public class EigenOps extends Object
Constructor and Description |
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EigenOps() |
Modifier and Type | Method and Description |
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static double[] |
boundLargestEigenValue(DenseMatrix64F A,
double[] bound)
Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius
theorem.
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static double |
computeEigenValue(DenseMatrix64F A,
DenseMatrix64F eigenVector)
Given matrix A and an eigen vector of A, compute the corresponding eigen value.
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static Eigenpair |
computeEigenVector(DenseMatrix64F A,
double eigenvalue)
Given an eigenvalue it computes an eigenvector using inverse iteration:
for i=1:MAX { (A - μI)z(i) = q(i-1) q(i) = z(i) / ||z(i)|| λ(i) = q(i)T A q(i) } |
static DenseMatrix64F |
createMatrixD(EigenDecomposition eig)
A diagonal matrix where real diagonal element contains a real eigenvalue.
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static DenseMatrix64F |
createMatrixV(EigenDecomposition<DenseMatrix64F> eig)
Puts all the real eigenvectors into the columns of a matrix.
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static Eigenpair |
dominantEigenpair(DenseMatrix64F A)
Computes the dominant eigen vector for a matrix.
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public static double computeEigenValue(DenseMatrix64F A, DenseMatrix64F eigenVector)
Given matrix A and an eigen vector of A, compute the corresponding eigen value. This is
the Rayleigh quotient.
xTAx / xTx
A
- Matrix. Not modified.eigenVector
- An eigen vector of A. Not modified.public static Eigenpair computeEigenVector(DenseMatrix64F A, double eigenvalue)
Given an eigenvalue it computes an eigenvector using inverse iteration:
for i=1:MAX {
(A - μI)z(i) = q(i-1)
q(i) = z(i) / ||z(i)||
λ(i) = q(i)T A q(i)
}
NOTE: If there is another eigenvalue that is very similar to the provided one then there is a chance of it converging towards that one instead. The larger a matrix is the more likely this is to happen.
A
- Matrix whose eigenvector is being computed. Not modified.eigenvalue
- The eigenvalue in the eigen pair.public static Eigenpair dominantEigenpair(DenseMatrix64F A)
Computes the dominant eigen vector for a matrix. The dominant eigen vector is an eigen vector associated with the largest eigen value.
WARNING: This function uses the power method. There are known cases where it will not converge. It also seems to converge to non-dominant eigen vectors some times. Use at your own risk.
A
- A matrix. Not modified.public static double[] boundLargestEigenValue(DenseMatrix64F A, double[] bound)
Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius theorem. This function only applies to non-negative real matrices.
For "stochastic" matrices (Markov process) this should return one for the upper and lower bound.
A
- Square matrix with positive elements. Not modified.bound
- Where the results are stored. If null then a matrix will be declared. Modified.public static DenseMatrix64F createMatrixD(EigenDecomposition eig)
A diagonal matrix where real diagonal element contains a real eigenvalue. If an eigenvalue is imaginary then zero is stored in its place.
eig
- An eigenvalue decomposition which has already decomposed a matrix.public static DenseMatrix64F createMatrixV(EigenDecomposition<DenseMatrix64F> eig)
Puts all the real eigenvectors into the columns of a matrix. If an eigenvalue is imaginary then the corresponding eigenvector will have zeros in its column.
eig
- An eigenvalue decomposition which has already decomposed a matrix.Copyright © 2014. All Rights Reserved.