Mercurial > octave-nkf
view scripts/special-matrix/hilb.m @ 18840:4a4edf0f2077 nkf-ready
fix LLVM 3.4 build (bug #41061)
* configure.ac: Call new functions OCTAVE_LLVM_RAW_FD_OSTREAM_API and
OCTAVE_LLVM_LEGACY_PASSMANAGER_API, check for Verifier.h header file
* m4/acinclude.m4 (OCTAVE_LLVM_RAW_FD_OSTREAM_API): New function to
detect correct raw_fd_ostream API
* m4/acinclude.m4 (OCTAVE_LLVM_LEGACY_PASSMANAGER_API): New function
to detect legacy passmanager API
* libinterp/corefcn/jit-util.h: Use legacy passmanager namespace if
necessary
* libinterp/corefcn/pt-jit.h (class tree_jit): Use legacy passmanager
class if necessary
* libinterp/corefcn/pt-jit.cc: Include appropriate header files
* libinterp/corefcn/pt-jit.cc (tree_jit::initialize): Use legacy
passmanager if necessary
* libinterp/corefcn/pt-jit.cc (tree_jit::optimize): Use correct API
* libinterp/corefcn/jit-typeinfo.cc: Include appropriate header file
author | Stefan Mahr <dac922@gmx.de> |
---|---|
date | Sun, 11 May 2014 02:28:33 +0200 |
parents | d63878346099 |
children | 4197fc428c7d |
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## Copyright (C) 1993-2013 John W. Eaton ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} hilb (@var{n}) ## Return the Hilbert matrix of order @var{n}. The @math{i,j} element ## of a Hilbert matrix is defined as ## @tex ## $$ ## H(i, j) = {1 \over (i + j - 1)} ## $$ ## @end tex ## @ifnottex ## ## @example ## H(i, j) = 1 / (i + j - 1) ## @end example ## ## @end ifnottex ## ## Hilbert matrices are close to being singular which make them difficult to ## invert with numerical routines. ## Comparing the condition number of a random matrix 5x5 matrix with that of ## a Hilbert matrix of order 5 reveals just how difficult the problem is. ## ## @example ## @group ## cond (rand (5)) ## @result{} 14.392 ## cond (hilb (5)) ## @result{} 4.7661e+05 ## @end group ## @end example ## ## @seealso{invhilb} ## @end deftypefn ## Author: jwe function retval = hilb (n) if (nargin != 1) print_usage (); elseif (! isscalar (n)) 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++; endfor endfunction %!assert (hilb (2), [1, 1/2; 1/2, 1/3]) %!assert (hilb (3), [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5]) %!error hilb () %!error hilb (1, 2) %!error <N must be a scalar integer> hilb (ones (2))