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

Class SvdImplicitQrDecompose_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.svd.SvdImplicitQrDecompose_DDRM
All Implemented Interfaces:
DecompositionInterface<DMatrixRMaj>, SingularValueDecomposition<DMatrixRMaj>, SingularValueDecomposition_F64<DMatrixRMaj>
Direct Known Subclasses:
SvdImplicitQrDecompose_MT_DDRM
public class SvdImplicitQrDecompose_DDRM extends Object implements SingularValueDecomposition_F64<DMatrixRMaj>

Computes the Singular value decomposition of a matrix using the implicit QR algorithm for singular value decomposition. It works by first by transforming the matrix to a bidiagonal A=U*B*VT form, then it implicitly computing the eigenvalues of the BTB matrix, which are the same as the singular values in the original A matrix.

Based off of the description provided in:

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

  • Field Details

    • numRows

      protected int numRows

    • numCols

      protected int numCols

    • numRowsT

      protected int numRowsT

    • numColsT

      protected int numColsT

    • canUseTallBidiagonal

      protected boolean canUseTallBidiagonal

    • bidiag

      protected BidiagonalDecomposition_F64<DMatrixRMaj> bidiag

    • qralg

      protected SvdImplicitQrAlgorithm_DDRM qralg

    • compact

      protected boolean compact

    • computeU

      protected boolean computeU

    • computeV

      protected boolean computeV

    • prefComputeU

      protected boolean prefComputeU

    • prefComputeV

      protected boolean prefComputeV

    • transposed

      protected boolean transposed

  • Constructor Details

    • SvdImplicitQrDecompose_DDRM

      public SvdImplicitQrDecompose_DDRM(boolean compact, boolean computeU, boolean computeV, boolean canUseTallBidiagonal)
      Configures the class
      Parameters:
      compact - Compute a compact SVD
      computeU - If true it will compute the U matrix
      computeV - If true it will compute the V matrix
      canUseTallBidiagonal - If true then it can choose to use a tall Bidiagonal decomposition to improve runtime performance.

  • Method Details

    • getSingularValues

      public double[] getSingularValues()
      Description copied from interface: SingularValueDecomposition_F64
      Returns the singular values. This is the diagonal elements of the W matrix in the decomposition. Ordering of singular values is not guaranteed..
      Specified by:
      getSingularValues in interface SingularValueDecomposition_F64<DMatrixRMaj>
      Returns:
      Singular values. Note this array can be longer than the number of singular values. Extra elements have no meaning.

    • numberOfSingularValues

      public int numberOfSingularValues()
      Description copied from interface: SingularValueDecomposition
      The number of singular values in the matrix. This is equal to the length of the smallest side.
      Specified by:
      numberOfSingularValues in interface SingularValueDecomposition<DMatrixRMaj>
      Returns:
      Number of singular values in the matrix.

    • isCompact

      public boolean isCompact()
      Description copied from interface: SingularValueDecomposition
      If true then compact matrices are returned.
      Specified by:
      isCompact in interface SingularValueDecomposition<DMatrixRMaj>
      Returns:
      true if results use compact notation.

    • getU

      public DMatrixRMaj getU(@Nullable @Nullable DMatrixRMaj U, boolean transpose)
      Description copied from interface: SingularValueDecomposition

      Returns the orthogonal 'U' matrix.

      Internally the SVD algorithm might compute U transposed or it might not. To avoid an unnecessary double transpose the option is provided to select if the transpose is returned.

      Specified by:
      getU in interface SingularValueDecomposition<DMatrixRMaj>
      Parameters:
      U - Optional storage for U. If null a new instance or internally maintained matrix is returned. Modified.
      transpose - If the returned U is transposed.
      Returns:
      An orthogonal matrix.

    • getV

      public DMatrixRMaj getV(@Nullable @Nullable DMatrixRMaj V, boolean transpose)
      Description copied from interface: SingularValueDecomposition

      Returns the orthogonal 'V' matrix.

      Internally the SVD algorithm might compute V transposed or it might not. To avoid an unnecessary double transpose the option is provided to select if the transpose is returned.

      Specified by:
      getV in interface SingularValueDecomposition<DMatrixRMaj>
      Parameters:
      V - Optional storage for v. If null a new instance or internally maintained matrix is returned. Modified.
      transpose - If the returned V is transposed.
      Returns:
      An orthogonal matrix.

    • transpose

      protected void transpose(@NotNull @NotNull DMatrixRMaj V, DMatrixRMaj Vt)

    • getW

      public DMatrixRMaj getW(@Nullable @Nullable DMatrixRMaj W)
      Description copied from interface: SingularValueDecomposition
      Returns a diagonal matrix with the singular values. Order of the singular values is not guaranteed.
      Specified by:
      getW in interface SingularValueDecomposition<DMatrixRMaj>
      Parameters:
      W - Optional storage for W. If null a new instance or internally maintained matrix is returned. Modified.
      Returns:
      Diagonal matrix with singular values along the diagonal.

    • decompose

      public boolean decompose(DMatrixRMaj orig)
      Description copied from interface: DecompositionInterface
      Computes the decomposition of the input matrix. Depending on the implementation the input matrix might be stored internally or modified. If it is modified then the function DecompositionInterface.inputModified() will return true and the matrix should not be modified until the decomposition is no longer needed.
      Specified by:
      decompose in interface DecompositionInterface<DMatrixRMaj>
      Parameters:
      orig - The matrix which is being decomposed. Modification is implementation dependent.
      Returns:
      Returns if it was able to decompose the matrix.

    • inputModified

      public boolean inputModified()
      Description copied from interface: DecompositionInterface
      Checks if the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.
      Specified by:
      inputModified in interface DecompositionInterface<DMatrixRMaj>
      Returns:
      true if the input matrix to decompose() is modified.

    • declareBidiagonalDecomposition

      protected void declareBidiagonalDecomposition()

    • numRows

      public int numRows()
      Description copied from interface: SingularValueDecomposition
      Number of rows in the decomposed matrix.
      Specified by:
      numRows in interface SingularValueDecomposition<DMatrixRMaj>
      Returns:
      Number of rows in the decomposed matrix.

    • numCols

      public int numCols()
      Description copied from interface: SingularValueDecomposition
      Number of columns in the decomposed matrix.
      Specified by:
      numCols in interface SingularValueDecomposition<DMatrixRMaj>
      Returns:
      Number of columns in the decomposed matrix.