--- /dev/null
+// vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+//
+// Trabajo Práctico I de Análisis Numérico I
+// Este programa resuelve un sistema de ecuaciones lineales ralo
+// resultante de la discretización mediante diferencias finitas
+// de ecuaciones diferenciales.
+// Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+//
+// Este programa es Software Libre; usted puede redistribuirlo
+// y/o modificarlo bajo los términos de la "GNU General Public
+// License" como lo publica la "FSF Free Software Foundation",
+// o (a su elección) de cualquier versión posterior.
+//
+// Este programa es distribuido con la esperanza de que le será
+// útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+// implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+// particular. Vea la "GNU General Public License" para más
+// detalles.
+//
+// Usted debe haber recibido una copia de la "GNU General Public
+// License" junto con este programa, si no, escriba a la "FSF
+// Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+// Boston, MA 02111-1307, USA.
+//
+// $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/77891.cpp $
+// $Date: 2002-10-13 23:38:45 -0300 (dom, 13 oct 2002) $
+// $Rev: 9 $
+// $Author: luca $
+//
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+// Tipos de datos.
+typedef unsigned int Indice;
+typedef float Numero;
+typedef struct {
+ Indice N;
+ Numero w;
+ Numero rtol;
+ Numero TS;
+ Numero TO;
+ Numero TN;
+ Numero TE;
+ Numero* X;
+} Datos;
+
+// Constantes.
+const Numero DEFAULT_W = 1.0,
+ DEFAULT_RTOL = 0.01,
+ DEFAULT_T = 1.0;
+
+// Calcula la iteración para un nodo.
+Numero procesarNodo( Datos&, Indice );
+
+// Calcula la iteración para un nodo dependiendo del tipo de nodo.
+Numero procesarNodo( Datos&, Indice, bool, bool, bool, bool, Numero = 0 );
+
+// Calcula la norma 2 de un vector.
+Numero norma2( Numero*, Indice );
+
+// Imprime un vector por la salida estándar.
+void imprimirVector( Indice, Numero* );
+
+// Imprime un vector por la salida estándar.
+void imprimirVector( Numero*, Indice );
+
+// Resuelve el sistema de ecuaciones lineales por el método S.O.R.
+// (o Gasuss-Seidel si w=1).
+void resolver( Datos& );
+
+int main( int argc, char* argv[] ) {
+
+ // Se fija que tenga los argumentos necesarios para correr.
+ if ( argc < 2 ) {
+ printf( "Faltan argumentos. Modo de uso:\n" );
+ printf( "\t%s N w RTOL TS TO TN TE\n", argv[0] );
+ printf( "Desde w en adelante son opcionales. Los valores por defecto son:\n" );
+ printf( "\tw = %f\n", DEFAULT_W );
+ printf( "\tRTOL = %f\n", DEFAULT_RTOL );
+ printf( "\tTS = TO = TN = TE = %f\n", DEFAULT_T );
+ return EXIT_FAILURE;
+ }
+
+ // Se inicializan los datos.
+ Datos D;
+ D.N = Indice( atol( argv[1] ) );
+ if ( D.N < 3 ) {
+ printf( "N Debe ser un entero mayor o igual a 3\n" );
+ return EXIT_FAILURE;
+ }
+ D.w = DEFAULT_W;
+ D.rtol = DEFAULT_RTOL;
+ D.TS =
+ D.TO =
+ D.TN =
+ D.TE = DEFAULT_T;
+ // Se aloca uno más de lo necesario para usar el rango [1,n]
+ D.X = new Numero[Indice(pow(D.N-1,2))+1];
+
+ // Si se pasaron datos como argumento, se los va agregando.
+ switch ( argc ) {
+ case 8: D.TE = Numero( atof( argv[7] ) );
+ case 7: D.TN = Numero( atof( argv[6] ) );
+ case 6: D.TO = Numero( atof( argv[5] ) );
+ case 5: D.TS = Numero( atof( argv[4] ) );
+ case 4: D.rtol = Numero( atof( argv[3] ) );
+ case 3: D.w = Numero( atof( argv[2] ) );
+ }
+
+ resolver( D );
+
+ delete D.X;
+
+ return EXIT_SUCCESS;
+
+}
+
+Numero procesarNodo( Datos& D, Indice i ) {
+
+ Indice N = D.N;
+
+ // Si es el primero, es SO.
+ if ( i == 1 )
+ return procesarNodo( D, i,
+ false, false, true, true,
+ D.TS + D.TO );
+
+ // Si es N - 1 es NO.
+ if ( i == ( N - 1 ) )
+ return procesarNodo( D, i,
+ false, true, false, true,
+ D.TN + D.TO );
+
+ // Si es N² - 3N + 3 es SE.
+ if ( i == ( N*N - 3*N + 3 ) )
+ return procesarNodo( D, i,
+ true, false, true, false,
+ D.TS + D.TE );
+
+ // Si es N² - 2N + 1 es NE.
+ if ( i == ( N*N - 2*N + 1 ) )
+ return procesarNodo( D, i,
+ true, true, false, false,
+ D.TN + D.TE );
+
+ // Si pertenece al intervalo [2;N-1] es O.
+ if ( ( 1 < i ) && ( i < ( N - 1 ) ) )
+ return procesarNodo( D, i,
+ false, true, true, true,
+ D.TO );
+
+ // Si pertenece al intervalo [N² - 3N + 3;N² - 2N + 1] es E.
+ if ( ( ( N*N - 3*N + 3 ) < i ) && ( i < ( N*N - 2*N + 1 ) ) )
+ return procesarNodo( D, i,
+ true, true, true, false,
+ D.TE );
+
+ // Si i - 1 es múltiplo de N - 1 (y no es NE, SE, NO, SO) es S.
+ if ( ( ( i - 1 ) % ( N - 1 ) ) == 0 )
+ return procesarNodo( D, i,
+ true, false, true, true,
+ D.TS );
+
+ // Si i es múltiplo de N - 1 (y no es NE, SE, NO, SO) es N.
+ if ( ( i % ( N - 1 ) ) == 0 )
+ return procesarNodo( D, i,
+ true, true, false, true,
+ D.TN );
+
+ return procesarNodo( D, i, true, true, true, true );
+
+}
+
+Numero procesarNodo( Datos& D, Indice i,
+ bool i_n1, bool i_1, bool i1, bool in_1,
+ Numero b ) {
+
+ Numero x = 0,
+ Xo = D.X[i];
+
+ // Voy sumando los elementos que corresponden.
+ if ( i_n1 )
+ x += D.X[i-D.N+1];
+ if ( i_1 )
+ x += D.X[i-1];
+ if ( i1 )
+ x += D.X[i+1];
+ if ( in_1 )
+ x += D.X[i+D.N-1];
+
+ // Calculo el elemento i.
+ D.X[i] = ( 1 - D.w ) * D.X[i] + ( b + x ) * D.w / 4;
+
+ // Devuelve parte de la sumatoria para calcular la norma 2.
+ return pow( D.X[i] - Xo, 2 );
+
+}
+
+Numero norma2( Numero* X, Indice n ) {
+
+ Numero sum = 0;
+
+ for ( Indice i = 1; i <= n; i++ )
+ sum += pow( X[i], 2 );
+
+ return sqrt( sum );
+
+}
+
+void imprimirVector( Indice n, Numero* X ) {
+
+ for ( Indice i = 1; i <= n; i++ )
+ printf( "%.7e%s", X[i], ( i == n ) ? "\n" : " " );
+
+}
+
+void resolver( Datos& D ) {
+
+ Indice ite = 0,
+ n = Indice( pow( D.N - 1, 2) );
+ Numero r = D.rtol + 1,
+ Ek = 0,
+ Ek_1 = 0;
+
+ // Imprime datos iniciales.
+ // Formato de salida:
+ // iteración R S <vector X>
+ // (si no se puede calcular S, se muestra 0)
+ printf( "%d %.2e 0.00000000 ", ite, r );
+ imprimirVector( n, D.X );
+
+ while ( r > D.rtol ) {
+
+ for ( Indice i = 1; i <= n; i++ )
+ Ek += procesarNodo( D, i );
+ Ek = sqrt( Ek );
+ r = Ek / norma2( D.X, n );
+ printf( "%d %.2e %.8f ", ++ite, r, Ek_1 ? ( Ek / Ek_1 ) : 0 );
+ imprimirVector( n, D.X );
+ Ek_1 = Ek;
+ Ek = 0;
+
+ }
+
+}
--- /dev/null
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--- /dev/null
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+distribute and/or modify the software.
+
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+that everyone understands that there is no warranty for this free
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+
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+
+ The precise terms and conditions for copying, distribution and
+modification follow.
+\f
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. This License applies to any program or other work which contains
+a notice placed by the copyright holder saying it may be distributed
+under the terms of this General Public License. The "Program", below,
+refers to any such program or work, and a "work based on the Program"
+means either the Program or any derivative work under copyright law:
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+
+Activities other than copying, distribution and modification are not
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+running the Program is not restricted, and the output from the Program
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+Whether that is true depends on what the Program does.
+
+ 1. You may copy and distribute verbatim copies of the Program's
+source code as you receive it, in any medium, provided that you
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+along with the Program.
+
+You may charge a fee for the physical act of transferring a copy, and
+you may at your option offer warranty protection in exchange for a fee.
+
+ 2. You may modify your copy or copies of the Program or any portion
+of it, thus forming a work based on the Program, and copy and
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+above, provided that you also meet all of these conditions:
+
+ a) You must cause the modified files to carry prominent notices
+ stating that you changed the files and the date of any change.
+
+ b) You must cause any work that you distribute or publish, that in
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+ part thereof, to be licensed as a whole at no charge to all third
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+
+ c) If the modified program normally reads commands interactively
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+ the Program is not required to print an announcement.)
+\f
+These requirements apply to the modified work as a whole. If
+identifiable sections of that work are not derived from the Program,
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+on the Program, the distribution of the whole must be on the terms of
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+entire whole, and thus to each and every part regardless of who wrote it.
+
+Thus, it is not the intent of this section to claim rights or contest
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+
+In addition, mere aggregation of another work not based on the Program
+with the Program (or with a work based on the Program) on a volume of
+a storage or distribution medium does not bring the other work under
+the scope of this License.
+
+ 3. You may copy and distribute the Program (or a work based on it,
+under Section 2) in object code or executable form under the terms of
+Sections 1 and 2 above provided that you also do one of the following:
+
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+compelled to copy the source along with the object code.
+\f
+ 4. You may not copy, modify, sublicense, or distribute the Program
+except as expressly provided under this License. Any attempt
+otherwise to copy, modify, sublicense or distribute the Program is
+void, and will automatically terminate your rights under this License.
+However, parties who have received copies, or rights, from you under
+this License will not have their licenses terminated so long as such
+parties remain in full compliance.
+
+ 5. You are not required to accept this License, since you have not
+signed it. However, nothing else grants you permission to modify or
+distribute the Program or its derivative works. These actions are
+prohibited by law if you do not accept this License. Therefore, by
+modifying or distributing the Program (or any work based on the
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+all its terms and conditions for copying, distributing or modifying
+the Program or works based on it.
+
+ 6. Each time you redistribute the Program (or any work based on the
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+
+ 7. If, as a consequence of a court judgment or allegation of patent
+infringement or for any other reason (not limited to patent issues),
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+refrain entirely from distribution of the Program.
+
+If any portion of this section is held invalid or unenforceable under
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+
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+implemented by public license practices. Many people have made
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+
+This section is intended to make thoroughly clear what is believed to
+be a consequence of the rest of this License.
+\f
+ 8. If the distribution and/or use of the Program is restricted in
+certain countries either by patents or by copyrighted interfaces, the
+original copyright holder who places the Program under this License
+may add an explicit geographical distribution limitation excluding
+those countries, so that distribution is permitted only in or among
+countries not thus excluded. In such case, this License incorporates
+the limitation as if written in the body of this License.
+
+ 9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation. If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
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+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
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+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+\f
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ 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
+ (at your option) 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
--- /dev/null
+#
+# Este programa resuelve un sistema de ecuaciones lineales ralo
+# resultante de la discretización mediante diferencias finitas
+# de ecuaciones diferenciales.
+# Copyright (C) 2002 Leandro Lucarella
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/Makefile $
+# $Date: 2002-10-17 15:46:08 -0300 (jue, 17 oct 2002) $
+# $Rev: 18 $
+# $Author: luca $
+#
+
+CPP_OPTS=-g3 -Wall
+LIBS=-lm
+
+all: ca4.txt ca8.txt ca16.txt ca32.txt cb4.txt cb8.txt cb16.txt cb32.txt eg.txt fg.txt \
+ d4.eps d8.eps d16.eps d32.eps eg.eps fg.eps grilla.eps regiones.eps mother.eps \
+ informe.ps informe.pdf informe.tex
+
+77891: 77891.cpp
+ c++ $(CPP_OPTS) $(LIBS) -o 77891 77891.cpp
+
+calc.sh: 77891 resultado.awk
+
+ca4.txt: calc.sh
+ ./calc.sh
+
+ca8.txt: calc.sh
+ ./calc.sh
+
+ca16.txt: calc.sh
+ ./calc.sh
+
+ca32.txt: calc.sh
+ ./calc.sh
+
+cb4.txt: calc.sh
+ ./calc.sh
+
+cb8.txt: calc.sh
+ ./calc.sh
+
+cb16.txt: calc.sh
+ ./calc.sh
+
+cb32.txt: calc.sh
+ ./calc.sh
+
+plot.sh: d.gnuplot efg.gnuplot cb4.txt cb8.txt cb16.txt cb32.txt eg.txt fg.txt
+
+d4.eps: plot.sh
+ ./plot.sh
+
+d8.eps: plot.sh
+ ./plot.sh
+
+d16.eps: plot.sh
+ ./plot.sh
+
+d32.eps: plot.sh
+ ./plot.sh
+
+eg.eps: plot.sh
+ ./plot.sh
+
+fg.eps: plot.sh
+ ./plot.sh
+
+grilla.eps: plot.sh grilla.xcf
+ ./plot.sh
+
+regiones.eps: plot.sh regiones.xcf
+ ./plot.sh
+
+mother.eps: plot.sh mother.xcf
+ ./plot.sh
+
+informe.ps: informe.lyx grilla.eps d4.eps d8.eps d16.eps d32.eps eg.eps fg.eps \
+ regiones.eps mother.eps
+ lyx -e ps informe.lyx
+
+informe.pdf: informe.lyx grilla.eps d4.eps d8.eps d16.eps d32.eps eg.eps fg.eps \
+ regiones.eps mother.eps
+ lyx -e pdf informe.lyx
+
+informe.tex: informe.lyx
+ lyx -e latex informe.lyx
+
+clean-plot:
+ rm -f *.eps
+
+clean-informe:
+ rm -f informe.ps informe.tex informe.pdf
+
+clean: clean-plot clean-informe
+ rm -f *.o 77891 ca*.txt cb*.txt ?g.txt *~ parte2.txt isolineas.txt
--- /dev/null
+vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+
+Trabajo Práctico I de Análisis Numérico I
+
+$URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/README $
+$Date: 2002-10-17 15:48:39 -0300 (jue, 17 oct 2002) $
+$Rev: 20 $
+$Author: luca $
+
+Para generar el Informe del trabajo práctico basta con hacer:
+
+ make all
+
+(ver Makefile para otras opciones)
+
+Para que esto funcione debe tener instalados los siguientes programas:
+* GNU make - http://www.gnu.org/software/make/ (o compatible)
+* GNU AWK - http://www.gnu.org/software/gawk/ (o compatible)
+* GNU bash - http://www.gnu.org/software/bash/ (o compatible)
+* GNU GCC - http://gcc.gnu.org/ (o compilador de C++ compatible)
+* gnuplot - http://www.gnuplot.info/
+* netpbm - http://netpbm.sourceforge.net/
+* LyX - http://www.lyx.org/
+* KMatPlot - http://kmatplot.sourceforge.net/
+
+El gnuplot y el netpbm son necesarios para generar los gráficos, el LyX es
+necesario para generar el informe (y es probable que necesite otras
+herramientas para generar el informe en distintos formatos).
+El KMatPlot es opcional ya que se incluye en el paquete el gráfico
+resultante en formato Postscript.
+
+Todos los programas de este paquete se encuentran bajo licencia GPL y
+los documentos bajo licencia GFDL. Ambas se incluyen en el paquete.
--- /dev/null
+#!/bin/sh
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Realiza los cálculos del punto c (y a y b).
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/calc.sh $
+# $Date: 2002-10-17 00:08:00 -0300 (jue, 17 oct 2002) $
+# $Rev: 16 $
+# $Author: luca $
+#
+
+# Calculo soluciones del punto a, b y c.
+for (( n=4; n <= 32; n*=2 )); do
+ ./77891 $n | tail -n1 | ./resultado.awk > ca$n.txt
+done
+
+# Calculo iteraciones y S en función de w.
+for (( n=4; n <= 32; n*=2 )); do
+ echo "Procesando N = $n ..."
+ for (( i=0; i < 100; i+=1 )); do
+ w=`printf "1.%02d\n" $i`
+ echo -n "$w "
+ # Iteraciones en función de w.
+ ./77891 $n $w | wc -l | awk '{printf "%-4d", $1-1}'
+ echo -n " "
+ # S en función de w.
+ ./77891 $n $w | tail -n1 | awk '{print $3}'
+ done > cb$n.txt
+done
+
+# Calculo los puntos e-g
+./77891 16 1.35 0.001 | awk '{print $1 " " log($2) " " $3 " " $116}' > eg.txt
+# Calculo los puntos f-g
+./77891 16 1.85 0.001 | awk '{print $1 " " log($2) " " $3 " " $116}' > fg.txt
+
+# Calculo la Parte II
+ej2="./77891 8 1.446467 0.001 71 79 78 77"
+$ej2 | tail -n1 | ./isolineas.awk > isolineas.txt
+$ej2 | tail -n1 | awk '{ printf "Radio espectral: %.2f\nX25 = %.3f ± 0.001%%\n", $3, $28 }' > parte2.txt
--- /dev/null
+#!/usr/bin/gnuplot
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Genera gráficos con los resultados de las corridas utilizando
+# GNU Plot.
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/d.gnuplot $
+# $Date: 2002-10-14 15:17:56 -0300 (lun, 14 oct 2002) $
+# $Rev: 10 $
+# $Author: luca $
+#
+
+# Seteo terminal para que "dibuje" en un PS.
+set term postscript eps enhanced color
+set encoding iso_8859_1
+set output "d<N>.eps"
+
+# Seteos generales.
+set title "Variacion de iteraciones y S en funcion de w para N = <N>"
+set key left top
+
+# Eje X.
+set xlabel "Factor de sobrerelajacion (w)"
+set mxtics 5
+
+# Eje Y.
+set ylabel "Iteraciones"
+set ytics nomirror
+set mytics 5
+
+# Eje Y secundario.
+set y2label "Radio espectral (S)"
+set y2range [0:1]
+set y2tics 0, 0.1
+set my2tics 5
+
+# Plotea
+plot 'cb<N>.txt' using 1:2 smooth csplines axes x1y1 title "Iteraciones" with lines linetype 1, \
+ 'cb<N>.txt' using 1:3 smooth csplines axes x1y2 title "Radio espectral" with lines linetype 3
--- /dev/null
+#!/usr/bin/gnuplot
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Genera gráficos con los resultados de las corridas utilizando
+# GNU Plot.
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/efg.gnuplot $
+# $Date: 2002-10-14 15:17:56 -0300 (lun, 14 oct 2002) $
+# $Rev: 10 $
+# $Author: luca $
+#
+
+# Seteo terminal para que "dibuje" en un PS.
+set term postscript eps enhanced color
+set encoding iso_8859_1
+set output "<A>g.eps"
+
+# Seteos generales.
+set title "Variacion R y S en funcion de las iteraciones N = 16 y w = <B>"
+set key bottom
+
+# Eje X.
+set xlabel "Iteraciones"
+set mxtics 5
+
+# Eje Y.
+set ylabel "R (en escala logaritmica)"
+set ytics nomirror
+set mytics 5
+
+# Eje Y secundario.
+set y2label "Radio espectral (S) / Valor del nodo central (113)"
+set y2range [0:1.2]
+set y2tics 0, 0.1
+set my2tics 5
+
+# Plotea
+plot '<A>g.txt' every ::2 using 1:2 smooth csplines axes x1y1 title "ln(R)" with lines linetype 1, \
+ '<A>g.txt'every ::2 using 1:3 smooth csplines axes x1y2 title "S" with lines linetype 3, \
+ '<A>g.txt'every ::2 using 1:4 smooth csplines axes x1y2 title "Nodo central (113)" with lines linetype 4
--- /dev/null
+#LyX 1.1 created this file. For more info see http://www.lyx.org/
+\lyxformat 218
+\textclass book
+\language spanish
+\inputencoding auto
+\fontscheme default
+\graphics default
+\paperfontsize default
+\spacing single
+\papersize Default
+\paperpackage a4
+\use_geometry 0
+\use_amsmath 0
+\paperorientation portrait
+\secnumdepth 2
+\tocdepth 2
+\paragraph_separation indent
+\defskip medskip
+\quotes_language english
+\quotes_times 2
+\papercolumns 1
+\papersides 2
+\paperpagestyle default
+
+\layout Title
+
+Análisis Numérico I
+\newline
+Trabajo Práctico N° 1
+\layout Author
+
+Leandro Lucarella (77.891)
+\layout Date
+
+$Date: 2002-10-25 23:44:39 -0300 (vie, 25 oct 2002) $ ($Rev: 21 $)
+\layout Standard
+
+Copyright (C) 2002 Leandro Lucarella.
+\layout Standard
+
+Tiene permiso para copiar, distribuir y/o modificar este documento bajo
+ los términos de la GNU Free Documentation License (Licencia de Documentación
+ Libre GNU), Versión 1.1 o cualquier versión posterior publicada por la Free
+ Software Foundation (Fundación de Software Libre); sin Invariant Sections
+ (Secciones Invariantes), sin Front-Cover Texts (Texto de Portada-Delantera),
+ y sin Back-Cover Texts (Texto de Portada-Trasera).
+ Puede obtener una copia de la licencia en inglés en
+\begin_inset LatexCommand \url{http://www.gnu.org/licenses/fdl.txt}
+
+\end_inset
+
+ o en español (sin validez legal) en
+\begin_inset LatexCommand \url{http://www.geocities.com/larteaga/gnu/gfdl.html}
+
+\end_inset
+
+.
+\layout Standard
+
+
+\begin_inset LatexCommand \tableofcontents{}
+
+\end_inset
+
+
+\layout Chapter
+
+Introducción.
+\layout Section
+
+Objetivo.
+\layout Standard
+
+El objetivo de este trabajo práctico es adquirir experiencia en el uso de
+ métodos iterativos para la resolución de sistemas de ecuaciones lineales
+ ralos resultantes de la discretización mediante diferencias finitas de
+ ecuaciones diferenciales.
+ Mediante experimentación numérica se optimiza la velocidad de convergencia
+ del proceso iterativo en función de la discretización empleada.
+ Los resultados de la optimización numérica se comparan con resultados teóricos.
+ Finalmente se efectúa una aplicación práctica.
+\layout Section
+
+Generalidades.
+\layout Standard
+
+La solución aproximada
+\begin_inset Formula \( f_{i} \)
+\end_inset
+
+ de la ecuación de Laplace
+\begin_inset Formula \( \nabla ^{2}\phi =0 \)
+\end_inset
+
+ en un dominio bidimensional cuadrado discretizado usando una grilla uniforme
+
+\begin_inset Formula \( (x_{i}=x_{0}+ih\; ;\; y_{j}=y_{0}+jh) \)
+\end_inset
+
+ puede obtenerse resolviendo el sistema de ecuaciones lineales que surge
+ de aplicar el siguiente operador a cada uno de los nodos de la grilla:
+\begin_inset Formula \[
+4f_{i,j}-f_{i-1,j}-f_{i+1,j}-f_{i,j-1}-f_{i,j+1}=0\]
+
+\end_inset
+
+ La matriz de coeficientes del sistema de ecuaciones lineales resultante
+ es rala (a lo sumo 5 elementos por fila son distintos de cero) y presenta
+ una estructura tri-diagonal en bloques.
+ La resolución de este sistema de ecuaciones fue ampliamente estudiada en
+ forma teórica durante la época del auge del método de las diferencias finitas
+ (aproximadamente a mediados del siglo XX).
+ Estos resultados muestran que el método de Gauss-Seidel converge cuando
+ se aplican condiciones de borde de tipo Dirichlet pero que la velocidad
+ de convergencia disminuye a medida que se mejora la discretización (reducción
+ de h).
+ Esta situación es revertida utilizando sobre-relajación con un valor óptimo
+ que también se estableció en forma teórica para dominios cuadrados y rectangula
+res.
+ Entre las aplicaciones más importantes efectuadas en ese momento con esta
+ técnica se encuentra el desarrollo de reactores nucleares.
+\layout Section
+
+Planteo del Trabajo Práctico.
+\layout Standard
+
+El trabajo práctico se divide en dos partes: en la primera se analiza la
+ optimización del proceso iterativo y en la segunda se efectúa una aplicación
+ practica consistente en determinar la distribución de temperaturas sobre
+ una región del
+\emph on
+\lang english
+motherboard
+\emph default
+\lang spanish
+ de una computadora.
+\layout Chapter
+
+Primera Parte.
+\layout Section
+
+Introducción.
+\layout Standard
+
+En la figura
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:grilla}
+
+\end_inset
+
+Discretización de un dominio cuadrado (N=4).
+\layout Standard
+\align center
+
+\begin_inset Figure size 216 216
+file grilla.eps
+subcaption Grilla
+flags 11
+
+\end_inset
+
+
+\end_float
+
+\begin_inset LatexCommand \vref{fig:grilla}
+
+\end_inset
+
+ se muestra la discretización de un dominio cuadrado cuyos lados se dividieron
+ en N = 4 partes iguales.
+ Sobre los contornos el valor de se encuentra impuesto (condición de tipo
+ Dirichlet).
+ La solución aproximada
+\begin_inset Formula \( f_{i} \)
+\end_inset
+
+ en los
+\begin_inset Formula \( (N-1)\cdot (N-1) \)
+\end_inset
+
+ nodos interiores se obtienen como solución de un sistema de ecuaciones
+ lineales cuya matriz de coeficientes, para N = 4, es de la forma:
+\begin_inset Formula \[
+A=\left[ \begin{array}{ccc}
+T & -I & 0\\
+-I & T & -I\\
+0 & -I & T
+\end{array}\right] \, con\, T=\left[ \begin{array}{ccc}
+4 & -1 & 0\\
+-1 & 4 & -1\\
+0 & -1 & 4
+\end{array}\right] \]
+
+\end_inset
+
+
+\layout Standard
+
+donde
+\begin_inset Formula \( I \)
+\end_inset
+
+ es la matriz identidad de dimensión N - 1.
+ Si se aplica el método de Gauss-Seidel a este sistema de ecuaciones el
+ radio espectral de la matriz de iteración resulta
+\begin_inset Formula \( \rho _{\left( T_{GS}\right) }=\cos \left( \frac{\pi }{N}\right) \)
+\end_inset
+
+.
+ Observar que si bien el método converge para todo N > 0, la convergencia
+ es muy lenta para valores grandes de N pues
+\begin_inset Formula \( \rho _{\left( T_{GS}\right) } \)
+\end_inset
+
+ tiende a 1.
+ En cambio, el método SOR optimizado presenta un
+\begin_inset Formula \( \rho _{\left( T_{\omega }\right) _{optimo}}=\omega _{optimo}-1 \)
+\end_inset
+
+ donde el factor de relajación óptimo es:
+\layout Standard
+
+
+\begin_inset Formula \[
+\omega _{optimo}=\frac{2}{1+\sqrt{\rho _{\left( T_{GS}\right) }}}=\frac{2}{1+\sin \left( \frac{\pi }{N}\right) }\]
+
+\end_inset
+
+Dado que las propiedades de convergencia no dependen del valor de arranque
+ ni del valor sobre los contornos, en la primera parte de este trabajo se
+ asume, por simplicidad, que en los contornos
+\begin_inset Formula \( \phi =1 \)
+\end_inset
+
+ y se toma
+\begin_inset Formula \( f_{i}=0 \)
+\end_inset
+
+ como valor de arranque.
+ Además se indica utilizar el siguiente criterio de convergencia:
+\begin_inset Formula \[
+R\leq R_{TOL}\, donde\, R=\frac{\left\Vert f^{k+1}-f^{k}\right\Vert _{2}}{\left\Vert f^{k+1}\right\Vert _{2}}\]
+
+\end_inset
+
+
+\begin_inset LatexCommand \label{sec:s}
+
+\end_inset
+
+Para estimar el radio espectral de la matriz de iteración,
+\begin_inset Formula \( \rho _{\left( T_{\omega }\right) } \)
+\end_inset
+
+, se usará la expresión:
+\begin_inset Formula \[
+S=\frac{\left\Vert f^{k+1}-f^{k}\right\Vert _{2}}{\left\Vert f^{k}-f^{k-1}\right\Vert _{2}}\]
+
+\end_inset
+
+
+\layout Section
+
+Construcción del programa principal.
+\layout Standard
+
+Para comenzar se describirá brevemente el proceso de construcción del programa
+ principal que resuelve este particular problema por el método de SOR (o
+ Gauss-Seidel si
+\begin_inset Formula \( \omega =1 \)
+\end_inset
+
+).
+\layout Standard
+
+Primero se identificaron los tipos de nodos presentes, dividiéndolos en
+ tres grandes grupos:
+\layout Description
+
+Nodos\SpecialChar ~
+de\SpecialChar ~
+los\SpecialChar ~
+vértices Tienen dos condiciones de borde.
+\layout Description
+
+Nodos\SpecialChar ~
+de\SpecialChar ~
+los\SpecialChar ~
+bordes Tienen una condición de borde.
+\layout Description
+
+Nodos\SpecialChar ~
+centrales No tienen condiciones de borde.
+\layout Standard
+
+A su vez, cada grupo (exceptuando los nodos centrales) se divide en cuatro
+ subgrupos, según la ubicación de los bordes, tomando como nomenclatura
+ a los puntos cardinales como se ve en la figura
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:regiones}
+
+\end_inset
+
+Regiones según tipo de nodo.
+\layout Standard
+\align center
+
+\begin_inset Figure size 216 216
+file regiones.eps
+subcaption Regiones
+flags 11
+
+\end_inset
+
+
+\end_float
+
+\begin_inset LatexCommand \vref{fig:regiones}
+
+\end_inset
+
+.
+ De esta forma, podeNordestemos distinguir N nodos en los vértices (en orden
+ ascendente según el número de nodo):
+\layout Itemize
+
+Sudoeste (SO).
+\layout Itemize
+
+Noroeste (NO).
+\layout Itemize
+
+Sudeste (SE).
+\layout Itemize
+
+Nordeste (NE).
+\layout Standard
+
+De la misma manera se distinguen cuatro subgrupos de los nodos de los bordes
+ (con N - 3 nodos cada uno):
+\layout Itemize
+
+Oeste (O).
+\layout Itemize
+
+Norte (N).
+\layout Itemize
+
+Sur (S).
+\layout Itemize
+
+Este (E).
+\layout Standard
+
+Podemos observar entonces que se tiene 9 tipos distintos de nodos, contenidos
+ en 3 grandes grupos.
+\layout Standard
+
+El problema siguiente es la identificación de cada nodo.
+ Probando con distintos N podemos hallar las siguientes condiciones para
+ que un nodo sea de un tipo particular, a saber:
+\layout Description
+
+SO Si es el primer nodo.
+\layout Description
+
+NO Si es el nodo número N - 1.
+\layout Description
+
+SE Si es el nodo número
+\begin_inset Formula \( \left( N-1\right) \cdot \left( N-2\right) +1=N^{2}-3\cdot N+3 \)
+\end_inset
+
+.
+\layout Description
+
+NE Si es el nodo número
+\begin_inset Formula \( \left( N-1\right) ^{2}=N^{2}-2\cdot N+1 \)
+\end_inset
+
+.
+\layout Description
+
+O Si el número de nodo pertenece al intervalo
+\begin_inset Formula \( \left[ 2;N-1\right] \)
+\end_inset
+
+.
+\layout Description
+
+N Si el número de nodo es múltiplo de N - 1.
+\layout Description
+
+S Si el número de nodo menos 1 es múltiplo de N - 1.
+\layout Description
+
+E Si el número de nodo pertenece al intervalo
+\begin_inset Formula \( \left[ N^{2}-3\cdot N+4;N^{2}-2\cdot N\right] \)
+\end_inset
+
+.
+\layout Description
+
+C El resto de los nodos son centrales.
+\layout Standard
+
+Finalmente el método SOR para este caso se reduce a:
+\begin_inset Formula \[
+\phi _{i}^{k+1}=\left( 1-\omega \right) \cdot \phi _{i}^{k}+\frac{\omega }{4}\cdot \left( b_{i}+\phi _{i-N+1}^{k+1}+\phi _{i-1}^{k+1}+\phi _{i+1}^{k}+\phi _{i+N-1}^{k}\right) \]
+
+\end_inset
+
+
+\layout Standard
+
+Siendo necesario sumar sólo algunos términos de
+\begin_inset Formula \( \phi \)
+\end_inset
+
+ según el tipo de nodo.
+\layout Section
+
+Puntos a), b) y c).
+\layout Standard
+
+En los primeros tres puntos del trabajo se propone hallar la solución para
+ N = 4, 8, 16 y 32, primero con
+\begin_inset Formula \( R_{TOL}=0.01 \)
+\end_inset
+
+ y
+\begin_inset Formula \( \omega =1.0 \)
+\end_inset
+
+ y luego con incrementos de
+\begin_inset Formula \( \Delta \omega =0.05 \)
+\end_inset
+
+.
+\layout Standard
+
+A continuación se presentan los resultados de las corridas para
+\begin_inset Formula \( \omega =1.0 \)
+\end_inset
+
+, en orden de nodo ascendente de izquierda a derecha y de arriba a abajo.
+\layout Subsection
+
+
+\begin_inset LatexCommand \label{sec:resultadosN}
+
+\end_inset
+
+Resultados para distintos N.
+\layout Subsubsection
+
+N = 4.
+\layout LyX-Code
+
+Iteraciones: 8
+\layout LyX-Code
+
+Radio espectral experimental: 0.50
+\layout LyX-Code
+
+0.99 0.99 1.00 0.99 0.99 1.00 1.00 1.00
+\layout Subsubsection
+
+N = 8.
+\layout LyX-Code
+
+Iteraciones: 19
+\layout LyX-Code
+
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+
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+
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+
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+
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+
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+
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+\layout LyX-Code
+
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+\layout LyX-Code
+
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+\layout LyX-Code
+
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+
+0.89 0.89 0.89 0.89 0.89 0.89 0.90 0.90 0.91
+\layout LyX-Code
+
+0.92 0.93 0.94 0.95 0.96 0.97
+\layout Subsection
+
+Gráficos.
+\layout Standard
+
+
+\begin_inset LatexCommand \label{sec:graficos}
+
+\end_inset
+
+En el punto c) se pide realizar gráficos con la evolución de las iteraciones
+ en función de
+\begin_inset Formula \( \omega \)
+\end_inset
+
+ con
+\begin_inset Formula \( \Delta \omega =0.05 \)
+\end_inset
+
+ o menor.
+ Para realizar estos gráficos se tomo un
+\begin_inset Formula \( \Delta \omega =0.01 \)
+\end_inset
+
+ y se grafica también el radio espectral
+\begin_inset Formula \( \rho _{\left( T_{\omega }\right) } \)
+\end_inset
+
+ estimado por S (ver sección
+\begin_inset LatexCommand \vref{sec:s}
+
+\end_inset
+
+) para la última iteración.
+\layout Standard
+\added_space_top 0.3cm \added_space_bottom 0.3cm \align center
+
+\begin_inset Figure size 360 252
+file d4.eps
+subcaption d4
+flags 11
+
+\end_inset
+
+
+\layout Standard
+\added_space_top 0.3cm \added_space_bottom 0.3cm \align center
+
+\begin_inset Figure size 360 252
+file d8.eps
+subcaption d8
+flags 11
+
+\end_inset
+
+
+\layout Standard
+\added_space_top 0.3cm \added_space_bottom 0.3cm \align center
+
+\begin_inset Figure size 360 252
+file d16.eps
+subcaption d16
+flags 11
+
+\end_inset
+
+
+\layout Standard
+\added_space_top 0.3cm \added_space_bottom 0.3cm \align center
+
+\begin_inset Figure size 360 252
+file d32.eps
+subcaption d32
+flags 11
+
+\end_inset
+
+
+\layout Section
+
+Puntos e), f) y g).
+\layout Standard
+
+En estos tres puntos se pide graficar la evolución de R, S (radio espectral
+ calculado experimentalmente) y
+\begin_inset Formula \( \phi _{113} \)
+\end_inset
+
+ (nodo central) a través del proceso iterativo.
+ En el gráfico
+\begin_inset LatexCommand \vref{fig:eg}
+
+\end_inset
+
+ se presentan los resultados para N = 8 y
+\begin_inset Formula \( \omega =1.35 \)
+\end_inset
+
+ (inferior al
+\begin_inset Formula \( \omega _{optimo} \)
+\end_inset
+
+)
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:eg}
+
+\end_inset
+
+Evolución de R, S y
+\begin_inset Formula \( \phi _{113} \)
+\end_inset
+
+ para N = 8 y
+\begin_inset Formula \( \omega =1.85 \)
+\end_inset
+
+.
+\layout Standard
+
+
+\begin_inset Figure size 360 252
+file eg.eps
+subcaption eg
+flags 11
+
+\end_inset
+
+
+\end_float
+, y en el gráfico
+\begin_inset LatexCommand \vref{fig:fg}
+
+\end_inset
+
+, para N = 8 y
+\begin_inset Formula \( \omega =1.85 \)
+\end_inset
+
+ (superior al
+\begin_inset Formula \( \omega _{optimo} \)
+\end_inset
+
+)
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:fg}
+
+\end_inset
+
+Evolución de R, S y
+\begin_inset Formula \( \phi _{113} \)
+\end_inset
+
+ para N = 8 y
+\begin_inset Formula \( \omega =1.85 \)
+\end_inset
+
+.
+\layout Standard
+
+
+\begin_inset Figure size 360 252
+file fg.eps
+subcaption fg
+flags 11
+
+\end_inset
+
+
+\end_float
+.
+\layout Section
+
+Conclusiones.
+\layout Standard
+
+En la sección
+\begin_inset LatexCommand \vref{sec:resultadosN}
+
+\end_inset
+
+ podemos ver que para tener una noción sobre el orden del error relativo
+ de truncamiento no siempre podemos observar el
+\begin_inset Formula \( R_{TOL}=0.01 \)
+\end_inset
+
+ y tomarlo como cota.
+ Esta aproximación es válida sólo para N = 4 ya que se puede aplicar sólo
+ si la norma de la matriz de Gauss-Seidel
+\begin_inset Formula \( \left\Vert T_{GS}\right\Vert \leq \frac{1}{2} \)
+\end_inset
+
+.
+ Considerando que en este trabajo se utiliza la norma 2 y la matriz es simétrica
+
+\begin_inset Formula \( \left( T_{GS}^{t}=T_{GS}\right) \)
+\end_inset
+
+ observamos que:
+\begin_inset Formula \[
+\left\Vert T_{GS}\right\Vert _{2}=\sqrt{\rho _{\left( T^{t}_{GS}\cdot T_{GS}\right) }}=\sqrt{\rho _{\left( T^{2}_{GS}\right) }}=\sqrt{\rho ^{2}_{\left( T_{GS}\right) }}=\left| \rho _{\left( T_{GS}\right) }\right| \]
+
+\end_inset
+
+
+\layout Standard
+
+Por lo que la condición para que la aproximación sea válida se transforma
+ en:
+\begin_inset Formula \( \left| \rho _{\left( T_{GS}\right) }\right| \leq \frac{1}{2} \)
+\end_inset
+
+ y para el único N que se cumple es para N = 4.
+\layout Standard
+
+En los gráficos de la sección
+\begin_inset LatexCommand \vref{sec:graficos}
+
+\end_inset
+
+ podemos ver como el radio espectral de la matriz para SOR va disminuyendo
+ a medida que
+\begin_inset Formula \( \omega \)
+\end_inset
+
+ se acerca a
+\begin_inset Formula \( \omega _{optimo} \)
+\end_inset
+
+.
+ Una vez alcanzado
+\begin_inset Formula \( \omega _{optimo} \)
+\end_inset
+
+, el método para calcular
+\begin_inset Formula \( \rho _{\left( T_{\omega }\right) } \)
+\end_inset
+
+ (ver sección
+\begin_inset LatexCommand \vref{sec:s}
+
+\end_inset
+
+) deja de ser válido y es por esto que pierde
+\emph on
+estabilidad
+\emph default
+ y los resultados no pueden ser tenidos en cuenta.
+\layout Standard
+
+Finalmente en la gráfico
+\begin_inset LatexCommand \vref{fig:eg}
+
+\end_inset
+
+ podemos ver como evoluciona el orden del error de truncamiento a través
+ de las iteraciones de forma no sólo monótona sino que prácticamente lineal.
+ El radio espectral de la matriz calculado experimentalmente también evoluciona
+ de forma monótona, pero creciendo de forma muy acelerada en las primeras
+ 10 iteraciones y estabilizándose en un valor cercano a 0,9, lo que indicaría
+ que en cada iteración esta bajando el error en un 10% aproximadamente (el
+ método converge de forma bastante lenta).
+ Por último vemos también que el valor del nodo central crece monótonamente
+ tendiendo a 1, pero llegando siempre a un valor inferior.
+\layout Standard
+
+Este comportamiento monótono de las variables R, S y
+\begin_inset Formula \( \phi _{113} \)
+\end_inset
+
+ se debe a que
+\begin_inset Formula \( \omega \leq \omega _{optimo} \)
+\end_inset
+
+.
+\layout Standard
+
+En el gráfico
+\begin_inset LatexCommand \vref{fig:fg}
+
+\end_inset
+
+, donde
+\begin_inset Formula \( \omega >\omega _{optimo} \)
+\end_inset
+
+ (caso inverso al anterior), se observa un comportamiento mucho más caótico.
+ El comportamiento de S ya fue explicado.
+ El nodo central
+\begin_inset Formula \( \phi _{113} \)
+\end_inset
+
+ sigue tendiendo a 1 pero superando este valor en varias oportunidades y
+ de forma para nada monótona.
+ La variable que menos cambios presenta es el orden del error de truncamiento
+ que, aunque su comportamiento es mucho menos caótico, tampoco evoluciona
+ de forma monótona como en el caso de que
+\begin_inset Formula \( \omega \leq \omega _{optimo} \)
+\end_inset
+
+.
+\layout Chapter
+
+Segunda Parte.
+\layout Section
+
+Introducción.
+\layout Standard
+
+En la figura
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:mother}
+
+\end_inset
+
+Esquema de placa madre.
+\layout Standard
+\align center
+
+\begin_inset Figure size 216 216
+file mother.eps
+subcaption mother
+flags 11
+
+\end_inset
+
+
+\end_float
+
+\begin_inset LatexCommand \vref{fig:mother}
+
+\end_inset
+
+ se representa una región de la plaqueta madre de una computadora, los cuadrados
+ indican procesadores que se encuentran operando a distintas temperaturas.
+ En el centro falta un procesador y se desea conocer la distribución de
+ temperaturas en esa zona.
+ Despreciando las perdidas de calor de la plaqueta, las temperaturas en
+ cuestión se pueden calcular resolviendo la ecuación de Laplace usando
+\begin_inset Formula \( T_{S} \)
+\end_inset
+
+,
+\begin_inset Formula \( T_{O} \)
+\end_inset
+
+,
+\begin_inset Formula \( T_{N} \)
+\end_inset
+
+ y
+\begin_inset Formula \( T_{E} \)
+\end_inset
+
+ como condiciones de borde aplicadas en las líneas punteadas.
+ Tomar N = 8,
+\begin_inset Formula \( R_{TOL}=0.001 \)
+\end_inset
+
+ y el
+\begin_inset Formula \( \omega _{optimo} \)
+\end_inset
+
+.
+\layout Standard
+
+Cada grupo obtendrá los datos de temperatura en °C descomponiendo la parte
+ entera del promedio de los N° de padrón de los integrantes del grupo, NPP,
+ de la siguiente manera:
+\begin_inset Formula \[
+NPP=a\cdot 10^{4}+b\cdot 10^{3}+c\cdot 10^{2}+d\cdot 10+e\]
+
+\end_inset
+
+
+\layout Standard
+
+En mi caso:
+\layout Itemize
+
+a = 7
+\layout Itemize
+
+b = 7
+\layout Itemize
+
+c = 8
+\layout Itemize
+
+d = 9
+\layout Itemize
+
+e = 1
+\layout Standard
+
+Las temperaturas de los bordes se calculan entonces de la siguiente forma:
+\layout Itemize
+
+
+\begin_inset Formula \( T_{1}=T_{S}=a\cdot 10+e=71^{\circ } \)
+\end_inset
+
+
+\layout Itemize
+
+
+\begin_inset Formula \( T_{2}=T_{O}=a\cdot 10+d=79^{\circ } \)
+\end_inset
+
+
+\layout Itemize
+
+
+\begin_inset Formula \( T_{3}=T_{N}=a\cdot 10+c=78^{\circ } \)
+\end_inset
+
+
+\layout Itemize
+
+
+\begin_inset Formula \( T_{4}=T_{E}=a\cdot 10+b=77^{\circ } \)
+\end_inset
+
+
+\layout Standard
+
+Cada grupo deberá reportar el valor de temperatura en el centro.
+ En forma opcional se propone graficar las isolíneas (o isobandas) de temperatur
+a calculadas.
+
+\layout Section
+
+Resultado.
+\layout Standard
+
+Al correr el programa para N = 8, R = 0.001 y
+\begin_inset Formula \( \omega =\omega _{optimo}=1.44647 \)
+\end_inset
+
+ y las condiciones de borde expuestas anteriormente, se obtienen los siguientes
+ resultado (mostrados gráficamente con los números de nodos ubicados igual
+ que en la figura
+\begin_inset LatexCommand \vref{fig:grilla}
+
+\end_inset
+
+):
+\layout LyX-Code
+
+
+\latex no_latex
+78.336 77.999 77.801 77.680 77.606 77.542 77.412
+\layout LyX-Code
+
+
+\latex no_latex
+78.348 77.858 77.521 77.312 77.201 77.150 77.105
+\layout LyX-Code
+
+
+\latex no_latex
+78.205 77.565 77.113 76.843 76.732 76.750 76.856
+\layout LyX-Code
+
+
+\latex no_latex
+77.928 77.089 76.521 76.211 76.131 76.259 76.569
+\layout LyX-Code
+
+
+\latex no_latex
+77.466 76.359 75.676 75.346 75.319 75.584 76.158
+\layout LyX-Code
+
+
+\latex no_latex
+76.646 75.239 74.493 74.183 74.212 74.599 75.477
+\layout LyX-Code
+
+
+\latex no_latex
+74.954 73.507 72.908 72.700 72.754 73.124 74.149
+\layout Standard
+
+Donde se ve que el nodo central es
+\begin_inset Formula \( \phi _{25}=76.211^{\circ } \)
+\end_inset
+
+.
+ Considerando que el radio espectral de la matriz en la última iteración
+ es del órden de
+\begin_inset Formula \( \frac{1}{2}\left( \approx 0.58\right) \)
+\end_inset
+
+ podemos aproximar el órden de la cota del error relativo con
+\begin_inset Formula \( R_{TOL}=0.001 \)
+\end_inset
+
+.
+ El error absoluto es entonces:
+\begin_inset Formula \[
+\Delta E=R_{TOL}\cdot \phi _{25}\cong 0.001\cdot 76\cong 0.076\cong 0.1\]
+
+\end_inset
+
+
+\layout Standard
+
+De esta forma, la temperatura del nodo central sería
+\begin_inset Formula \( \phi _{25}=76.2^{\circ }\pm 0.1^{\circ } \)
+\end_inset
+
+.
+\layout Standard
+
+Puede verse también gráficamente
+\begin_float fig
+\layout Caption
+
+
+\begin_inset LatexCommand \label{fig:isolineas}
+
+\end_inset
+
+Isolíneas de temperatura.
+\layout Standard
+
+
+\begin_inset Figure size 499 355
+file isolineas.ps
+subcaption isolineas
+angle -90
+flags 11
+
+\end_inset
+
+
+\end_float
+ la distribución de las temperaturas en la figura
+\begin_inset LatexCommand \vref{fig:isolineas}
+
+\end_inset
+
+.
+\layout Chapter
+
+Código Fuente.
+\layout Section
+
+Programa Principal (
+\family typewriter
+77891.cpp
+\family default
+).
+\layout LyX-Code
+
+// vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+//
+\layout LyX-Code
+
+// Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+// Este programa resuelve un sistema de ecuaciones lineales ralo
+\layout LyX-Code
+
+// resultante de la discretización mediante diferencias finitas
+\layout LyX-Code
+
+// de ecuaciones diferenciales.
+\layout LyX-Code
+
+// Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+//
+\layout LyX-Code
+
+// Este programa es Software Libre; usted puede redistribuirlo
+\layout LyX-Code
+
+// y/o modificarlo bajo los términos de la "GNU General Public
+\layout LyX-Code
+
+// License" como lo publica la "FSF Free Software Foundation",
+\layout LyX-Code
+
+// o (a su elección) de cualquier versión posterior.
+\layout LyX-Code
+
+//
+\layout LyX-Code
+
+// Este programa es distribuido con la esperanza de que le será
+\layout LyX-Code
+
+// útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+\layout LyX-Code
+
+// implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+\layout LyX-Code
+
+// particular.
+ Vea la "GNU General Public License" para más
+\layout LyX-Code
+
+// detalles.
+\layout LyX-Code
+
+//
+\layout LyX-Code
+
+// Usted debe haber recibido una copia de la "GNU General Public
+\layout LyX-Code
+
+// License" junto con este programa, si no, escriba a la "FSF
+\layout LyX-Code
+
+// Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+\layout LyX-Code
+
+// Boston, MA 02111-1307, USA.
+\layout LyX-Code
+
+//
+\layout LyX-Code
+
+\layout LyX-Code
+
+#include <stdio.h>
+\layout LyX-Code
+
+#include <stdlib.h>
+\layout LyX-Code
+
+#include <math.h>
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Tipos de datos.
+\layout LyX-Code
+
+typedef unsigned int Indice;
+\layout LyX-Code
+
+typedef float Numero;
+\layout LyX-Code
+
+typedef struct {
+\layout LyX-Code
+
+ Indice N;
+\layout LyX-Code
+
+ Numero w;
+\layout LyX-Code
+
+ Numero rtol;
+\layout LyX-Code
+
+ Numero TS;
+\layout LyX-Code
+
+ Numero TO;
+\layout LyX-Code
+
+ Numero TN;
+\layout LyX-Code
+
+ Numero TE;
+\layout LyX-Code
+
+ Numero* X;
+\layout LyX-Code
+
+} Datos;
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Constantes.
+\layout LyX-Code
+
+const Numero DEFAULT_W = 1.0,
+\layout LyX-Code
+
+ DEFAULT_RTOL = 0.01,
+\layout LyX-Code
+
+ DEFAULT_T = 1.0;
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Calcula la iteración para un nodo.
+ Numero procesarNodo( Datos&, Indice );
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Calcula la iteración para un nodo dependiendo del tipo de nodo.
+\layout LyX-Code
+
+Numero procesarNodo( Datos&, Indice, bool, bool, bool, bool, Numero = 0
+ );
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Calcula la norma 2 de un vector.
+\layout LyX-Code
+
+Numero norma2( Numero*, Indice );
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Imprime un vector por la salida estándar.
+\layout LyX-Code
+
+void imprimirVector( Indice, Numero* );
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Imprime un vector por la salida estándar.
+\layout LyX-Code
+
+void imprimirVector( Numero*, Indice );
+\layout LyX-Code
+
+\layout LyX-Code
+
+// Resuelve el sistema de ecuaciones lineales por el método S.O.R.
+\layout LyX-Code
+
+// (o Gasuss-Seidel si w=1).
+\layout LyX-Code
+
+void resolver( Datos& );
+\layout LyX-Code
+
+\layout LyX-Code
+
+int main( int argc, char* argv[] ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Se fija que tenga los argumentos necesarios para correr.
+\layout LyX-Code
+
+ if ( argc < 2 ) {
+\layout LyX-Code
+
+ printf( "Faltan argumentos.
+ Modo de uso:
+\backslash
+n" );
+\layout LyX-Code
+
+ printf( "
+\backslash
+t%s N w RTOL TS TO TN TE
+\backslash
+n", argv[0] );
+\layout LyX-Code
+
+ printf( "Desde w en adelante son opcionales.
+ Los valores por defecto son:
+\backslash
+n" );
+\layout LyX-Code
+
+ printf( "
+\backslash
+tw = %f
+\backslash
+n", DEFAULT_W );
+\layout LyX-Code
+
+ printf( "
+\backslash
+tRTOL = %f
+\backslash
+n", DEFAULT_RTOL );
+\layout LyX-Code
+
+ printf( "
+\backslash
+tTS = TO = TN = TE = %f
+\backslash
+n", DEFAULT_T );
+\layout LyX-Code
+
+ return EXIT_FAILURE;
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Se inicializan los datos.
+\layout LyX-Code
+
+ Datos D;
+\layout LyX-Code
+
+ D.N = Indice( atol( argv[1] ) );
+\layout LyX-Code
+
+ if ( D.N < 3 ) {
+\layout LyX-Code
+
+ printf( "N Debe ser un entero mayor o igual a 3
+\backslash
+n" );
+\layout LyX-Code
+
+ return EXIT_FAILURE;
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+ D.w = DEFAULT_W;
+\layout LyX-Code
+
+ D.rtol = DEFAULT_RTOL;
+\layout LyX-Code
+
+ D.TS = D.TO = D.TN = D.TE = DEFAULT_T;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Se aloca uno más de lo necesario para usar el rango [1,n]
+\layout LyX-Code
+
+ D.X = new Numero[Indice(pow(D.N-1,2))+1];
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si se pasaron datos como argumento, se los va agregando.
+\layout LyX-Code
+
+ switch ( argc ) {
+\layout LyX-Code
+
+ case 8: D.TE = Numero( atof( argv[7] ) );
+\layout LyX-Code
+
+ case 7: D.TN = Numero( atof( argv[6] ) );
+\layout LyX-Code
+
+ case 6: D.TO = Numero( atof( argv[5] ) );
+\layout LyX-Code
+
+ case 5: D.TS = Numero( atof( argv[4] ) );
+\layout LyX-Code
+
+ case 4: D.rtol = Numero( atof( argv[3] ) );
+\layout LyX-Code
+
+ case 3: D.w = Numero( atof( argv[2] ) );
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+\layout LyX-Code
+
+ resolver( D );
+\layout LyX-Code
+
+ delete D.X;
+\layout LyX-Code
+
+ return EXIT_SUCCESS;
+\layout LyX-Code
+
+}
+\layout LyX-Code
+
+\layout LyX-Code
+
+Numero procesarNodo( Datos& D, Indice i ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ Indice N = D.N;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si es el primero, es SO.
+\layout LyX-Code
+
+ if ( i == 1 )
+\layout LyX-Code
+
+ return procesarNodo( D, i, false, false, true, true, D.TS + D.TO );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si es N - 1 es NO.
+\layout LyX-Code
+
+ if ( i == ( N - 1 ) )
+\layout LyX-Code
+
+ return procesarNodo( D, i, false, true, false, true, D.TN + D.TO );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si es N² - 3N + 3 es SE.
+\layout LyX-Code
+
+ if ( i == ( N*N - 3*N + 3 ) )
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, false, true, false, D.TS + D.TE );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si es N² - 2N + 1 es NE.
+\layout LyX-Code
+
+ if ( i == ( N*N - 2*N + 1 ) )
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, true, false, false, D.TN + D.TE );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si pertenece al intervalo [2;N-1] es O.
+\layout LyX-Code
+
+ if ( ( 1 < i ) && ( i < ( N - 1 ) ) )
+\layout LyX-Code
+
+ return procesarNodo( D, i, false, true, true, true, D.TO );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si pertenece al intervalo [N² - 3N + 3;N² - 2N + 1] es E.
+\layout LyX-Code
+
+ if ( ( ( N*N - 3*N + 3 ) < i ) && ( i < ( N*N - 2*N + 1 ) ) )
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, true, true, false, D.TE );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si i - 1 es múltiplo de N - 1 (y no es NE, SE, NO, SO) es S.
+\layout LyX-Code
+
+ if ( ( ( i - 1 ) % ( N - 1 ) ) == 0 )
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, false, true, true, D.TS );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Si i es múltiplo de N - 1 (y no es NE, SE, NO, SO) es N.
+\layout LyX-Code
+
+ if ( ( i % ( N - 1 ) ) == 0 )
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, true, false, true, D.TN );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ return procesarNodo( D, i, true, true, true, true );
+\layout LyX-Code
+
+}
+\layout LyX-Code
+
+\layout LyX-Code
+
+Numero procesarNodo( Datos& D, Indice i,
+\layout LyX-Code
+
+ bool i_n1, bool i_1, bool i1, bool in_1,
+\layout LyX-Code
+
+ Numero b ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ Numero x = 0,
+\layout LyX-Code
+
+ Xo = D.X[i];
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Voy sumando los elementos que corresponden.
+\layout LyX-Code
+
+ if ( i_n1 )
+\layout LyX-Code
+
+ x += D.X[i-D.N+1];
+\layout LyX-Code
+
+ if ( i_1 )
+\layout LyX-Code
+
+ x += D.X[i-1];
+\layout LyX-Code
+
+ if ( i1 )
+\layout LyX-Code
+
+ x += D.X[i+1];
+\layout LyX-Code
+
+ if ( in_1 )
+\layout LyX-Code
+
+ x += D.X[i+D.N-1];
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Calculo el elemento i.
+\layout LyX-Code
+
+ D.X[i] = ( 1 - D.w ) * D.X[i] + ( b + x ) * D.w / 4;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Devuelve parte de la sumatoria para calcular la norma 2.
+\layout LyX-Code
+
+ return pow( D.X[i] - Xo, 2 );
+\layout LyX-Code
+
+\layout LyX-Code
+
+}
+\layout LyX-Code
+
+\layout LyX-Code
+
+Numero norma2( Numero* X, Indice n ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ Numero sum = 0;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ for ( Indice i = 1; i <= n; i++ )
+\layout LyX-Code
+
+ sum += pow( X[i], 2 );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ return sqrt( sum );
+\layout LyX-Code
+
+\layout LyX-Code
+
+}
+\layout LyX-Code
+
+\layout LyX-Code
+
+void imprimirVector( Indice n, Numero* X ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ for ( Indice i = 1; i <= n; i++ )
+\layout LyX-Code
+
+ printf( "%.7e%s", X[i], ( i == n ) ? "
+\backslash
+n" : " " );
+\layout LyX-Code
+
+\layout LyX-Code
+
+}
+\layout LyX-Code
+
+\layout LyX-Code
+
+void resolver( Datos& D ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ Indice ite = 0,
+\layout LyX-Code
+
+ n = Indice( pow( D.N - 1, 2) );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ Numero r = D.rtol + 1,
+\layout LyX-Code
+
+ Ek = 0,
+\layout LyX-Code
+
+ Ek_1 = 0;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ // Imprime datos iniciales.
+\layout LyX-Code
+
+ // Formato de salida:
+\layout LyX-Code
+
+ // iteración R S <vector X>
+\layout LyX-Code
+
+ // (si no se puede calcular S, se muestra 0)
+\layout LyX-Code
+
+ printf( "%d %.2e 0.00000000 ", ite, r );
+\layout LyX-Code
+
+ imprimirVector( n, D.X );
+\layout LyX-Code
+
+\layout LyX-Code
+
+ while ( r > D.rtol ) {
+\layout LyX-Code
+
+\layout LyX-Code
+
+ for ( Indice i = 1; i <= n; i++ )
+\layout LyX-Code
+
+ Ek += procesarNodo( D, i );
+\layout LyX-Code
+
+ Ek = sqrt( Ek );
+\layout LyX-Code
+
+ r = Ek / norma2( D.X, n );
+\layout LyX-Code
+
+ printf( "%d %.2e %.8f ", ++ite, r, Ek_1 ? ( Ek / Ek_1 ) : 0 );
+\layout LyX-Code
+
+ imprimirVector( n, D.X ); Ek_1 = Ek; Ek = 0;
+\layout LyX-Code
+
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+\layout LyX-Code
+
+}
+\layout Section
+
+Utilidades.
+\layout Standard
+
+Todas las utilidades listadas aquí son Software Libre; puede redistribuirlas
+ y/o modificarlas bajo los términos de la "GNU General Public License" como
+ lo publica la "FSF Free Software Foundation", o (a su elección) de cualquier
+ versión posterior.
+\layout Subsection
+
+
+\family typewriter
+calc.sh
+\layout LyX-Code
+
+#!/bin/sh
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Realiza los cálculos del punto c (y a y b).
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Calculo soluciones del punto a, b y c.
+\layout LyX-Code
+
+for (( n=4; n <= 32; n*=2 )); do
+\layout LyX-Code
+
+ ./77891 $n | tail -n1 | ./resultado.awk > ca$n.txt
+\layout LyX-Code
+
+done
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Calculo iteraciones y S en función de w.
+\layout LyX-Code
+
+for (( n=4; n <= 32; n*=2 )); do
+\layout LyX-Code
+
+ echo "Procesando N = $n ..."
+\layout LyX-Code
+
+ for (( i=0; i < 100; i+=1 )); do
+\layout LyX-Code
+
+ w=`printf "1.%02d
+\backslash
+n" $i`
+\layout LyX-Code
+
+ echo -n "$w "
+\layout LyX-Code
+
+ # Iteraciones en función de w.
+\layout LyX-Code
+
+ ./77891 $n $w | wc -l | awk '{printf "%-4d", $1-1}'
+\layout LyX-Code
+
+ echo -n " "
+\layout LyX-Code
+
+ # S en función de w.
+\layout LyX-Code
+
+ ./77891 $n $w | tail -n1 | awk '{print $3}'
+\layout LyX-Code
+
+ done > cb$n.txt
+\layout LyX-Code
+
+done
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Calculo los puntos e-g
+\layout LyX-Code
+
+./77891 16 1.35 0.001 | awk '{print $1 " " log($2) " " $3 " " $116}'
+\backslash
+
+\layout LyX-Code
+
+ > eg.txt
+\layout LyX-Code
+
+# Calculo los puntos f-g
+\layout LyX-Code
+
+./77891 16 1.85 0.001 | awk '{print $1 " " log($2) " " $3 " " $116}'
+\backslash
+
+\layout LyX-Code
+
+ > fg.txt
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Calculo la Parte II
+\layout LyX-Code
+
+ej2="./77891 8 1.446467 0.001 71 79 78 77"
+\layout LyX-Code
+
+$ej2 | tail -n1 | ./isolineas.awk > isolineas.txt
+\layout LyX-Code
+
+$ej2 | tail -n1 | awk '{ printf "X25 = %.3f ± 0.001
+\backslash
+n", $28 }'
+\backslash
+
+\layout LyX-Code
+
+ > parte2.txt
+\layout Subsection
+
+
+\family typewriter
+plot.sh
+\layout LyX-Code
+
+#!/bin/sh
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Genera gráficos con los resultados de las corridas utilizando
+\layout LyX-Code
+
+# GNU Plot.
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Genera todos los gráficos del punto d
+\layout LyX-Code
+
+for (( n=4; n <= 32; n*=2 )); do
+\layout LyX-Code
+
+ sed "s/<N>/$n/g" d.gnuplot | gnuplot
+\layout LyX-Code
+
+done
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Genera gráficos del punto e-g
+\layout LyX-Code
+
+sed "s/<A>/e/g" efg.gnuplot | sed "s/<B>/1.35/g" | gnuplot
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Genera gráficos del punto f-g
+\layout LyX-Code
+
+sed "s/<A>/f/g" efg.gnuplot | sed "s/<B>/1.85/g" | gnuplot
+\layout Subsection
+
+
+\family typewriter
+d.gnuplot
+\layout LyX-Code
+
+#!/usr/bin/gnuplot
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Genera gráficos con los resultados de las corridas utilizando
+\layout LyX-Code
+
+# GNU Plot.
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Seteo terminal para que "dibuje" en un PS.
+\layout LyX-Code
+
+set term postscript eps enhanced color
+\layout LyX-Code
+
+set encoding iso_8859_1
+\layout LyX-Code
+
+set output "d<N>.eps"
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Seteos generales.
+\layout LyX-Code
+
+set title "Variacion de iteraciones y S en funcion de w para N = <N>"
+\layout LyX-Code
+
+set key left top
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje X.
+\layout LyX-Code
+
+set xlabel "Factor de sobrerelajacion (w)"
+\layout LyX-Code
+
+set mxtics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje Y.
+\layout LyX-Code
+
+set ylabel "Iteraciones"
+\layout LyX-Code
+
+set ytics nomirror
+\layout LyX-Code
+
+set mytics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje Y secundario.
+\layout LyX-Code
+
+set y2label "Radio espectral (S)"
+\layout LyX-Code
+
+set y2range [0:1]
+\layout LyX-Code
+
+set y2tics 0, 0.1
+\layout LyX-Code
+
+set my2tics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Plotea
+\layout LyX-Code
+
+plot 'cb<N>.txt' using 1:2 smooth csplines axes x1y1
+\backslash
+
+\layout LyX-Code
+
+ title "Iteraciones" with lines linetype 1,
+\backslash
+
+\layout LyX-Code
+
+ 'cb<N>.txt' using 1:3 smooth csplines axes x1y2
+\backslash
+
+\layout LyX-Code
+
+ title "Radio espectral" with lines linetype 3
+\layout Subsection
+
+
+\family typewriter
+efg.gnuplot
+\layout LyX-Code
+
+#!/usr/bin/gnuplot
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Genera gráficos con los resultados de las corridas utilizando
+\layout LyX-Code
+
+# GNU Plot.
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Seteo terminal para que "dibuje" en un PS.
+\layout LyX-Code
+
+set term postscript eps enhanced color
+\layout LyX-Code
+
+set encoding iso_8859_1
+\layout LyX-Code
+
+set output "<A>g.eps"
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Seteos generales.
+\layout LyX-Code
+
+set title "Variacion R y S en funcion de las iteraciones N = 16 y w = <B>"
+\layout LyX-Code
+
+set key bottom
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje X.
+\layout LyX-Code
+
+set xlabel "Iteraciones"
+\layout LyX-Code
+
+set mxtics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje Y.
+\layout LyX-Code
+
+set ylabel "R (en escala logaritmica)"
+\layout LyX-Code
+
+set ytics nomirror
+\layout LyX-Code
+
+set mytics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Eje Y secundario.
+\layout LyX-Code
+
+set y2label "Radio espectral (S) / Valor del nodo central (113)"
+\layout LyX-Code
+
+set y2range [0:1.2]
+\layout LyX-Code
+
+set y2tics 0, 0.1
+\layout LyX-Code
+
+set my2tics 5
+\layout LyX-Code
+
+\layout LyX-Code
+
+# Plotea
+\layout LyX-Code
+
+plot '<A>g.txt' every ::2 using 1:2 smooth csplines axes x1y1
+\backslash
+
+\layout LyX-Code
+
+ title "ln(R)" with lines linetype 1,
+\backslash
+
+\layout LyX-Code
+
+ '<A>g.txt' every ::2 using 1:3 smooth csplines axes x1y2
+\backslash
+
+\layout LyX-Code
+
+ title "S" with lines linetype 3,
+\backslash
+
+\layout LyX-Code
+
+ '<A>g.txt' every ::2 using 1:4 smooth csplines axes x1y2
+\backslash
+
+\layout LyX-Code
+
+ title "Nodo central (113)" with lines linetype 4
+\layout Subsection
+
+
+\family typewriter
+resultado.awk
+\layout LyX-Code
+
+#!/usr/bin/awk -f
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Muestra el resultado de una iteración de forma más agradable.
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+{
+\layout LyX-Code
+
+ print "Iteraciones: " $1
+\layout LyX-Code
+
+ printf "Radio espectral experimental: %.2f
+\backslash
+n", $3
+\layout LyX-Code
+
+ for ( i = 4; i <= NF; i+=9 ) {
+\layout LyX-Code
+
+ for ( j = 0; (j < 9) && (i+j < NF); j++ ) {
+\layout LyX-Code
+
+ printf "%5.2f ", $(i+j)
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+ printf "
+\backslash
+n"
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+}
+\layout Subsection
+
+
+\family typewriter
+isolineas.awk
+\layout LyX-Code
+
+#!/usr/bin/awk -f
+\layout LyX-Code
+
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+# Trabajo Práctico I de Análisis Numérico I
+\layout LyX-Code
+
+# Muestra el resultado de una iteración de forma más agradable.
+\layout LyX-Code
+
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+\layout LyX-Code
+
+#
+\layout LyX-Code
+
+\layout LyX-Code
+
+{
+\layout LyX-Code
+
+ for ( i = 7; i >= 1; i-- ) {
+\layout LyX-Code
+
+ for ( j = 0; j < 7; j++ ) {
+\layout LyX-Code
+
+ printf "%7.3f ", $(3+i+j*7)
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+ printf "
+\backslash
+n"
+\layout LyX-Code
+
+ }
+\layout LyX-Code
+
+}
+\the_end
--- /dev/null
+#!/usr/bin/awk -f
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Muestra el resultado de una iteración de forma más agradable.
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: file:///var/lib/subversion/facultad/75.12/2002/1/resultado.awk $
+# $Date: 2002-10-13 23:38:45 -0300 (dom, 13 oct 2002) $
+# $Rev: 9 $
+# $Author: luca $
+#
+
+{
+ for ( i = 7; i >= 1; i-- ) {
+ for ( j = 0; j < 7; j++ ) {
+ printf "%7.3f ", $(3+i+j*7)
+ }
+ printf "\n"
+ }
+}
--- /dev/null
+<?xml version='1.0' encoding='UTF-8'?>
+<!DOCTYPE kmatplot>
+<kmatplot mime='application/x-kmatplot' editor='KMatplot' version='0.3' url='http://kmatplot.sourceforge.net' program-author='K. Dobkowski'>
+ <canvas page-size='B6' orientation='Landscape' dpi='72'>
+ <sheets number='1'>
+ <sheet number='0' name='unnamed'>
+ <matrix title='unnamed' rows='8' cols='7' element-type='double' data-channel='0'>
+ <row>1 2 3 4 5 6 7 </row>
+ <row>74.954323 73.50705 72.9077 72.699631 72.754166 73.12426 74.149315 </row>
+ <row>76.646347 75.239304 74.49337 74.183144 74.212029 74.59877 75.476501 </row>
+ <row>77.466202 76.359474 75.675934 75.346451 75.318771 75.584038 76.158051 </row>
+ <row>77.928444 77.088737 76.521362 76.211227 76.131165 76.259239 76.569138 </row>
+ <row>78.20549 77.564507 77.112808 76.842842 76.731865 76.749901 76.856445 </row>
+ <row>78.348427 77.857697 77.521088 77.31189 77.200523 77.149765 77.104813 </row>
+ <row>78.335838 77.998528 77.800644 77.680397 77.606285 77.542267 77.411942 </row>
+ </matrix>
+ </sheet>
+ </sheets>
+ <page number='0' title='Page 1'>
+ <axes2d>
+ <area xmm='7' ymm='7' wmm='110' hmm='110'/>
+ <draw-in-background enabled='1'/>
+ <title-attributes>
+ </title-attributes>
+ <background-attributes>
+ <fill element-number='-1' style='transparent' color='ff000000'/>
+ </background-attributes>
+ <frame width='1'/>
+ <axis type='X' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='0' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='-20'/>
+ <tics format='' visible='0' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='<html><head><meta name="qrichtext" content="1" /></head><body style="font-size:12pt;font-family:Helvetica"> <p>T<span style="vertical-align:sub">S</span> = 71°</p> </body></html> '/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
+ <line element-number='2' style='invisible' width='0' color='ff000000'/>
+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <axis type='Y' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='1' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='-20'/>
+ <tics format='' visible='0' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='<html><head><meta name="qrichtext" content="1" /></head><body style="font-size:12pt;font-family:Helvetica"> <p>T<span style="vertical-align:sub">E</span> = 77°</p> </body></html> '/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
+ <line element-number='2' style='invisible' width='0' color='ff000000'/>
+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <axis type='Z' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='0' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='-20'/>
+ <tics format='(TIC)' visible='1' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0.05'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='Z'/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
+ <line element-number='2' style='invisible' width='0' color='ff000000'/>
+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <axis type='V' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='0' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='0'/>
+ <tics format='(TIC)' visible='1' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0.05'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='V'/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
+ <line element-number='2' style='invisible' width='0' color='ff000000'/>
+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <axis type='Y' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='0' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='-20'/>
+ <tics format='' visible='0' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='<html><head><meta name="qrichtext" content="1" /></head><body style="font-size:12pt;font-family:Helvetica"> <p>T<span style="vertical-align:sub">O</span> = 79°</p> </body></html> '/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
+ <line element-number='2' style='invisible' width='0' color='ff000000'/>
+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <axis type='X' visible='1' scrollable='1'>
+ <dart element-number='1' style='none' size='3' />
+ <dart element-number='2' style='none' size='3' />
+ <display position='0' default='1' opposite='1' />
+ <range min='0' max='0' rounded='0'/>
+ <scale type='linear' base='10' reversed='0'/>
+ <grid-step major='-4' minor='-20'/>
+ <tics format='' visible='0' outer='0' angle='0' pos1='0.01' pos2='0.01'/>
+ <title-position pos='0.5' distance='0'/>
+ <remembered-view number='0' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='1' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <remembered-view number='2' min='0' max='0' scale='linear' base='10' reversed='0' rounded='0'/>
+ <title text='<html><head><meta name="qrichtext" content="1" /></head><body style="font-size:12pt;font-family:Helvetica"> <p>T<span style="vertical-align:sub">N</span> = 78°</p> </body></html> '/>
+ <line element-number='0' style='solid' width='0' color='ff000000'/>
+ <line element-number='1' style='invisible' width='0' color='ff000000'/>
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+ <font element-number='0' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ <font element-number='1' family='helvetica' size='10' bold='0' italic='0' color='ff000000'/>
+ </axis>
+ <title text=''/>
+ <fill element-number='0' style='transparent' color='ff000000'/>
+ <fill element-number='1' style='solid' color='ff000000'/>
+ <gridded-contour stack-order='0'>
+ <legend-item visible='1'/>
+ <default-axis x-axis='0' y-axis='1' z-axis='2' v-axis='3'/>
+ <gradient type='five-colors'>
+ <fill element-number='0' style='solid' color='ff0000ff'/>
+ <fill element-number='1' style='solid' color='ff000080'/>
+ <fill element-number='2' style='solid' color='ff008000'/>
+ <fill element-number='3' style='solid' color='ffff0000'/>
+ <fill element-number='4' style='solid' color='ffffff00'/>
+ </gradient>
+ <filled enabled='1'/>
+ <lines enabled='1'/>
+ <labels enabled='1' spacing='0.2'/>
+ <title text='Distribución de Temperaturas'/>
+ <line element-number='0' style='invisible' width='0' color='ff000000'/>
+ <point element-number='0' style='invisible' fill='transparent' size='9' color='ff000000'/>
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+ <matrixref title='unnamed' sheet='0' row-from='0' row-step='1' row-to='0' col-from='0' col-step='1' col-to='-1' transposition='0' data-channel='1'/>
+ <matrixref title='unnamed' sheet='0' row-from='1' row-step='1' row-to='-1' col-from='0' col-step='1' col-to='-1' transposition='0' data-channel='2'/>
+ </gridded-contour>
+ </axes2d>
+ </page>
+ </canvas>
+</kmatplot>
--- /dev/null
+%!PS-Adobe-1.0
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+%%CreationDate: lun oct 14 15:16:25 2002
+%%Orientation: Landscape
+%%Pages: 1
+%%DocumentFonts: Helvetica
+
+%%EndComments
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+
+QP
+%%Trailer
+%%Pages: 1
+%%DocumentFonts: Helvetica
+%%EOF
--- /dev/null
+#!/bin/sh
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Genera gráficos con los resultados de las corridas utilizando
+# GNU Plot.
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/plot.sh $
+# $Date: 2002-10-17 00:08:00 -0300 (jue, 17 oct 2002) $
+# $Rev: 16 $
+# $Author: luca $
+#
+
+# Genera todos los gráficos del punto d
+for (( n=4; n <= 32; n*=2 )); do
+ sed "s/<N>/$n/g" d.gnuplot | gnuplot
+done
+
+# Genera gráficos del punto e-g
+sed "s/<A>/e/g" efg.gnuplot | sed "s/<B>/1.35/g" | gnuplot
+
+# Genera gráficos del punto f-g
+sed "s/<A>/f/g" efg.gnuplot | sed "s/<B>/1.85/g" | gnuplot
+
+# Genera gráficos para el informe.
+for f in regiones grilla mother; do
+ xcftopnm $f.xcf | pnmtops -imagewidth 3 -dpi 360 > $f.eps
+done
--- /dev/null
+#!/usr/bin/awk -f
+# vim: set tabstop=4 softtabstop=4 shiftwidth=4 expandtab:
+#
+# Trabajo Práctico I de Análisis Numérico I
+# Muestra el resultado de una iteración de forma más agradable.
+# Copyright (C) 2002 Leandro Lucarella <leandro@lucarella.com.ar>
+#
+# Este programa es Software Libre; usted puede redistribuirlo
+# y/o modificarlo bajo los términos de la "GNU General Public
+# License" como lo publica la "FSF Free Software Foundation",
+# o (a su elección) de cualquier versión posterior.
+#
+# Este programa es distribuido con la esperanza de que le será
+# útil, pero SIN NINGUNA GARANTIA; incluso sin la garantía
+# implícita por el MERCADEO o EJERCICIO DE ALGUN PROPOSITO en
+# particular. Vea la "GNU General Public License" para más
+# detalles.
+#
+# Usted debe haber recibido una copia de la "GNU General Public
+# License" junto con este programa, si no, escriba a la "FSF
+# Free Software Foundation, Inc.", 59 Temple Place - Suite 330,
+# Boston, MA 02111-1307, USA.
+#
+# $URL: http://www.llucax.hn.org:81/svn/facultad/75.12/tp1/resultado.awk $
+# $Date: 2002-10-16 21:52:18 -0300 (mié, 16 oct 2002) $
+# $Rev: 13 $
+# $Author: luca $
+#
+
+{
+ print "Iteraciones: " $1
+ printf "Radio espectral experimental: %.2f\n", $3
+ for ( i = 4; i <= NF; i+=9 ) {
+ for ( j = 0; (j < 9) && (i+j < NF); j++ ) {
+ printf "%5.2f ", $(i+j)
+ }
+ printf "\n"
+ }
+}
projects / z.facultad / 75.12 / tp1.git / commitdiff