# MathInteg Package

Numerical integration (quadrature) algorithms for OCCT.

## Overview

The MathInteg package provides a collection of numerical integration methods for computing definite integrals of functions. It includes both classical quadrature rules and advanced adaptive methods suitable for various types of integrands, including those with singularities or over infinite intervals.

## Components

### MathInteg_Gauss.hxx
Gauss-Legendre quadrature methods:
- `Gauss` - Fixed-order Gauss-Legendre integration (orders >= 1)
- `GaussAdaptive` - Adaptive subdivision with error control using `IntegConfig.InitialOrder/MaxOrder`
- `GaussComposite` - Composite rule over multiple subintervals

### MathInteg_Kronrod.hxx
Gauss-Kronrod quadrature with embedded error estimation:
- `KronrodRule` - Single application of Gauss-Kronrod rule
- `Kronrod` - Adaptive Gauss-Kronrod integration
- `KronrodAuto` - Automatic order selection
- `KronrodSemiInfinite` - Integration over [a, +infinity)
- `KronrodInfinite` - Integration over (-infinity, +infinity)

### MathInteg_DoubleExp.hxx
Double exponential (tanh-sinh) quadrature:
- `TanhSinh` - Finite interval integration with endpoint singularity handling
- `ExpSinh` - Semi-infinite interval [a, +infinity)
- `SinhSinh` - Infinite interval (-infinity, +infinity)
- `DoubleExponential` - Automatic interval type detection
- `TanhSinhSingular` - Optimized for singular integrands
- `TanhSinhWithSingularity` - Known interior singularity

### MathInteg_Multiple.hxx
Multi-dimensional integration:
- `GaussMultiple` - N-dimensional Gauss-Legendre quadrature
- `GaussMultipleUniform` - Uniform order for all dimensions

### MathInteg_Set.hxx
Vector-valued function integration:
- `GaussSet` - Gauss-Legendre integration of R -> R^N functions

## Usage

All functions are template-based and accept functor types with appropriate `Value()` methods. Results are returned as `IntegResult` or `SetResult` structures containing the integral value, error estimates, and status information.

```cpp
#include <MathInteg_Gauss.hxx>

class MyFunc
{
public:
  bool Value(double theX, double& theF)
  {
    theF = theX * theX;
    return true;
  }
};

MyFunc aFunc;
MathInteg::IntegResult aResult = MathInteg::Gauss(aFunc, 0.0, 1.0, 15);
if (aResult.IsDone())
{
  double aValue = *aResult.Value; // Should be ~0.333...
}
```

## Dependencies

- MathUtils package for core types, configuration, and helper functions
- math_Vector, math_IntegerVector, math_Matrix for multi-dimensional integration
