Gridding for Interpolation
nSpiner performs interpolation on Cartesian-product grids. There are two lower-level objects:
RegularGrid1DPiecewiseGrid1D
These objects contain the metadata required for interpolation operations and have a few useful userspace functions, which are described here.
Like DataBox, these grid objects are templated on
underlying data type, the default type being a Real as provided by
ports-of-call. You may wish to specialize to a specific type with
a type alias such as:
using RegularGrid1D = Spiner::RegularGrid1D<double>;
using PiecewiseGrid1D = Spiner::PiecewiseGrid1D<double>;
Note
In the function signature below we refer to T and Real as
the underlying arithmetic data type.
When constructing a DataBox, you may wish to specify which
interpolation object you are using. It is a template parameter.
RegularGrid1D
We begin by discussing RegularGrid1D, as the PiecewiseGrid1D
object is built on top of it.
Construction
A RegularGrid1D requires three values to specify an interpolation
grid: the minimum value of the independent variable, the maximum value
of the independent variable, and the number of points on the
grid. These are passed into the constructor:
-
RegularGrid1D::RegularGrid1D(T min, T max, size_t N);
Default constructors and copy constructors are also provided.
Mapping an index to a real number and vice-versa
The function
-
T RegularGrid1D::x(const int i) const;
returns a “physical” position on the grid given an index i.
The function
-
int RegularGrid1D::index(const T x) const;
returns the index on the grid of a “physical” value x.
The function
-
T RegularGrid1D::min() const;
returns the minimum value on the independent variable grid.
The function
-
T RegularGrid1D::max() const;
returns the maximum value on the independent variable grid.
The function
-
T RegularGrid1D::dx() const;
returns the grid spacing for the independent variable.
The function
-
int RegularGrid1D::nPoints() const;
returns the number of points in the independent variable grid.
The PiecewiseGrid1D
A PiecewiseGrid1D is a non-intersecting, contiguous, ordered
collection RegularGrid1D s. It can be used to construct grids with
non-uniform spacing, so long as the grid spacing is piecewise
constant.
The maximum number of RegularGrid1D``s that can be used to construct
a ``PiecewiseGrid1D is a compile-time parameter (default is 5). You
can specify a different value with, e.g.,
// Maximum number of "pieces" in a grid = 10
using PiecewiseGrid1D = Spiner::PiecewiseGrid1D<double, 10>;
Constructiong a PiecewiseGrid1D
A PiecewiseGrid1D is constructed from either a std::vector or
a std::initializer_list of RegularGrid1D s. For example:
// Initialize the regular grids
// Note that the start and end points match
// for each consecutive pair of grids.
// g1 ends when g2 starts, etc.
Spiner::RegularGrid1D<double> g1(0, 0.25, 3);
Spiner::RegularGrid1D<double> g2(0.25, 0.75, 11);
Spiner::RegularGrid1D<double> g3(0.75, 1, 7);
// Build the piecewise grid. The double bracket notation
// is an "initalizer list" and is very convenient,
// as it is a C++ language feature.
Spiner::PiecewiseGrid1D<double> h = {{g1, g2, g3}};
Default constructors and copy constructors are also provided.
Index Mapping with PiecewiseGrid1D
A PiecewiseGrid1D has all the same functionality as
RegularGrid1D, but it automatically uses the relevant underlying
grid spacing.
The function
-
T PiecewiseGrid1D::x(const int i) const;
returns a “physical” position on the grid given an index i.
The function
-
int PiecewiseGrid1D::index(const T x) const;
returns the index on the grid of a “physical” value x.
The function
-
T PiecewiseGrid1D::min() const;
returns the minimum value on the independent variable grid.
The function
-
T PiecewiseGrid1D::max() const;
returns the maximum value on the independent variable grid.
The function
-
T PiecewiseGrid1D::dx() const;
returns the grid spacing for the independent variable.
The function
-
int PiecewiseGrid1D::nPoints() const;
returns the number of points in the independent variable grid.
Developer functionality
For developers, additional functionality is available. Please consult the code.