Package org.ejml.dense.block.decomposition.hessenberg

Class TridiagonalHelper_FDRB

java.lang.Object
org.ejml.dense.block.decomposition.hessenberg.TridiagonalHelper_FDRB
@Generated("org.ejml.dense.block.decomposition.hessenberg.TridiagonalHelper_DDRB") public class TridiagonalHelper_FDRB extends Object

  • Constructor Summary

    Constructors
    Constructor
    Description
    TridiagonalHelper_FDRB()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static void
    applyReflectorsToRow(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row)
    Applies the reflectors that have been computed previously to the specified row.
    static void
    computeRowOfV(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row, float gamma)
    Final computation for a single row of 'v':

    v = y -(1/2)γ(y^T*u)*u
    static void
    computeV_blockVector(int blockLength, org.ejml.data.FSubmatrixD1 A, float[] gammas, org.ejml.data.FSubmatrixD1 V)
    Given an already computed tridiagonal decomposition, compute the V row block vector.

    y(:) = A*u
    v(i) = y - (1/2)*γ*(y^T*u)*u
    static void
    computeW_row(int blockLength, org.ejml.data.FSubmatrixD1 Y, org.ejml.data.FSubmatrixD1 W, float[] beta, int betaIndex)
    Computes W from the householder reflectors stored in the columns of the row block submatrix Y.
    static void
    computeY(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row, float gamma)
    Computes the 'y' vector and stores the result in 'v'

    y = -γ(A + U*V^T + V*U^T)u
    static float
    innerProdRowSymm(int blockLength, org.ejml.data.FSubmatrixD1 A, int rowA, org.ejml.data.FSubmatrixD1 B, int rowB, int zeroOffset)
     
    static void
    multA_u(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row)
    Multiples the appropriate submatrix of A by the specified reflector and stores the result ('y') in V.

    y = A*u
    static void
    tridiagUpperRow(int blockLength, org.ejml.data.FSubmatrixD1 A, float[] gammas, org.ejml.data.FSubmatrixD1 V)
    Performs a tridiagonal decomposition on the upper row only.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • TridiagonalHelper_FDRB

      public TridiagonalHelper_FDRB()

  • Method Details

    • tridiagUpperRow

      public static void tridiagUpperRow(int blockLength, org.ejml.data.FSubmatrixD1 A, float[] gammas, org.ejml.data.FSubmatrixD1 V)

      Performs a tridiagonal decomposition on the upper row only.

      For each row 'a' in 'A':
      Compute 'u' the householder reflector.
      y(:) = A*u
      v(i) = y - (1/2)*(y^T*u)*u
      a(i+1) = a(i) - u*γ*v^T - v*u^t

      Parameters:
      blockLength - Size of a block
      A - is the row block being decomposed. Modified.
      gammas - Householder gammas.
      V - Where computed 'v' are stored in a row block. Modified.

    • computeW_row

      public static void computeW_row(int blockLength, org.ejml.data.FSubmatrixD1 Y, org.ejml.data.FSubmatrixD1 W, float[] beta, int betaIndex)

      Computes W from the householder reflectors stored in the columns of the row block submatrix Y.

      Y = v(1)
      W = -β1v(1)
      for j=2:r
        z = -β(I +WYT)v(j)
        W = [W z]
        Y = [Y v(j)]
      end

      where v(.) are the house holder vectors, and r is the block length. Note that Y already contains the householder vectors so it does not need to be modified.

      Y and W are assumed to have the same number of rows and columns.

    • computeV_blockVector

      public static void computeV_blockVector(int blockLength, org.ejml.data.FSubmatrixD1 A, float[] gammas, org.ejml.data.FSubmatrixD1 V)

      Given an already computed tridiagonal decomposition, compute the V row block vector.

      y(:) = A*u
      v(i) = y - (1/2)*γ*(y^T*u)*u

    • applyReflectorsToRow

      public static void applyReflectorsToRow(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row)

      Applies the reflectors that have been computed previously to the specified row.
      A = A + u*v^T + v*u^T only along the specified row in A.

      Parameters:
      A - Contains the reflectors and the row being updated.
      V - Contains previously computed 'v' vectors.
      row - The row of 'A' that is to be updated.

    • computeY

      public static void computeY(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row, float gamma)

      Computes the 'y' vector and stores the result in 'v'

      y = -γ(A + U*V^T + V*U^T)u

      Parameters:
      A - Contains the reflectors and the row being updated.
      V - Contains previously computed 'v' vectors.
      row - The row of 'A' that is to be updated.

    • multA_u

      public static void multA_u(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row)

      Multiples the appropriate submatrix of A by the specified reflector and stores the result ('y') in V.

      y = A*u

      Parameters:
      A - Contains the 'A' matrix and 'u' vector.
      V - Where resulting 'y' row vectors are stored.
      row - row in matrix 'A' that 'u' vector and the row in 'V' that 'y' is stored in.

    • innerProdRowSymm

      public static float innerProdRowSymm(int blockLength, org.ejml.data.FSubmatrixD1 A, int rowA, org.ejml.data.FSubmatrixD1 B, int rowB, int zeroOffset)

    • computeRowOfV

      public static void computeRowOfV(int blockLength, org.ejml.data.FSubmatrixD1 A, org.ejml.data.FSubmatrixD1 V, int row, float gamma)

      Final computation for a single row of 'v':

      v = y -(1/2)γ(y^T*u)*u