diff --git a/inc/Lau1DCubicSpline.hh b/inc/Lau1DCubicSpline.hh
index ba922b9..87cd324 100644
--- a/inc/Lau1DCubicSpline.hh
+++ b/inc/Lau1DCubicSpline.hh
@@ -1,224 +1,228 @@
 
 /*
 Copyright 2015 University of Warwick
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
 
     http://www.apache.org/licenses/LICENSE-2.0
 
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
 
 /*
 Laura++ package authors:
 John Back
 Paul Harrison
 Thomas Latham
 */
 
 /*! \file Lau1DCubicSpline.hh
     \brief File containing declaration of Lau1DCubicSpline class.
  */
 
 /*! \class Lau1DCubicSpline
     \brief Class for defining a 1D cubic spline based on a set of knots.
 
     Class for defining a 1D cubic spline based on a set of knots.
     Interpolation between the knots is performed either by one of 
     two types of cubic spline (standard or Akima) or by linear interpolation.
     The splines are defined by a piecewise cubic function which, between knots i and i+1, has the form
 
     f_i(x) = (1 - t)*y_i + t*y_i+1 + t*(1 - t)(a*(1 - t) + b*t)
 
     where t = (x - x_i)/(x_i+1 - x_i),
     a =  k_i  *(x_i+1 - x_i) - (y_i+1 - y_i),
     b = -k_i+1*(x_i+1 - x_i) + (y_i+1 - y_i)
 
     and k_i is (by construction) the first derivative at knot i.
     f(x) and f'(x) are continuous at the internal knots by construction.
     
     For the standard splines, f''(x) is required to be continuous 
     at all internal knots placing n-2 constraints on the n parameters, k_i.
     The final two constraints are set by the boundary conditions.
     At each boundary, the function may be:
 
     (i)   Clamped :     f'(x) = C at the last knot
     (ii)  Natural :     f''(x) = 0 at the last knot
     (iii) Not a knot :  f'''(x) continuous at the second last knot
 
     The algorithms used in these splines can be found on:
     http://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline
     http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
 
     For the Akima splines, the values of k_i are determined from the slopes of the four nearest segments (a_i-1, a_i, a_i+1 and a_i+2) as
 
     k_i = ( | a_i+2 - a_i+1 | a_i  +  | a_i - a_i-1 | a_i+1 ) / ( | a_i+2 - a_i+1 |  +  | a_i - a_i-1 | )
 
     and as
 
     k_i = ( a_i + a_i+1 ) / 2
 
     in the special case a_i-1 == a_i != a_i+1 == a_i+2.
 
     Boundary conditions are specified by the relations
     a_2 - a_1 = a_1 - a_0 = a_0 - a_-1 and 
     a_n-1 - a_n-2 = a_n - a_n-1 = a_n+1 - a_n
 
     The algorithms used in these splines can be found in:
     J.ACM vol. 17 no. 4 pp 589-602
  */
 
 #ifndef LAU_1DCUBICSPLINE
 #define LAU_1DCUBICSPLINE
 
 #include <vector>
 #include <array>
 #include "LauParameter.hh"
 #include "Rtypes.h"
 #include "TF1.h"
 
 class Lau1DCubicSpline {
 
 	public:
 		//! Define the allowed interpolation types
 		enum LauSplineType {
 			StandardSpline, /*!< standard cubic splines with f''(x) continuous at all internal knots */
 			AkimaSpline, /*!< Akima cubic splines with f'(x) at each knot defined locally by the positions of only five knots */
 			LinearInterpolation /*! Linear interpolation between each pair of knots */
 		};
 
 		//! Define the allowed boundary condition types
 		/*!
 		    These are only supported by standard splines
 		*/
 		enum LauSplineBoundaryType {
 			Clamped, /*!< clamped boundary - f'(x) = C */
 			Natural, /*!< natural boundary - f''(x) = 0 */
 			NotAKnot /*!< 'not a knot' boundary - f'''(x) continuous at second last knot */
 		};
 
 		//! Constructor
 		/*!
 		    /param [in] xs the x-values of the knots
 		    /param [in] ys the y-values of the knots
 		    /param [in] leftBound the left-hand boundary condition
 		    /param [in] rightBound the right-hand boundary condition
 		    /param [in] dydx0 the gradient at the left-hand boundary of a clamped spline
 		    /param [in] dydxn the gradient at the right-hand boundary of a clamped spline
 		*/
 		Lau1DCubicSpline(const std::vector<Double_t>& xs, const std::vector<Double_t>& ys,
 				 LauSplineType type = Lau1DCubicSpline::StandardSpline,
 				 LauSplineBoundaryType leftBound = Lau1DCubicSpline::NotAKnot, 
 				 LauSplineBoundaryType rightBound = Lau1DCubicSpline::NotAKnot,
 				 Double_t dydx0 = 0.0, Double_t dydxn = 0.0);
 
 		//! Destructor
 		virtual ~Lau1DCubicSpline();
 
 		//! Evaluate the function at given point
 		/*!
 		    \param [in] x the x-coordinate
 		    \return the value of the spline at x
 		*/
 		Double_t evaluate(Double_t x) const;
 
 		//! Update the y-values of the knots
 		/*!
 		    \param [in] ys the y-values of the knots
 		*/
 		void updateYValues(const std::vector<Double_t>& ys);
 		void updateYValues(const std::vector<LauParameter*>& ys);
 
 		//! Update the type of interpolation to perform
 		/*!
 		    \param [in] type the type of interpolation
 		*/
 		void updateType(LauSplineType type);
 
 		//! Update the boundary conditions for the spline
 		/*!
 		    /param [in] leftBound the left-hand boundary condition
 		    /param [in] rightBound the right-hand boundary condition
 		    /param [in] dydx0 the gradient at the left-hand boundary of a clamped spline
 		    /param [in] dydxn the gradient at the right-hand boundary of a clamped spline
 		*/
 		void updateBoundaryConditions(LauSplineBoundaryType leftBound, 
 					      LauSplineBoundaryType rightBound, 
 					      Double_t dydx0 = 0.0,
 					      Double_t dydxn = 0.0);
 
 		//! Return the number of knots
 		UInt_t getnKnots() const {return nKnots_;}
 
 		//! Get y values
 		std::vector<Double_t> getYValues(){return y_;}
 
 		//! Get the coefficients of spline section i in the form a + bx + cx^2 + dx^3
 		/*!
-		    /params [in] i refers to the left-hand index of the knot (i = 0 gets the params between x_0 and x_1)
-		 */
-		std::array<Double_t,4> getCoefficients(UInt_t i);
+			\params [in] i refers to the left-hand index of the knot (i = 0 gets the params between x_0 and x_1)
+			\return coefficients {a, b, c, d}
+		*/
+		std::array<Double_t,4> getCoefficients(const UInt_t i) const;
 
-		//! Make a TF1 showing the spline with its current knot values. Mostly as a sanity check
-		TF1* makeTF1();
+		//! Make a TF1 showing the spline with its current knot values
+		/*!
+			\return 1D function object
+		*/
+		TF1* makeTF1() const;
 
 	private:
 		//! Copy constructor - not implemented
 		Lau1DCubicSpline( const Lau1DCubicSpline& rhs );
 
 		//! Copy assignment operator - not implemented
 		Lau1DCubicSpline& operator=(const Lau1DCubicSpline& rhs);
 
 		//! Initialise the class
 		void init();
 
 		//! Calculate the first derivative at each knot
 		void calcDerivatives();
 
 		//! Calculate the first derivatives according to the standard method
 		void calcDerivativesStandard();
 		//! Calculate the first derivatives according to the Akima method
 		void calcDerivativesAkima();
 
 		//! The number of knots in the spline
 		const UInt_t nKnots_;
 
 		//! The x-value at each knot
 		std::vector<Double_t> x_;
 		//! The y-value at each knot
 		std::vector<Double_t> y_;
 		//! The first derivative at each knot
 		std::vector<Double_t> dydx_;
 
 		//! The 'a' coefficients used to determine the derivatives
 		std::vector<Double_t> a_;
 		//! The 'b' coefficients used to determine the derivatives
 		std::vector<Double_t> b_;
 		//! The 'c' coefficients used to determine the derivatives
 		std::vector<Double_t> c_;
 		//! The 'd' coefficients used to determine the derivatives
 		std::vector<Double_t> d_;
 
 		//! The type of interpolation to be performed
 		LauSplineType type_;
 
 		//! The left-hand boundary condition on the spline
 		LauSplineBoundaryType leftBound_;
 		//! The right-hand boundary condition on the spline
 		LauSplineBoundaryType rightBound_;
 
 		//! The gradient at the left boundary for a clamped spline
 		Double_t dydx0_;
 		//! The gradient at the right boundary for a clamped spline
 		Double_t dydxn_;
 
 		ClassDef(Lau1DCubicSpline, 0); // Class for defining a 1D cubic spline
 };
 
 #endif
diff --git a/src/Lau1DCubicSpline.cc b/src/Lau1DCubicSpline.cc
index e0c05a6..26c43e9 100644
--- a/src/Lau1DCubicSpline.cc
+++ b/src/Lau1DCubicSpline.cc
@@ -1,455 +1,455 @@
 
 /*
 Copyright 2015 University of Warwick
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
 
     http://www.apache.org/licenses/LICENSE-2.0
 
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
 
 /*
 Laura++ package authors:
 John Back
 Paul Harrison
 Thomas Latham
 */
 
 /*! \file Lau1DCubicSpline.cc
   \brief File containing implementation of Lau1DCubicSpline class.
  */
 
 #include <cmath>
 #include <cstdlib>
 #include <iostream>
 
 #include <TH2.h>
 #include <TSystem.h>
 
 #include "Lau1DCubicSpline.hh"
 
 ClassImp(Lau1DCubicSpline)
 
 
 Lau1DCubicSpline::Lau1DCubicSpline(const std::vector<Double_t>& xs, const std::vector<Double_t>& ys,
 				   LauSplineType type, 
 				   LauSplineBoundaryType leftBound, 
 				   LauSplineBoundaryType rightBound,
 				   Double_t dydx0, Double_t dydxn) :
 	nKnots_(xs.size()),
 	x_(xs),
 	y_(ys),
 	type_(type),
 	leftBound_(leftBound),
 	rightBound_(rightBound),
 	dydx0_(dydx0),
 	dydxn_(dydxn)
 {
 	init();
 }
 
 Lau1DCubicSpline::~Lau1DCubicSpline()
 {
 }
 
 Double_t Lau1DCubicSpline::evaluate(Double_t x) const
 {
 	// do not attempt to extrapolate the spline
 	if( x<x_[0] || x>x_[nKnots_-1] ) {
 		std::cerr << "WARNING in Lau1DCubicSpline::evaluate : function is only defined between " << x_[0] << " and " << x_[nKnots_-1] << std::endl;
 		std::cerr << "                                        value at " << x << " returned as 0" << std::endl;
 		return 0.;
 	}
 
 	// first determine which 'cell' of the spline x is in
 	// cell i runs from knot i to knot i+1
 	Int_t cell(0);
 
 	while( x > x_[cell+1] ) {
 		++cell;
 	}
 
 	// obtain x- and y-values of the neighbouring knots
 	Double_t xLow  = x_[cell];
 	Double_t xHigh = x_[cell+1];
 	Double_t yLow  = y_[cell];
 	Double_t yHigh = y_[cell+1];
 
 	if(type_ == Lau1DCubicSpline::LinearInterpolation) {
 		return yHigh*(x-xLow)/(xHigh-xLow) + yLow*(xHigh-x)/(xHigh-xLow);
 	}
 
 	// obtain t, the normalised x-coordinate within the cell, 
 	// and the coefficients a and b, which are defined in cell i as:
 	//
 	//      a_i =  k_i  *(x_i+1 - x_i) - (y_i+1 - y_i),
 	//      b_i = -k_i+1*(x_i+1 - x_i) + (y_i+1 - y_i)
 	//
 	// where k_i is (by construction) the first derivative at knot i
 	Double_t t = (x - xLow) / (xHigh - xLow);
 	Double_t a =     dydx_[cell]   * (xHigh - xLow) - (yHigh - yLow);
 	Double_t b = -1.*dydx_[cell+1] * (xHigh - xLow) + (yHigh - yLow);
 
 	Double_t retVal = (1 - t) * yLow + t * yHigh + t * (1 - t) * ( a * (1 - t) + b * t );
 
 	return retVal;
 }
 
 void Lau1DCubicSpline::updateYValues(const std::vector<Double_t>& ys)
 {
 	y_ = ys;
 	this->calcDerivatives();
 }
 
 void Lau1DCubicSpline::updateYValues(const std::vector<LauParameter*>& ys)
 {
 	for (UInt_t i=0; i<nKnots_; ++i){
 		y_[i] = ys[i]->unblindValue();
 	}
 	this->calcDerivatives();
 }
 
 void Lau1DCubicSpline::updateType(LauSplineType type)
 {
 	if(type_ != type) {
 		type_ = type;
 		this->calcDerivatives();
 	}
 }
 
 void Lau1DCubicSpline::updateBoundaryConditions(LauSplineBoundaryType leftBound,
 		LauSplineBoundaryType rightBound,
 		Double_t dydx0, Double_t dydxn)
 {
 	Bool_t updateDerivatives(kFALSE);
 
 	if(leftBound_ != leftBound || rightBound_ != rightBound) {
 		leftBound_ = leftBound;
 		rightBound_ = rightBound;
 		updateDerivatives = kTRUE;
 	}
 
 	if(dydx0_ != dydx0) {
 		dydx0_ = dydx0;
 		if(leftBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = kTRUE;
 	}
 
 	if(dydxn_ != dydxn) {
 		dydxn_ = dydxn;
 		if(rightBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = kTRUE;
 	}
 
 	if(updateDerivatives) {
 		this->calcDerivatives();
 	}
 }
 
-std::array<Double_t,4> Lau1DCubicSpline::getCoefficients(UInt_t i)
+std::array<Double_t,4> Lau1DCubicSpline::getCoefficients(const UInt_t i) const
 {
 	std::array<Double_t,4> result = {0.,0.,0.,0.};
 	if(i >= nKnots_)
 	{
 		std::cerr << "ERROR in Lau1DCubicSpline::getCoefficients requested for too high a knot value" << std::endl;
 		return result;
 	}
 	
 	Double_t xL = x_[i]   , xH = x_[i+1];
 	Double_t yL = y_[i]   , yH = y_[i+1];
 	Double_t h = xH-xL; //This number comes up a lot
 	
 	switch(type_)
 	{
 		case Lau1DCubicSpline::StandardSpline:
 		case Lau1DCubicSpline::AkimaSpline:
 			{
 				Double_t kL = dydx_[i], kH = dydx_[i+1];
 
 				//a and b based on definitions from https://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline
 				Double_t a = kL*h-(yH-yL);
 				Double_t b =-kH*h+(yH-yL);
 
 				Double_t denom = -h*h*h;//The terms have a common demoninator
 
 				result[0] = -b*xL*xL*xH + a*xL*xH*xH + h*h*(xL*yH - xH*yL);
 				result[1] = -a*xH*(2*xL+xH) + b*xL*(xL+2*xH) + h*h*(yL-yH);
 				result[2] = -b*(2*xL+xH) + a*(xL+2*xH);
 				result[3] = -a+b;
 
 				for(auto& res : result){res /= denom;}
 				break;
 			}
 /*		case Lau1DCubicSpline::AkimaSpline: // Double check the Akima description of splines (in evaluate) right now they're the same except for the first derivatives
 			{
 				//using fomulae from https://asmquantmacro.com/2015/09/01/akima-spline-interpolation-in-excel/
 				std::function<Double_t(Int_t)> m = [&](Int_t j) //formula to get the straight line gradient
 				{
 					if(j < 0){return 2*m(j+1)-m(j+2);}
 					if(j >= nKnots_){return 2*m(j-1)-m(j-2);}
 					return (y_[j+1]-y_[j]) / (x_[j+1]-x_[j]);
 				};
 				
 				auto t = [&](Int_t j)
 				{
 					Double_t res = 0.; //originally res was called 't' but that produced a shadow warning
 					Double_t denom = TMath::Abs(m(j+1)-m(j)) + TMath::Abs(m(j-1)-m(j-2));
 					if(denom == 0){res = (m(j)-m(j-1))/2;} //Special case for when denom = 0
 					else
 					{
 						res = TMath::Abs(m(j+1)-m(j))*m(j-1) + TMath::Abs(m(j-1)-m(j-2))*m(j);
 						res /= denom;
 					}
 					return res;
 				};
 
 				//These are the p's to get the spline in the form p_k(x-xL)^k
 				Double_t pDenom = x_[i+1]/x_[i]; //a denominator used for p[2] and p[3]
 				std::array<Double_t,4> p = {y_[i],t(i),0.,0.}; //we'll do the last 2 below
 				
 				p[2] = 3*m(i)-2*t(i)-t(i+1);
 				p[2]/= pDenom;
 
 				p[3] = t(i)+t(i+1)-2*m(i);
 				p[3]/= pDenom*pDenom;
 
 				//Now finally rearranging the p's into the desired results
 				result[0] = p[0]-p[1]*xL+p[2]*xL*xL-p[3]*xL*xL*xL;
 				result[1] = p[1]-2*p[2]*xL+3*p[3]*xL*xL;
 				result[2] = p[2]-3*p[3]*xL;
 				result[3] = p[3];
 
 				break;
 			}*/
 		case Lau1DCubicSpline::LinearInterpolation:
 			{
 				result[0] = xH*yL-xL*yH;
 				result[1] = yH-yL;
 
 				for(auto& res : result){res /= h;}
 				break;
 			}
 	}
 
 	return result;
 }
 
-TF1* Lau1DCubicSpline::makeTF1()
+TF1* Lau1DCubicSpline::makeTF1() const
 {
 	TString functionString = ""; //make a long piecewise construction of all the spline pieces
 	for(UInt_t i = 0; i < nKnots_-1; ++i)
 	{
 		functionString += Form("(x>%f && x<= %f)*",x_[i],x_[i+1]);//get the bounds of this piece
 		std::array<Double_t,4> coeffs = this->getCoefficients(i);
 		functionString += Form("(%f + %f*x + %f*x^2 + %f*x^3)",coeffs[0],coeffs[1],coeffs[2],coeffs[3]);
 		if(i < nKnots_ -2){functionString += " + \n";}//add to all lines except the last
 	}
 
 	TF1* func = new TF1("SplineFunction", functionString, x_.front(), x_.back());
 
 	return func;
 }
 
 void Lau1DCubicSpline::init()
 {
 	if( y_.size() != x_.size()) {
 		std::cerr << "ERROR in Lau1DCubicSpline::init : The number of y-values given does not match the number of x-values" << std::endl;
 		std::cerr << "                                  Found " <<  y_.size() << ", expected " << x_.size() << std::endl;
 		gSystem->Exit(EXIT_FAILURE);
 	}
 
 	dydx_.insert(dydx_.begin(),nKnots_,0.);
 
 	a_.insert(a_.begin(),nKnots_,0.);
 	b_.insert(b_.begin(),nKnots_,0.);
 	c_.insert(c_.begin(),nKnots_,0.);
 	d_.insert(d_.begin(),nKnots_,0.);
 
 	this->calcDerivatives();
 }
 
 void Lau1DCubicSpline::calcDerivatives()
 {
 	switch ( type_ ) {
 		case Lau1DCubicSpline::StandardSpline :
 			this->calcDerivativesStandard();
 			break;
 		case Lau1DCubicSpline::AkimaSpline :
 			this->calcDerivativesAkima();
 			break;
 		case Lau1DCubicSpline::LinearInterpolation :
 			//derivatives not needed for linear interpolation
 			break;
 	}
 }
 
 void Lau1DCubicSpline::calcDerivativesStandard()
 {
 	// derivatives are determined such that the second derivative is continuous at internal knots
 
 	// derivatives, k_i, are the solutions to a set of linear equations of the form:
 	// a_i * k_i-1  +  b_i * k+i  +  c_i * k_i+1  =  d_i with a_0 = 0, c_n-1 = 0
 
 	// this is solved using the tridiagonal matrix algorithm as on en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
 
 	// first and last equations give boundary conditions
 	// - for natural boundary, require f''(x) = 0 at end knot
 	// - for 'not a knot' boundary, require f'''(x) continuous at second knot
 	// - for clamped boundary, require predefined value of f'(x) at end knot
 
 	// non-zero values of a_0 and c_n-1 would give cyclic boundary conditions
 	a_[0] = 0.;
 	c_[nKnots_-1] = 0.;
 
 	// set left boundary condition
 	if(leftBound_ == Lau1DCubicSpline::Natural) {
 		b_[0] = 2./(x_[1]-x_[0]);
 		c_[0] = 1./(x_[1]-x_[0]);
 		d_[0] = 3.*(y_[1]-y_[0])/((x_[1]-x_[0])*(x_[1]-x_[0]));
 
 	} else if(leftBound_ == Lau1DCubicSpline::NotAKnot) {
 		// define the width, h, and the 'slope', delta, of the first cell
 		Double_t h1(x_[1]-x_[0]), h2(x_[2]-x_[0]);
 		Double_t delta1((y_[1]-y_[0])/h1), delta2((y_[2]-y_[1])/h2);
 
 		// these coefficients can be determined by requiring f'''_0(x_1) = f'''_1(x_1)
 		// the requirement f''_0(x_1) = f''_1(x_1) has been used to remove the dependence on k_2
 		b_[0] = h2;
 		c_[0] = h1+h2;
 		d_[0] = delta1*(2.*h2*h2 + 3.*h1*h2)/(h1+h2) + delta2*5.*h1*h1/(h1+h2);
 
 	} else { //Clamped
 		b_[0] = 1.;
 		c_[0] = 0.;
 		d_[0] = dydx0_;
 	}
 
 	// set right boundary condition
 	if(rightBound_ == Lau1DCubicSpline::Natural) {
 		a_[nKnots_-1] = 1./(x_[nKnots_-1]-x_[nKnots_-2]);
 		b_[nKnots_-1] = 2./(x_[nKnots_-1]-x_[nKnots_-2]);
 		d_[nKnots_-1] = 3.*(y_[nKnots_-1]-y_[nKnots_-2])/((x_[nKnots_-1]-x_[nKnots_-2])*(x_[nKnots_-1]-x_[nKnots_-2]));
 
 	} else if(rightBound_ == Lau1DCubicSpline::NotAKnot) {
 		// define the width, h, and the 'slope', delta, of the last cell
 		Double_t hnm1(x_[nKnots_-1]-x_[nKnots_-2]), hnm2(x_[nKnots_-2]-x_[nKnots_-3]);
 		Double_t deltanm1((y_[nKnots_-1]-y_[nKnots_-2])/hnm1), deltanm2((y_[nKnots_-2]-y_[nKnots_-3])/hnm2);
 
 		// these coefficients can be determined by requiring f'''_n-3(x_n-2) = f'''_n-2(x_n-2)
 		// the requirement f''_n-3(x_n-2) = f''_n-2(x_n-2) has been used to remove 
 		// the dependence on k_n-3
 		a_[nKnots_-1] = hnm2 + hnm1;
 		b_[nKnots_-1] = hnm1;
 		d_[nKnots_-1] = deltanm2*hnm1*hnm1/(hnm2+hnm1) + deltanm1*(2.*hnm2*hnm2 + 3.*hnm2*hnm1)/(hnm2+hnm1);
 
 	} else { //Clamped
 		a_[nKnots_-1] = 0.;
 		b_[nKnots_-1] = 1.;
 		d_[nKnots_-1] = dydxn_;
 	}
 
 	// the remaining equations ensure that f_i-1''(x_i) = f''_i(x_i) for all internal knots
 	for(UInt_t i=1; i<nKnots_-1; ++i) {
 		a_[i] = 1./(x_[i]-x_[i-1]);
 		b_[i] = 2./(x_[i]-x_[i-1]) + 2./(x_[i+1]-x_[i]);
 		c_[i] =                      1./(x_[i+1]-x_[i]);
 		d_[i] = 3.*(y_[i]-y_[i-1])/((x_[i]-x_[i-1])*(x_[i]-x_[i-1])) + 3.*(y_[i+1]-y_[i])/((x_[i+1]-x_[i])*(x_[i+1]-x_[i]));
 	}
 
 	// forward sweep - replace c_i and d_i with
 	//
 	// c'_i =  c_i /  b_i                 for i = 0
 	//         c_i / (b_i - a_i * c_i-1)  otherwise
 	//
 	// and 
 	//
 	// d'_i =   d_i                /  b_i                 for i = 0
 	//         (d_i - a_i * d_i-1) / (b_i - a_i * c_i-1)  otherwise
 
 	c_[0] /= b_[0];
 	d_[0] /= b_[0];
 
 	for(UInt_t i=1; i<nKnots_-1; ++i) {
 		c_[i] =  c_[i]                  / (b_[i] - a_[i]*c_[i-1]);
 		d_[i] = (d_[i] - a_[i]*d_[i-1]) / (b_[i] - a_[i]*c_[i-1]);
 	}
 
 	d_[nKnots_-1] = (d_[nKnots_-1] - a_[nKnots_-1]*d_[nKnots_-2]) / (b_[nKnots_-1] - a_[nKnots_-1]*c_[nKnots_-2]);
 
 	// back substitution - calculate k_i = dy/dx at each knot
 	//
 	// k_i = d'_i                   for i = n-1
 	//       d'_i - c'_i * k_i+1    otherwise
 
 	dydx_[nKnots_-1] = d_[nKnots_-1];
 
 	for(Int_t i=nKnots_-2; i>=0; --i) {
 		dydx_[i] = d_[i] - c_[i]*dydx_[i+1];
 	}
 }
 
 void Lau1DCubicSpline::calcDerivativesAkima() {
 	//derivatives are calculated according to the Akima method
 	// J.ACM vol. 17 no. 4 pp 589-602
 
 	Double_t am1(0.), an(0.), anp1(0.);
 
 	// a[i] is the slope of the segment from point i-1 to point i
 	//
 	// n.b. segment 0 is before point 0 and segment n is after point n-1
 	//      internal segments are numbered 1 - n-1
 	for(UInt_t i=1; i<nKnots_; ++i) {
 		a_[i] = (y_[i]-y_[i-1])/(x_[i]-x_[i-1]);
 	}
 
 	// calculate slopes between additional points on each end according to the Akima method
 	// method assumes that the additional points follow a quadratic defined by the last three points
 	// this leads to the relations a[2] - a[1] = a[1] - a[0] = a[0] - a[-1] and a[n-1] - a[n-2] = a[n] - a[n-1] = a[n+1] - a[n]
 	a_[0]         = 2*a_[1]         - a_[2];
 	am1           = 2*a_[0]         - a_[1];
 
 	an            = 2*a_[nKnots_-1] - a_[nKnots_-2];
 	anp1          = 2*an            - a_[nKnots_-1];
 
 	// b[i] is the weight of a[i]   towards dydx[i]
 	// c[i] is the weight of a[i+1] towards dydx[i]
 	// See Appendix A of J.ACM vol. 17 no. 4 pp 589-602 for a justification of these weights
 	b_[0] = TMath::Abs(a_[1] - a_[0]);
 	b_[1] = TMath::Abs(a_[2] - a_[1]);
 
 	c_[0] = TMath::Abs(a_[0] - am1  );
 	c_[1] = TMath::Abs(a_[1] - a_[0]);
 
 	for(UInt_t i=2; i<nKnots_-2; ++i) {
 		b_[i] = TMath::Abs(a_[i+2] - a_[i+1]);
 		c_[i] = TMath::Abs(a_[i]   - a_[i-1]);
 	}
 
 	b_[nKnots_-2] = TMath::Abs(an            - a_[nKnots_-1]);
 	b_[nKnots_-1] = TMath::Abs(anp1          - an           );
 
 	c_[nKnots_-2] = TMath::Abs(a_[nKnots_-2] - a_[nKnots_-3]);
 	c_[nKnots_-1] = TMath::Abs(a_[nKnots_-1] - a_[nKnots_-2]);
 
 	// dy/dx calculated as the weighted average of a[i] and a[i+1]:
 	// dy/dx_i = ( | a_i+2 - a_i+1 | a_i  +  | a_i - a_i-1 | a_i+1 ) / ( | a_i+2 - a_i+1 |  +  | a_i - a_i-1 | )
 	// in the special case a_i-1 == a_i != a_i+1 == a_i+2 this function is undefined so dy/dx is then defined as (a_i + a_i+1) / 2
 	for(UInt_t i=0; i<nKnots_-2; ++i) {
 		if(b_[i]==0 && c_[i]==0) {
 			dydx_[i] = ( a_[i] + a_[i+1] ) / 2.;
 		} else {
 			dydx_[i] = ( b_[i] * a_[i] + c_[i] * a_[i+1] ) / ( b_[i] + c_[i] );
 		}
 	}
 
 	if(b_[nKnots_-1]==0 && c_[nKnots_-1]==0) {
 		dydx_[nKnots_-1] = ( a_[nKnots_-1] + an ) / 2.;
 	} else {
 		dydx_[nKnots_-1] = ( b_[nKnots_-1] * a_[nKnots_-1] + c_[nKnots_-1] * an ) / ( b_[nKnots_-1] + c_[nKnots_-1] );
 	}
 }