SplineInterpolation Class Reference

This class interpolates tabulated functions with cubic splines. More...

#include <SplineInterpolation.h>

Inheritance diagram for SplineInterpolation:

Public Member Functions
	SplineInterpolation ()
	SplineInterpolation (const std::vector< Real > &x, const std::vector< Real > &y, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	Construct the object. More...
virtual	~SplineInterpolation ()=default
void	setData (const std::vector< Real > &x, const std::vector< Real > &y, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	Set the x-, y- values and first derivatives. More...
void	errorCheck ()
Real	sample (Real x) const
	This function will take an independent variable input and will return the dependent variable based on the generated fit. More...
ADReal	sample (const ADReal &x) const
Real	sampleDerivative (Real x) const
Real	sample2ndDerivative (Real x) const
unsigned int	getSampleSize ()
	This function returns the size of the array holding the points, i.e. More...
Real	domain (int i) const
Real	range (int i) const
Real	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const
ADReal	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, const ADReal &x_int) const
Real	sampleDerivative (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const
Real	sample2ndDerivative (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, Real x_int) const

Protected Member Functions
void	solve ()
template<typename T >
T	sample (const std::vector< Real > &x, const std::vector< Real > &y, const std::vector< Real > &y2, const T &x_int, unsigned int klo, unsigned int khi) const
	Sample value at point x_int given the indices of the vector of dependent values that bound the point. More...
void	spline (const std::vector< Real > &x, const std::vector< Real > &y, std::vector< Real > &y2, Real yp1=_deriv_bound, Real ypn=_deriv_bound)
	This function calculates the second derivatives based on supplied x and y-vectors. More...
void	findInterval (const std::vector< Real > &x, Real x_int, unsigned int &klo, unsigned int &khi) const
template<typename T >
void	computeCoeffs (const std::vector< Real > &x, unsigned int klo, unsigned int khi, const T &x_int, Real &h, T &a, T &b) const

Protected Attributes
std::vector< Real >	_x
std::vector< Real >	_y
Real	_yp1
	boundary conditions More...
Real	_ypn
std::vector< Real >	_y2
	Second derivatives. More...

Static Protected Attributes
static int	_file_number = 0
static const Real	_deriv_bound = std::numeric_limits<Real>::max()

Detailed Description

This class interpolates tabulated functions with cubic splines.

Adopted from Numerical Recipes in C (section 3.3).

Definition at line 20 of file SplineInterpolation.h.

Constructor & Destructor Documentation

SplineInterpolation() [1/2]

SplineInterpolation::SplineInterpolation

(

)

Definition at line 20 of file SplineInterpolation.C.

{}

SplineInterpolation() [2/2]

SplineInterpolation::SplineInterpolation	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		Real	yp1 = _deriv_bound,
		Real	ypn = _deriv_bound
	)

Construct the object.

Parameters

x	Tabulated function (x-positions)
y	Tabulated function (y-positions)
yp1	First derivative of the interpolating function at point 1
ypn	First derivative of the interpolating function at point n

If yp1, ypn are not specified or greater or equal that _deriv_bound, we use natural spline

Definition at line 22 of file SplineInterpolation.C.

  : SplineInterpolationBase(), _x(x), _y(y), _yp1(yp1), _ypn(ypn)
{
  errorCheck();
  solve();
}

~SplineInterpolation()

virtual SplineInterpolation::~SplineInterpolation ( )

virtualdefault

Member Function Documentation

computeCoeffs()

template<typename T >

void SplineInterpolationBase::computeCoeffs ( const std::vector< Real > &  x, unsigned int  klo, unsigned int  khi, const T &  x_int, Real &  h, T &  a, T &  b  ) const

protectedinherited

Definition at line 85 of file SplineInterpolationBase.C.

Referenced by SplineInterpolationBase::sample(), SplineInterpolationBase::sample2ndDerivative(), and SplineInterpolationBase::sampleDerivative().

{
  h = x[khi] - x[klo];
  if (h == 0)
    mooseError("The values of x must be distinct");
  a = (x[khi] - x_int) / h;
  b = (x_int - x[klo]) / h;
}

domain()

Real SplineInterpolation::domain

(

int

i

)

const

Definition at line 92 of file SplineInterpolation.C.

{
  return _x[i];
}

errorCheck()

void SplineInterpolation::errorCheck

(

)

Definition at line 47 of file SplineInterpolation.C.

Referenced by setData(), and SplineInterpolation().

{
  if (_x.size() != _y.size())
    mooseError("SplineInterpolation: vectors are not the same length");

  bool error = false;
  for (unsigned i = 0; !error && i + 1 < _x.size(); ++i)
    if (_x[i] >= _x[i + 1])
      error = true;

  if (error)
    mooseError("x-values are not strictly increasing");
}

findInterval()

void SplineInterpolationBase::findInterval ( const std::vector< Real > &  x, Real  x_int, unsigned int &  klo, unsigned int &  khi  ) const

protectedinherited

Definition at line 65 of file SplineInterpolationBase.C.

Referenced by BicubicSplineInterpolation::constructColumnSpline(), BicubicSplineInterpolation::constructRowSpline(), SplineInterpolationBase::sample(), SplineInterpolationBase::sample2ndDerivative(), and SplineInterpolationBase::sampleDerivative().

{
  klo = 0;
  mooseAssert(x.size() >= 2, "You must have at least two knots to create a spline.");
  khi = x.size() - 1;
  while (khi - klo > 1)
  {
    unsigned int k = (khi + klo) >> 1;
    if (x[k] > x_int)
      khi = k;
    else
      klo = k;
  }
}

getSampleSize()

unsigned int SplineInterpolation::getSampleSize

(

)

This function returns the size of the array holding the points, i.e.

the number of sample points

Definition at line 104 of file SplineInterpolation.C.

{
  return _x.size();
}

range()

Real SplineInterpolation::range

(

int

i

)

const

Definition at line 98 of file SplineInterpolation.C.

{
  return _y[i];
}

sample() [1/5]

Real SplineInterpolationBase::sample ( const std::vector< Real > &  x, const std::vector< Real > &  y, const std::vector< Real > &  y2, Real  x_int  ) const

inherited

Definition at line 101 of file SplineInterpolationBase.C.

Referenced by BicubicSplineInterpolation::constructColumnSpline(), BicubicSplineInterpolation::constructRowSpline(), SplineInterpolationBase::sample(), sample(), BicubicSplineInterpolation::sample(), and BicubicSplineInterpolation::sampleValueAndDerivatives().

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);

  return sample(x, y, y2, x_int, klo, khi);
}

sample() [2/5]

ADReal SplineInterpolationBase::sample ( const std::vector< Real > &  x, const std::vector< Real > &  y, const std::vector< Real > &  y2, const ADReal &  x_int  ) const

inherited

Definition at line 113 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, MetaPhysicL::raw_value(x_int), klo, khi);

  return sample(x, y, y2, x_int, klo, khi);
}

sample() [3/5]

Real SplineInterpolation::sample

(

Real

x

)

const

This function will take an independent variable input and will return the dependent variable based on the generated fit.

Definition at line 68 of file SplineInterpolation.C.

Referenced by SplineFunction::value().

{
  return SplineInterpolationBase::sample(_x, _y, _y2, x);
}

sample() [4/5]

ADReal SplineInterpolation::sample

(

const ADReal &

x

)

const

Definition at line 74 of file SplineInterpolation.C.

{
  return SplineInterpolationBase::sample(_x, _y, _y2, x);
}

sample() [5/5]

template<typename T >

T SplineInterpolationBase::sample ( const std::vector< Real > &  x, const std::vector< Real > &  y, const std::vector< Real > &  y2, const T &  x_int, unsigned int  klo, unsigned int  khi  ) const

protectedinherited

Sample value at point x_int given the indices of the vector of dependent values that bound the point.

This method is useful in bicubic spline interpolation, where several spline evaluations are needed to sample from a 2D point.

Definition at line 157 of file SplineInterpolationBase.C.

{
  Real h;
  T a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);

  return a * y[klo] + b * y[khi] +
         ((a * a * a - a) * y2[klo] + (b * b * b - b) * y2[khi]) * (h * h) / 6.0;
}

sample2ndDerivative() [1/2]

Real SplineInterpolationBase::sample2ndDerivative ( const std::vector< Real > &  x, const std::vector< Real > &  y, const std::vector< Real > &  y2, Real  x_int  ) const

inherited

Definition at line 141 of file SplineInterpolationBase.C.

Referenced by sample2ndDerivative(), and BicubicSplineInterpolation::sample2ndDerivative().

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);

  Real h, a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);

  return a * y2[klo] + b * y2[khi];
}

sample2ndDerivative() [2/2]

Real SplineInterpolation::sample2ndDerivative

(

Real

x

)

const

Definition at line 86 of file SplineInterpolation.C.

Referenced by SplineFunction::secondDerivative().

{
  return SplineInterpolationBase::sample2ndDerivative(_x, _y, _y2, x);
}

sampleDerivative() [1/2]

Real SplineInterpolationBase::sampleDerivative ( const std::vector< Real > &  x, const std::vector< Real > &  y, const std::vector< Real > &  y2, Real  x_int  ) const

inherited

Definition at line 125 of file SplineInterpolationBase.C.

Referenced by sampleDerivative(), BicubicSplineInterpolation::sampleDerivative(), and BicubicSplineInterpolation::sampleValueAndDerivatives().

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);

  Real h, a, b;
  computeCoeffs(x, klo, khi, x_int, h, a, b);

  return (y[khi] - y[klo]) / h -
         (((3.0 * a * a - 1.0) * y2[klo] + (3.0 * b * b - 1.0) * -y2[khi]) * h / 6.0);
}

sampleDerivative() [2/2]

Real SplineInterpolation::sampleDerivative

(

Real

x

)

const

Definition at line 80 of file SplineInterpolation.C.

Referenced by SplineFunction::derivative().

{
  return SplineInterpolationBase::sampleDerivative(_x, _y, _y2, x);
}

setData()

void SplineInterpolation::setData	(	const std::vector< Real > &	x,
		const std::vector< Real > &	y,
		Real	yp1 = _deriv_bound,
		Real	ypn = _deriv_bound
	)

Set the x-, y- values and first derivatives.

Definition at line 33 of file SplineInterpolation.C.

{
  _x = x;
  _y = y;
  _yp1 = yp1;
  _ypn = ypn;
  errorCheck();
  solve();
}

solve()

void SplineInterpolation::solve ( )

protected

Definition at line 62 of file SplineInterpolation.C.

Referenced by setData(), and SplineInterpolation().

{
  spline(_x, _y, _y2, _yp1, _ypn);
}

spline()

void SplineInterpolationBase::spline ( const std::vector< Real > &  x, const std::vector< Real > &  y, std::vector< Real > &  y2, Real  yp1 = _deriv_bound, Real  ypn = _deriv_bound  )

protectedinherited

This function calculates the second derivatives based on supplied x and y-vectors.

Definition at line 19 of file SplineInterpolationBase.C.

Referenced by BicubicSplineInterpolation::constructColumnSpline(), BicubicSplineInterpolation::constructColumnSplineSecondDerivativeTable(), BicubicSplineInterpolation::constructRowSpline(), BicubicSplineInterpolation::constructRowSplineSecondDerivativeTable(), and solve().

{
  auto n = x.size();
  if (n < 2)
    mooseError("You must have at least two knots to create a spline.");

  std::vector<Real> u(n, 0.);
  y2.assign(n, 0.);

  if (yp1 >= 1e30)
    y2[0] = u[0] = 0.;
  else
  {
    y2[0] = -0.5;
    u[0] = (3.0 / (x[1] - x[0])) * ((y[1] - y[0]) / (x[1] - x[0]) - yp1);
  }
  // decomposition of tri-diagonal algorithm (y2 and u are used for temporary storage)
  for (decltype(n) i = 1; i < n - 1; i++)
  {
    Real sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]);
    Real p = sig * y2[i - 1] + 2.0;
    y2[i] = (sig - 1.0) / p;
    u[i] = (y[i + 1] - y[i]) / (x[i + 1] - x[i]) - (y[i] - y[i - 1]) / (x[i] - x[i - 1]);
    u[i] = (6.0 * u[i] / (x[i + 1] - x[i - 1]) - sig * u[i - 1]) / p;
  }

  Real qn, un;
  if (ypn >= 1e30)
    qn = un = 0.;
  else
  {
    qn = 0.5;
    un = (3.0 / (x[n - 1] - x[n - 2])) * (ypn - (y[n - 1] - y[n - 2]) / (x[n - 1] - x[n - 2]));
  }

  y2[n - 1] = (un - qn * u[n - 2]) / (qn * y2[n - 2] + 1.);
  // back substitution
  for (auto k = n - 1; k >= 1; k--)
    y2[k - 1] = y2[k - 1] * y2[k] + u[k - 1];
}

Member Data Documentation

_deriv_bound

const Real SplineInterpolationBase::_deriv_bound = std::numeric_limits<Real>::max()

staticprotectedinherited

Definition at line 79 of file SplineInterpolationBase.h.

Referenced by BicubicSplineInterpolation::errorCheck().

_file_number

int SplineInterpolation::_file_number = 0

staticprotected

Definition at line 80 of file SplineInterpolation.h.

_x

std::vector<Real> SplineInterpolation::_x

protected

Definition at line 71 of file SplineInterpolation.h.

Referenced by domain(), errorCheck(), getSampleSize(), sample(), sample2ndDerivative(), sampleDerivative(), setData(), and solve().

_y

std::vector<Real> SplineInterpolation::_y

protected

Definition at line 72 of file SplineInterpolation.h.

Referenced by errorCheck(), range(), sample(), sample2ndDerivative(), sampleDerivative(), setData(), and solve().

_y2

std::vector<Real> SplineInterpolation::_y2

protected

Second derivatives.

Definition at line 76 of file SplineInterpolation.h.

Referenced by sample(), sample2ndDerivative(), sampleDerivative(), and solve().

_yp1

Real SplineInterpolation::_yp1

protected

boundary conditions

Definition at line 74 of file SplineInterpolation.h.

Referenced by setData(), and solve().

_ypn

Real SplineInterpolation::_ypn

protected

Definition at line 74 of file SplineInterpolation.h.

Referenced by setData(), and solve().

---

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

• include/utils/SplineInterpolation.h
• src/utils/SplineInterpolation.C