Detailed Description

Definition at line 39 of file orthoPoly1D.H.

Public Member Functions
	orthoPoly1D (int _order, const std::vector< double > &x)

	orthoPoly1D ()=default

	orthoPoly1D (const orthoPoly1D &op)

orthoPoly1D &	operator= (const orthoPoly1D &op)

	~orthoPoly1D ()=default

double	EvaluateOrthogonal (int power, double xk) const

void	ComputeAB (const std::vector< double > &x)

void	EvaluateOrthogonals (const std::vector< double > &x)

void	ComputePhiTPhiInv (const std::vector< double > &x)

Public Attributes
int	order

std::vector< double >	a

std::vector< double >	b

Eigen::MatrixXd	phi

Eigen::MatrixXd	phiTphiInv

Constructor & Destructor Documentation

◆ orthoPoly1D() [1/3]

orthoPoly1D::orthoPoly1D	(	int	_order,
		const std::vector< double > &	x
	)

Definition at line 37 of file orthoPoly1D.C.

References a, b, ComputePhiTPhiInv(), phi, and phiTphiInv.

     : order(_order)
 {
   a.resize(_order + 1);
   b.resize(_order);
   phi.resize(x.size(), _order + 1);
   phiTphiInv.resize(_order + 1, _order + 1);
   ComputePhiTPhiInv(x);
 }

◆ orthoPoly1D() [2/3]

orthoPoly1D::orthoPoly1D ( )

default

◆ orthoPoly1D() [3/3]

orthoPoly1D::orthoPoly1D ( const orthoPoly1D & op )

Definition at line 47 of file orthoPoly1D.C.

References a, b, order, phi, and phiTphiInv.

 {
   order = op.order;
   a = op.a;
   b = op.b;
   phi = op.phi;
   phiTphiInv = op.phiTphiInv;
 }

◆ ~orthoPoly1D()

orthoPoly1D::~orthoPoly1D ( )

default

Member Function Documentation

◆ ComputeAB()

void orthoPoly1D::ComputeAB ( const std::vector< double > & x )

Definition at line 91 of file orthoPoly1D.C.

References a, b, EvaluateOrthogonal(), and order.

Referenced by EvaluateOrthogonals().

 {
   a[0] = 0.;
   int n = x.size();
   for (int i = 0; i < n; ++i)
   {
     a[0] += x[i];
   }
   a[0] /= n;
 
   for (int i = 1; i < order; ++i)
   {
     double sum0, sum1, sum2;
     sum0 = sum1 = sum2 = 0.0;
     for (int j = 0; j < n; ++j)
     {
       double tmp0 = EvaluateOrthogonal(i - 1, x[j]);
       double tmp1 = EvaluateOrthogonal(i, x[j]);
       sum0 += tmp0 * tmp0;
       sum1 += tmp1 * tmp1;
       sum2 += x[j] * tmp1 * tmp1;
     }
     a[i] = sum2 / sum1;
     b[i - 1] = sum1 / sum0;
   }
 }

◆ ComputePhiTPhiInv()

void orthoPoly1D::ComputePhiTPhiInv ( const std::vector< double > & x )

Definition at line 131 of file orthoPoly1D.C.

References EvaluateOrthogonals(), phi, and phiTphiInv.

Referenced by orthoPoly1D().

 {
   EvaluateOrthogonals(x);
   VectorXd tmp = (phi.transpose() * phi).diagonal();
   for (int i = 0; i < tmp.rows(); ++i)
     tmp(i) = 1. / tmp(i);
   phiTphiInv = tmp.asDiagonal();
 }

◆ EvaluateOrthogonal()

double orthoPoly1D::EvaluateOrthogonal	(	int	power,
		double	xk
	)		const

Definition at line 69 of file orthoPoly1D.C.

References a, and b.

Referenced by ComputeAB(), and EvaluateOrthogonals().

 {
   double p0 = 1.;
   if (power == 0)
     return p0;
   double p1 = xk - a[0];
   if (power == 1)
     return p1;
   double p2 = std::numeric_limits<double>::quiet_NaN();
   for (int i = 1; i < power; ++i)
   {
     p2 = (xk - a[i]) * p1 - b[i - 1] * p0;
     p0 = p1;
     p1 = p2;
   }
   return p2;
 }

◆ EvaluateOrthogonals()

void orthoPoly1D::EvaluateOrthogonals ( const std::vector< double > & x )

Definition at line 120 of file orthoPoly1D.C.

References ComputeAB(), EvaluateOrthogonal(), order, and phi.

Referenced by ComputePhiTPhiInv().

 {
   ComputeAB(x);
   for (int i = 0; i < order + 1; ++i)
   {
     for (int j = 0; j < x.size(); ++j)
       phi(j, i) = EvaluateOrthogonal(i, x[j]);
   }
 }

◆ operator=()

orthoPoly1D & orthoPoly1D::operator= ( const orthoPoly1D & op )

Definition at line 56 of file orthoPoly1D.C.

References a, b, order, phi, and phiTphiInv.

 {
   if (this != &op)
   {
     order = op.order;
     a = op.a;
     b = op.b;
     phi = op.phi;
     phiTphiInv = op.phiTphiInv;
   }
   return *this;
 }