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compute_normal_form.cpp 10.77 KiB
/*
COMPUTE_NORMAL_FORM
Hermite and Smith normal forms of integer matrices.
Implementation: Dense matrix with GMP-library's mpz_t elements to
hold huge integers.
Algorithm: Kannan - Bachem algorithm with improvement by
Chou and Collins. Expects a large number of unit invariant
factors and takes advantage of them as they appear.
References:
[1] Ravindran Kannan, Achim Bachem:
"Polynomial algorithms for computing the Smith and Hermite normal
forms of an integer matrix",
SIAM J. Comput., vol. 8, no. 5, pp. 499-507, 1979.
[2] Tsu-Wu J.Chou, George E. Collins:
"Algorithms for the solution of systems of linear Diophantine
equations",
SIAM J. Comput., vol. 11, no. 4, pp. 687-708, 1982.
[3] GMP homepage http://www.swox.com/gmp/
[4] GNU gmp page http://www.gnu.org/software/gmp/
Copyright (C) 3.11.2003 Saku Suuriniemi TUT/CEM
This program 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 2 of the License, or
any later version.
This program 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 this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Saku Suuriniemi, TUT/Electromagetics
P.O.Box 692, FIN-33101 Tampere, Finland
saku.suuriniemi@tut.fi
$Id: compute_normal_form.c,v 1.1 2009-03-30 14:10:57 matti Exp $
*/
#include<stdlib.h>
#include<stdio.h>
#include<string.h>
#include"gmp_matrix_io.h"
#include"gmp_normal_form.h"
typedef enum {HERMITE, SMITH} nf_flag;
typedef enum {NOT_WANTED, WANTED} w_flag;
static int nf_parse_options(int arg_counter, char ** args,
char ** p_infile_name, char ** p_outfile_name,
nf_flag * p_normal_form_requested,
inverted_flag * p_left_inverted,
inverted_flag * p_right_inverted,
w_flag * p_help_wanted,
w_flag * p_verbose_wanted)
{
size_t ind1, ind2;
size_t outfilename_length;
/* If no infile is specified, the error is indisputable.
=> Print help and exit. Infile should be the last argument. */
if(strncmp(args[arg_counter-1], "-", 1) == 0)
{
*(p_help_wanted) = WANTED;
return EXIT_SUCCESS;
}
/* Should I find arguments? */
if(arg_counter > 2)
{
for(ind1 = 1; ind1 < arg_counter-1; ind1++)
{
/* No multiple infile names ! */
if(strncmp(args[ind1], "-", 1) != 0)
{
*(p_help_wanted) = WANTED;
return EXIT_SUCCESS;
}
/* Parse the option letters after '-' one by one */
for(ind2 = 1; ind2 < strlen(args[ind1]); ind2++)
{
switch(args[ind1][ind2])
{
case 'h':
*(p_help_wanted) = WANTED;
return EXIT_SUCCESS;
break;
case 'H':
*(p_normal_form_requested) = HERMITE;
break;
case 'S':
*(p_normal_form_requested) = SMITH;
break;
case 'l':
*(p_left_inverted) = INVERTED;
break;
case 'r':
*(p_right_inverted) = INVERTED;
break;
case 'v':
*(p_verbose_wanted) = WANTED;
break;
}
}
}
}
/* Get the infile name */
* p_infile_name = (char *) calloc(strlen(args[arg_counter-1]) + 1,
sizeof(char));
if(* p_infile_name == NULL)
{
return EXIT_FAILURE;
}
strcpy(* p_infile_name, args[arg_counter-1]);
/* Create the outfile name */
outfilename_length = strcspn( * p_infile_name, ".");
* p_outfile_name = (char *) calloc(outfilename_length + 1,
sizeof(char));
if( * p_outfile_name == NULL)
{
free( * p_infile_name);
return EXIT_FAILURE;
}
strncpy(* p_outfile_name, * p_infile_name, outfilename_length); (* p_outfile_name)[outfilename_length] = '\0';
return EXIT_SUCCESS;
}
static int nf_print_help(void)
{
fprintf(stdout, "Usage: compute_normal_form [-hHSlrv] infile\n");
fprintf(stdout, "\n");
fprintf(stdout, "Description: Compute the Hermite/Smith normal form of an integer matrix.\n");
fprintf(stdout, "\n");
fprintf(stdout, "Input: \"infile\" is an ascii file, which contains an integer matrix\n");
fprintf(stdout, " in the sparse coordinate format:\n");
fprintf(stdout, "\n");
fprintf(stdout, " # All comments before the data\n");
fprintf(stdout, " rows columns nonzeros\n");
fprintf(stdout, " row1 col1 value1\n");
fprintf(stdout, " row2 col2 value2\n");
fprintf(stdout, " ...\n");
fprintf(stdout, "\n");
fprintf(stdout, " No multiple infiles, please.\n");
fprintf(stdout, "\n");
fprintf(stdout, "Options: -h This help\n");
fprintf(stdout, " -H Compute the Hermite normal form (default)\n");
fprintf(stdout, " -S Compute the Smith normal form\n");
fprintf(stdout, " -l Left factor inverted (A = P^(T)LU instead of PA = LU for Hermite, \n");
fprintf(stdout, " U^(-1)A = SV instead of A = USV for Smith)\n");
fprintf(stdout, " -r Right factor inverted (PAU^(-1) = L instead of PA = LU for Hermite, \n");
fprintf(stdout, " AV^(-1) = US instead of A = USV for Smith)\n");
fprintf(stdout, " -v Verbose. Print the matrix and the decomposition to sdtout, \n");
fprintf(stdout, " so that the user may check that the problem is read and written\n");
fprintf(stdout, " correctly.\n");
fprintf(stdout, "\n");
fprintf(stdout, "Output: For inpur matrix in e.g. \"infile.coord\", writes ascii files\n");
fprintf(stdout, " \"infile.left\", \"infile.can\", and \"infile.right\", which \n");
fprintf(stdout, " contain the left factor, canonical form, and the right factor, \n");
fprintf(stdout, " respectively. The matrices are written in the sparse coordinate\n");
fprintf(stdout, " format.\n");
fprintf(stdout, "\n");
fprintf(stdout, "Note: The return values may be big enough to not fit the standard integer types.\n");
fprintf(stdout, "\n");
fprintf(stdout, "Copyright (C) 3.11.2003 Saku Suuriniemi, Tampere University of Technology/Electromagnetics\n");
fprintf(stdout, " P.O.Box 692, FIN-33101 Tampere, Finland. saku.suuriniemi@tut.fi\n");
fprintf(stdout, "\n");
fprintf(stdout, "Licenced under GNU General Public Licence (GPL) version 2 or later, ABSOLUTELY NO WARRANTY.\n");
return EXIT_SUCCESS;
}
static char* append_suffix(const char * file_base_name, const char * suffix)
{
char * filename;
if((file_base_name == NULL) || (suffix == NULL))
{
return NULL;
}
filename =
(char*) calloc(strlen(file_base_name)+strlen(suffix)+2,
sizeof(char));
if(filename == NULL)
{
return NULL;
}
strcpy(filename, file_base_name);
strcat(filename, "."); strcat(filename, suffix);
return filename;
}
int main(int argc, char * argv[])
{
char * infile_name;
char * file_base_name;
char * outfile_name;
gmp_matrix * A;
gmp_normal_form * normal_form;
w_flag help_wanted;
w_flag verbose_wanted;
nf_flag normal_form_requested;
inverted_flag left_inverted;
inverted_flag right_inverted;
if(argc == 1)
{
fprintf(stdout, "Please try \"compute_normal_form -h\" for help.\n");
return EXIT_SUCCESS;
}
/* Default settings before option parsing */
normal_form_requested = HERMITE;
left_inverted = NOT_INVERTED;
right_inverted = NOT_INVERTED;
help_wanted = NOT_WANTED;
verbose_wanted = NOT_WANTED;
if( nf_parse_options(argc, argv,
&infile_name, &file_base_name,
&normal_form_requested,
&left_inverted, &right_inverted,
&help_wanted,
&verbose_wanted)
== EXIT_FAILURE )
{
return EXIT_FAILURE;
}
/* In this case, no dynamical memory has been allocated by
nf_parse_options ! */
if(help_wanted == WANTED)
{
return nf_print_help();
}
if(verbose_wanted == WANTED)
{
fprintf(stdout, "Computing ");
if(normal_form_requested == HERMITE)
{
fprintf(stdout, "Hermite");
}
else
{
fprintf(stdout, "Smith");
}
fprintf(stdout, " normal form\n");
if(left_inverted == INVERTED)
{
fprintf(stdout, "The left factor will be inverted.\n");
}
if(right_inverted == INVERTED)
{
fprintf(stdout, "The right factor will be inverted.\n"); }
fprintf(stdout, "Matrix read from file %s\n", infile_name);
}
/*************************************************************/
/* We have all we need to get to the computational business: */
/*************************************************************/
/* Read the matrix */
A = gmp_matrix_read_coord(infile_name);
free(infile_name);
if(verbose_wanted == WANTED)
{
fprintf(stdout, "Input matrix:\n");
gmp_matrix_fprintf(stdout, A);
}
/* Compute the requested normal form */
switch(normal_form_requested)
{
case SMITH:
normal_form = create_gmp_Smith_normal_form(A, left_inverted, right_inverted);
break;
default:
normal_form = create_gmp_Hermite_normal_form(A, left_inverted, right_inverted);
break;
}
if(verbose_wanted == WANTED)
{
fprintf(stdout, "Left factor:\n");
gmp_matrix_fprintf(stdout, normal_form->left);
fprintf(stdout, "Canonical form:\n");
gmp_matrix_fprintf(stdout, normal_form->canonical);
fprintf(stdout, "Right factor:\n");
gmp_matrix_fprintf(stdout, normal_form->right);
}
/* Save the result to the output files */
outfile_name = append_suffix(file_base_name, "left");
if( gmp_matrix_write_coord(outfile_name, normal_form -> left)
== EXIT_SUCCESS)
{
if(verbose_wanted == WANTED)
fprintf(stdout, "Left factor successfully writen to file %s\n", outfile_name);
}
free(outfile_name);
outfile_name = append_suffix(file_base_name, "can");
if( gmp_matrix_write_coord(outfile_name, normal_form -> canonical)
== EXIT_SUCCESS)
{
if(verbose_wanted == WANTED)
fprintf(stdout, "Canonical form successfully writen to file %s\n", outfile_name);
}
free(outfile_name);
outfile_name = append_suffix(file_base_name, "right");
if( gmp_matrix_write_coord(outfile_name, normal_form -> right)
== EXIT_SUCCESS)
{
if(verbose_wanted == WANTED)
fprintf(stdout, "Right factor successfully writen to file %s\n", outfile_name);
}
free(outfile_name);
free(file_base_name);
destroy_gmp_normal_form(normal_form);
return EXIT_SUCCESS;
}