Class interp2_seq (o2scl)

O2scl : Class List

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>, class mat_row_t = boost::numeric::ublas::matrix_row<mat_t>>
class interp2_seq : public o2scl::interp2_base<boost::numeric::ublas::vector<double>, boost::numeric::ublas::matrix<double>>

Two-dimensional interpolation class by successive one-dimensional interpolation.

This class implements two-dimensional interpolation by iterating the one-dimensional interpolation routines. Derivatives and integrals along both x- and y-directions can be computed. This class is likely a bit slower than interp2_direct but more flexible.

The convention used by this class is that the first (row) index of the matrix enumerates the x coordinate and that the second (column) index enumerates the y coordinate. See the discussion in the User’s guide in the section called Rows and columns vs. x and y.

The function set_data() does not copy the data, it stores pointers to the data. If the data is modified, then the function reset_interp() must be called to reset the interpolation information with the original pointer information. The storage for the data, including the arrays x_grid and y_grid are all managed by the user.

By default, cubic spline interpolation with natural boundary conditions is used. This can be changed by calling set_interp() again with the same data and the new interpolation type.

There is an example for the usage of this class given in examples/ex_interp2_seq.cpp.

Because of the way this class creates pointers to the data, copy construction is not currently allowed.

Idea for Future:

Implement an improved caching system in case, for example xfirst is true and the last interpolation used the same value of x.

Public Types

typedef boost::numeric::ublas::vector<double> ubvector

Public Functions

inline interp2_seq()

inline virtual ~interp2_seq()

inline void set_data(size_t n_x, size_t n_y, vec_t &x_grid, vec_t &y_grid, mat_t &data, size_t interp_type = itp_cspline)

Initialize the data for the 2-dimensional interpolation.

If x_first is true, then set_data() creates interpolation objects for each of the rows. Calls to interp() then uses these to create a column at the specified value of x. An interpolation object is created at this column to find the value of the function at the specified value y. If x_first is false, the opposite strategy is employed. These two options may give slightly different results.

inline void reset_interp()

Reset the stored interpolation since the data has changed.

This will throw an exception if the set_data() has not been called.

inline virtual double eval(double x, double y) const

Perform the 2-d interpolation.

inline virtual double operator()(double x, double y) const

Perform the 2-d interpolation.

inline virtual double deriv_x(double x, double y) const

Compute the partial derivative in the x-direction.

inline virtual double deriv_xx(double x, double y) const

Compute the partial second derivative in the x-direction.

inline virtual double integ_x(double x0, double x1, double y) const

Compute the integral in the x-direction between x=x0 and x=x1.

inline virtual double deriv_y(double x, double y) const

Compute the partial derivative in the y-direction.

inline virtual double deriv_yy(double x, double y) const

Compute the partial second derivative in the y-direction.

inline virtual double integ_y(double x, double y0, double y1) const

Compute the integral in the y-direction between y=y0 and y=y1.

inline virtual double deriv_xy(double x, double y) const

Compute the mixed partial derivative \( \frac{\partial^2 f}{\partial x \partial y} \).

inline virtual double eval_gen(int ix, int iy, double x0, double x1, double y0, double y1) const

Compute a general interpolation result.

This computes

\[ \frac{\partial^m}{\partial x^m} \frac{\partial^n}{\partial y^n} f(x,y) \]

for \( m \in (-1,0,1,2) \) and \( n \in (-1,0,1,2) \) with the notation

\[\begin{split}\begin{eqnarray*} \frac{\partial^{-1}}{\partial x^{-1}} &\equiv & \int_{x_0}^{x_1} f~dx \nonumber \\ \frac{\partial^0}{\partial x^0} &\equiv & \left.f\right|_{x=x_0} \nonumber \\ \frac{\partial^1}{\partial x^1} &\equiv & \left(\frac{\partial f}{\partial x}\right)_{x=x_0} \nonumber \\ \frac{\partial^2}{\partial x^2} &\equiv & \left(\frac{\partial^2 f}{\partial x^2}\right)_{x=x_0} \end{eqnarray*}\end{split}\]

and the value of \( x_1 \) is ignored when \( m \geq 0 \) and the value of \( y_1 \) is ignored when \( n \geq 0 \).

Protected Attributes

std::vector<interp_vec<vec_t, mat_row_t>*> itps

The array of interpolation objects.

std::vector<mat_row_t*> vecs

An array of rows.

size_t nx

The number of x grid points.

size_t ny

The number of y grid points.

bool data_set

True if the data has been specified by the user.

vec_t *xfun

The x grid.

vec_t *yfun

The y grid.

mat_t *datap

The data.

size_t itype

Interpolation type.

Private Functions

interp2_seq(const interp2_seq<vec_t, mat_t, mat_row_t>&)

interp2_seq<vec_t, mat_t, mat_row_t> &operator=(const interp2_seq<vec_t, mat_t, mat_row_t>&)