Class SvdImplicitQrAlgorithm_FDRM

java.lang.Object
org.ejml.dense.row.decomposition.svd.implicitqr.SvdImplicitQrAlgorithm_FDRM

@Generated("org.ejml.dense.row.decomposition.svd.implicitqr.SvdImplicitQrAlgorithm_DDRM") public class SvdImplicitQrAlgorithm_FDRM extends Object

Computes the QR decomposition of a bidiagonal matrix. Internally this matrix is stored as two arrays. Shifts can either be provided to it or it can generate the shifts on its own. It optionally computes the U and V matrices. This comparability allows it to be used to compute singular values and associated matrices efficiently.

A = U*S*VT
where A is the original m by n matrix.

Based off of the outline provided in:

David S. Watkins, "Fundamentals of Matrix Computations," Second Edition. Page 404-411

Note: To watch it process the matrix step by step uncomment commented out code.

  • Field Details

    • rand

      protected Random rand
    • Ut

      @Nullable protected @Nullable FMatrixRMaj Ut
    • Vt

      @Nullable protected @Nullable FMatrixRMaj Vt
    • totalSteps

      protected int totalSteps
    • maxValue

      protected float maxValue
    • N

      protected int N
    • eigenSmall

      protected EigenvalueSmall_F32 eigenSmall
    • numExceptional

      protected int numExceptional
    • nextExceptional

      protected int nextExceptional
    • diag

      protected float[] diag
    • off

      protected float[] off
    • x1

      protected int x1
    • x2

      protected int x2
    • splits

      protected int[] splits
    • numSplits

      protected int numSplits
  • Constructor Details

    • SvdImplicitQrAlgorithm_FDRM

      public SvdImplicitQrAlgorithm_FDRM(boolean fastValues)
    • SvdImplicitQrAlgorithm_FDRM

      public SvdImplicitQrAlgorithm_FDRM()
  • Method Details

    • getUt

      @Nullable public @Nullable FMatrixRMaj getUt()
    • setUt

      public void setUt(@Nullable @Nullable FMatrixRMaj ut)
    • getVt

      @Nullable public @Nullable FMatrixRMaj getVt()
    • setVt

      public void setVt(@Nullable @Nullable FMatrixRMaj vt)
    • setMatrix

      public void setMatrix(int numRows, int numCols, float[] diag, float[] off)
    • swapDiag

      public float[] swapDiag(float[] diag)
    • swapOff

      public float[] swapOff(float[] off)
    • setMaxValue

      public void setMaxValue(float maxValue)
    • initParam

      public void initParam(int M, int N)
    • process

      public boolean process()
    • process

      public boolean process(float[] values)
      Perform a sequence of steps based off of the singular values provided.
    • _process

      public boolean _process()
    • incrementSteps

      public void incrementSteps()
    • isOffZero

      public boolean isOffZero(int i)
    • isDiagonalZero

      public boolean isDiagonalZero(int i)
    • resetSteps

      public void resetSteps()
    • nextSplit

      public boolean nextSplit()
      Tells it to process the submatrix at the next split. Should be called after the current submatrix has been processed.
    • performImplicitSingleStep

      public void performImplicitSingleStep(float scale, float lambda, boolean byAngle)
      Given the lambda value perform an implicit QR step on the matrix. B^T*B-lambda*I
      Parameters:
      lambda - Stepping factor.
    • updateRotator

      protected void updateRotator(FMatrixRMaj Q, int m, int n, float c, float s)
      Multiplied a transpose orthogonal matrix Q by the specified rotator. This is used to update the U and V matrices. Updating the transpose of the matrix is faster since it only modifies the rows.
      Parameters:
      Q - Orthogonal matrix
      m - Coordinate of rotator.
      n - Coordinate of rotator.
      c - cosine of rotator.
      s - sine of rotator.
    • createBulge

      protected void createBulge(int x1, float p, float scale, boolean byAngle)
      Performs a similar transform on BTB-pI
    • computeRotator

      protected void computeRotator(float rise, float run)
      Computes a rotator that will set run to zero (?)
    • removeBulgeLeft

      protected void removeBulgeLeft(int x1, boolean notLast)
    • removeBulgeRight

      protected void removeBulgeRight(int x1)
    • setSubmatrix

      public void setSubmatrix(int x1, int x2)
    • selectWilkinsonShift

      public float selectWilkinsonShift(float scale)
      Selects the Wilkinson's shift for BTB. See page 410. It is guaranteed to converge and converges fast in practice.
      Parameters:
      scale - Scale factor used to help prevent overflow/underflow
      Returns:
      Shifting factor lambda/(scale*scale)
    • eigenBB_2x2

      protected void eigenBB_2x2(int x1)
      Computes the eigenvalue of the 2 by 2 matrix BTB
    • checkForAndHandleZeros

      protected boolean checkForAndHandleZeros()
      Checks to see if either the diagonal element or off diagonal element is zero. If one is then it performs a split or pushes it off the matrix.
      Returns:
      True if there was a zero.
    • exceptionShift

      public void exceptionShift()
      It is possible for the QR algorithm to get stuck in a loop because of symmetries. This happens more often with larger matrices. By taking a random step it can break the symmetry and finish.
    • printMatrix

      public void printMatrix()
    • getNumberOfSingularValues

      public int getNumberOfSingularValues()
    • getSingularValue

      public float getSingularValue(int index)
    • setFastValues

      public void setFastValues(boolean b)
    • getSingularValues

      public float[] getSingularValues()
    • getDiag

      public float[] getDiag()
    • getOff

      public float[] getOff()
    • getMaxValue

      public float getMaxValue()