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 Details

    • TridiagonalHelper_FDRB

      public TridiagonalHelper_FDRB()
  • Method Details

    • tridiagUpperRow

      public static void tridiagUpperRow(int blockLength, FSubmatrixD1 A, float[] gammas, 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, FSubmatrixD1 Y, 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, FSubmatrixD1 A, float[] gammas, 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, FSubmatrixD1 A, 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, FSubmatrixD1 A, 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, FSubmatrixD1 A, 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, FSubmatrixD1 A, int rowA, FSubmatrixD1 B, int rowB, int zeroOffset)
    • computeRowOfV

      public static void computeRowOfV(int blockLength, FSubmatrixD1 A, FSubmatrixD1 V, int row, float gamma)

      Final computation for a single row of 'v':

      v = y -(1/2)γ(y^T*u)*u