CubSpline Class Reference

The CubSpline class is a third-order spline representation of a function. More...

Collaboration diagram for CubSpline:

Public Member Functions
int	size ()
	Returns the interpolated value. More...
double	operator() (double x)
double	Deriv (double x)
	Returns the interpolated first derivative. More...
double	Deriv2 (double x)
	Returns the interpolated second derivative. More...
double	Deriv3 (double x)
	Returns the interpolated third derivative. More...
void	Update ()
	Recompute the second derivatives from the function values. More...
std::vector< double > &	Data ()
void	Init (SimpleGrid &newGrid, std::vector< double > yvals, double startderiv, double endderiv)
	Initialize the cubic spline. More...
void	Init (SimpleGrid &newGrid, std::vector< double > &yvals)
	Simplified form which assumes that the second derivative at both boundaries are zero. More...
	CubSpline (SimpleGrid &newGrid, std::vector< double > &yvals)
	Simplified constructor. More...
	CubSpline (SimpleGrid &newGrid, std::vector< double > &yvals, double startderiv, double endderiv)
	Full constructor. More...
double	operator() (int i) const
	Returns the value of the function at the ith grid point. More...
double &	operator() (int i)
	Returns a reference to the value at the ith grid point. More...
	CubSpline ()
	Trivial constructor. More...

Public Attributes
SimpleGrid	grid
bool	Initialized

Private Attributes
bool	UpToDate
	This flag records whether or not the stored second derivatives are in sync with the function values. More...
std::vector< double >	y
	The function values on the grid points. More...
std::vector< double >	d2y
	The second derivatives of the function. More...
double	StartDeriv
	The values of the derivative of the represented function on the boundary. More...
double	EndDeriv

Detailed Description

The CubSpline class is a third-order spline representation of a function.

It stores a pointer to a grid and the values of the function and its second derivative at the points defined by the grid.

Definition at line 26 of file CubicSpline.h.

Constructor & Destructor Documentation

CubSpline() [1/3]

CubSpline ( SimpleGrid &  newGrid, std::vector< double > &  yvals  )

inline

Simplified constructor.

Definition at line 91 of file CubicSpline.h.

References EndDeriv, Init(), StartDeriv, and Update().

  {
    StartDeriv = EndDeriv = 5.0e30;
    Init(newGrid, yvals, 5.0e30, 5.0e30);
    Update();
  }

CubSpline() [2/3]

CubSpline ( SimpleGrid &  newGrid, std::vector< double > &  yvals, double  startderiv, double  endderiv  )

inline

Full constructor.

Definition at line 99 of file CubicSpline.h.

References Init(), and Update().

  {
    Init(newGrid, yvals, startderiv, endderiv);
    Update();
  }

CubSpline() [3/3]

CubSpline ( )

inline

Trivial constructor.

Definition at line 115 of file CubicSpline.h.

References Initialized, and UpToDate.

              : StartDeriv(0.), EndDeriv(0.)
  {
    UpToDate    = false;
    Initialized = false;
  }

Member Function Documentation

Data()

std::vector<double>& Data ( )

inline

Definition at line 59 of file CubicSpline.h.

References y.

{ return y; }

Deriv()

double Deriv ( double  x )

inline

Returns the interpolated first derivative.

Definition at line 163 of file CubicSpline.h.

References d2y, grid, SimpleGrid::NumPoints(), SimpleGrid::ReverseMap(), Update(), UpToDate, and y.

{
  if (!UpToDate)
    Update();

  SimpleGrid& X = grid;
  int hi        = X.ReverseMap(x) + 1;
  int low       = hi - 1;
  if (low < 0)
  {
    low = 0;
    hi  = 1;
  }
  if (hi > (X.NumPoints() - 1))
  {
    hi  = (X.NumPoints() - 1);
    low = hi - 1;
  }

  double h      = X[hi] - X[low];
  double hinv   = 1.0 / h;
  double a      = (X[hi] - x) * hinv;
  double b      = (x - X[low]) * hinv;
  double sixinv = 0.1666666666666666666;

  return ((y[hi] - y[low]) * hinv + (h * sixinv) * ((3.0 * b * b - 1.0) * d2y[hi] - (3.0 * a * a - 1.0) * d2y[low]));
}

Deriv2()

double Deriv2 ( double  x )

inline

Returns the interpolated second derivative.

Definition at line 191 of file CubicSpline.h.

References d2y, grid, SimpleGrid::NumPoints(), SimpleGrid::ReverseMap(), Update(), and UpToDate.

{
  if (!UpToDate)
    Update();
  SimpleGrid& X = grid;
  int hi        = X.ReverseMap(x) + 1;
  int low       = hi - 1;
  if (low < 0)
  {
    low = 0;
    hi  = 1;
  }
  if (hi > (X.NumPoints() - 1))
  {
    hi  = (X.NumPoints() - 1);
    low = hi - 1;
  }


  double h    = X[hi] - X[low];
  double hinv = 1.0 / h;
  double a    = (X[hi] - x) * hinv;
  double b    = (x - X[low]) * hinv;
  return (a * d2y[low] + b * d2y[hi]);
}

Deriv3()

double Deriv3 ( double  x )

inline

Returns the interpolated third derivative.

Definition at line 218 of file CubicSpline.h.

References d2y, grid, SimpleGrid::NumPoints(), SimpleGrid::ReverseMap(), Update(), and UpToDate.

{
  if (!UpToDate)
    Update();
  SimpleGrid& X = grid;
  int hi        = X.ReverseMap(x) + 1;
  int low       = hi - 1;
  if (low < 0)
  {
    low = 0;
    hi  = 1;
  }
  if (hi > (X.NumPoints() - 1))
  {
    hi  = (X.NumPoints() - 1);
    low = hi - 1;
  }

  double h = X[hi] - X[low];

  return ((d2y[hi] - d2y[low]) / h);
}

Init() [1/2]

void Init ( SimpleGrid &  newGrid, std::vector< double >  yvals, double  startderiv, double  endderiv  )

inline

Initialize the cubic spline.

See notes about start and end deriv above.

Definition at line 63 of file CubicSpline.h.

References d2y, EndDeriv, grid, Initialized, SimpleGrid::NumPoints(), StartDeriv, Update(), and y.

Referenced by CubSpline(), and Init().

  {
    StartDeriv = startderiv;
    EndDeriv   = endderiv;
    if (newGrid.NumPoints() != yvals.size())
    {
      std::cerr << "Size mismatch in CubSpline.\n";
      std::cerr << "Grid Points = " << newGrid.NumPoints() << std::endl;
      std::cerr << "Y points    = " << yvals.size() << std::endl;
      abort();
    }
    grid = newGrid;
    y.resize(grid.NumPoints());
    d2y.resize(grid.NumPoints());
    y = yvals;
    Update();
    Initialized = true;
  }

Init() [2/2]

void Init ( SimpleGrid &  newGrid, std::vector< double > &  yvals  )

inline

Simplified form which assumes that the second derivative at both boundaries are zero.

Definition at line 84 of file CubicSpline.h.

References Init(), and Update().

  {
    Init(newGrid, yvals, 5.0e30, 5.0e30);
    Update();
  }

operator()() [1/3]

double operator() ( double  x )

inline

Definition at line 122 of file CubicSpline.h.

References d2y, SimpleGrid::End(), grid, SimpleGrid::NumPoints(), SimpleGrid::ReverseMap(), Update(), UpToDate, and y.

{
  if (!UpToDate)
    Update();

  SimpleGrid& X = grid;
#ifdef DEBUG
  if (x > X.End())
  {
    if (x < (X.End() * 1.000000001))
      x = X.End();
    else
    {
      std::cerr << "x outside grid in CubSpline.\n";
      std::cerr << "x = " << x << " X.End = " << X.End() << "\n";
      abort();
    }
  }
#endif
  int hi  = X.ReverseMap(x) + 1;
  int low = hi - 1;
  if (low < 0)
  {
    low = 0;
    hi  = 1;
  }
  if (hi > (X.NumPoints() - 1))
  {
    hi  = (X.NumPoints() - 1);
    low = hi - 1;
  }

  double h      = X[hi] - X[low];
  double hinv   = 1.0 / h;
  double a      = (X[hi] - x) * hinv;
  double b      = (x - X[low]) * hinv;
  double sixinv = 0.1666666666666666666;

  return (a * y[low] + b * y[hi] + ((a * a * a - a) * d2y[low] + (b * b * b - b) * d2y[hi]) * (h * h * sixinv));
}

operator()() [2/3]

double operator() ( int  i ) const

inline

Returns the value of the function at the ith grid point.

Definition at line 106 of file CubicSpline.h.

References y.

{ return (y[i]); }

operator()() [3/3]

double& operator() ( int  i )

inline

Returns a reference to the value at the ith grid point.

Definition at line 108 of file CubicSpline.h.

References UpToDate, and y.

  {
    UpToDate = false;
    return (y[i]);
  }

size()

int size ( void  )

inline

Returns the interpolated value.

Definition at line 49 of file CubicSpline.h.

References grid, and SimpleGrid::NumPoints().

{ return grid.NumPoints(); }

Update()

void Update

(

)

Recompute the second derivatives from the function values.

Referenced by CubSpline(), Deriv(), Deriv2(), Deriv3(), Init(), and operator()().

Member Data Documentation

d2y

std::vector<double> d2y

private

The second derivatives of the function.

Definition at line 36 of file CubicSpline.h.

Referenced by Deriv(), Deriv2(), Deriv3(), Init(), and operator()().

EndDeriv

double EndDeriv

private

Definition at line 42 of file CubicSpline.h.

Referenced by CubSpline(), and Init().

grid

SimpleGrid grid

Definition at line 45 of file CubicSpline.h.

Referenced by Deriv(), Deriv2(), Deriv3(), Init(), operator()(), and size().

Initialized

bool Initialized

Definition at line 46 of file CubicSpline.h.

Referenced by CubSpline(), and Init().

StartDeriv

double StartDeriv

private

The values of the derivative of the represented function on the boundary.

If each value is greater that 1e30, we compute boundary conditions assuming that the second derivative is zero at that boundary.

Definition at line 42 of file CubicSpline.h.

Referenced by CubSpline(), and Init().

UpToDate

bool UpToDate

private

This flag records whether or not the stored second derivatives are in sync with the function values.

It is used to determine whether the second derivatives need recomputation.

Definition at line 32 of file CubicSpline.h.

Referenced by CubSpline(), Deriv(), Deriv2(), Deriv3(), and operator()().

y

std::vector<double> y

private

The function values on the grid points.

Definition at line 34 of file CubicSpline.h.

Referenced by Data(), Deriv(), Init(), and operator()().

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The documentation for this class was generated from the following file:

• /home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/QMCTools/ppconvert/src/CubicSpline.h