Class and methods for cubic splines

Functions
dvar_vector	d3_np_fs (int n, const dvar_vector &_a, const dvar_vector &_b)
	factors and solves a D3 system. More...
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, double yp1, double ypn)
	Cubic spline interpolation. More...
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, dvariable yp1, dvariable ypn)
	Cubic spline interpolation. More...
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, dvariable yp1, double ypn)
	Cubic spline interpolation. More...
dvar_vector	spline_cubic_set (int n, const dvector &t, const dvar_vector &y, int ibcbeg, dvariable ybcbeg, int ibcend, dvariable ybcend)
	Computes the second derivatives of a piecewise cubic spline. More...
dvariable	spline_cubic_val (int n, const dvector &_t, double tval, const dvar_vector &_y, const dvar_vector &_ypp)
	Evaluates a piecewise cubic spline at a point. More...
dvariable	spline_cubic_val2 (int n, const dvector &_t, const prevariable &tval, const dvar_vector &_y, const dvar_vector &_ypp)
	Evaluates a piecewise cubic spline at a point. More...
dvariable	splint (const dvector &_xa, const dvar_vector &_ya, const dvar_vector &_y2a, double x)
	Cubic spline interpolation allows users to model natural cubic spline (2nd derivative of boundary nodes is set to zero) as an alternative of use of 1st derivative of boundary nodes. More...
dvariable	splint (const dvector &_xa, const dvar_vector &_ya, const dvar_vector &_y2a, const prevariable &_x)
	Cubic spline interpolation. More...

Detailed Description

Function Documentation

dvar_vector d3_np_fs	(	int	n,
		const dvar_vector &	_a,
		const dvar_vector &	_b
	)

factors and solves a D3 system.

Parameters

n	the order of the linear system
_a	On input, the nonzero diagonals of the linear system
_b	the right hand side

Returns

the solution of the linear system

Definition at line 530 of file vspline.cpp.

Referenced by spline_cubic_set().

dvar_vector spline	(	const dvector &	_x,
		const dvar_vector &	_y,
		double	yp1,
		double	ypn
	)

Cubic spline interpolation.

Parameters

_x	array of abscissa
_y	array of corresponding values
yp1	value of the first derivative of at the left end point
ypn	value of the first derivative of at the right end point

Returns

an array containing the second derivatives

Definition at line 189 of file vspline.cpp.

dvar_vector spline	(	const dvector &	_x,
		const dvar_vector &	_y,
		dvariable	yp1,
		dvariable	ypn
	)

Cubic spline interpolation.

Parameters

_x	array of abscissa
_y	array of corresponding values
yp1	value of the first derivative of at the left end point
ypn	value of the first derivative of at the right end point

Returns

an array containing the second derivatives

Definition at line 142 of file vspline.cpp.

dvar_vector spline	(	const dvector &	_x,
		const dvar_vector &	_y,
		dvariable	yp1,
		double	ypn
	)

Cubic spline interpolation.

Parameters

_x	array of abscissa
_y	array of corresponding values
yp1	value of the first derivative of at the left end point
ypn	value of the first derivative of at the right end point

Returns

an array containing the second derivatives

Definition at line 236 of file vspline.cpp.

dvar_vector spline_cubic_set	(	int	n,
		const dvector &	t,
		const dvar_vector &	y,
		int	ibcbeg,
		dvariable	ybcbeg,
		int	ibcend,
		dvariable	ybcend
	)

Computes the second derivatives of a piecewise cubic spline.

Parameters

n	The number of data points. must be at least 2. In the special case where and ibcend = ibcend = 0, the spline will actually be linear.
t	The knot values. The knot values should be distinct, and increasing.
y	The data values to be interpolated
ibcbeg	The left boundary flag, 0: the cubic spline should be a quadratic over the first interval; 1: the first derivative at the left endpoint should be ybcbeg; 2: the second derivative at the left endpoint should be ybcbeg.
ybcbeg	The values to be used in the boundary conditions
ibcend	The right boundary flag, 0: the cubic spline should be a quadratic over the last interval; 1: the first derivative at the right endpoint should be YBCEND; 2: the second derivative at the right endpoint should be YBCEND.
ybcend	the values to be used in the boundary conditions

Returns

the second derivatives of the cubic spline

Definition at line 643 of file vspline.cpp.

Referenced by spline().

dvariable spline_cubic_val	(	int	n,
		const dvector &	_t,
		double	tval,
		const dvar_vector &	_y,
		const dvar_vector &	_ypp
	)

Evaluates a piecewise cubic spline at a point.

Parameters

n	the number of knots
t	the knot values
tval	a point, typically between t[0] and t[N-1], at which the spline is to be evalulated. If tval lies outside this range, extrapolation is used.
y	the data values at the knots
ypp	the second derivatives of the spline at the knots

Returns

the value of the spline at tval

Definition at line 284 of file vspline.cpp.

Referenced by splint().

dvariable spline_cubic_val2	(	int	n,
		const dvector &	_t,
		const prevariable &	tval,
		const dvar_vector &	_y,
		const dvar_vector &	_ypp
	)

Evaluates a piecewise cubic spline at a point.

Parameters

n	the number of knots
t	the knot values
tval	a point, typically between t[0] and t[n-1], at which the spline is to be evalulated. If tval lies outside this range, extrapolation is used.
y	the data values at the knots
ypp	the second derivatives of the spline at the knots

Returns

the value of the spline at tval

Definition at line 409 of file vspline.cpp.

Referenced by splint().

dvariable splint	(	const dvector &	_xa,
		const dvar_vector &	_ya,
		const dvar_vector &	_y2a,
		double	x
	)

Cubic spline interpolation allows users to model natural cubic spline (2nd derivative of boundary nodes is set to zero) as an alternative of use of 1st derivative of boundary nodes.

This can be accomplished b setting yp1 and ypn of function spline to >0.99e30

Parameters

_xa	array of abscissa
_ya	array of corresponding values
_y2a	array of 2nd derivatives computed from dvar_vector spline()
x	the input coordinate to be used in the interpolation

Returns

a cubic-spline interpolation to

Definition at line 38 of file vspline.cpp.

dvariable splint	(	const dvector &	_xa,
		const dvar_vector &	_ya,
		const dvar_vector &	_y2a,
		const prevariable &	_x
	)

Cubic spline interpolation.

Parameters

_xa	array of abscissa
_ya	array of corresponding values
_y2a	array of 2nd derivatives computed from dvar_vector spline()
x	the input coordinate to be used in the interpolation

Returns

a cubic-spline interpolation to

Definition at line 57 of file vspline.cpp.