ecl_statistics Documentation

### ecl_statistics

Common statistical structures and algorithms for control systems.

## packageSummary

This group mostly contains classes relevant to the probabilistics of mobile robot slam.

Include the following at the top of any translation unit that requires the ecl probabilistic tools.

## CompilingLinking

Include the following at the top of any translation unit which requires this library:

```        #include <ecl/statistics.hpp>

// Statistics Classes
using ecl::CovarianceEllipsoid;
using ecl::CovarianceEllipsoid2f; // also 2d, 3f, 3d typedef variants
```

You will also need to link to -lecl_statistics.

## usage

### Covariance Ellipsoids

mplemented by the template class `CovarianceEllipsoid` - this takes two template parameters. The first is the float type used (usually `float`/`double`) and the second, the dimension of the ellipsoid to be determined.

Specialisations are enabled for 2 and 3 dimensional types only as we haven't had a need to develop a general implementation.

== Typedefs ==

Typedefs exist for the template class in the eigen style:

{{{ #!cplusplus using ecl::CovarianceEllipsoid2f; using ecl::CovarianceEllipsoid2d; using ecl::CovarianceEllipsoid3f; using ecl::CovarianceEllipsoid3d; }}}

== Usage ==

You typically feed the covariance ellipsoid with a positive definite symmetric matrix (eigen matrix). Take care entering the positive definite symmetric matrix - the class does not yet do checking to make sure it is positive definite symmetric.

You can either input the matrix via the constructor - in which case it will automatically calculate the ellipsoid properties, or pass it in later via the `compute()` method:

```Matrix2d M;
M << 3.0, 1.0, 1.0, 5.0; // must be a positive definite, symmetric matrix

CovarianceEllipsoid2d ellipse(M);

// OR

CovarianceEllipsoid2d ellipse;
ellipse.compute(M);
```
```Matrix2d M;
M << 3.0, 1.0, 1.0, 5.0;
CovarianceEllipsoid2d ellipse(M);

// ellipse minor and major axis lengths
const Vector2d& lengths = ellipse.lengths();
double eigen_value_0 = lengths*lengths;

// angle between x-axis and major axis of the ellipse
double angle = ellipse.rotation();

// values of the intercepts of the ellipse with x and y axes
const Vector2d& intercepts = ellipse.intercepts();

// the ellipse axes/covariance eigenvectors as column vectors in a matrix
const Matrix2d& axes = ellipse.axes();
```

The 3d version is similar, but will only calculate intercepts and axes respectively. Note that the axes are sorted (to ensure a right-handed co-ordinate system) and normalised.

```Matrix3d P;
double sigmaX(0.1);
double sigmaY(0.5);
double sigmaT(0.3);
P << sigmaX*sigmaX, 0, 0, 0, sigmaY*sigmaY, 0, 0, 0, sigmaT*sigmaT;
CovarianceEllipsoid3d ellipse(P);

const Vector3d& lengths = ellipse.lengths();
double eigen_value_0 = lengths*lengths;
const Matrix3d& axes = ellipse.axes();
```

## ChangeLog

ecl_statistics
Author(s): Daniel Stonier
autogenerated on Sun Oct 5 2014 23:35:31