Class ComplexUnitaryDecomposition

java.lang.Object
org.flag4j.linalg.decompositions.unitary.UnitaryDecomposition<CMatrix,Complex128[]>
org.flag4j.linalg.decompositions.unitary.ComplexUnitaryDecomposition
All Implemented Interfaces:
Decomposition<CMatrix>
Direct Known Subclasses:
ComplexHess, ComplexQR
public abstract class ComplexUnitaryDecomposition extends UnitaryDecomposition<CMatrix,Complex128[]>
This class is the base class for complex matrix decompositions which proceed by using unitary transformations (specifically Householder reflectors) to bring a matrix into an upper triangular/Hessenburg matrix. Specifically, the QR and Hessenburg decompositions.

  • Field Details

    • normRe

      protected double normRe
      To store norms of columns in UnitaryDecomposition.transformMatrix. Will be real.

    • norm

      protected Complex128 norm
      For storing the scaled, phase-adjusted norm. This may be complex.

    • currentFactor

      protected Complex128 currentFactor
      Scalar factor of the currently computed Householder reflector.

  • Constructor Details

    • ComplexUnitaryDecomposition

      public ComplexUnitaryDecomposition(int subDiagonal)
      Creates a real unitary decomposer which will reduce the matrix to an upper triangular/Hessenburg matrix which is has zeros below the specified sub-diagonal.
      Parameters:
      subDiagonal - Sub-diagonal of the upper triangular/Hessenburg matrix. That is, the sub-diagonal for which all data below will be zero in the final upper quasi-triangular matrix. Must be Zero or one. If zero, it will be upper triangular. If one, it will be upper Hessenburg.

    • ComplexUnitaryDecomposition

      public ComplexUnitaryDecomposition(int subDiagonal, boolean storeReflectors)
      Creates a real unitary decomposer which will reduce the matrix to an upper triangular/Hessenburg matrix which is has zeros below the specified sub-diagonal.

      Allows for specification if the reflectors used to bring matrix to upper triangular/Hessenburg form to be stored or not.

      If the Q matrix is need, then storeReflectors must be true. If Q is NOT needed, then not storing the reflectors may improve performance slightly by avoiding unneeded copies.

      It should be noted that if performance is improved, it will be a very slight improvement compared to the total time to compute the decomposition. This is because the computation of Q is only evaluated lazily once getQ() is called, so this will only save on copy ops.

      Parameters:
      subDiagonal - Sub-diagonal of the upper triangular/Hessenburg matrix. That is, the sub-diagonal for which all data below will be zero in the final upper quasi-triangular matrix. Must be Zero or one. If zero, it will be upper triangular. If one, it will be upper Hessenburg.
      storeReflectors - Flag indicating if the reflectors used to bring the matrix to upper triangular/Hessenburg form should be stored.

  • Method Details

    • getQ

      public CMatrix getQ()

      Gets the unitary Q matrix from the QR decomposition.

      Note, if the reflectors for this decomposition were not saved, then Q can not be computed and this method will be null.

      Specified by:
      getQ in class UnitaryDecomposition<CMatrix,Complex128[]>
      Returns:
      The Q matrix from the QR decomposition. Note, if the reflectors for this decomposition were not saved, then Q can not be computed and this method will return null.

    • getUpper

      protected CMatrix getUpper(CMatrix H)
      Gets the upper triangular/Hessenburg matrix from the last decomposition.
      Specified by:
      getUpper in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      H - Storage for upper triangular/Hessenburg matrix. Assumed to be the zero matrix of an appropriate size.
      Returns:
      The upper triangular/Hessenburg matrix from the last decomposition.

    • initWorkArrays

      protected void initWorkArrays(int maxAxisSize)
      Initialized any work arrays to be used in computing the decomposition with the proper size.
      Specified by:
      initWorkArrays in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      maxAxisSize - Length of the largest axis in the matrix to be decomposed. That is, max(numRows, numCols)

    • computeHouseholder

      protected void computeHouseholder(int j)
      Computes the Householder vector for the first column of the sub-matrix with upper left corner at (j, j).
      Specified by:
      computeHouseholder in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      j - Index of the upper left corner of the sub-matrix for which to compute the Householder vector for the first column. That is, a Householder vector will be computed for the portion of column j below row j.

    • computePhasedNorm

      protected void computePhasedNorm(int j, double maxAbs)
      Computes the norm of column j below the jth row of the matrix to be decomposed. The norm will have the same parity as the first entry in the sub-column.
      Specified by:
      computePhasedNorm in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      j - Column to compute norm of below the jth row.
      maxAbs - Maximum absolute value in the column. Used for scaling norm to minimize potential overflow issues.

    • findMaxAndInit

      protected double findMaxAndInit(int j)
      Finds the maximum value in UnitaryDecomposition.transformMatrix at column j at or below the jth row. This method also initializes the first numRows-j data of the storage array UnitaryDecomposition.householderVector to the data of this column.
      Specified by:
      findMaxAndInit in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      j - Index of column (and starting row) to compute max of.
      Returns:
      The maximum value in UnitaryDecomposition.transformMatrix at column j at or below the jth row.

    • updateData

      protected void updateData(int j)
      Updates the UnitaryDecomposition.transformMatrix matrix using the computed Householder vector from computeHouseholder(int).
      Specified by:
      updateData in class UnitaryDecomposition<CMatrix,Complex128[]>
      Parameters:
      j - Index of sub-matrix for which the Householder reflector was computed for.