Class and methods for cubic splines.

Functions
dvector	spline (const dvector &_x, const dvector &_y, double yp1, double ypn)
	Cubic spline interpolation.
double	splint (const dvector &_xa, const dvector &_ya, const dvector &_y2a, double x)
	Cubic spline interpolation.
double	spline_cubic_val (int n, const dvector &t, double tval, const dvector &y, const dvector &ypp)
	Evaluates a piecewise cubic spline at a point.
double *	d3_np_fs (int n, const dvector &_a, const dvector &_b)
	factors and solves a D3 system.
dvector	spline_cubic_set (int n, const dvector &t, const dvector &y, int ibcbeg, double ybcbeg, int ibcend, double ybcend)
	Computes the second derivatives of a piecewise cubic spline.
dvariable	splint (const dvector &_xa, const dvar_vector &_ya, const dvar_vector &_y2a, double x)
	Cubic spline interpolation.
dvariable	splint (const dvector &_xa, const dvar_vector &_ya, const dvar_vector &_y2a, const prevariable &_x)
	Cubic spline interpolation.
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, dvariable yp1, dvariable ypn)
	Cubic spline interpolation.
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, double yp1, double ypn)
	Cubic spline interpolation.
dvar_vector	spline (const dvector &_x, const dvar_vector &_y, dvariable yp1, double ypn)
	Cubic spline interpolation.
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.
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.
dvar_vector	d3_np_fs (int n, const dvar_vector &_a, const dvar_vector &_b)
	factors and solves a D3 system.
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.

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Function Documentation

dvector spline	(	const dvector &	_x,
		const dvector &	_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 70 of file cspline.cpp.

Referenced by cubic_spline_function::cubic_spline_function(), splie2(), splin2(), and vcubic_spline_function::vcubic_spline_function().

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

Cubic spline interpolation.

Parameters:

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

Returns:

a cubic-spline interpolation to

Definition at line 112 of file cspline.cpp.

Referenced by vcubic_spline_function::operator()(), cubic_spline_function::operator()(), and splin2().

double spline_cubic_val	(	int	n,
		const dvector &	t,
		double	tval,
		const dvector &	y,
		const dvector &	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 129 of file cspline.cpp.

Referenced by splint().

double* d3_np_fs	(	int	n,
		const dvector &	_a,
		const dvector &	_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 237 of file cspline.cpp.

Referenced by spline_cubic_set().

dvector spline_cubic_set	(	int	n,
		const dvector &	t,
		const dvector &	y,
		int	ibcbeg,
		double	ybcbeg,
		int	ibcend,
		double	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 351 of file cspline.cpp.

Referenced by spline().

dvariable splint	(	const dvector &	_xa,
		const dvar_vector &	_ya,
		const dvar_vector &	_y2a,
		double	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 35 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 53 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 137 of file vspline.cpp.

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 183 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 229 of file vspline.cpp.

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 276 of file vspline.cpp.

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 400 of file vspline.cpp.

Referenced by splint().

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 520 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 633 of file vspline.cpp.