CubicSplineCommon Class Reference

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

Collaboration diagram for CubicSplineCommon:

Public Member Functions
Array< double, 1 > &	Data ()
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...
void	Init (std::shared_ptr< Grid > &NewGrid, Array< double, 1 > NewYs, double startderiv, double endderiv)
	Initialize the cubic spline. More...
void	Init (std::shared_ptr< Grid > &NewGrid, Array< double, 1 > NewYs)
	Simplified form which assumes that the second derivative at both boundaries are zero. More...
	CubicSplineCommon (std::shared_ptr< Grid > &NewGrid, Array< double, 1 > NewYs)
	Simplified constructor. More...
	CubicSplineCommon (std::shared_ptr< Grid > &NewGrid, Array< double, 1 > NewYs, 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...
double	Params (int i) const
	Returns the value of the function at the ith grid point. More...
double &	Params (int i)
	Returns a reference to the value at the ith grid point. More...
void	Write (IOSectionClass &outSection)
void	Read (IOSectionClass &inSection)
CubicSplineCommon &	operator= (const CubicSplineCommon &spline)
	CubicSplineCommon ()
	Trivial constructor. More...

Public Attributes
int	NumParams
std::shared_ptr< Grid >	grid
double	StartDeriv
	The values of the derivative of the represented function on the boundary. More...
double	EndDeriv

Private Attributes
int	UpToDate
	This flag records whether or not the stored second derivatives are in sync with the function values. More...
Array< double, 1 >	y
	The function values on the grid points. More...
Array< double, 1 >	d2y
	The second derivatives of the function. More...

Detailed Description

The CubicSplineCommon 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 28 of file CubicSplineCommon.h.

Constructor & Destructor Documentation

CubicSplineCommon() [1/3]

CubicSplineCommon ( std::shared_ptr< Grid > &  NewGrid, Array< double, 1 >  NewYs  )

inline

Simplified constructor.

Definition at line 88 of file CubicSplineCommon.h.

References EndDeriv, Init(), and StartDeriv.

  {
    StartDeriv = EndDeriv = 5.0e30;
    Init(NewGrid, NewYs, 5.0e30, 5.0e30);
  }

CubicSplineCommon() [2/3]

CubicSplineCommon ( std::shared_ptr< Grid > &  NewGrid, Array< double, 1 >  NewYs, double  startderiv, double  endderiv  )

inline

Full constructor.

Definition at line 95 of file CubicSplineCommon.h.

References Init(), and Update().

  {
    Init(NewGrid, NewYs, startderiv, endderiv);
    Update();
  }

CubicSplineCommon() [3/3]

CubicSplineCommon ( )

inline

Trivial constructor.

Definition at line 140 of file CubicSplineCommon.h.

References EndDeriv, grid, NumParams, StartDeriv, and UpToDate.

  {
    UpToDate = 0;
    NumParams = 0;
    StartDeriv = 0;
    EndDeriv = 0;
    grid     = NULL;
  }

Member Function Documentation

Data()

Array< double, 1 > & Data ( )

inline

Definition at line 151 of file CubicSplineCommon.h.

References UpToDate, and y.

{
  UpToDate = false;
  return y;
}

Deriv()

double Deriv ( double  x )

inline

Returns the interpolated first derivative.

Definition at line 200 of file CubicSplineCommon.h.

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

{
  if (!UpToDate)
    Update();

  Grid& 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 228 of file CubicSplineCommon.h.

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

{
  if (!UpToDate)
    Update();
  Grid& 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 255 of file CubicSplineCommon.h.

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

{
  if (!UpToDate)
    Update();
  Grid& 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 ( std::shared_ptr< Grid > &  NewGrid, Array< double, 1 >  NewYs, double  startderiv, double  endderiv  )

inline

Initialize the cubic spline.

See notes about start and end deriv above.

Definition at line 64 of file CubicSplineCommon.h.

References d2y, EndDeriv, grid, NumParams, Array< T, D, ALLOC >::resize(), Array< T, D, ALLOC >::rows(), StartDeriv, Update(), and y.

Referenced by CubicSplineCommon().

  {
    StartDeriv = startderiv;
    EndDeriv   = endderiv;
    if (NewGrid->NumPoints != NewYs.rows())
    {
      std::cerr << "Size mismatch in CubicSplineCommon.\n";
      std::cerr << "Grid Points = " << NewGrid->NumPoints << std::endl;
      std::cerr << "Y points    = " << NewYs.rows() << std::endl;
      exit(1);
    }
    grid      = NewGrid;
    NumParams = grid->NumPoints;
    y.resize(grid->NumPoints);
    d2y.resize(grid->NumPoints);
    y = NewYs;
    Update();
  }

Init() [2/2]

void Init ( std::shared_ptr< Grid > &  NewGrid, Array< double, 1 >  NewYs  )

inline

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

Definition at line 85 of file CubicSplineCommon.h.

References Init().

Referenced by Init().

{ Init(NewGrid, NewYs, 5.0e30, 5.0e30); }

operator()() [1/3]

double operator() ( double  x )

inline

Definition at line 158 of file CubicSplineCommon.h.

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

{
  if (!UpToDate)
    Update();


  Grid& X = *grid;
#ifdef BZ_DEBUG
  if (x > X.End)
  {
    if (x < (X.End * 1.000000001))
      x = X.End;
    else
    {
      std::cerr << "x outside grid in CubicSplineCommon.\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 102 of file CubicSplineCommon.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 104 of file CubicSplineCommon.h.

References UpToDate, and y.

  {
    UpToDate = 0;
    return (y(i));
  }

operator=()

CubicSplineCommon& operator=

(

const CubicSplineCommon &

spline

)

Params() [1/2]

double Params ( int  i ) const

inline

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

Definition at line 111 of file CubicSplineCommon.h.

References y.

{ return (y(i)); }

Params() [2/2]

double& Params ( int  i )

inline

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

Definition at line 113 of file CubicSplineCommon.h.

References y.

{ return (y(i)); }

Read()

void Read ( IOSectionClass &  inSection )

inline

Definition at line 124 of file CubicSplineCommon.h.

References IOSectionClass::CloseSection(), d2y, EndDeriv, grid, NumParams, IOSectionClass::OpenSection(), ReadGrid(), IOSectionClass::ReadVar(), Array< T, D, ALLOC >::resize(), Array< T, D, ALLOC >::size(), StartDeriv, Update(), and y.

  {
    assert(inSection.ReadVar("StartDeriv", StartDeriv));
    assert(inSection.ReadVar("EndDeriv", EndDeriv));
    assert(inSection.ReadVar("y", y));
    NumParams = y.size();
    d2y.resize(NumParams);
    assert(inSection.OpenSection("Grid"));
    grid = ReadGrid(inSection);
    inSection.CloseSection();
    Update();
  }

size()

int size ( void  )

inline

Returns the interpolated value.

Definition at line 51 of file CubicSplineCommon.h.

References grid.

{ return grid->NumPoints; }

Update()

void Update

(

)

Recompute the second derivatives from the function values.

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

Write()

void Write ( IOSectionClass &  outSection )

inline

Definition at line 114 of file CubicSplineCommon.h.

References IOSectionClass::CloseSection(), EndDeriv, grid, IOSectionClass::NewSection(), StartDeriv, IOSectionClass::WriteVar(), and y.

  {
    outSection.WriteVar("StartDeriv", StartDeriv);
    outSection.WriteVar("EndDeriv", EndDeriv);
    outSection.WriteVar("y", y);

    outSection.NewSection("Grid");
    grid->Write(outSection);
    outSection.CloseSection();
  }

Member Data Documentation

d2y

Array<double, 1> d2y

private

The second derivatives of the function.

Definition at line 38 of file CubicSplineCommon.h.

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

EndDeriv

double EndDeriv

Definition at line 47 of file CubicSplineCommon.h.

Referenced by CubicSplineCommon(), Init(), Read(), and Write().

grid

std::shared_ptr<Grid> grid

Definition at line 42 of file CubicSplineCommon.h.

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

NumParams

int NumParams

Definition at line 41 of file CubicSplineCommon.h.

Referenced by CubicSplineCommon(), Init(), and Read().

StartDeriv

double StartDeriv

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 47 of file CubicSplineCommon.h.

Referenced by CubicSplineCommon(), Init(), Read(), and Write().

UpToDate

int 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 34 of file CubicSplineCommon.h.

Referenced by CubicSplineCommon(), Data(), Deriv(), Deriv2(), Deriv3(), and operator()().

y

Array<double, 1> y

private

The function values on the grid points.

Definition at line 36 of file CubicSplineCommon.h.

Referenced by Data(), Deriv(), Init(), operator()(), Params(), Read(), and Write().

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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/common/CubicSplineCommon.h