# HG changeset patch
# User Kai T. Ohlhus <k.ohlhus@gmail.com>
# Date 1593587021 -32400
# Node ID 627da618dcc4b7e84732c9c132c35ea5738070b3
# Parent  49f4d7814760957f2fc5ca5514929eea577a95af
hilb.m: Speed-up function using broadcasting.

* scripts/special-matrix/hilb.m: Speed-up function using broadcasting.  For more
 information read https://octave.discourse.group/t/boosting-hilb/48 .

diff -r 49f4d7814760 -r 627da618dcc4 scripts/special-matrix/hilb.m
--- a/scripts/special-matrix/hilb.m	Mon Jun 29 15:01:27 2020 -0400
+++ b/scripts/special-matrix/hilb.m	Wed Jul 01 16:03:41 2020 +0900
@@ -66,12 +66,10 @@
     error ("hilb: N must be a scalar integer");
   endif
 
-  retval = zeros (n);
-  tmp = 1:n;
-  for i = 1:n
-    retval(i, :) = 1.0 ./ tmp;
-    tmp += 1;
-  endfor
+  ## Very elegant solution by N. Higham
+  ## https://nhigham.com/2020/06/30/what-is-the-hilbert-matrix/
+  j = 1:n;
+  retval = 1 ./ (j' + j - 1);
 
 endfunction