class cubspline

1D Cubic spline class accomodating several boundary condition types including not-a-knot and periodic.

Public Fields

Vec x

vector of abscissae

Vec y

vector of ordinates

bool init

true if spline coefficients have been initialized

bool periodic

true if periodic

Vec_int bc_type

A 2-integer vector defining the type of boundary conditions

Vec bc_value

Boundary condition values

double xmin

Min of abscissae

double xmax

Max of abscissae

double ymin

Min of ordinates

double ymax

Max of ordinates

Public Methods

cubspline()

Constructor.

cubspline(const Vec &x1, const Vec &y1, Vec_int bc_type1=cubspline_itwo_zeros, Vec bc_value1=cubspline_two_zeros)

Constructor.

cubspline(const Vec &x1, const Vec &y1, std::string per)

Constructor for splines with periodic boundary conditions.

void load(const Vec &x, const Vec &y, Vec_int bc_type1, Vec bc_value1)

Build spline object.

void load(const Vec &x, const Vec &y)

Build spline object.

void load(const Vec &x, const Vec &y, std::string per)

Build spline object.

bool is_below(Vec &xi)

Check if xi < xmin.

bool is_above(Vec &xi)

Check if xi > xmax.

bool is_extra(Vec &xi)

Check if xi < xmin and xi > xmax.

Vec mask(const Vec &xi)

Return 1's for all nodes xi that are inside [min(x), max(x)].

Vec_int bra(const Vec &xi)

Return indices of nodes closest to the left of xi.

size_t bra(const double xi)

Return index of node closest to the left of xi.

Vec_int near(const Vec &xi)

Return indices of nodes nearest to xi.

size_t near(const double xi)

Return index of node nearest xi.

Vec_int ket(const Vec &xi)

Return indices of nodes closest to the right of xi.

size_t ket(const double xi)

Return index of node closest to the right of xi.

Vec step(const Vec &xi)

Step function interpolation.

double step(const double xi)

Step function interpolation.

Vec linear(const Vec &xi)

Linear function interpolation.

double linear(const double xi)

Linear function interpolation.

Vec cubic(const Vec &xi)

Cubic function interpolation.

double cubic(const double xi)

Cubic function interpolation.

Vec prime(const Vec &xi, std::string method="cubic")

First derivative.

double prime(const double xi, std::string method="cubic")

First derivative.

Vec second(const Vec &xi)

Second derivative.

double second(const double xi)

Second derivative.

Vec third(const Vec &xi)

Third derivative.

double third(const double xi)

Third derivative.

Vec integrate(const Vec &xi_to)

Integrate from xmin to xi_to.

double integrate(const double xi_to)

Integrate from xmin to xi_to.

Documentation

1D Cubic spline class accomodating several boundary condition types including not-a-knot and periodic. Once cubic spline coefficients are computed using either the constructor call or 'load' method, interpolation as well as derivatives up to and including order three can be obtained either pointwise or on grids. Integration routines are also provided. All vectors Vec are Vector<double> whereas Vec_int are Vector<size_t>.

Vec x

vector of abscissae

Vec y

vector of ordinates

bool init

true if spline coefficients have been initialized

bool periodic

true if periodic

Vec_int bc_type

A 2-integer vector defining the type of boundary conditions

Vec bc_value

Boundary condition values

double xmin

Min of abscissae

double xmax

Max of abscissae

double ymin

Min of ordinates

double ymax

Max of ordinates

cubspline()

Constructor.

cubspline(const Vec &x1, const Vec &y1, Vec_int bc_type1=cubspline_itwo_zeros, Vec bc_value1=cubspline_two_zeros)

Constructor. Build object given a set of (x, y) coordinates and some boundary condition constraints.

Parameters:

x1 - original abscissae
y1 - original ordinates
bc_type1 - Boundary condition types: 0 for not a knot, 1 for setting the derivative, 2 for imposing the second derivative.
bc_value1 - Values of the boundary conditions (not used for not-a-knot).

cubspline(const Vec &x1, const Vec &y1, std::string per)

Constructor for splines with periodic boundary conditions.

Parameters:

x1 - original abscissae
y1 - original ordinates
per - if ="periodic" then periodic boundary conditions

void load(const Vec &x, const Vec &y, Vec_int bc_type1, Vec bc_value1)

Build spline object.

Parameters:

- x original abscissae
- y original ordinates
bc_type1 - Boundary condition types: 0 for not a knot, 1 for setting the derivative, 2 for imposing the second derivative.

See Also:

cubspline()

void load(const Vec &x, const Vec &y)

Build spline object. Not-a-knot boundary conditions.

Parameters:

- x original abscissae
- y original ordinates
bc_type1 - Boundary condition types: 0 for not a knot, 1 for setting the derivative, 2 for imposing the second derivative.

See Also:

cubspline()

void load(const Vec &x, const Vec &y, std::string per)

Build spline object. Periodic boundary conditions.

Parameters:

- x original abscissae
- y original ordinates
bc_type1 - Boundary condition types: 0 for not a knot, 1 for setting the derivative, 2 for imposing the second derivative.

See Also:

cubspline()

bool is_below(Vec &xi)

Check if xi < xmin. Look for nodes below interval.

Parameters:

xi - grid

Returns:

true if there is a node such that xi < xmin

bool is_above(Vec &xi)

Check if xi > xmax. Look for nodes above interval.

Parameters:

xi - grid

Returns:

true if there is a node such that xi > xmax

bool is_extra(Vec &xi)

Check if xi < xmin and xi > xmax. Look for nodes outside interval.

Parameters:

xi - grid

Returns:

true if there is a node such that xi > xmax and xi < xmin

Vec mask(const Vec &xi)

Return 1's for all nodes xi that are inside [min(x), max(x)].

Parameters:

xi - grid

Returns:

vector 0's for nodes outside [xmin, xmax], resp 1's for nodes inside.

Vec_int bra(const Vec &xi)

Return indices of nodes closest to the left of xi.

Parameters:

xi - abscissae

Returns:

result = node indices

size_t bra(const double xi)

Return index of node closest to the left of xi.

Parameters:

xi - abscissa

Returns:

result = node index

Vec_int near(const Vec &xi)

Return indices of nodes nearest to xi.

Parameters:

xi - abscissae

Returns:

result = node indices

size_t near(const double xi)

Return index of node nearest xi.

Parameters:

xi - abscissa

Returns:

result = node index

Vec_int ket(const Vec &xi)

Return indices of nodes closest to the right of xi.

Parameters:

xi - abscissae

Returns:

result = node indices

size_t ket(const double xi)

Return index of node closest to the right of xi.

Parameters:

xi - abscissa

Returns:

result = node index

Vec step(const Vec &xi)

Step function interpolation.

Parameters:

xi - abscissae

Returns:

result = piecewise constant interpolation.

double step(const double xi)

Step function interpolation.

Parameters:

xi - abscissa

Returns:

result = piecewise constant interpolation.

Vec linear(const Vec &xi)

Linear function interpolation.

Parameters:

xi - abscissae

Returns:

result = piecewise linear interpolation.

double linear(const double xi)

Linear function interpolation.

Parameters:

xi - abscissa

Returns:

result = piecewise linear interpolation.

Vec cubic(const Vec &xi)

Cubic function interpolation.

Parameters:

xi - abscissae

Returns:

result = piecewise linear interpolation.

double cubic(const double xi)

Cubic function interpolation.

Parameters:

xi - abscissa

Returns:

result = piecewise linear interpolation.

Vec prime(const Vec &xi, std::string method="cubic")

First derivative.

Parameters:

xi - abscissae
method - can be "cubic" or "linear"

Returns:

result = df/dx

double prime(const double xi, std::string method="cubic")

First derivative.

Parameters:

xi - abscissa
method - can be "cubic" or "linear"

Returns:

result = df/dx

Vec second(const Vec &xi)

Second derivative.

Parameters:

xi - abscissae

Returns:

result = d2f/dx2

double second(const double xi)

Second derivative.

Parameters:

xi - abscissa

Returns:

result = d2f/dx2

Vec third(const Vec &xi)

Third derivative.

Parameters:

xi - abscissae

Returns:

result = d3f/dx3

double third(const double xi)

Third derivative.

Parameters:

xi - abscissa

Returns:

result = d3f/dx3

Vec integrate(const Vec &xi_to)

Integrate from xmin to xi_to.

Parameters:

xi_to - right end point (array)

Returns:

integral

double integrate(const double xi_to)

Integrate from xmin to xi_to.

Parameters:

xi_to - right end point

Returns:

integral

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