Class ChebyshevApproximation

Namespace

ChebyshevSharp

Assembly

ChebyshevSharp.dll

Multi-dimensional Chebyshev tensor interpolation with analytical derivatives. Uses barycentric interpolation with pre-computed weights.

public class ChebyshevApproximation

Inheritance

object

ChebyshevApproximation

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

Constructors

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

Create a new ChebyshevApproximation.

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

Parameters

function Func<double[], object, double>

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

numDimensions int

Number of input dimensions.

domain double[][]

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

nNodes int[]

Number of Chebyshev nodes per dimension.

maxDerivativeOrder int

Maximum derivative order to support (default 2).

Properties

BuildTime

Time taken by Build() in seconds.

public double BuildTime { get; }

Property Value

double

DiffMatrices

Spectral differentiation matrices per dimension.

public double[][,]? DiffMatrices { get; }

Property Value

double[][,]

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 or from_values.

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

NEvaluations

Number of function evaluations during Build().

public int NEvaluations { get; }

Property Value

int

NNodes

Number of Chebyshev nodes per dimension.

public int[] NNodes { get; }

Property Value

int[]

NodeArrays

Chebyshev nodes per dimension, each sorted ascending.

public double[][] NodeArrays { get; }

Property Value

double[][]

NumDimensions

Number of input dimensions.

public int NumDimensions { get; }

Property Value

int

TensorValues

Flat tensor of function values at all node combinations (C-order).

public double[]? TensorValues { get; }

Property Value

double[]

Weights

Barycentric weights per dimension.

public double[][]? Weights { get; }

Property Value

double[][]

Methods

Build(bool)

Evaluate the function at all node combinations and pre-compute weights.

public void Build(bool verbose = true)

Parameters

verbose bool

If true, print build progress.

ChebyshevCoefficients1D(double[])

Get Chebyshev coefficients for a 1D array of values at Type I nodes. Public for testing.

public static double[] ChebyshevCoefficients1D(double[] values)

Parameters

values double[]

Returns

double[]

ErrorEstimate()

Estimate the supremum-norm interpolation error using Chebyshev coefficient decay.

public double ErrorEstimate()

Returns

double

Estimated maximum interpolation error.

Eval(double[], int[])

Evaluate using dimensional decomposition with barycentric interpolation. Loop-based implementation matching Python eval().

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

Parameters

point double[]

Query point, one coordinate per dimension.

derivativeOrder int[]

Derivative order per dimension.

Returns

double

Interpolated value or derivative at the query point.

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

Add new dimensions where the function is constant.

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

Parameters

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

Returns

ChebyshevApproximation

FromValues(double[], int, double[][], int[], int)

Create an interpolant from pre-computed function values.

public static ChebyshevApproximation FromValues(double[] tensorValues, int numDimensions, double[][] domain, int[] nNodes, int maxDerivativeOrder = 2)

Parameters

tensorValues double[]

numDimensions int

domain double[][]

nNodes int[]

maxDerivativeOrder int

Returns

ChebyshevApproximation

GetDerivativeId(int[])

Return derivative order as-is (for API compatibility).

public int[] GetDerivativeId(int[] derivativeOrder)

Parameters

derivativeOrder int[]

Returns

int[]

Integrate(int[]?, (double lo, double hi)[]?)

Integrate the interpolant over one or more dimensions.

public object Integrate(int[]? dims = null, (double lo, double hi)[]? bounds = null)

Parameters

dims int[]

Dimensions to integrate out. Null = all.

bounds (double lo, double hi)[]

Sub-interval bounds per dim. Null = full domain.

Returns

object

Scalar if all dims integrated, otherwise a lower-dimensional interpolant.

Load(string)

Load a previously saved interpolant from a file.

public static ChebyshevApproximation Load(string path)

Parameters

path string

Path to the saved file.

Returns

ChebyshevApproximation

The restored interpolant.

Maximize(int?, Dictionary<int, double>?)

Find the maximum value of the interpolant along a dimension.

public (double value, double location) Maximize(int? dim = null, Dictionary<int, double>? fixedDims = null)

Parameters

dim int?

fixedDims Dictionary<int, double>

Returns

(double value, double location)

Minimize(int?, Dictionary<int, double>?)

Find the minimum value of the interpolant along a dimension.

public (double value, double location) Minimize(int? dim = null, Dictionary<int, double>? fixedDims = null)

Parameters

dim int?

fixedDims Dictionary<int, double>

Returns

(double value, double location)

Nodes(int, double[][], int[])

Generate Chebyshev nodes without evaluating any function.

public static NodeInfo Nodes(int numDimensions, double[][] domain, int[] nNodes)

Parameters

numDimensions int

Number of dimensions.

domain double[][]

Lower and upper bounds for each dimension.

nNodes int[]

Number of Chebyshev nodes per dimension.

Returns

NodeInfo

Dictionary with "NodesPerDim", "FullGrid", and "Shape".

Roots(int?, Dictionary<int, double>?)

Find all roots of the interpolant along a specified dimension.

public double[] Roots(int? dim = null, Dictionary<int, double>? fixedDims = null)

Parameters

dim int?

fixedDims Dictionary<int, double>

Returns

double[]

Save(string)

Save the built interpolant to a file using JSON serialization.

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

Parameters

sliceParams (int dimIndex, double value)[]

Returns

ChebyshevApproximation

ToReprString()

Compact representation of the interpolant.

public string ToReprString()

Returns

string

ToString()

Returns a string that represents the current object.

public override string ToString()

Returns

string

A string that represents the current object.

VectorizedEval(double[], int[])

Fully vectorized evaluation using matrix operations. Replaces the Python loop with BLAS-style matrix-vector products.

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

Parameters

point double[]

Query point, one coordinate per dimension.

derivativeOrder int[]

Derivative order per dimension.

Returns

double

Interpolated value or derivative.

VectorizedEvalBatch(double[][], int[])

Evaluate at multiple points.

public double[] VectorizedEvalBatch(double[][] points, int[] derivativeOrder)

Parameters

points double[][]

Points as double[N][numDimensions].

derivativeOrder int[]

Derivative order per dimension.

Returns

double[]

Results array of length N.

VectorizedEvalMulti(double[], int[][])

Evaluate multiple derivative orders at the same point, sharing barycentric weights.

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

Parameters

point double[]

Query point.

derivativeOrders int[][]

Each inner array specifies derivative order per dimension.

Returns

double[]

One result per derivative order.

Operators

operator +(ChebyshevApproximation, ChebyshevApproximation)

Add two interpolants with the same grid.

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

Parameters

a ChebyshevApproximation

b ChebyshevApproximation

Returns

ChebyshevApproximation

operator /(ChebyshevApproximation, double)

Divide interpolant by a scalar.

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

Parameters

a ChebyshevApproximation

scalar double

Returns

ChebyshevApproximation

operator *(ChebyshevApproximation, double)

Multiply interpolant by a scalar.

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

Parameters

a ChebyshevApproximation

scalar double

Returns

ChebyshevApproximation

operator *(double, ChebyshevApproximation)

Multiply scalar by interpolant.

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

Parameters

scalar double

a ChebyshevApproximation

Returns

ChebyshevApproximation

operator -(ChebyshevApproximation, ChebyshevApproximation)

Subtract two interpolants with the same grid.

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

Parameters

a ChebyshevApproximation

b ChebyshevApproximation

Returns

ChebyshevApproximation

operator -(ChebyshevApproximation)

Negate interpolant.

public static ChebyshevApproximation operator -(ChebyshevApproximation a)

Parameters

a ChebyshevApproximation

Returns

ChebyshevApproximation