#!/bin/sh
#
#	Ajustement de courbes
#	~~~~~~~~~~~~~~~~~~~~~
#
#	lr        : Linear Regression      (Regression lineaire)
#	ecf       : Exponential Curve Fit  (Ajustement de fonction exponentielle)
#	lcf       : Logarithmic Curve Fit  (Ajustement de fonction logarithmique)
#	pcf       : Power Curve Fit        (Ajustement de fonction puissance)
#

# Fonction d'affichage de l'usage
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
usage()
{
	echo "Usage: $pgm_name data_file"
	echo "       cat data_file | $pgm_name"
	echo "       $pgm_name [-h|-help|--help]"
	echo ""
	echo "lr  : Linear Regression     : Regression lineaire"
	echo "ecf : Exponential Curve Fit : Ajustement de fonction exponentielle"
	echo "lcf : Logarithmic Curve Fit : Ajustement de fonction logarithmique"
	echo "pcf : Power Cuve Fit        : Ajustement de fonction puissance"
}

# Controle du nom du script
# ~~~~~~~~~~~~~~~~~~~~~~~~~
pgm_name=`basename $0`
case "$pgm_name" in
	lr)       FX=id  ; FY=id  ; FB=id  ; FCT="y  = a.x + b"
	          ;;

	ecf)      FX=id  ; FY=log ; FB=exp ; FCT="y  = b.e^(a.x)"
	          ;;

	lcf)      FX=log ; FY=id  ; FB=id  ; FCT="y  = a.Log(x) + b"
	          ;;

	pcf)      FX=log ; FY=log ; FB=exp ; FCT="y  = b.x^a"
	          ;;

	*)        echo "*** lr,ecf,lcf,pcf : nom $pgm_name inconnu"
	          usage
	          exit 1
	          ;;
esac

# Controle des arguments
# ~~~~~~~~~~~~~~~~~~~~~~
case "$1" in
	-h|-help|--help)    usage
	                    exit 1
	                    ;;

	*)                  ;;
esac

if [ "$1" != "" ]
then
	DATA_FILE="$1"
fi

awk 'BEGIN {
	# Initialisation des variables
	# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	sum_x     = 0;
	sum_x2    = 0;
	sum_y     = 0;
	sum_y2    = 0;
	sum_xy    = 0;
	N         = 0;
}
# Fonction identite
# ~~~~~~~~~~~~~~~~~
function id(x)
{
	return x;
}
NF == 2 && $1 !~ /^[ 	]*#/ {
	x         = '"$FX"'($1);
	y         = '"$FY"'($2);

	sum_x     += x;
	sum_x2    += x*x;

	sum_y     += y;
	sum_y2    += y*y;

	sum_xy    += x*y;

	N++;
}
END {
	a         = (sum_xy - ((sum_x * sum_y)/N))/(sum_x2 -((sum_x^2)/N));
	b         = '"$FB"'((sum_y/N) - a*(sum_x/N));
	r2        = ((sum_xy - ((sum_x*sum_y)/N))^2)/((sum_x2 - ((sum_x^2)/N))*(sum_y2 - ((sum_y^2)/N)));

	printf("%s\n", "'"$FCT"'");
	printf("a  = %+f\n", a);
	printf("b  = %+f\n", b);
	printf("r2 =  %f\n", r2);
}' "$DATA_FILE"