CovarianceMatrix class
A 2D covariance matrix for computation with 2D vertices.
Contents
The matrix is real, symmetric, positive semidefinite. See dip::Polygon::CovarianceMatrix
for how to create a covariance matrix.
The elements stored are xx, xy and yy, with xx the top-left element, and xy both
the off-diagonal elements, which are equal by definition.
Constructors, destructors, assignment and conversion operators
- CovarianceMatrix() defaulted
- Default-initialized covariance matrix is all zeros.
- CovarianceMatrix(dip::VertexFloat v) explicit
- Construct a covariance matrix as the outer product of a vector and itself.
- CovarianceMatrix(dip::dfloat xx, dip::dfloat yy, dip::dfloat xy) explicit
- Construct a covariance matrix with the three components.
Classes
- struct Eigenvalues
- Container for matrix eigenvalues.
- struct EllipseParameters
- Container for ellipse parameters.
Functions
- auto xx() const -> dip::dfloat
- Read matrix element.
- auto xy() const -> dip::dfloat
- Read matrix element.
- auto yy() const -> dip::dfloat
- Read matrix element.
- auto Det() const -> dip::dfloat
- Compute determinant of matrix.
- auto Inv() const -> dip::CovarianceMatrix
- Compute inverse of matrix.
- auto Project(dip::VertexFloat const& v) const -> dip::dfloat
- Computes v’ * C * v, with v’ the transpose of v. This is a positive scalar if v is non-zero, because C (this matrix) is positive semidefinite.
- auto Eig() const -> dip::CovarianceMatrix::Eigenvalues
- Compute eigenvalues of matrix.
- auto Ellipse(bool solid = false) const -> dip::CovarianceMatrix::EllipseParameters
- Compute parameters of ellipse with same covariance matrix.
Operators
- auto operator+=(dip::CovarianceMatrix const& other) -> dip::CovarianceMatrix&
- Add other matrix to this matrix.
- auto operator*=(dip::dfloat d) -> dip::CovarianceMatrix&
- Scale matrix.
- auto operator/=(dip::dfloat d) -> dip::CovarianceMatrix&
- Scale matrix.
Class documentation
struct EllipseParameters
Container for ellipse parameters.
| Variables | |
|---|---|
| dip::dfloat majorAxis | Major axis length |
| dip::dfloat minorAxis | Minor axis length |
| dip::dfloat orientation | Orientation of major axis |
| dip::dfloat eccentricity | Ellipse eccentricity |
Function documentation
dip::CovarianceMatrix::EllipseParameters Ellipse(bool solid = false) const
Compute parameters of ellipse with same covariance matrix.
If solid is false (default), then it is assumed that the covariance matrix corresponds to an ellipse
shell (e.g. obtained through dip::Polygon::CovarianceMatrixVertices). This is the default for
backwards-compatibility. If true, the covariance matrix corresponds to a solid ellipse (e.g. obtained
though dip::Polygon::CovarianceMatrixSolid).