Plots exercise

exercises/plots/Erf.c

+#include<math.h>
+
+double Erf(double x){
+/// single precision error function (Abramowitz and Stegun, from Wikipedia)
+if(x<0) return -Erf(-x);
+double a[]={0.254829592,-0.284496736,1.421413741,-1.453152027,1.061405429};
+double t=1/(1+0.3275911*x);
+double sum=t*(a[0]+t*(a[1]+t*(a[2]+t*(a[3]+t*a[4]))));/* the right thing */
+return 1-sum*exp(-x*x);
+} 
\ No newline at end of file

exercises/plots/Makefile

+CFLAGS = $(shell gsl-config --cflags)
+LDLIBS = $(shell gsl-config --libs)
+
+default: Makefile erf.gnuplot.png gam.gnuplot.png
+
+erf.gnuplot.png: err_data.txt tabulated_err_data.txt
+	echo '\
+	set terminal png;\
+	set output "$@";\
+	set key bottom right;\
+	set tics out;\
+	set xlabel "x";\
+	set ylabel "y";\
+	set title "Error function";\
+	plot\
+	"$<" using 1:2 with line title "Erf from math.h",\
+	"$<" using 1:3 with line title "Erf from GSL",\
+	"$<" using 1:4 with line title "Erf from homemade approx.",\
+	"tabulated_err_data.txt" using 1:2 with points title "Tabulated data";\
+	' | gnuplot
+
+gam.gnuplot.png: gam_data.txt tabulated_gam_data.txt
+	echo '\
+	set terminal png;\
+	set output "$@";\
+	set key top left;\
+	set tics out;\
+	set xlabel "x";\
+	set ylabel "y";\
+	set title "Gamma function";\
+	plot\
+	"$<" using 1:2 with line title "Gamma from math.h",\
+	"$<" using 1:3 with line title "Gamma from GSL",\
+	"$<" using 1:4 with line title "Gamma from homemade approx.",\
+	"tabulated_gam_data.txt" using 1:2 with points title "Tabulated data";\
+	' | gnuplot
+
+err_data.txt gam_data.txt: main
+	./main
+	
+main: main.c Erf.c stirling.c
+
+
+.PHONEY: test clean
+clean:
+	$(RM) main err_data.txt gam_data.txt erf.gnuplot.png gam.gnuplot.png
+
+test:
+	echo $(CFLAGS)
+	echo $(LDLIBS)
\ No newline at end of file

exercises/plots/main.c

+#include<stdio.h>
+#include<math.h>
+#include<gsl/gsl_sf_erf.h>
+#include<gsl/gsl_sf_gamma.h>
+
+double Erf(double);
+double Gamma(double);
+
+int main() {
+	FILE* err_stream = fopen("err_data.txt","w");
+	double xmin=-2,xmax=2;
+	for(double x=xmin;x<=xmax;x+=1.0/8) {
+		fprintf(err_stream,"%10g %10g %10g %10g\n",x,erf(x),gsl_sf_erf(x),Erf(x));
+	}
+	fclose(err_stream);
+	
+	FILE* gam_stream = fopen("gam_data.txt","w");
+	double ymin=0.25,ymax=5;
+	for(double y=ymin;y<=ymax;y+=1.0/32) {
+		fprintf(gam_stream,"%10g %10g %10g %10g\n",y,tgamma(y),gsl_sf_gamma(y),Gamma(y));
+	}
+	fclose(gam_stream);
+	
+return 0;
+}
\ No newline at end of file

exercises/plots/stirling.c

+#include<math.h>
+
+double Gamma(double x){
+///single precision gamma function (Gergo Nemes, from Wikipedia)
+if(x<0)return M_PI/sin(M_PI*x)/Gamma(1-x);
+if(x<9)return Gamma(x+1)/x;
+double lnGamma=x*log(x+1/(12*x-1/x/10))-x+log(2*M_PI/x)/2;
+return exp(lnGamma);
+}
\ No newline at end of file

exercises/plots/tabulated_err_data.txt

+0	0	1
+0.02	0.022564575	0.977435425
+0.04	0.045111106	0.954888894
+0.06	0.067621594	0.932378406
+0.08	0.090078126	0.909921874
+0.1	0.112462916	0.887537084
+0.2	0.222702589	0.777297411
+0.3	0.328626759	0.671373241
+0.4	0.428392355	0.571607645
+0.5	0.520499878	0.479500122
+0.6	0.603856091	0.396143909
+0.7	0.677801194	0.322198806
+0.8	0.742100965	0.257899035
+0.9	0.796908212	0.203091788
+1	0.842700793	0.157299207
+1.1	0.88020507	0.11979493
+1.2	0.910313978	0.089686022
+1.3	0.934007945	0.065992055
+1.4	0.95228512	0.04771488
+1.5	0.966105146	0.033894854
+1.6	0.976348383	0.023651617
+1.7	0.983790459	0.016209541
+1.8	0.989090502	0.010909498
+1.9	0.992790429	0.007209571
+2	0.995322265	0.004677735
+2.1	0.997020533	0.002979467
+2.2	0.998137154	0.001862846
+2.3	0.998856823	0.001143177
+2.4	0.999311486	0.000688514
+2.5	0.999593048	0.000406952
+3	0.99997791	0.00002209
+3.5	0.999999257	0.000000743

exercises/plots/tabulated_gam_data.txt

+1	1
+2	1
+3	2
+4	6
+5	24