Class ChebyshevSlider

Namespace

ChebyshevSharp

Assembly

ChebyshevSharp.dll

Chebyshev Sliding approximation for high-dimensional functions. Decomposes f(x₁, …, xₙ) into a sum of low-dimensional Chebyshev interpolants (slides) around a pivot point z: f(x) ≈ f(z) + Σᵢ [sᵢ(x_groupᵢ) - f(z)] where each slide sᵢ is a ChebyshevApproximation built on a subset of dimensions with the remaining dimensions fixed at z.

public class ChebyshevSlider

Inheritance

object

ChebyshevSlider

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

Remarks

This trades accuracy for dramatically reduced build cost: instead of evaluating f at n₁ × n₂ × … × nₐ grid points (exponential), the slider evaluates at n₁ × n₂ + n₃ × n₄ + … (sum of products within each group). Reference: Ruiz & Zeron (2022), Ch. 7.

Constructors

ChebyshevSlider(Func<double[], object?, double>, int, double[][], int[], int[][], double[], int)

Create a new ChebyshevSlider.

public ChebyshevSlider(Func<double[], object?, double> function, int numDimensions, double[][] domain, int[] nNodes, int[][] partition, double[] pivotPoint, int maxDerivativeOrder = 2)

Parameters

function Func<double[], object, double>

Function to approximate: f(point, data) → double.

numDimensions int

Total number of input dimensions.

domain double[][]

Bounds for each dimension as double[ndim][2].

nNodes int[]

Number of Chebyshev nodes per dimension.

partition int[][]

Grouping of dimension indices into slides. Each dimension must appear exactly once.

pivotPoint double[]

Reference point z around which slides are built.

maxDerivativeOrder int

Maximum derivative order to support (default 2).

Properties

BuildTime

Wall-clock time (seconds) for the most recent Build() call.

public double BuildTime { get; }

Property Value

double

Built

Whether Build() has been called.

public bool Built { get; }

Property Value

bool

Domain

Domain bounds for each dimension, as list of [lo, hi].

public double[][] Domain { get; }

Property Value

double[][]

Function

The function to approximate. Null after load.

public Func<double[], object?, double>? Function { get; }

Property Value

Func<double[], object, double>

MaxDerivativeOrder

Maximum supported derivative order.

public int MaxDerivativeOrder { get; }

Property Value

int

NNodes

Number of Chebyshev nodes per dimension.

public int[] NNodes { get; }

Property Value

int[]

NumDimensions

Number of input dimensions.

public int NumDimensions { get; }

Property Value

int

Partition

Grouping of dimension indices into slides.

public int[][] Partition { get; }

Property Value

int[][]

PivotPoint

Reference point z around which slides are built.

public double[] PivotPoint { get; }

Property Value

double[]

PivotValue

Function value at the pivot point: f(z).

public double PivotValue { get; }

Property Value

double

TotalBuildEvals

Total number of function evaluations used during build.

public int TotalBuildEvals { get; }

Property Value

int

Methods

Build(bool)

Build all slides by evaluating the function at slide-specific grids. For each slide, dimensions outside the group are fixed at pivot values.

public void Build(bool verbose = true)

Parameters

verbose bool

If true, print build progress.

ErrorEstimate()

Estimate the sliding approximation error. Returns the sum of per-slide Chebyshev error estimates. Note: this captures per-slide interpolation error only; cross-group interaction error inherent to the sliding decomposition is not included.

public double ErrorEstimate()

Returns

double

Estimated interpolation error (per-slide sum).

Eval(double[], int[])

Evaluate the slider approximation at a point. Uses Equation 7.5: f(x) ≈ f(z) + Σᵢ [sᵢ(x_groupᵢ) - f(z)]. For derivatives, only the slide containing that dimension contributes. Cross-group mixed partials are exactly zero.

public double Eval(double[] point, int[] derivativeOrder)

Parameters

point double[]

Evaluation point in the full n-dimensional space.

derivativeOrder int[]

Derivative order for each dimension (0 = function value).

Returns

double

Approximated function value or derivative.

EvalMulti(double[], int[][])

Evaluate slider at multiple derivative orders for the same point.

public double[] EvalMulti(double[] point, int[][] derivativeOrders)

Parameters

point double[]

Evaluation point.

derivativeOrders int[][]

Each inner array specifies derivative order per dimension.

Returns

double[]

Results for each derivative order.

Extrude(params (int dimIndex, double[] bounds, int nNodes)[])

Add new dimensions where the function is constant. Each new dimension becomes its own single-dim slide group with constant tensor values equal to PivotValue, so it contributes nothing to the sliding sum.

public ChebyshevSlider Extrude(params (int dimIndex, double[] bounds, int nNodes)[] extrudeParams)

Parameters

extrudeParams (int dimIndex, double[] bounds, int nNodes)[]

Tuples of (dimIndex, bounds, nNodes).

Returns

ChebyshevSlider

A new, higher-dimensional slider (already built).

Load(string)

Load a previously saved slider from a JSON file.

public static ChebyshevSlider Load(string path)

Parameters

path string

Path to the saved file.

Returns

ChebyshevSlider

A fully functional slider with Function=null.

Save(string)

Save the built slider to a JSON file.

public void Save(string path)

Parameters

path string

Destination file path.

Slice(params (int dimIndex, double value)[])

Fix one or more dimensions at given values, reducing dimensionality.

public ChebyshevSlider Slice(params (int dimIndex, double value)[] sliceParams)

Parameters

sliceParams (int dimIndex, double value)[]

Tuples of (dimIndex, value).

Returns

ChebyshevSlider

A new, lower-dimensional slider (already built).

ToReprString()

Compact repr string.

public string ToReprString()

Returns

string

ToString()

Multi-line display string.

public override string ToString()

Returns

string

Operators

operator +(ChebyshevSlider, ChebyshevSlider)

Pointwise addition of two sliders on the same grid.

public static ChebyshevSlider operator +(ChebyshevSlider a, ChebyshevSlider b)

Parameters

a ChebyshevSlider

b ChebyshevSlider

Returns

ChebyshevSlider

operator /(ChebyshevSlider, double)

Scalar division.

public static ChebyshevSlider operator /(ChebyshevSlider a, double scalar)

Parameters

a ChebyshevSlider

scalar double

Returns

ChebyshevSlider

operator *(ChebyshevSlider, double)

Scalar multiplication.

public static ChebyshevSlider operator *(ChebyshevSlider a, double scalar)

Parameters

a ChebyshevSlider

scalar double

Returns

ChebyshevSlider

operator *(double, ChebyshevSlider)

Scalar multiplication (scalar on left).

public static ChebyshevSlider operator *(double scalar, ChebyshevSlider a)

Parameters

scalar double

a ChebyshevSlider

Returns

ChebyshevSlider

operator -(ChebyshevSlider, ChebyshevSlider)

Pointwise subtraction of two sliders on the same grid.

public static ChebyshevSlider operator -(ChebyshevSlider a, ChebyshevSlider b)

Parameters

a ChebyshevSlider

b ChebyshevSlider

Returns

ChebyshevSlider

operator -(ChebyshevSlider)

Unary negation.

public static ChebyshevSlider operator -(ChebyshevSlider a)

Parameters

a ChebyshevSlider

Returns

ChebyshevSlider