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public interface EigenDecomposition
An interface to classes that implement an algorithm to calculate the eigen decomposition of a real matrix.
The eigen decomposition of matrix A is a set of two matrices: V and D such that A = V × D × VT. A, V and D are all m × m matrices.
This interface is similar in spirit to the EigenvalueDecomposition
class from the JAMA
library, with the following changes:
getVt method has been added,getRealEigenvalue and getImagEigenvalue methods to pick up a single eigenvalue have been added,getEigenvector method to pick up a single
eigenvector has been added,getDeterminant method has been added.getSolver method has been added.
| Method Summary | |
|---|---|
RealMatrix |
getD()
Returns the block diagonal matrix D of the decomposition. |
double |
getDeterminant()
Return the determinant of the matrix |
RealVector |
getEigenvector(int i)
Returns a copy of the ith eigenvector of the original matrix. |
double |
getImagEigenvalue(int i)
Returns the imaginary part of the ith eigenvalue of the original matrix. |
double[] |
getImagEigenvalues()
Returns a copy of the imaginary parts of the eigenvalues of the original matrix. |
double |
getRealEigenvalue(int i)
Returns the real part of the ith eigenvalue of the original matrix. |
double[] |
getRealEigenvalues()
Returns a copy of the real parts of the eigenvalues of the original matrix. |
DecompositionSolver |
getSolver()
Get a solver for finding the A × X = B solution in exact linear sense. |
RealMatrix |
getV()
Returns the matrix V of the decomposition. |
RealMatrix |
getVT()
Returns the transpose of the matrix V of the decomposition. |
| Method Detail |
|---|
RealMatrix getV()
V is an orthogonal matrix, i.e. its transpose is also its inverse.
The columns of V are the eigenvectors of the original matrix.
RealMatrix getD()
D is a block diagonal matrix.
Real eigenvalues are on the diagonal while complex values are on 2x2 blocks { {real +imaginary}, {-imaginary, real} }.
getRealEigenvalues(),
getImagEigenvalues()RealMatrix getVT()
V is an orthogonal matrix, i.e. its transpose is also its inverse.
The columns of V are the eigenvectors of the original matrix.
double[] getRealEigenvalues()
getD(),
getRealEigenvalue(int),
getImagEigenvalues()double getRealEigenvalue(int i)
i - index of the eigenvalue (counting from 0)
getD(),
getRealEigenvalues(),
getImagEigenvalue(int)double[] getImagEigenvalues()
getD(),
getImagEigenvalue(int),
getRealEigenvalues()double getImagEigenvalue(int i)
i - index of the eigenvalue (counting from 0)
getD(),
getImagEigenvalues(),
getRealEigenvalue(int)RealVector getEigenvector(int i)
i - index of the eigenvector (counting from 0)
getD()double getDeterminant()
DecompositionSolver getSolver()
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