Public Types | Public Member Functions | Protected Attributes | Private Member Functions | List of all members
o2scl::interp2_seq< vec_t, mat_t, mat_row_t > Class Template Reference

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

#include <interp2_seq.h>

Inheritance diagram for o2scl::interp2_seq< vec_t, mat_t, mat_row_t >:
o2scl::interp2_base< boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double > >

Detailed Description

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 o2scl::interp2_seq< vec_t, mat_t, mat_row_t >

This class implements two-dimensional interpolation by iterating the O2scl 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.

Definition at line 82 of file interp2_seq.h.

Public Types

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

Public Member Functions

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. More...
 
void reset_interp ()
 Reset the stored interpolation since the data has changed. More...
 
double eval (double x, double y) const
 Perform the 2-d interpolation.
 
double operator() (double x, double y) const
 Perform the 2-d interpolation.
 
double deriv_x (double x, double y) const
 Compute the partial derivative in the x-direction.
 
double deriv_xx (double x, double y) const
 Compute the partial second derivative in the x-direction.
 
double integ_x (double x0, double x1, double y) const
 Compute the integral in the x-direction between x=x0 and x=x1.
 
double deriv_y (double x, double y) const
 Compute the partial derivative in the y-direction.
 
double deriv_yy (double x, double y) const
 Compute the partial second derivative in the y-direction.
 
double integ_y (double x, double y0, double y1) const
 Compute the integral in the y-direction between y=y0 and y=y1.
 
double deriv_xy (double x, double y) const
 Compute the mixed partial derivative $ \frac{\partial^2 f}{\partial x \partial y} $.
 
double eval_gen (int ix, int iy, double x0, double x1, double y0, double y1) const
 Compute a general interpolation result. More...
 

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.
 
- Protected Attributes inherited from o2scl::interp2_base< boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double > >
size_t nx
 The number of x grid points.
 
size_t ny
 The number of y grid points.
 
boost::numeric::ublas::vector< double > * xfun
 The x grid.
 
boost::numeric::ublas::vector< double > * yfun
 The y grid.
 
boost::numeric::ublas::matrix< double > * datap
 The data.
 

Private Member 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 > &)
 

Member Function Documentation

◆ eval_gen()

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>>
double o2scl::interp2_seq< vec_t, mat_t, mat_row_t >::eval_gen ( int  ix,
int  iy,
double  x0,
double  x1,
double  y0,
double  y1 
) const
inlinevirtual

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{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*}

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

Implements o2scl::interp2_base< boost::numeric::ublas::vector< double >, boost::numeric::ublas::matrix< double > >.

Definition at line 347 of file interp2_seq.h.

◆ reset_interp()

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>>
void o2scl::interp2_seq< vec_t, mat_t, mat_row_t >::reset_interp ( )
inline

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

Definition at line 154 of file interp2_seq.h.

◆ set_data()

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>>
void o2scl::interp2_seq< vec_t, mat_t, mat_row_t >::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 
)
inline

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.

Definition at line 115 of file interp2_seq.h.

The documentation for this class was generated from the following file:

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).