Git commit 4cc356dfc00c1ca25e31622d4ba1c9f65cf1a168 by Stefan Gerlach.
Committed on 30/04/2016 at 18:29.
Pushed by sgerlach into branch 'analysis_interpolation'.

added rational function interpolation

M  +56   -5    src/backend/worksheet/plots/cartesian/XYInterpolationCurve.c=
pp
M  +1    -1    src/backend/worksheet/plots/cartesian/XYInterpolationCurve.h
M  +1    -0    src/backend/worksheet/plots/cartesian/XYInterpolationCurvePr=
ivate.h
M  +1    -1    src/kdefrontend/dockwidgets/XYInterpolationCurveDock.cpp

http://commits.kde.org/labplot/4cc356dfc00c1ca25e31622d4ba1c9f65cf1a168

diff --git a/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.cpp=
 b/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.cpp
index 0c855b3..3567552 100644
--- a/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.cpp
+++ b/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.cpp
@@ -41,6 +41,7 @@
 #include "backend/lib/commandtemplates.h"
 =

 #include <cmath>	// isnan
+#include <values.h>	// DBL_MIN
 #include <gsl_errno.h>
 #include <gsl/gsl_interp.h>
 #include <gsl/gsl_spline.h>
@@ -239,6 +240,53 @@ void XYInterpolationCurvePrivate::integ(double *x, dou=
ble *y, unsigned n) {
 	y[n-1]=3Dy[n-2]+vold;
 }
 =

+// calculates rational interpolation of n points of xy-data at xn using Bu=
rlisch-Stoer method. result in v (error dv)
+void XYInterpolationCurvePrivate::ratint(double *x, double *y, int n, doub=
le xn, double *v, double *dv) {
+	int i,j,a=3D0,b=3Dn-1;
+	while(b-a>1) {	// find interval using bisection
+		j=3Dfloor((a+b)/2.);
+		if(x[j]>xn)
+			b=3Dj;
+		else
+			a=3Dj;
+	}
+
+	int ns=3Da;// nearest index
+	if(fabs(xn-x[a])>fabs(xn-x[b]))
+		ns=3Db;
+
+	if(xn=3D=3Dx[ns]) {	// exact point
+		*v=3Dy[ns];
+		*dv=3D0;
+		return;
+	}
+
+	double *c =3D (double*)malloc(n*sizeof(double));
+	double *d =3D (double*)malloc(n*sizeof(double));
+	for(i=3D0;i<n;i++)
+		c[i]=3Dd[i]=3Dy[i];
+
+	*v=3Dy[ns--];
+
+	double t,dd;
+	for(int m=3D1;m<n;m++) {
+		for(i=3D0;i<n-m;i++) {
+			t=3D(x[i]-xn)*d[i]/(x[i+m]-xn);
+			dd=3Dt-c[i+1];
+			if(dd=3D=3D0.0) // pole
+				dd+=3DDBL_MIN;
+			dd=3D(c[i+1]-d[i])/dd;
+			d[i]=3Dc[i+1]*dd;
+			c[i]=3Dt*dd;
+		}
+
+		*dv =3D (2*(ns+1) < (n-m) ? c[ns+1] : d[ns--]);
+		*v +=3D *dv;
+	}
+
+	free(c);free(d);
+}
+
 void XYInterpolationCurvePrivate::recalculate() {
 	QElapsedTimer timer;
 	timer.start();
@@ -427,10 +475,6 @@ void XYInterpolationCurvePrivate::recalculate() {
 			t =3D (x-xdata[a])/(xdata[b]-xdata[a]);
 			(*yVector)[i] =3D ydata[a]*pow(ydata[b]/ydata[a],t);
 			break;
-		case XYInterpolationCurve::Rational:
-			//TODO
-			//(*yVector)[i] =3D =

-			break;
 		case XYInterpolationCurve::PCH: {
 			t =3D (x-xdata[a])/(xdata[b]-xdata[a]);
 			double h1=3D2.*t*t*t-3.*t*t+1, h2=3D-2.*t*t*t+3.*t*t, h3=3Dt*t*t-2*t*t+=
t, h4=3Dt*t*t-t*t;
@@ -492,6 +536,13 @@ void XYInterpolationCurvePrivate::recalculate() {
 			(*yVector)[i] =3D ydata[a]*h1+ydata[b]*h2+(xdata[b]-xdata[a])*(m1*h3+m2=
*h4);
 		}
 			break;
+		case XYInterpolationCurve::Rational: {
+			double v,dv;
+			ratint(xdata, ydata, n, x, &v, &dv);
+			(*yVector)[i] =3D v;
+			//TODO: use dv
+		}
+			break;
 		}
 	}
 =

@@ -499,8 +550,8 @@ void XYInterpolationCurvePrivate::recalculate() {
 	switch(type) {
 	case XYInterpolationCurve::Cosine:
 	case XYInterpolationCurve::Exponential:
-	case XYInterpolationCurve::Rational:
 	case XYInterpolationCurve::PCH:
+	case XYInterpolationCurve::Rational:
 		switch(evaluate) {
 		case XYInterpolationCurve::Function:
 			break;
diff --git a/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.h b=
/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.h
index 6d77b76..cf3fb08 100644
--- a/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.h
+++ b/src/backend/worksheet/plots/cartesian/XYInterpolationCurve.h
@@ -37,7 +37,7 @@ class XYInterpolationCurve: public XYCurve {
 	Q_OBJECT
 =

 	public:
-		enum InterpolationType {Linear,Polynomial,CSpline,CSplinePeriodic,Akima,=
AkimaPeriodic,Steffen,Cosine,Exponential,Rational,PCH};
+		enum InterpolationType {Linear,Polynomial,CSpline,CSplinePeriodic,Akima,=
AkimaPeriodic,Steffen,Cosine,Exponential,PCH,Rational};
 		enum CubicHermiteVariant {FiniteDifference,CatmullRom,Cardinal,KochanekB=
artels};
 		enum InterpolationEval {Function,Derivative,Derivative2,Integral};
 =

diff --git a/src/backend/worksheet/plots/cartesian/XYInterpolationCurvePriv=
ate.h b/src/backend/worksheet/plots/cartesian/XYInterpolationCurvePrivate.h
index d2f6f2d..4fba513 100644
--- a/src/backend/worksheet/plots/cartesian/XYInterpolationCurvePrivate.h
+++ b/src/backend/worksheet/plots/cartesian/XYInterpolationCurvePrivate.h
@@ -65,6 +65,7 @@ class XYInterpolationCurvePrivate: public XYCurvePrivate {
 		void deriv(double *x, double *y, unsigned n);
 		void deriv2(double *x, double *y, unsigned n);
 		void integ(double *x, double *y, unsigned n);
+		void ratint(double *x, double *y, int n, double xn, double *v, double *d=
v);
 };
 =

 #endif
diff --git a/src/kdefrontend/dockwidgets/XYInterpolationCurveDock.cpp b/src=
/kdefrontend/dockwidgets/XYInterpolationCurveDock.cpp
index 416a51f..90344d7 100644
--- a/src/kdefrontend/dockwidgets/XYInterpolationCurveDock.cpp
+++ b/src/kdefrontend/dockwidgets/XYInterpolationCurveDock.cpp
@@ -93,8 +93,8 @@ void XYInterpolationCurveDock::setupGeneral() {
 #endif
 	uiGeneralTab.cbType->addItem(i18n("cosine"));
 	uiGeneralTab.cbType->addItem(i18n("exponential"));
-	uiGeneralTab.cbType->addItem(i18n("rational functions"));
 	uiGeneralTab.cbType->addItem(i18n("piecewise cubic Hermite (PCH)"));
+	uiGeneralTab.cbType->addItem(i18n("rational functions"));
 =

 	uiGeneralTab.cbVariant->addItem(i18n("finite differences"));
 	uiGeneralTab.cbVariant->addItem(i18n("Catmull-Rom"));