Examples of org.ejml.alg.block.decomposition.qr.BlockMatrix64HouseholderQR

org.ejml.alg.block.decomposition.qr.BlockMatrix64HouseholderQR

QR decomposition for {@link BlockMatrix64F} using householder reflectors. The decomposition isperformed by computing a QR decomposition for each block column as is normally done, see {@link org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder}. The reflectors are then combined and applied to the remainder of the matrix. This process is repeated until all the block columns have been processed

The input matrix is modified and used to store the decomposition. Reflectors are stored in the lower triangle columns. The first element of the reflector is implicitly assumed to be one.

Each iteration can be sketched as follows:

 QR_Decomposition( A(:,i-r to i) ) W=computeW( A(:,i-r to i) ) A(:,i:n) = (I + W*Y^T)^TA(:,i:n)

Where r is the block size, i is the submatrix being considered, A is the input matrix, Y is a matrix containing the reflectors just computed, and W is computed using {@link BlockHouseHolder#computeW_Column}.

Based upon "Block Householder QR Factorization" pg 255 in "Matrix Computations" 3rd Ed. 1996 by Gene H. Golub and Charles F. Van Loan.

@author Peter Abeles

 */
public class QRDecompositionBlock64
        extends BaseDecompositionBlock64 implements QRDecomposition<DenseMatrix64F>  {


    public QRDecompositionBlock64() {
        super(new BlockMatrix64HouseholderQR(), EjmlParameters.BLOCK_WIDTH);
    }

    }


    public static long block( DenseMatrix64F orig , int numTrials ) {


        BlockMatrix64F A = BlockMatrixOps.convert(orig);
        BlockMatrix64HouseholderQR alg = new BlockMatrix64HouseholderQR();


        BlockMatrix64F B;


        long prev = System.currentTimeMillis();


        for( long i = 0; i < numTrials; i++ ) {
            if( alg.inputModified())
                B = A.copy();
            else
                B = A;
            if( !alg.decompose(B) ) {
                throw new RuntimeException("Bad matrix");
            }
        }


        return System.currentTimeMillis() - prev;

Examples of org.ejml.alg.block.decomposition.qr.BlockMatrix64HouseholderQR

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