpy.fft.fft(a,r) * numpy.fft.fft(b,r),r)
+    return numpy.trim_zeros(numpy.around(numpy.real(y),decimals=6))
+
+def deconv(a, b):
+    p = len(a)
+    q = len(b)
+    n = p - q + 1
+    r = shift_bit_length(max(p, q))
+    y = numpy.fft.ifft(numpy.fft.fft(a,r) / numpy.fft.fft(b,r), r)
+    return numpy.trim_zeros(numpy.around(numpy.real(y),decimals=6))
+
+# should return g
+
+print(conv(h,f))
+
+# should return h
+
+print(deconv(g,f))
+
+# should return f
+
+print(deconv(g,h))