Frobenius norm of a null matrix is not zero
Rolf Fabian
Rolf.Fabian at gmx.de
Fri Jan 11 05:03:58 CST 2008
This fixes the problem.
Sorry, no time to send patches etc ....
Rolf Fabian
< r dot fabian at jacobs-university dot de >
## Copyright (C) 1996, 1997, 2007 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/>.
## Undocumented internal function.
## Author: jwe
function retval = __norm__ (x, p)
if (nargin < 1 || nargin > 2)
print_usage ();
endif
if (isempty (x))
retval = [];
return;
endif
if (ndims (x) > 2)
error ("norm: only valid on 2-D objects")
endif
if (nargin == 1)
p = 2;
endif
## Do we have a vector or matrix as the first argument?
if (ndims(x) == 2 && (rows (x) == 1 || columns (x) == 1))
if (ischar (p))
if (strcmp (p, "fro"))
inf_norm = norm (x, "inf");
if ( inf_norm )
retval = inf_norm .* sqrt (sum (abs (x ./ inf_norm) .^ 2));
else
retval = inf_norm;
endif
elseif (strcmp (p, "inf"))
retval = max (abs (x));
else
error ("norm: unrecognized norm");
endif
else
if (p == Inf)
retval = max (abs (x));
elseif (p == -Inf)
retval = min (abs (x));
elseif (p == 1)
retval = sum (abs (x));
elseif (p == 2)
if (iscomplex (x))
x = abs (x);
endif
retval = sqrt (sumsq (x));
else
retval = sum (abs (x) .^ p) ^ (1/p);
endif
endif
else
if (ischar (p))
if (strcmp (p, "fro"))
inf_norm = norm (x, "inf");
if ( inf_norm )
retval = inf_norm .* sqrt (sum (sum (abs (x ./ inf_norm) .^ 2)));
else
retval = inf_norm;
endif
elseif (strcmp (p, "inf"))
retval = max (sum (abs (x.')));
else
error ("norm: unrecognized vector norm");
endif
else
if (p == 1)
retval = max (sum (abs (x)));
elseif (p == 2)
s = svd (x);
retval = s (1);
elseif (p == Inf)
retval = max (sum (abs (x.')));
else
error ("norm: unrecognized matrix norm");
endif
endif
endif
endfunction
Jean-Francois Cardoso wrote:
>
> --------
> Bug report for Octave 3.0.0 configured for i386-apple-darwin8.11.1
>
> Description:
> -----------
>
> The Frobenius norm of a null matrix is reported to be NaN
> and a warning is raised.
>
> Repeat-By:
> ---------
>
> norm(zeros(5), "fro" )
>
>
> Configuration (please do not edit this section):
> -----------------------------------------------
>
> uname output: Darwin rajif 8.11.1 Darwin Kernel Version 8.11.1: Wed
> Oct 10 18:23:28 PDT 2007; root:xnu-792.25.20~1/RELEASE_I386 i386 i386
> configure opts: 'LDFLAGS=-L/usr/local/lib'
> 'CPPFLAGS=-I/usr/local/include/readline'
> Fortran compiler: gfortran
> FFLAGS: -O -mieee-fp
> F2C: @F2C@
> F2CFLAGS: @F2CFLAGS@
> FLIBS: -L/usr/local/lib
> -L/usr/local/lib/gcc/i386-apple-darwin8.8.1/4.2.0
> -L/usr/local/lib/gcc/i386-apple-darwin8.8.1/4.2.0/../../.. -lz -lm
> -lgfortranbegin -lgfortran
> CPPFLAGS: -I/usr/local/include/readline -I/usr/local/include
> INCFLAGS: -I. -I. -I./liboctave -I./src -I./libcruft/misc
> C compiler: gcc, version 4.0.1 (Apple Computer, Inc. build 5367)
> CFLAGS: -g -O2
> CPICFLAG: -fPIC
> C++ compiler: g++, version 4.0.1
> CXXFLAGS: -g -O2
> CXXPICFLAG: -fPIC
> LD_CXX: g++
> LDFLAGS: -L/usr/local/lib
> LIBFLAGS: -L.
> RLD_FLAG:
> BLAS_LIBS: -Wl,-framework -Wl,vecLib
> FFTW_LIBS: -lfftw3
> LIBS: -lreadline -lncurses -lz -lm
> LEXLIB:
> LIBGLOB:
> SED: /usr/local/bin/sed
> DEFS:
>
> -DPACKAGE_NAME="" -DPACKAGE_TARNAME="" -DPACKAGE_VERSION=""
> -DPACKAGE_STRING="" -DPACKAGE_BUGREPORT="" -DOCTAVE_SOURCE=1
> -D_GNU_SOURCE=1 -DSTDC_HEADERS=1 -DHAVE_SYS_TYPES_H=1
> -DHAVE_SYS_STAT_H=1
> -DHAVE_STDLIB_H=1 -DHAVE_STRING_H=1 -DHAVE_MEMORY_H=1
> -DHAVE_STRINGS_H=1
> -DHAVE_INTTYPES_H=1 -DHAVE_STDINT_H=1 -DHAVE_UNISTD_H=1 -DSEPCHAR=':'
> -DSEPCHAR_STR=":" -D__NO_MATH_INLINES=1
> -DCXX_NEW_FRIEND_TEMPLATE_DECL=1
> -DCXX_ISO_COMPLIANT_LIBRARY=1 -DCXX_ABI=gnu_v3
> -DCXX_PREPENDS_UNDERSCORE=1
> -DHAVE_LIBM=1 -DHAVE_QHULL=1 -DHAVE_PCRE=1 -DHAVE_REGEXEC=1
> -DHAVE_REGEX=1 -DHAVE_ZLIB_H=1 -DHAVE_ZLIB=1 -DHAVE_FFTW3=1
> -DHAVE_GLPK_H=1 -DHAVE_GLPK=1 -DHAVE_IEEE754_DATA_FORMAT=1
> -DF77_FUNC(name,NAME)=name ## _ -DF77_FUNC_(name,NAME)=name ## _
> -DHAVE_BLAS=1 -DHAVE_GETHOSTNAME=1 -DHAVE_GETPWNAM=1 -DHAVE_DEV_T=1
> -DHAVE_INO_T=1 -DHAVE_NLINK_T=1 -DHAVE_NLINK_T=1 -DHAVE_LONG_LONG_INT=1
> -DHAVE_UNSIGNED_LONG_LONG_INT=1 -DHAVE_SIGSET_T=1 -DHAVE_SIG_ATOMIC_T=1
> -DSIZEOF_SHORT=2 -DSIZEOF_INT=4 -DSIZEOF_LONG=4 -DSIZEOF_LONG_LONG=8
> -DHAVE_ALLOCA_H=1 -DHAVE_ALLOCA=1 -DNPOS=std::string::npos
> -DHAVE_PLACEMENT_DELETE=1 -DHAVE_DYNAMIC_AUTO_ARRAYS=1 -DSTDC_HEADERS=1
> -DHAVE_DIRENT_H=1 -DTIME_WITH_SYS_TIME=1 -DHAVE_SYS_WAIT_H=1
> -DHAVE_ASSERT_H=1 -DHAVE_CURSES_H=1 -DHAVE_DLFCN_H=1 -DHAVE_FCNTL_H=1
> -DHAVE_FLOAT_H=1 -DHAVE_GRP_H=1 -DHAVE_INTTYPES_H=1 -DHAVE_LIMITS_H=1
> -DHAVE_LOCALE_H=1 -DHAVE_MEMORY_H=1 -DHAVE_NCURSES_H=1 -DHAVE_POLL_H=1
> -DHAVE_PWD_H=1 -DHAVE_STDINT_H=1 -DHAVE_STDLIB_H=1 -DHAVE_STRING_H=1
> -DHAVE_SYS_IOCTL_H=1 -DHAVE_SYS_PARAM_H=1 -DHAVE_SYS_POLL_H=1
> -DHAVE_SYS_RESOURCE_H=1 -DHAVE_SYS_SELECT_H=1 -DHAVE_SYS_STAT_H=1
> -DHAVE_SYS_TIME_H=1 -DHAVE_SYS_TIMES_H=1 -DHAVE_SYS_TYPES_H=1
> -DHAVE_SYS_UTSNAME_H=1 -DHAVE_TERMCAP_H=1 -DHAVE_UNISTD_H=1
> -DHAVE_UTIME_H=1 -DHAVE_SSTREAM=1 -DHAVE_SGTTY_H=1 -DHAVE_GLOB_H=1
> -DHAVE_FNMATCH_H=1 -DHAVE_FNMATCH=1 -DHAVE_GLOB=1 -DHAVE_ATEXIT=1
> -DHAVE_BASENAME=1 -DHAVE_BCOPY=1 -DHAVE_BZERO=1 -DHAVE_CHMOD=1
> -DHAVE_DUP2=1 -DHAVE_ENDGRENT=1 -DHAVE_ENDPWENT=1 -DHAVE_EXECVP=1
> -DHAVE_FCNTL=1 -DHAVE_FORK=1 -DHAVE_GETCWD=1 -DHAVE_GETEGID=1
> -DHAVE_GETEUID=1 -DHAVE_GETGID=1 -DHAVE_GETGRENT=1 -DHAVE_GETGRGID=1
> -DHAVE_GETGRNAM=1 -DHAVE_GETPGRP=1 -DHAVE_GETPID=1 -DHAVE_GETPPID=1
> -DHAVE_GETPWENT=1 -DHAVE_GETPWUID=1 -DHAVE_GETTIMEOFDAY=1
> -DHAVE_GETUID=1
> -DHAVE_GETWD=1 -DHAVE_KILL=1 -DHAVE_LGAMMA=1 -DHAVE_LINK=1
> -DHAVE_LOCALTIME_R=1 -DHAVE_LSTAT=1 -DHAVE_MEMMOVE=1 -DHAVE_MKDIR=1
> -DHAVE_MKFIFO=1 -DHAVE_MKSTEMP=1 -DHAVE_PIPE=1 -DHAVE_POLL=1
> -DHAVE_PUTENV=1 -DHAVE_RAISE=1 -DHAVE_READLINK=1 -DHAVE_REALPATH=1
> -DHAVE_RENAME=1 -DHAVE_RINDEX=1 -DHAVE_RMDIR=1 -DHAVE_ROUND=1
> -DHAVE_SELECT=1 -DHAVE_SETGRENT=1 -DHAVE_SETLOCALE=1 -DHAVE_SETPWENT=1
> -DHAVE_SETVBUF=1 -DHAVE_SIGACTION=1 -DHAVE_SIGLONGJMP=1
> -DHAVE_SIGPENDING=1
> -DHAVE_SIGPROCMASK=1 -DHAVE_SIGSUSPEND=1 -DHAVE_SNPRINTF=1
> -DHAVE_STAT=1
> -DHAVE_STRCASECMP=1 -DHAVE_STRDUP=1 -DHAVE_STRERROR=1
> -DHAVE_STRNCASECMP=1
> -DHAVE_STRPTIME=1 -DHAVE_STRSIGNAL=1 -DHAVE_SYMLINK=1 -DHAVE_TEMPNAM=1
> -DHAVE_TGAMMA=1 -DHAVE_UMASK=1 -DHAVE_UNAME=1 -DHAVE_UNLINK=1
> -DHAVE_USLEEP=1 -DHAVE_UTIME=1 -DHAVE_VFPRINTF=1 -DHAVE_VSPRINTF=1
> -DHAVE_VSNPRINTF=1 -DHAVE_WAITPID=1 -DHAVE_STRFTIME=1
> -DOCTAVE_HAVE_BROKEN_STRPTIME=1 -DHAVE_DYLD_API=1
> -DENABLE_DYNAMIC_LINKING=1 -DHAVE_TIMEVAL=1 -DHAVE_FINITE=1
> -DHAVE_ISNAN=1 -DHAVE_ISINF=1 -DHAVE_COPYSIGN=1 -DHAVE_DECL_SIGNBIT=1
> -DHAVE_ACOSH=1 -DHAVE_ASINH=1 -DHAVE_ATANH=1 -DHAVE_ERF=1 -DHAVE_ERFC=1
> -DHAVE_EXP2=1 -DHAVE_LOG2=1 -DHAVE_STRUCT_STAT_ST_BLKSIZE=1
> -DHAVE_STRUCT_STAT_ST_BLOCKS=1 -DHAVE_STRUCT_STAT_ST_RDEV=1
> -DHAVE_STRUCT_TM_TM_ZONE=1 -DHAVE_TM_ZONE=1 -DUSE_READLINE=1
> -DEXCEPTION_IN_MATH=1 -DRETSIGTYPE=void -DHAVE_DECL_SYS_SIGLIST=1
> -DHAVE_POSIX_SIGNALS=1 -DRETSIGTYPE_IS_VOID=1 -DHAVE_GETRUSAGE=1
> -DHAVE_TIMES=1 -DYYTEXT_POINTER=1 -DGNUPLOT_BINARY="gnuplot"
>
> User-preferences (please do not edit this section):
> --------------------------------------------------
>
> EDITOR = emacs
> EXEC_PATH =
> /usr/local/libexec/octave/3.0.0/site/exec/i386-apple-darwin8.11.1:/usr/local/libexec/octave/api-v32/site/exec/i386-apple-darwin8.11.1:/usr/local/libexec/octave/site/exec/i386-apple-darwin8.11.1:/usr/local/libexec/octave/3.0.0/exec/i386-apple-darwin8.11.1:/usr/local/bin:/sw/bin:/sw/sbin:/bin:/sbin:/usr/bin:/usr/sbin:/usr/X11R6/bin:/usr/local/bin:/Users/cardoso/bin:/Users/cardoso/bin:/Users/cardoso/local/bin:/Volumes/partage/Soft/Astro/Healpix_2.01/src/cxx/generic_gcc/bin
> IMAGE_PATH = .:/usr/local/share/octave/3.0.0/imagelib
> PAGER = less
> PS1 = \s:\#>
> PS2 = >
> PS4 = +
> beep_on_error = 0
> completion_append_char =
> crash_dumps_octave_core = 1
> echo_executing_commands = 0
> fixed_point_format = 0
> gnuplot_binary = /usr/local/bin/gnuplot
> gnuplot_command_end =
>
> gnuplot_command_plot = pl
> gnuplot_command_replot = rep
> gnuplot_command_splot = sp
> gnuplot_command_title = t
> gnuplot_command_using = u
> gnuplot_command_with = w
> history_file = /Users/cardoso/.octave_hist
> history_size = 1024
> ignore_function_time_stamp = system
> info_file = /usr/local/share/info/octave.info
> info_program = info
> makeinfo_program = makeinfo
> max_recursion_depth = 256
> output_max_field_width = 5
> output_precision = 5
> page_output_immediately = 1
> page_screen_output = 0
> print_answer_id_name = 1
> print_empty_dimensions = 1
> save_precision = 16
> saving_history = 1
> sighup_dumps_octave_core = 1
> sigterm_dumps_octave_core = 1
> silent_functions = 0
> split_long_rows = 1
> string_fill_char =
> struct_levels_to_print = 2
> suppress_verbose_help_message = 0
> _______________________________________________
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>
>
-----
Rolf Fabian
<r dot fabian at jacobs-university dot de>
--
View this message in context: http://www.nabble.com/Frobenius-norm-of-a-null-matrix-is-not-zero-tp14484096p14753647.html
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