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Commit a391a1ef authored by Taddeüs Kroes's avatar Taddeüs Kroes
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ModSim ass3: Changed integration methods.

parent 596700c1
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Showing with 107 additions and 61 deletions
modsim/ass3/compare_osc.sh 0 → 100644
View file @ a391a1ef
./main 0
cat report/osc_euler | ./plot.py report/osc_euler.pdf
cat report/osc_rk2 | ./plot.py report/osc_rk2.pdf
cat report/osc_rk4 | ./plot.py report/osc_rk4.pdf
rm report/osc_euler report/osc_rk2 report/osc_rk4
modsim/ass3/integration.c
View file @ a391a1ef
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "integration.h"
#include "logger.h"
......@@ -21,29 +22,27 @@ occurs (overflow, NaN or such)
int Euler(double t0, double t1, double dt, double *y0, double *y1, int N,
f_ptr f, void *params) {
int i, j, intervals = (t1 - t0) / dt;
double dy[N], t = t0;
int i;
double dy[N], t;
// Initialize with first values (specified)
for( j = 0; j < N; j++ )
y1[j] = y0[j];
for( i = 0; i < N; i++ )
y1[i] = y0[i];
logger(t0, N, y0);
// Estimate for each interval
for( i = 0; i < intervals; i++ ) {
for( t = t0; t < t1; t = t + dt > t1 ? t1 : t + dt ) {
if( f(t, y1, dy, params) ) {
puts("Error calculating slope.");
return -1;
}
for( j = 0; j < N; j++ )
y1[j] = y1[j] + dy[j] * dt;
for( i = 0; i < N; i++ )
y1[i] = y1[i] + dy[i] * dt;
// Value can be printed/logged here
logger(t, N, y1);
t = t0 + i * dt;
}
return 0;
......@@ -51,29 +50,27 @@ int Euler(double t0, double t1, double dt, double *y0, double *y1, int N,
int RungeKutta2(double t0, double t1, double dt, double *y0, double *y1, int N,
f_ptr f, void *params) {
int i, j, intervals = (t1 - t0) / dt;
double dy1[N], dy2[N], t = t0;
int i;
double dy1[N], dy2[N], t;
// Initialize with first values (specified)
for( j = 0; j < N; j++ )
y1[j] = y0[j];
for( i = 0; i < N; i++ )
y1[i] = y0[i];
logger(t0, N, y0);
// Estimate for each interval
for( i = 0; i < intervals; i++ ) {
for( t = t0; t < t1; t = t + dt > t1 ? t1 : t + dt ) {
if( f(t, y1, dy1, params) || f(t + dt, y1, dy2, params) ) {
puts("Error calculating slope.");
return -1;
}
for( j = 0; j < N; j++ )
y1[j] = y1[j] + .5 * (dy1[j] + dy2[j]) * dt;
for( i = 0; i < N; i++ )
y1[i] = y1[i] + .5 * (dy1[i] + dy2[i]) * dt;
// Value can be printed/logged here
logger(t, N, y1);
t = t0 + i * dt;
}
return 0;
......@@ -81,25 +78,25 @@ int RungeKutta2(double t0, double t1, double dt, double *y0, double *y1, int N,
int RungeKutta4(double t0, double t1, double dt, double *y0, double *y1, int N,
f_ptr f, void *params) {
int i, j, intervals = (t1 - t0) / dt;
double y[N], dy[N], e1[N], e2[N], e3[N], e4, t = t0, half_dt = .5 * dt;
int i;
double y[N], dy[N], e1[N], e2[N], e3[N], e4, t, half_dt = .5 * dt;
// Initialize with first values (specified)
for( j = 0; j < N; j++ )
y[j] = y1[j] = y0[j];
for( i = 0; i < N; i++ )
y1[i] = y0[i];
logger(t0, N, y0);
// Estimate for each interval
for( i = 0; i < intervals; i++ ) {
for( t = t0; t < t1; t = t + dt > t1 ? t1 : t + dt ) {
if( f(t, y1, dy, params) ) {
puts("Error calculating first estimate.");
return -1;
}
for( j = 0; j < N; j++ ) {
e1[j] = dy[j] * dt;
y[j] = y1[j] + .5 * e1[j];
for( i = 0; i < N; i++ ) {
e1[i] = dy[i] * dt;
y[i] = y1[i] + .5 * e1[i];
}
if( f(t + half_dt, y1, dy, params) ) {
......@@ -107,9 +104,9 @@ int RungeKutta4(double t0, double t1, double dt, double *y0, double *y1, int N,
return -1;
}
for( j = 0; j < N; j++ ) {
e2[j] = dy[j] * dt;
y[j] = y1[j] + .5 * e2[j];
for( i = 0; i < N; i++ ) {
e2[i] = dy[i] * dt;
y[i] = y1[i] + .5 * e2[i];
}
if( f(t + half_dt, y1, dy, params) ) {
......@@ -117,9 +114,9 @@ int RungeKutta4(double t0, double t1, double dt, double *y0, double *y1, int N,
return -1;
}
for( j = 0; j < N; j++ ) {
e3[j] = dy[j] * dt;
y[j] = y0[j] + e3[j];
for( i = 0; i < N; i++ ) {
e3[i] = dy[i] * dt;
y[i] = y0[i] + e3[i];
}
if( f(t + dt, y1, dy, params) ) {
......@@ -127,15 +124,13 @@ int RungeKutta4(double t0, double t1, double dt, double *y0, double *y1, int N,
return -1;
}
for( j = 0; j < N; j++ ) {
e4 = dy[j] * dt;
y1[j] = y1[j] + (e1[j] + 2 * (e2[j] + e3[j]) + e4) / 6;
for( i = 0; i < N; i++ ) {
e4 = dy[i] * dt;
y1[i] = y1[i] + (e1[i] + 2 * (e2[i] + e3[i]) + e4) / 6;
}
// Value can be printed/logged here
logger(t, N, y1);
t = t0 + i * dt;
}
return 0;
......
modsim/ass3/logger.c
View file @ a391a1ef
......@@ -13,10 +13,10 @@ void logger(double t, int N, double *y) {
if( !logfile )
logfile = stdout;
fprintf(logfile, "%e", t);
fprintf(logfile, "%.12e", t);
for( int i = 0; i < N; i++ )
fprintf(logfile, ",%e", y[i]);
fprintf(logfile, ",%.12e", y[i]);
fprintf(logfile, "\n");
}
......
modsim/ass3/main.c
View file @ a391a1ef
......@@ -5,6 +5,16 @@
#include "models.h"
#include "logger.h"
#define DEFAULT_DT .001
#define COMPARE_DT .5
#define INTEGRATE(method, t0, t1, dt, N, FN) { \
if( method(t0, t1, dt, y0, y1, N, &f_ ## FN, (void *)args_ ## FN) ) \
puts("FAIL"); \
}
extern FILE *logfile;
int main(int argc, char **argv) {
if( argc < 2 ) {
printf("Usage: %s ODE\n", argv[0]);
......@@ -14,7 +24,7 @@ int main(int argc, char **argv) {
double y0[3] = {.0, 5.0, .0},
y1[3] = {.0, .0, .0};
const double args_osc[1] = {.5}, // {k}
const double args_osc[1] = {1.0}, // {k}
args_forced_osc[3] = {1.0, 0.1, 2.0}, // {k, D, w}
args_lottka_volt[4] = {.5, 1.0, .1, .1}, // {a, b, c, d}
args_modified_pp[5] = {.5, 1.0, .1, .1, 100.0}, // {a, b, c, d, y_m}
......@@ -22,7 +32,19 @@ int main(int argc, char **argv) {
*args_gilpin = NULL;
switch( atoi(argv[1]) ) {
case 0: COMPARE(.0, 15.0, osc); break;
case 0:
logfile = fopen("report/osc_euler", "w");
puts("Integrating Euler method...");
INTEGRATE(Euler, .0, 40.0, COMPARE_DT, 2, osc);
logger_close();
logfile = fopen("report/osc_rk2", "w");
puts("Integrating Runge-Kutta 2 method...");
INTEGRATE(RungeKutta2, .0, 40.0, COMPARE_DT, 2, osc);
logger_close();
logfile = fopen("report/osc_rk4", "w");
puts("Integrating Runge-Kutta 4 method...");
INTEGRATE(RungeKutta4, .0, 40.0, COMPARE_DT, 2, osc);
break;
case 1: INTEGRATE(RungeKutta4, .0, 20.0, DEFAULT_DT, 2, forced_osc); break;
case 2: INTEGRATE(RungeKutta4, .0, 20.0, DEFAULT_DT, 2, lottka_volt); break;
case 3: INTEGRATE(RungeKutta4, .0, 20.0, DEFAULT_DT, 2, modified_pp); break;
......
modsim/ass3/models.h
View file @ a391a1ef
#ifndef __MODELS_H__
#define __MODELS_H__
#define DEFAULT_DT .001
#define INTEGRATE(method, t0, t1, dt, N, FN) { \
if( method(t0, t1, dt, y0, y1, N, &f_ ## FN, (void *)args_ ## FN) ) \
puts("FAIL"); \
}
#define COMPARE(t0, t1, fn) { \
INTEGRATE(Euler, t0, t1, DEFAULT_DT, 2, fn); \
INTEGRATE(RungeKutta2, t0, t1, DEFAULT_DT, 2, fn); \
INTEGRATE(RungeKutta4, t0, t1, DEFAULT_DT, 2, fn); \
}
#define PARAM(n) ((const double *) params)[n]
double *v_buf, *s_buf;
......
modsim/ass3/plot.py
View file @ a391a1ef
......@@ -3,6 +3,7 @@ from sys import argv, stdin
from pylab import figure, clf, plot, show, savefig
# Collect data
lines = stdin.readlines()
x = []
y = [[] for i in range(lines[0].count(','))]
for i in range(len(lines)):
......@@ -18,7 +19,7 @@ for i in range(len(lines)):
figure(1)
clf()
for i in range(len(y)):
plot(x, y[i], '-')
plot(x, y[i], 'x')
if len(argv) == 2:
savefig(argv[1])
show()
modsim/ass3/report/report.tex
View file @ a391a1ef
......@@ -73,6 +73,25 @@ verassend, want RK4 voert de meeste operaties uit).
\subsection{Harmonische oscillator}
De vergelijking van de drie integratiemethoden kan worden uitgevoerd met:
\begin{verbatim}
$ sh ./compare_osc.sh
\end{verbatim}
In de volgende grafieken staan hiervan de resultaten (blauw
\begin{figure}[H]
\includegraphics[scale=.5]{osc_euler.pdf}
\caption{Euler}
\end{figure}
\begin{figure}[H]
\includegraphics[scale=.5]{osc_rk2.pdf}
\caption{Runge-Kutta 2}
\end{figure}
\begin{figure}[H]
\includegraphics[scale=.5]{osc_rk4.pdf}
\caption{Runge-Kutta 4}
\end{figure}
\subsection{Damped, forced harmonic oscillator}
......
modsim/ass3/test.c
View file @ a391a1ef
......@@ -4,8 +4,6 @@
#include "integration.h"
#include "logger.h"
#define DT .01
extern FILE *logfile;
int f_test_1(double t, double *y, double *dy, void *params) {
......@@ -40,9 +38,20 @@ int f_test_4(double t, double *y, double *dy, void *params) {
}
}
int f_cos(double t, double *y, double *dy, void *params) {
double result = cos(t);
if( isnan(result) ) {
return -1;
} else {
*dy = result;
return 0;
}
}
#define INTEGRATE(method, y_start, t0, t1, dy) { \
*y0 = y_start; \
if( method(t0, t1, DT, y0, y1, 1, &dy, NULL) ) \
if( method(t0, t1, dt, y0, y1, 1, &dy, NULL) ) \
puts("FAIL"); \
else \
printf("y1 for dy = " #dy " using %-12s %.10f\n", #method ":", *y1); \
......@@ -53,9 +62,15 @@ int f_test_4(double t, double *y, double *dy, void *params) {
INTEGRATE(RungeKutta4, y_start, t0, t1, dy); \
}
int main(void) {
double y0[1] = {.0}, y1[1] = {.0};
int main(int argc, char **argv) {
double y0[1] = {.0}, y1[1] = {.0}, dt;
if( argc < 2 ) {
printf("Usage: %s DT\n", argv[0]);
exit(EXIT_FAILURE);
}
dt = atof(argv[1]);
logfile = fopen("/dev/null", "w");
COMPARE(.0, .0, 10.0, f_test_1);
......@@ -67,6 +82,8 @@ int main(void) {
COMPARE(1.0, -1.0, 1.0, f_test_4);
puts("");
COMPARE(-1.0, 1.0, 10.0, f_test_4);
puts("");
COMPARE(.0, .0, 5.0, f_cos);
return 0;
return EXIT_SUCCESS;
}
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