Package org.ejml.dense.row.decomposition.svd.implicitqr

Class SvdImplicitQrAlgorithm_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.svd.implicitqr.SvdImplicitQrAlgorithm_DDRM
public class SvdImplicitQrAlgorithm_DDRM 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 DMatrixRMaj Ut

    • Vt

      @Nullable protected @Nullable DMatrixRMaj Vt

    • totalSteps

      protected int totalSteps

    • maxValue

      protected double maxValue

    • N

      protected int N

    • eigenSmall

      protected EigenvalueSmall_F64 eigenSmall

    • numExceptional

      protected int numExceptional

    • nextExceptional

      protected int nextExceptional

    • diag

      protected double[] diag

    • off

      protected double[] off

    • x1

      protected int x1

    • x2

      protected int x2

    • splits

      protected int[] splits

    • numSplits

      protected int numSplits

  • Constructor Details

    • SvdImplicitQrAlgorithm_DDRM

      public SvdImplicitQrAlgorithm_DDRM(boolean fastValues)

    • SvdImplicitQrAlgorithm_DDRM

      public SvdImplicitQrAlgorithm_DDRM()

  • Method Details

    • getUt

      @Nullable public @Nullable DMatrixRMaj getUt()

    • setUt

      public void setUt(@Nullable @Nullable DMatrixRMaj ut)

    • getVt

      @Nullable public @Nullable DMatrixRMaj getVt()

    • setVt

      public void setVt(@Nullable @Nullable DMatrixRMaj vt)

    • setMatrix

      public void setMatrix(int numRows, int numCols, double[] diag, double[] off)

    • swapDiag

      public double[] swapDiag(double[] diag)

    • swapOff

      public double[] swapOff(double[] off)

    • setMaxValue

      public void setMaxValue(double maxValue)

    • initParam

      public void initParam(int M, int N)

    • process

      public boolean process()

    • process

      public boolean process(double[] 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(double scale, double 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(DMatrixRMaj Q, int m, int n, double c, double 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, double p, double scale, boolean byAngle)
      Performs a similar transform on BTB-pI

    • computeRotator

      protected void computeRotator(double rise, double 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 double selectWilkinsonShift(double 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 double getSingularValue(int index)

    • setFastValues

      public void setFastValues(boolean b)

    • getSingularValues

      public double[] getSingularValues()

    • getDiag

      public double[] getDiag()

    • getOff

      public double[] getOff()

    • getMaxValue

      public double getMaxValue()