SplineInterpolationBase Class Reference

#include <SplineInterpolationBase.h>

Inheritance diagram for SplineInterpolationBase:

Public Member Functions
	SplineInterpolationBase ()
virtual	~SplineInterpolationBase ()=default
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	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.
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
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.

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

Detailed Description

Definition at line 15 of file SplineInterpolationBase.h.

Constructor & Destructor Documentation

SplineInterpolationBase()

SplineInterpolationBase::SplineInterpolationBase

(

)

Definition at line 16 of file SplineInterpolationBase.C.

{}

~SplineInterpolationBase()

virtual SplineInterpolationBase::~SplineInterpolationBase ( )

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

protected

Definition at line 85 of file SplineInterpolationBase.C.

{
  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;
}

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

findInterval()

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

protected

Definition at line 65 of file SplineInterpolationBase.C.

{
  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;
  }
}

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

sample() [1/3]

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

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() [2/3]

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

protected

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;
}

sample() [3/3]

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

Definition at line 101 of file SplineInterpolationBase.C.

{
  unsigned int klo, khi;
  findInterval(x, x_int, klo, khi);
 
  return sample(x, y, y2, x_int, klo, khi);
}

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

sample2ndDerivative()

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

Definition at line 141 of file SplineInterpolationBase.C.

{
  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];
}

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

sampleDerivative()

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

Definition at line 125 of file SplineInterpolationBase.C.

{
  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);
}

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

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  )

protected

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

Definition at line 19 of file SplineInterpolationBase.C.

{
  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];
}

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

Member Data Documentation

_deriv_bound

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

staticprotected

Definition at line 79 of file SplineInterpolationBase.h.

Referenced by BicubicSplineInterpolation::errorCheck().

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

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