init exercise1

exercise1/Makefile

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+CFLAGS+= -std=c99 -O2 -Wall -Wextra
+LDLIBS+= -lm
+TARGETS=wave_1d
+IMAGES=$(shell find data -type f | sed s/\\.dat/.png/g | sed s/data/images/g )
+.PHONY: all clean dirs plot movie
+all: dirs ${TARGETS}
+dirs:
+	mkdir -p data images
+plot: ${IMAGES}
+images/%.png: data/%.dat
+	./plot_image.sh $<
+movie: ${IMAGES}
+	ffmpeg -y -an -i images/%5d.png -vcodec libx264 -pix_fmt yuv420p -profile:v baseline -level 3 -r 12 wave.mp4
+clean:
+	-rm -fr ${TARGETS} data images wave.mp4

exercise1/README.md

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+* make       : builds the executable 'wave_1d'
+* ./wave\_1d : fills the 'data/' directory with stored time steps
+* make plot  : converts saved time steps to png files under 'images/', using gnuplot. Runs faster if launched with e.g. 4 threads (make -j4 plot).
+* make movie : converts collection of png files under 'images' into an mp4 movie file

exercise1/plot_image.sh

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+#! /usr/bin/env bash
+SIZE=1024
+DATAFILE=$1
+IMAGEFILE=`echo $1 | sed s/dat$/png/ | sed s/data/images/`
+cat <<END_OF_SCRIPT | gnuplot -
+set term png
+set output "$IMAGEFILE"
+set yrange[-1:1]
+plot "$DATAFILE" binary array=${SIZE} format='%double' with lines
+END_OF_SCRIPT

exercise1/wave_1d.c

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+#define _XOPEN_SOURCE 600
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdint.h>
+#include <math.h>
+
+
+// Option to change numerical precision.
+typedef int64_t int_t;
+typedef double real_t;
+
+// Simulation parameters: size, step count, and how often to save the state.
+const int_t
+    N = 1024,
+    max_iteration = 4000,
+    snapshot_freq = 10;
+
+// Wave equation parameters, time step is derived from the space step.
+const real_t
+    c  = 1.0,
+    dx  = 1.0;
+real_t
+    dt;
+
+// Buffers for three time steps, indexed with 2 ghost points for the boundary.
+real_t
+    *buffers[3] = { NULL, NULL, NULL };
+
+
+#define U_prv(i) buffers[0][(i)+1]
+#define U(i)     buffers[1][(i)+1]
+#define U_nxt(i) buffers[2][(i)+1]
+
+
+// Save the present time step in a numbered file under 'data/'.
+void domain_save ( int_t step )
+{
+    char filename[256];
+    sprintf ( filename, "data/%.5ld.dat", step );
+    FILE *out = fopen ( filename, "wb" );
+    fwrite ( &U(0), sizeof(real_t), N, out );
+    fclose ( out );
+}
+
+
+// TASK: T1
+// Set up our three buffers, fill two with an initial cosine wave,
+// and set the time step.
+void domain_initialize ( void )
+{
+// BEGIN: T1
+    ;
+// END: T1
+}
+
+
+// TASK T2:
+// Return the memory to the OS.
+// BEGIN: T2
+void domain_finalize ( void )
+{
+    ;
+}
+// END: T2
+
+
+// TASK: T3
+// Rotate the time step buffers.
+// BEGIN: T3
+    ;
+// END: T3
+
+
+// TASK: T4
+// Derive step t+1 from steps t and t-1.
+// BEGIN: T4
+    ;
+// END: T4
+
+
+// TASK: T5
+// Neumann (reflective) boundary condition.
+// BEGIN: T5
+    ;
+// END: T5
+
+
+// TASK: T6
+// Main time integration.
+void simulate( void )
+{
+// BEGIN: T6
+    int_t iteration=0;
+    domain_save ( iteration / snapshot_freq );
+// END: T6
+}
+
+
+int main ( void )
+{
+    domain_initialize();
+
+    simulate();
+
+    domain_finalize();
+    exit ( EXIT_SUCCESS );
+}