Class MultiCubicSpline

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

N-dimensional cubic spline interpolation between discrete points, in 1 to 15 dimensions.

public sealed class MultiCubicSpline

Inheritance

object

MultiCubicSpline

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

QuantLib's recursion: at construction a natural cubic spline's second derivatives along the last dimension, for every line of it; at each evaluation the splines of the lower dimensions through the values the higher ones interpolate, the first dimension last, each step's arithmetic and order QuantLib's, so the values are QuantLib's.

Immutable and safe to share across threads: the grid and the values are copied, and each evaluation computes QuantLib's coefficients in scratch of its own, where QuantLib's spline holds references to its inputs and evaluates through mutable members. The dimension is the grid's, read at construction, where QuantLib's is a template parameter.

The last grid point of a dimension is interpolated on its last interval, where QuantLib refuses it as extrapolation (its documented bug, "cannot interpolate at the grid points on the boundary surface"), and with extrapolation allowed a point beyond it reads the last value, where QuantLib's flat value reads one value past the data; an argument that isn't a number is refused, where QuantLib's search reads past the grid (Divergences/MultiCubicSplineBoundaryTests.cs).

Constructors

MultiCubicSpline(ImmutableArray<ImmutableArray<double>>, ReadOnlySpan<double>, ReadOnlySpan<bool>)

Initializes a new instance of the MultiCubicSpline class.

public MultiCubicSpline(ImmutableArray<ImmutableArray<double>> grid, ReadOnlySpan<double> values, ReadOnlySpan<bool> extrapolation = default)

Parameters

grid ImmutableArray<ImmutableArray<double>>

The grid, one increasing list of at least four points per dimension.

values ReadOnlySpan<double>

The values at the grid's points, the first dimension slowest (QuantLib's nested data table, flattened), copied.

extrapolation ReadOnlySpan<bool>

Whether each dimension extrapolates flat beyond the grid; empty, QuantLib's default, for none.

Exceptions

ArgumentException

The grid's dimension isn't 1 to 15, a dimension is empty, holds fewer than four points or isn't increasing, the values don't fill the grid, or the extrapolation flags aren't one per dimension.

Fields

MaxDimension

The largest dimension, QuantLib's fifteen splines.

public const int MaxDimension = 15

Field Value

int

Properties

Dimension

Gets the dimension.

public int Dimension { get; }

Property Value

int

Grid

Gets the grid.

public ImmutableArray<ImmutableArray<double>> Grid { get; }

Property Value

ImmutableArray<ImmutableArray<double>>

Methods

Evaluate(ReadOnlySpan<double>)

The interpolated value at a point.

public double Evaluate(ReadOnlySpan<double> x)

Parameters

x ReadOnlySpan<double>

The point, one coordinate per dimension.

Returns

double

The value.

Exceptions

ArgumentException

x doesn't hold one coordinate per dimension, a coordinate isn't a number, or lies outside its dimension's grid where that dimension doesn't extrapolate.