TRadSpline5 Class Reference

#include <TRadSpline.h>

Inheritance diagram for TRadSpline5:

List of all members.

Public Member Functions
	TRadSpline5 ()
	TRadSpline5 (const char *title, double x[], double y[], int n, const char *opt=0, double b1=0, double e1=0, double b2=0, double e2=0)
	TRadSpline5 (const char *title, double xmin, double xmax, double y[], int n, const char *opt=0, double b1=0, double e1=0, double b2=0, double e2=0)
	TRadSpline5 (const char *title, double xmin, double xmax, double(*func)(const double &), int n, const char *opt=0, double b1=0, double e1=0, double b2=0, double e2=0)
int	FindX (double x) const
double	Eval (double x) const
double	Derivative (double x) const
	~TRadSpline5 ()
void	GetCoeff (int i, double &x, double &y, double &b, double &c, double &d, double &e, double &f)
void	GetKnot (int i, double &x, double &y) const
virtual void	SaveAs (const char *filename) const
virtual int	GetNpx () const
void	SetNpx (int n)
Static Public Member Functions
static void	Test ()
Protected Attributes
double	fDelta
double	fXmin
double	fXmax
int	fNp
bool	fKstep
int	fNpx
Private Member Functions
void	BuildCoeff ()
void	BoundaryConditions (const char *opt, int &beg, int &end, const char *&cb1, const char *&ce1, const char *&cb2, const char *&ce2)
void	SetBoundaries (double b1, double e1, double b2, double e2, const char *cb1, const char *ce1, const char *cb2, const char *ce2)
Private Attributes
TRadSplinePoly5 *	fPoly

---

Detailed Description

Definition at line 154 of file TRadSpline.h.

---

Constructor & Destructor Documentation

TRadSpline5::TRadSpline5

(

)

[inline]

Definition at line 167 of file TRadSpline.h.

Referenced by Test().

: fPoly(0) {}

TRadSpline5::TRadSpline5	(	const char *	title,
		double	x[],
		double	y[],
		int	n,
		const char *	opt = 0,
		double	b1 = 0,
		double	e1 = 0,
		double	b2 = 0,
		double	e2 = 0
	)

Definition at line 657 of file TRadSpline.C.

References BoundaryConditions(), BuildCoeff(), deljobs::end, TRadSpline::fNp, fPoly, genRecEmupikp::i, SetBoundaries(), and TRadSplinePoly::Y().

                                         :
  TRadSpline(title,-1, x[0], x[n-1], n, false)
{
  //
  // Quintic natural spline creator given an array of
  // arbitrary knots in increasing abscissa order and
  // possibly end point conditions
  //
  int beg, end;
  const char *cb1, *ce1, *cb2, *ce2;
  //
  // Check endpoint conditions
  BoundaryConditions(opt,beg,end,cb1,ce1,cb2,ce2);
  //
  // Create the plynomial terms and fill
  // them with node information
  fPoly = new TRadSplinePoly5[fNp];
  for (int i=0; i<n; ++i) {
    fPoly[i+beg].X() = x[i];
    fPoly[i+beg].Y() = y[i];
  }
  //
  // Set the double knots at boundaries
  SetBoundaries(b1,e1,b2,e2,cb1,ce1,cb2,ce2);
  //
  // Build the spline coefficients
  BuildCoeff();
}

TRadSpline5::TRadSpline5	(	const char *	title,
		double	xmin,
		double	xmax,
		double	y[],
		int	n,
		const char *	opt = 0,
		double	b1 = 0,
		double	e1 = 0,
		double	b2 = 0,
		double	e2 = 0
	)

Definition at line 690 of file TRadSpline.C.

References BoundaryConditions(), BuildCoeff(), deljobs::end, TRadSpline::fDelta, TRadSpline::fNp, fPoly, TRadSpline::fXmin, genRecEmupikp::i, SetBoundaries(), and TRadSplinePoly::Y().

                                         :
  TRadSpline(title,(xmax-xmin)/(n-1), xmin, xmax, n, true)
{
  //
  // Quintic natural spline creator given an array of
  // arbitrary function values on equidistant n abscissa
  // values from xmin to xmax and possibly end point conditions
  //
  int beg, end;
  const char *cb1, *ce1, *cb2, *ce2;
  //
  // Check endpoint conditions
  BoundaryConditions(opt,beg,end,cb1,ce1,cb2,ce2);
  //
  // Create the plynomial terms and fill
  // them with node information
  fPoly = new TRadSplinePoly5[fNp];
  for (int i=0; i<n; ++i) {
    fPoly[i+beg].X() = fXmin+i*fDelta;
    fPoly[i+beg].Y() = y[i];
  }
  //
  // Set the double knots at boundaries
  SetBoundaries(b1,e1,b2,e2,cb1,ce1,cb2,ce2);
  //
  // Build the spline coefficients
  BuildCoeff();
}

TRadSpline5::TRadSpline5	(	const char *	title,
		double	xmin,
		double	xmax,
		double(*)(const double &)	func,
		int	n,
		const char *	opt = 0,
		double	b1 = 0,
		double	e1 = 0,
		double	b2 = 0,
		double	e2 = 0
	)

Definition at line 723 of file TRadSpline.C.

References BoundaryConditions(), BuildCoeff(), deljobs::end, TRadSpline::fDelta, TRadSpline::fNp, fPoly, TRadSpline::fXmin, genRecEmupikp::i, SetBoundaries(), TRadSplinePoly::X(), x, and TRadSplinePoly::Y().

                                               :
  TRadSpline(title,(xmax-xmin)/(n-1), xmin, xmax, n, true)
{
  //
  // Quintic natural spline creator given a function to be
  // evaluated on n equidistand abscissa points between xmin
  // and xmax and possibly end point conditions
  //
  int beg, end;
  const char *cb1, *ce1, *cb2, *ce2;

  //
  // Check endpoint conditions
  BoundaryConditions(opt,beg,end,cb1,ce1,cb2,ce2);
  //
  // Create the plynomial terms and fill
  // them with node information
  fPoly = new TRadSplinePoly5[fNp];
  for (int i=0; i<n; ++i) {
    double x=fXmin+i*fDelta;
    fPoly[i+beg].X() = x;
    fPoly[i+beg].Y() = func(x);
  }
  //
  // Set the double knots at boundaries
  SetBoundaries(b1,e1,b2,e2,cb1,ce1,cb2,ce2);
  //
  // Build the spline coefficients
  BuildCoeff();
}

TRadSpline5::~TRadSpline5

(

)

[inline]

Definition at line 186 of file TRadSpline.h.

References fPoly.

{if (fPoly) delete [] fPoly;}

---

Member Function Documentation

void TRadSpline5::BoundaryConditions	(	const char *	opt,
		int &	beg,
		int &	end,
		const char *&	cb1,
		const char *&	ce1,
		const char *&	cb2,
		const char *&	ce2
	)			[private]

Definition at line 759 of file TRadSpline.C.

References TRadSpline::fNp.

Referenced by TRadSpline5().

{
  //
  // Check the boundary conditions and the
  // amount of extra double knots needed
  //
  cb1=ce1=cb2=ce2=0;
  beg=end=0;
  if(opt) {
    cb1 = strstr(opt,"b1");
    ce1 = strstr(opt,"e1");
    cb2 = strstr(opt,"b2");
    ce2 = strstr(opt,"e2");
    if(cb2) {
      fNp=fNp+2;
      beg=2;
    } else if(cb1) {
      fNp=fNp+1;
      beg=1;
    }
    if(ce2) {
      fNp=fNp+2;
      end=2;
    } else if(ce1) {
      fNp=fNp+1;
      end=1;
    }
  }
}

void TRadSpline5::BuildCoeff

(

)

[private, virtual]

Implements TRadSpline.

Definition at line 1081 of file TRadSpline.C.

References TRadSplinePoly5::B(), EvtCyclic3::B, TRadSplinePoly5::C(), EvtCyclic3::C, TRadSplinePoly5::D(), TRadSplinePoly5::E(), F, TRadSplinePoly5::F(), TRadSpline::fNp, fPoly, genRecEmupikp::i, pr, q, s, t(), v, TRadSplinePoly::X(), and TRadSplinePoly::Y().

Referenced by TRadSpline5().

{
  //
  //     algorithm 600, collected algorithms from acm.
  //     algorithm appeared in acm-trans. math. software, vol.9, no. 2,
  //     jun., 1983, p. 258-259.
  //
  //     TRadSpline5 computes the coefficients of a quintic natural quintic spli
  //     s(x) with knots x(i) interpolating there to given function values:
  //               s(x(i)) = y(i)  for i = 1,2, ..., n.
  //     in each interval (x(i),x(i+1)) the spline function s(xx) is a
  //     polynomial of fifth degree:
  //     s(xx) = ((((f(i)*p+e(i))*p+d(i))*p+c(i))*p+b(i))*p+y(i)    (*)
  //           = ((((-f(i)*q+e(i+1))*q-d(i+1))*q+c(i+1))*q-b(i+1))*q+y(i+1)
  //     where  p = xx - x(i)  and  q = x(i+1) - xx.
  //     (note the first subscript in the second expression.)
  //     the different polynomials are pieced together so that s(x) and
  //     its derivatives up to s"" are continuous.
  //
  //        input:
  //
  //     n          number of data points, (at least three, i.e. n > 2)
  //     x(1:n)     the strictly increasing or decreasing sequence of
  //                knots.  the spacing must be such that the fifth power
  //                of x(i+1) - x(i) can be formed without overflow or
  //                underflow of exponents.
  //     y(1:n)     the prescribed function values at the knots.
  //
  //        output:
  //
  //     b,c,d,e,f  the computed spline coefficients as in (*).
  //         (1:n)  specifically
  //                b(i) = s'(x(i)), c(i) = s"(x(i))/2, d(i) = s"'(x(i))/6,
  //                e(i) = s""(x(i))/24,  f(i) = s""'(x(i))/120.
  //                f(n) is neither used nor altered.  the five arrays
  //                b,c,d,e,f must always be distinct.
  //
  //        option:
  //
  //     it is possible to specify values for the first and second
  //     derivatives of the spline function at arbitrarily many knots.
  //     this is done by relaxing the requirement that the sequence of
  //     knots be strictly increasing or decreasing.  specifically:
  //
  //     if x(j) = x(j+1) then s(x(j)) = y(j) and s'(x(j)) = y(j+1),
  //     if x(j) = x(j+1) = x(j+2) then in addition s"(x(j)) = y(j+2).
  //
  //     note that s""(x) is discontinuous at a double knot and, in
  //     addition, s"'(x) is discontinuous at a triple knot.  the
  //     subroutine assigns y(i) to y(i+1) in these cases and also to
  //     y(i+2) at a triple knot.  the representation (*) remains
  //     valid in each open interval (x(i),x(i+1)).  at a double knot,
  //     x(j) = x(j+1), the output coefficients have the following values:
  //       y(j) = s(x(j))          = y(j+1)
  //       b(j) = s'(x(j))         = b(j+1)
  //       c(j) = s"(x(j))/2       = c(j+1)
  //       d(j) = s"'(x(j))/6      = d(j+1)
  //       e(j) = s""(x(j)-0)/24     e(j+1) = s""(x(j)+0)/24
  //       f(j) = s""'(x(j)-0)/120   f(j+1) = s""'(x(j)+0)/120
  //     at a triple knot, x(j) = x(j+1) = x(j+2), the output
  //     coefficients have the following values:
  //       y(j) = s(x(j))         = y(j+1)    = y(j+2)
  //       b(j) = s'(x(j))        = b(j+1)    = b(j+2)
  //       c(j) = s"(x(j))/2      = c(j+1)    = c(j+2)
  //       d(j) = s"'((x(j)-0)/6    d(j+1) = 0  d(j+2) = s"'(x(j)+0)/6
  //       e(j) = s""(x(j)-0)/24    e(j+1) = 0  e(j+2) = s""(x(j)+0)/24
  //       f(j) = s""'(x(j)-0)/120  f(j+1) = 0  f(j+2) = s""'(x(j)+0)/120
  //
  int i, m;
  double pqqr, p, q, r, s, t, u, v,
    b1, p2, p3, q2, q3, r2, pq, pr, qr;

  if (fNp <= 2) {
    return;
  }
  //
  //     coefficients of a positive definite, pentadiagonal matrix,
  //     stored in D, E, F from 1 to n-3.
  //
  m = fNp-2;
  q = fPoly[1].X()-fPoly[0].X();
  r = fPoly[2].X()-fPoly[1].X();
  q2 = q*q;
  r2 = r*r;
  qr = q+r;
  fPoly[0].D() = fPoly[0].E() = 0;
  if (q) fPoly[1].D() = q*6.*q2/(qr*qr);
  else fPoly[1].D() = 0;

  if (m > 1) {
    for (i = 1; i < m; ++i) {
      p = q;
      q = r;
      r = fPoly[i+2].X()-fPoly[i+1].X();
      p2 = q2;
      q2 = r2;
      r2 = r*r;
      pq = qr;
      qr = q+r;
      if (q) {
        q3 = q2*q;
        pr = p*r;
        pqqr = pq*qr;
        fPoly[i+1].D() = q3*6./(qr*qr);
        fPoly[i].D() += (q+q)*(pr*15.*pr+(p+r)*q
                               *(pr* 20.+q2*7.)+q2*
                               ((p2+r2)*8.+pr*21.+q2+q2))/(pqqr*pqqr);
        fPoly[i-1].D() += q3*6./(pq*pq);
        fPoly[i].E() = q2*(p*qr+pq*3.*(qr+r+r))/(pqqr*qr);
        fPoly[i-1].E() += q2*(r*pq+qr*3.*(pq+p+p))/(pqqr*pq);
        fPoly[i-1].F() = q3/pqqr;
      } else
        fPoly[i+1].D() = fPoly[i].E() = fPoly[i-1].F() = 0;
    }
  }
  if (r) fPoly[m-1].D() += r*6.*r2/(qr*qr);
  //
  //     First and second order divided differences of the given function
  //     values, stored in b from 2 to n and in c from 3 to n
  //     respectively. care is taken of double and triple knots.
  //
  for (i = 1; i < fNp; ++i) {
    if (fPoly[i].X() != fPoly[i-1].X()) {
      fPoly[i].B() =
        (fPoly[i].Y()-fPoly[i-1].Y())/(fPoly[i].X()-fPoly[i-1].X());
    } else {
      fPoly[i].B() = fPoly[i].Y();
      fPoly[i].Y() = fPoly[i-1].Y();
    }
  }
  for (i = 2; i < fNp; ++i) {
    if (fPoly[i].X() != fPoly[i-2].X()) {
      fPoly[i].C() =
        (fPoly[i].B()-fPoly[i-1].B())/(fPoly[i].X()-fPoly[i-2].X());
    } else {
      fPoly[i].C() = fPoly[i].B()*.5;
      fPoly[i].B() = fPoly[i-1].B();
    }
  }
  //
  //     Solve the linear system with c(i+2) - c(i+1) as right-hand side. */
  //
  if (m > 1) {
    p=fPoly[0].C()=fPoly[m-1].E()=fPoly[0].F()
      =fPoly[m-2].F()=fPoly[m-1].F()=0;
    fPoly[1].C() = fPoly[3].C()-fPoly[2].C();
    fPoly[1].D() = 1./fPoly[1].D();

    if (m > 2) {
      for (i = 2; i < m; ++i) {
        q = fPoly[i-1].D()*fPoly[i-1].E();
        fPoly[i].D() = 1./(fPoly[i].D()-p*fPoly[i-2].F()-q*fPoly[i-1].E());
        fPoly[i].E() -= q*fPoly[i-1].F();
        fPoly[i].C() = fPoly[i+2].C()-fPoly[i+1].C()-p*fPoly[i-2].C()
          -q*fPoly[i-1].C();
        p = fPoly[i-1].D()*fPoly[i-1].F();
      }
    }
  }

  fPoly[fNp-2].C() = fPoly[fNp-1].C() = 0;
  if (fNp > 3)
    for (i=fNp-3; i > 0; --i)
      fPoly[i].C() = (fPoly[i].C()-fPoly[i].E()*fPoly[i+1].C()
                      -fPoly[i].F()*fPoly[i+2].C())*fPoly[i].D();
  //
  //     Integrate the third derivative of s(x)
  //
  m = fNp-1;
  q = fPoly[1].X()-fPoly[0].X();
  r = fPoly[2].X()-fPoly[1].X();
  b1 = fPoly[1].B();
  q3 = q*q*q;
  qr = q+r;
  if (qr) {
    v = fPoly[1].C()/qr;
    t = v;
  } else
    v = t = 0;
  if (q) fPoly[0].F() = v/q;
  else fPoly[0].F() = 0;
  for (i = 1; i < m; ++i) {
    p = q;
    q = r;
    if (i != m-1) r = fPoly[i+2].X()-fPoly[i+1].X();
    else r = 0;
    p3 = q3;
    q3 = q*q*q;
    pq = qr;
    qr = q+r;
    s = t;
    if (qr) t = (fPoly[i+1].C()-fPoly[i].C())/qr;
    else t = 0;
    u = v;
    v = t-s;
    if (pq) {
      fPoly[i].F() = fPoly[i-1].F();
      if (q) fPoly[i].F() = v/q;
      fPoly[i].E() = s*5.;
      fPoly[i].D() = (fPoly[i].C()-q*s)*10;
      fPoly[i].C() =
        fPoly[i].D()*(p-q)+(fPoly[i+1].B()-fPoly[i].B()+(u-fPoly[i].E())*
                            p3-(v+fPoly[i].E())*q3)/pq;
      fPoly[i].B() = (p*(fPoly[i+1].B()-v*q3)+q*(fPoly[i].B()-u*p3))/pq-p
        *q*(fPoly[i].D()+fPoly[i].E()*(q-p));
    } else {
      fPoly[i].C() = fPoly[i-1].C();
      fPoly[i].D() = fPoly[i].E() = fPoly[i].F() = 0;
    }
  }
  //
  //     End points x(1) and x(n)
  //
  p = fPoly[1].X()-fPoly[0].X();
  s = fPoly[0].F()*p*p*p;
  fPoly[0].E() = fPoly[0].D() = 0;
  fPoly[0].C() = fPoly[1].C()-s*10;
  fPoly[0].B() = b1-(fPoly[0].C()+s)*p;

  q = fPoly[fNp-1].X()-fPoly[fNp-2].X();
  t = fPoly[fNp-2].F()*q*q*q;
  fPoly[fNp-1].E() = fPoly[fNp-1].D() = 0;
  fPoly[fNp-1].C() = fPoly[fNp-2].C()+t*10;
  fPoly[fNp-1].B() += (fPoly[fNp-1].C()-t)*q;
}

double TRadSpline5::Derivative

(

double

x

)

const

Definition at line 882 of file TRadSpline.C.

References TRadSplinePoly5::Derivative(), FindX(), and fPoly.

{
  int klow=FindX(x);
  return fPoly[klow].Derivative(x);
}

double TRadSpline5::Eval

(

double

x

)

const [virtual]

Implements TRadSpline.

Definition at line 875 of file TRadSpline.C.

References TRadSplinePoly5::Eval(), FindX(), and fPoly.

{
  int klow=FindX(x);
  return fPoly[klow].Eval(x);
}

int TRadSpline5::FindX

(

double

x

)

const

Definition at line 841 of file TRadSpline.C.

References TRadSpline::fDelta, TRadSpline::fKstep, TRadSpline::fNp, fPoly, TRadSpline::fXmax, and TRadSpline::fXmin.

Referenced by Derivative(), and Eval().

{

  int klow=0;
  //
  // If out of boundaries, extrapolate
  // It may be badly wrong
  if(x<=fXmin) klow=0;
  else if(x>=fXmax) klow=fNp-1;
  else {
    if(fKstep) {
      //
      // Equidistant knots, use histogramming
      klow = (int((x-fXmin)/fDelta)<fNp-1)?int((x-fXmin)/fDelta):fNp-1;
    } else {
      int khig=fNp-1, khalf;
      //
      // Non equidistant knots, binary search
      while(khig-klow>1)
        if(x>fPoly[khalf=(klow+khig)/2].X())
          klow=khalf;
        else
          khig=khalf;
    }
    //
    // This could be removed, sanity check
    if(!(fPoly[klow].X()<=x && x<=fPoly[klow+1].X()))
      printf("Binary search failed x(%d) = %f < %f < x(%d) = %f\n",
             klow,fPoly[klow].X(),x,klow+1,fPoly[klow+1].X());
  }
  return klow;
}

void TRadSpline5::GetCoeff	(	int	i,
		double &	x,
		double &	y,
		double &	b,
		double &	c,
		double &	d,
		double &	e,
		double &	f
	)			[inline]

Definition at line 187 of file TRadSpline.h.

References TRadSplinePoly5::B(), TRadSplinePoly5::C(), TRadSplinePoly5::D(), TRadSplinePoly5::E(), TRadSplinePoly5::F(), fPoly, TRadSplinePoly::X(), and TRadSplinePoly::Y().

Referenced by Test().

    {x=fPoly[i].X();y=fPoly[i].Y();b=fPoly[i].B();
    c=fPoly[i].C();d=fPoly[i].D();
    e=fPoly[i].E();f=fPoly[i].F();}

void TRadSpline5::GetKnot	(	int	i,
		double &	x,
		double &	y
	)			const [inline, virtual]

Implements TRadSpline.

Definition at line 192 of file TRadSpline.h.

References fPoly, TRadSplinePoly::X(), and TRadSplinePoly::Y().

    {x=fPoly[i].X(); y=fPoly[i].Y();}

virtual int TRadSpline::GetNpx

(

)

const [inline, virtual, inherited]

Definition at line 26 of file TRadSpline.h.

References TRadSpline::fNpx.

{return fNpx;}

void TRadSpline5::SaveAs

(

const char *

filename

)

const [virtual]

Reimplemented from TRadSpline.

Definition at line 889 of file TRadSpline.C.

References EvtCyclic3::B, EvtCyclic3::C, F, TRadSpline::fDelta, TRadSpline::fKstep, TRadSpline::fNp, fPoly, TRadSpline::fXmax, TRadSpline::fXmin, and genRecEmupikp::i.

{
  // write this spline as a C++ function that can be executed without ROOT
  // the name of the function is the name of the file up to the "." if any
    
   //open the file
   ofstream *f = new ofstream(filename,ios::out);
   if (f == 0) {
      printf("Cannot open file:%s\n",filename);
      return;
   }
   
   //write the function name and the spline constants
   char buffer[512];
   int nch = strlen(filename);
   sprintf(buffer,"double %s",filename);
   char *dot = strstr(buffer,".");
   if (dot) *dot = 0;
   strcat(buffer,"(double x) {\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   const int fNp = %d, fKstep = %d;\n",fNp,fKstep);
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   const double fDelta = %g, fXmin = %g, fXmax = %g;\n",fDelta,fXmin,fXmax);
   nch = strlen(buffer); f->write(buffer,nch);

   //write the spline coefficients
   //array fX
   sprintf(buffer,"   const double fX[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   int i;
   char numb[20];
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].X());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
   //array fY
   sprintf(buffer,"   const double fY[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].Y());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
   //array fB
   sprintf(buffer,"   const double fB[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].B());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
   //array fC
   sprintf(buffer,"   const double fC[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].C());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
    //array fD
   sprintf(buffer,"   const double fD[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].D());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
    //array fE
   sprintf(buffer,"   const double fE[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].E());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
    //array fF
   sprintf(buffer,"   const double fF[%d] = {",fNp);   
   nch = strlen(buffer); f->write(buffer,nch);
   buffer[0] = 0;
   for (i=0;i<fNp;i++) {
      sprintf(numb," %g,",fPoly[i].F());
      nch = strlen(numb);
      if (i == fNp-1) numb[nch-1]=0;
      strcat(buffer,numb);
      if (i%5 == 4 || i == fNp-1) {
         nch = strlen(buffer); f->write(buffer,nch);
         if (i != fNp-1) sprintf(buffer,"\n                       ");
      }
   }
   sprintf(buffer," };\n");
   nch = strlen(buffer); f->write(buffer,nch);
    
   //generate code for the spline evaluation
   sprintf(buffer,"   int klow=0;\n");
   nch = strlen(buffer); f->write(buffer,nch);

   sprintf(buffer,"   // If out of boundaries, extrapolate. It may be badly wrong\n");
   sprintf(buffer,"   if(x<=fXmin) klow=0;\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   else if(x>=fXmax) klow=fNp-1;\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   else {\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"     if(fKstep) {\n");
   nch = strlen(buffer); f->write(buffer,nch);

   sprintf(buffer,"       // Equidistant knots, use histogramming\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"       klow = int((x-fXmin)/fDelta);\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"       if (klow < fNp-1) klow = fNp-1;\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"     } else {\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"       int khig=fNp-1, khalf;\n");
   nch = strlen(buffer); f->write(buffer,nch);

   sprintf(buffer,"       // Non equidistant knots, binary search\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"       while(khig-klow>1)\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"      if(x>fX[khalf=(klow+khig)/2]) klow=khalf;\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"      else khig=khalf;\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"     }\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   }\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   // Evaluate now\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   double dx=x-fX[klow];\n");
   nch = strlen(buffer); f->write(buffer,nch);
   sprintf(buffer,"   return (fY[klow]+dx*(fB[klow]+dx*(fC[klow]+dx*(fD[klow]+dx*(fE[klow]+dx*fF[klow])))));\n");
   nch = strlen(buffer); f->write(buffer,nch);
    
   //close file
   f->write("}\n",2);
      
   if (f) { f->close(); delete f;}
}

void TRadSpline5::SetBoundaries	(	double	b1,
		double	e1,
		double	b2,
		double	e2,
		const char *	cb1,
		const char *	ce1,
		const char *	cb2,
		const char *	ce2
	)			[private]

Definition at line 792 of file TRadSpline.C.

References TRadSpline::fNp, fPoly, TRadSplinePoly::X(), and TRadSplinePoly::Y().

Referenced by TRadSpline5().

{
  //
  // Set the boundary conditions at double/triple knots
  //
  if(cb2) {
    //
    // Second derivative at the beginning
    fPoly[0].X() = fPoly[1].X() = fPoly[2].X();
    fPoly[0].Y() = fPoly[2].Y();
    fPoly[2].Y()=b2;
    //
    // If first derivative not given, we take the finite
    // difference from first and second point... not recommended
    if(cb1)
      fPoly[1].Y()=b1;
    else
      fPoly[1].Y()=(fPoly[3].Y()-fPoly[0].Y())/(fPoly[3].X()-fPoly[2].X());
  } else if(cb1) {
    //
    // First derivative at the end
    fPoly[0].X() = fPoly[1].X();
    fPoly[0].Y() = fPoly[1].Y();
    fPoly[1].Y()=b1;
  }
  if(ce2) {
    //
    // Second derivative at the end
    fPoly[fNp-1].X() = fPoly[fNp-2].X() = fPoly[fNp-3].X();
    fPoly[fNp-1].Y()=e2;
    //
    // If first derivative not given, we take the finite
    // difference from first and second point... not recommended
    if(ce1)
      fPoly[fNp-2].Y()=e1;
    else
      fPoly[fNp-2].Y()=
        (fPoly[fNp-3].Y()-fPoly[fNp-4].Y())
        /(fPoly[fNp-3].X()-fPoly[fNp-4].X());
  } else if(ce1) {
    //
    // First derivative at the end
    fPoly[fNp-1].X() = fPoly[fNp-2].X();
    fPoly[fNp-1].Y()=e1;
  }
}

void TRadSpline::SetNpx

(

int

n

)

[inline, inherited]

Definition at line 30 of file TRadSpline.h.

References TRadSpline::fNpx.

{fNpx=n;}

void TRadSpline5::Test

(

)

[static]

Definition at line 1308 of file TRadSpline.C.

References cos(), GetCoeff(), genRecEmupikp::i, ganga-rec::j, sin(), TRadSpline5(), and x.

{
  //
  // Test method for TRadSpline5
  //
  //
  //   n          number of data points.
  //   m          2*m-1 is order of spline.
  //                 m = 3 always for quintic spline.
  //   nn,nm1,mm,
  //   mm1,i,k,
  //   j,jj       temporary integer variables.
  //   z,p        temporary double precision variables.
  //   x[n]       the sequence of knots.
  //   y[n]       the prescribed function values at the knots.
  //   a[200][6]  two dimensional array whose columns are
  //                 the computed spline coefficients
  //   diff[5]    maximum values of differences of values and
  //                 derivatives to right and left of knots.
  //   com[5]     maximum values of coefficients.
  //
  //
  //   test of TRadSpline5 with nonequidistant knots and
  //      equidistant knots follows.
  //
  //
  double hx;
  double diff[5];
  double a[1200], c[6];
  int i, j, k, m, n;
  double p, x[200], y[200], z;
  int jj, mm, nn;
  int mm1, nm1;
  double com[5];

  printf("1         TEST OF TRadSpline5 WITH NONEQUIDISTANT KNOTS\n");
  n = 5;
  x[0] = -3;
  x[1] = -1;
  x[2] = 0;
  x[3] = 3;
  x[4] = 4;
  y[0] = 7;
  y[1] = 11;
  y[2] = 26;
  y[3] = 56;
  y[4] = 29;
  m = 3;
  mm = m << 1;
  mm1 = mm-1;
  printf("\n-N = %3d    M =%2d\n",n,m);
  TRadSpline5 *spline = new TRadSpline5("Test",x,y,n);
  for (i = 0; i < n; ++i)
    spline->GetCoeff(i,hx, a[i],a[i+200],a[i+400],
                     a[i+600],a[i+800],a[i+1000]);
  delete spline;
  for (i = 0; i < mm1; ++i) diff[i] = com[i] = 0;
  for (k = 0; k < n; ++k) {
    for (i = 0; i < mm; ++i) c[i] = a[k+i*200];
    printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
    printf("%12.8f\n",x[k]);
    if (k == n-1) {
      printf("%16.8f\n",c[0]);
    } else {
      for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
      printf("\n");
      for (i = 0; i < mm1; ++i)
        if ((z=fabs(a[k+i*200])) > com[i]) com[i] = z;
      z = x[k+1]-x[k];
      for (i = 1; i < mm; ++i)
        for (jj = i; jj < mm; ++jj) {
          j = mm+i-jj;
          c[j-2] = c[j-1]*z+c[j-2];
        }
      for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
      printf("\n");
      for (i = 0; i < mm1; ++i)
        if (!(k >= n-2 && i != 0))
          if((z = fabs(c[i]-a[k+1+i*200]))
             > diff[i]) diff[i] = z;
    }
  }
  printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
  for (i = 0; i < mm1; ++i) printf("%18.9E",diff[i]);
  printf("\n");
  printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
  if (fabs(c[0]) > com[0])
    com[0] = fabs(c[0]);
  for (i = 0; i < mm1; ++i) printf("%16.8f",com[i]);
  printf("\n");
  m = 3;
  for (n = 10; n <= 100; n += 10) {
    mm = m << 1;
    mm1 = mm-1;
    nm1 = n-1;
    for (i = 0; i < nm1; i += 2) {
      x[i] = i+1;
      x[i+1] = i+2;
      y[i] = 1;
      y[i+1] = 0;
    }
    if (n % 2 != 0) {
      x[n-1] = n;
      y[n-1] = 1;
    }
    printf("\n-N = %3d    M =%2d\n",n,m);
    spline = new TRadSpline5("Test",x,y,n);
    for (i = 0; i < n; ++i)
      spline->GetCoeff(i,hx,a[i],a[i+200],a[i+400],
                       a[i+600],a[i+800],a[i+1000]);
    delete spline;
    for (i = 0; i < mm1; ++i)
      diff[i] = com[i] = 0;
    for (k = 0; k < n; ++k) {
      for (i = 0; i < mm; ++i)
        c[i] = a[k+i*200];
      if (n < 11) {
        printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
        printf("%12.8f\n",x[k]);
        if (k == n-1) printf("%16.8f\n",c[0]);
      }
      if (k == n-1) break;
      if (n <= 10) {
        for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
        printf("\n");
      }
      for (i = 0; i < mm1; ++i)
        if ((z=fabs(a[k+i*200])) > com[i])
          com[i] = z;
      z = x[k+1]-x[k];
      for (i = 1; i < mm; ++i)
        for (jj = i; jj < mm; ++jj) {
          j = mm+i-jj;
          c[j-2] = c[j-1]*z+c[j-2];
        }
      if (n <= 10) {
        for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
        printf("\n");
      }
      for (i = 0; i < mm1; ++i)
        if (!(k >= n-2 && i != 0))
          if ((z = fabs(c[i]-a[k+1+i*200]))
              > diff[i]) diff[i] = z;
    }
    printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
    for (i = 0; i < mm1; ++i) printf("%18.9E",diff[i]);
    printf("\n");
    printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
    if (fabs(c[0]) > com[0])
      com[0] = fabs(c[0]);
    for (i = 0; i < mm1; ++i) printf("%16.8E",com[i]);
    printf("\n");
  }
  //
  //     Test of TRadSpline5 with nonequidistant double knots follows
  //
  printf("1  TEST OF TRadSpline5 WITH NONEQUIDISTANT DOUBLE KNOTS\n");
  n = 5;
  x[0] = -3;
  x[1] = -3;
  x[2] = -1;
  x[3] = -1;
  x[4] = 0;
  x[5] = 0;
  x[6] = 3;
  x[7] = 3;
  x[8] = 4;
  x[9] = 4;
  y[0] = 7;
  y[1] = 2;
  y[2] = 11;
  y[3] = 15;
  y[4] = 26;
  y[5] = 10;
  y[6] = 56;
  y[7] = -27;
  y[8] = 29;
  y[9] = -30;
  m = 3;
  nn = n << 1;
  mm = m << 1;
  mm1 = mm-1;
  printf("-N = %3d    M =%2d\n",n,m);
  spline = new TRadSpline5("Test",x,y,nn);
  for (i = 0; i < nn; ++i)
    spline->GetCoeff(i,hx,a[i],a[i+200],a[i+400],
                     a[i+600],a[i+800],a[i+1000]);
  delete spline;
  for (i = 0; i < mm1; ++i)
    diff[i] = com[i] = 0;
  for (k = 0; k < nn; ++k) {
    for (i = 0; i < mm; ++i)
      c[i] = a[k+i*200];
    printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
    printf("%12.8f\n",x[k]);
    if (k == nn-1) {
      printf("%16.8f\n",c[0]);
      break;
    }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if ((z=fabs(a[k+i*200])) > com[i]) com[i] = z;
    z = x[k+1]-x[k];
    for (i = 1; i < mm; ++i)
      for (jj = i; jj < mm; ++jj) {
        j = mm+i-jj;
        c[j-2] = c[j-1]*z+c[j-2];
      }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if (!(k >= nn-2 && i != 0))
        if ((z = fabs(c[i]-a[k+1+i*200]))
            > diff[i]) diff[i] = z;
  }
  printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
  for (i = 1; i <= mm1; ++i) {
    printf("%18.9E",diff[i-1]);
  }
  printf("\n");
  if (fabs(c[0]) > com[0])
    com[0] = fabs(c[0]);
  printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
  for (i = 0; i < mm1; ++i) printf("%16.8f",com[i]);
  printf("\n");
  m = 3;
  for (n = 10; n <= 100; n += 10) {
    nn = n << 1;
    mm = m << 1;
    mm1 = mm-1;
    p = 0;
    for (i = 0; i < n; ++i) {
      p += fabs(sin(i+1));
      x[(i << 1)] = p;
      x[(i << 1)+1] = p;
      y[(i << 1)] = cos(i+1)-.5;
      y[(i << 1)+1] = cos((i << 1)+2)-.5;
    }
    printf("-N = %3d    M =%2d\n",n,m);
    spline = new TRadSpline5("Test",x,y,nn);
    for (i = 0; i < nn; ++i)
      spline->GetCoeff(i,hx,a[i],a[i+200],a[i+400],
                       a[i+600],a[i+800],a[i+1000]);
    delete spline;
    for (i = 0; i < mm1; ++i)
      diff[i] = com[i] = 0;
    for (k = 0; k < nn; ++k) {
      for (i = 0; i < mm; ++i)
        c[i] = a[k+i*200];
      if (n < 11) {
        printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
        printf("%12.8f\n",x[k]);
        if (k == nn-1) printf("%16.8f\n",c[0]);
      }
      if (k == nn-1) break;
      if (n <= 10) {
        for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
        printf("\n");
      }
      for (i = 0; i < mm1; ++i)
        if ((z=fabs(a[k+i*200])) > com[i]) com[i] = z;
      z = x[k+1]-x[k];
      for (i = 1; i < mm; ++i) {
        for (jj = i; jj < mm; ++jj) {
          j = mm+i-jj;
          c[j-2] = c[j-1]*z+c[j-2];
        }
      }
      if (n <= 10) {
        for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
        printf("\n");
      }
      for (i = 0; i < mm1; ++i)
        if (!(k >= nn-2 && i != 0))
          if ((z = fabs(c[i]-a[k+1+i*200]))
              > diff[i]) diff[i] = z;
    }
    printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
    for (i = 0; i < mm1; ++i) printf("%18.9E",diff[i]);
    printf("\n");
    printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
    if (fabs(c[0]) > com[0])
      com[0] = fabs(c[0]);
    for (i = 0; i < mm1; ++i) printf("%18.9E",com[i]);
    printf("\n");
  }
  //
  //     test of TRadSpline5 with nonequidistant knots, one double knot,
  //        one triple knot, follows.
  //
  printf("1         TEST OF TRadSpline5 WITH NONEQUIDISTANT KNOTS,\n");
  printf("             ONE DOUBLE, ONE TRIPLE KNOT\n");
  n = 8;
  x[0] = -3;
  x[1] = -1;
  x[2] = -1;
  x[3] = 0;
  x[4] = 3;
  x[5] = 3;
  x[6] = 3;
  x[7] = 4;
  y[0] = 7;
  y[1] = 11;
  y[2] = 15;
  y[3] = 26;
  y[4] = 56;
  y[5] = -30;
  y[6] = -7;
  y[7] = 29;
  m = 3;
  mm = m << 1;
  mm1 = mm-1;
  printf("-N = %3d    M =%2d\n",n,m);
  spline=new TRadSpline5("Test",x,y,n);
  for (i = 0; i < n; ++i)
    spline->GetCoeff(i,hx,a[i],a[i+200],a[i+400],
                     a[i+600],a[i+800],a[i+1000]);
  delete spline;
  for (i = 0; i < mm1; ++i)
    diff[i] = com[i] = 0;
  for (k = 0; k < n; ++k) {
    for (i = 0; i < mm; ++i)
      c[i] = a[k+i*200];
    printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
    printf("%12.8f\n",x[k]);
    if (k == n-1) {
      printf("%16.8f\n",c[0]);
      break;
    }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if ((z=fabs(a[k+i*200])) > com[i]) com[i] = z;
    z = x[k+1]-x[k];
    for (i = 1; i < mm; ++i)
      for (jj = i; jj < mm; ++jj) {
        j = mm+i-jj;
        c[j-2] = c[j-1]*z+c[j-2];
      }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if (!(k >= n-2 && i != 0))
        if ((z = fabs(c[i]-a[k+1+i*200]))
            > diff[i]) diff[i] = z;
  }
  printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
  for (i = 0; i < mm1; ++i) printf("%18.9E",diff[i]);
  printf("\n");
  printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
  if (fabs(c[0]) > com[0])
    com[0] = fabs(c[0]);
  for (i = 0; i < mm1; ++i) printf("%16.8f",com[i]);
  printf("\n");
  //
  //     Test of TRadSpline5 with nonequidistant knots, two double knots,
  //        one triple knot,follows.
  //
  printf("1         TEST OF TRadSpline5 WITH NONEQUIDISTANT KNOTS,\n");
  printf("             TWO DOUBLE, ONE TRIPLE KNOT\n");
  n = 10;
  x[0] = 0;
  x[1] = 2;
  x[2] = 2;
  x[3] = 3;
  x[4] = 3;
  x[5] = 3;
  x[6] = 5;
  x[7] = 8;
  x[8] = 9;
  x[9] = 9;
  y[0] = 163;
  y[1] = 237;
  y[2] = -127;
  y[3] = 119;
  y[4] = -65;
  y[5] = 192;
  y[6] = 293;
  y[7] = 326;
  y[8] = 0;
  y[9] = -414;
  m = 3;
  mm = m << 1;
  mm1 = mm-1;
  printf("-N = %3d    M =%2d\n",n,m);
  spline = new TRadSpline5("Test",x,y,n);
  for (i = 0; i < n; ++i)
    spline->GetCoeff(i,hx,a[i],a[i+200],a[i+400],
                     a[i+600],a[i+800],a[i+1000]);
  delete spline;
  for (i = 0; i < mm1; ++i)
    diff[i] = com[i] = 0;
  for (k = 0; k < n; ++k) {
    for (i = 0; i < mm; ++i)
      c[i] = a[k+i*200];
    printf(" ---------------------------------------%3d --------------------------------------------\n",k+1);
    printf("%12.8f\n",x[k]);
    if (k == n-1) {
      printf("%16.8f\n",c[0]);
      break;
    }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if ((z=fabs(a[k+i*200])) > com[i]) com[i] = z;
    z = x[k+1]-x[k];
    for (i = 1; i < mm; ++i)
      for (jj = i; jj < mm; ++jj) {
        j = mm+i-jj;
        c[j-2] = c[j-1]*z+c[j-2];
      }
    for (i = 0; i < mm; ++i) printf("%16.8f",c[i]);
    printf("\n");
    for (i = 0; i < mm1; ++i)
      if (!(k >= n-2 && i != 0))
        if((z = fabs(c[i]-a[k+1+i*200]))
           > diff[i]) diff[i] = z;
  }
  printf("  MAXIMUM ABSOLUTE VALUES OF DIFFERENCES \n");
  for (i = 0; i < mm1; ++i) printf("%18.9E",diff[i]);
  printf("\n");
  printf("  MAXIMUM ABSOLUTE VALUES OF COEFFICIENTS \n");
  if (fabs(c[0]) > com[0])
    com[0] = fabs(c[0]);
  for (i = 0; i < mm1; ++i) printf("%16.8f",com[i]);
  printf("\n");
}

---

Member Data Documentation

double TRadSpline::fDelta [protected, inherited]

Definition at line 6 of file TRadSpline.h.

Referenced by FindX(), TRadSpline3::FindX(), SaveAs(), TRadSpline3::SaveAs(), TRadSpline3::TRadSpline3(), and TRadSpline5().

bool TRadSpline::fKstep [protected, inherited]

Definition at line 10 of file TRadSpline.h.

Referenced by FindX(), TRadSpline3::FindX(), SaveAs(), and TRadSpline3::SaveAs().

int TRadSpline::fNp [protected, inherited]

Definition at line 9 of file TRadSpline.h.

Referenced by BoundaryConditions(), BuildCoeff(), TRadSpline3::BuildCoeff(), FindX(), TRadSpline3::FindX(), SaveAs(), TRadSpline3::SaveAs(), SetBoundaries(), and TRadSpline5().

int TRadSpline::fNpx [protected, inherited]

Definition at line 11 of file TRadSpline.h.

Referenced by TRadSpline::GetNpx(), and TRadSpline::SetNpx().

TRadSplinePoly5* TRadSpline5::fPoly [private]

Definition at line 156 of file TRadSpline.h.

Referenced by BuildCoeff(), Derivative(), Eval(), FindX(), GetCoeff(), GetKnot(), SaveAs(), SetBoundaries(), TRadSpline5(), and ~TRadSpline5().

double TRadSpline::fXmax [protected, inherited]

Definition at line 8 of file TRadSpline.h.

Referenced by FindX(), TRadSpline3::FindX(), SaveAs(), and TRadSpline3::SaveAs().

double TRadSpline::fXmin [protected, inherited]

Definition at line 7 of file TRadSpline.h.

Referenced by FindX(), TRadSpline3::FindX(), SaveAs(), TRadSpline3::SaveAs(), TRadSpline3::TRadSpline3(), and TRadSpline5().

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