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

Class SvdImplicitQrAlgorithm_FDRM

  • public class SvdImplicitQrAlgorithm_FDRM
extends java.lang.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 Detail

      • rand

        protected java.util.Random rand

      • Ut

        protected org.ejml.data.FMatrixRMaj Ut

      • Vt

        protected org.ejml.data.FMatrixRMaj Vt

      • totalSteps

        protected int totalSteps

      • maxValue

        protected float maxValue

      • N

        protected int N

      • 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 Detail

      • SvdImplicitQrAlgorithm_FDRM

        public SvdImplicitQrAlgorithm_FDRM​(boolean fastValues)

      • SvdImplicitQrAlgorithm_FDRM

        public SvdImplicitQrAlgorithm_FDRM()

    • Method Detail

      • getUt

        public org.ejml.data.FMatrixRMaj getUt()

      • setUt

        public void setUt​(org.ejml.data.FMatrixRMaj ut)

      • getVt

        public org.ejml.data.FMatrixRMaj getVt()

      • setVt

        public void setVt​(org.ejml.data.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.
        Parameters:
        values -
        Returns:

      • _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​(org.ejml.data.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()