org.apache.mahout.math.decomposer.lanczos
Class LanczosSolver
java.lang.Object
org.apache.mahout.math.decomposer.lanczos.LanczosSolver
public class LanczosSolver
- extends Object
Simple implementation of the Lanczos algorithm for
finding eigenvalues of a symmetric matrix, applied to non-symmetric matrices by applying Matrix.timesSquared(vector)
as the "matrix-multiplication" method.
To avoid floating point overflow problems which arise in power-methods like Lanczos, an initial pass is made
through the input matrix to
- generate a good starting seed vector by summing all the rows of the input matrix, and
- compute the trace(inputMatrixt*matrix)
This latter value, being the sum of all of the singular values, is used to rescale the entire matrix, effectively
forcing the largest singular value to be strictly less than one, and transforming floating point overflow
problems into floating point underflow (ie, very small singular values will become invisible, as they
will appear to be zero and the algorithm will terminate).
This implementation uses EigenvalueDecomposition
to do the
eigenvalue extraction from the small (desiredRank x desiredRank) tridiagonal matrix. Numerical stability is
achieved via brute-force: re-orthogonalization against all previous eigenvectors is computed after every pass.
This can be made smarter if (when!) this proves to be a major bottleneck. Of course, this step can be parallelized
as well.
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SAFE_MAX
public static final double SAFE_MAX
- See Also:
- Constant Field Values
LanczosSolver
public LanczosSolver()
solve
public void solve(LanczosState state,
int desiredRank)
solve
public void solve(LanczosState state,
int desiredRank,
boolean isSymmetric)
calculateScaleFactor
protected double calculateScaleFactor(Vector nextVector)
orthoganalizeAgainstAllButLast
protected void orthoganalizeAgainstAllButLast(Vector nextVector,
LanczosState state)
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