Examples of org.ejml.factory.QRDecomposition

org.ejml.factory.QRDecomposition

QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix, and R ∈ ℜ ^{n × m} is an upper triangular matrix. Some implementations of QR decomposition require that A has full rank.

Some features of QR decompositions:

Can decompose rectangular matrices.
Numerically stable solutions to least-squares problem, but not as stable as SVD
Can incrementally add and remove columns from the decomposed matrix. See {@link org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr}

Orthogonal matrices have the following properties:

QQ^T=I
Q^T=Q^-1

@see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn @author Peter Abeles

        // compute what the A matrix would look like without the row
        DenseMatrix64F A_e = RandomMatrices.createRandom(m-1,n,rand);
        SubmatrixOps.setSubMatrix(A,A_e,0,0,0,0,remove,n);
        SubmatrixOps.setSubMatrix(A,A_e,remove+1,0,remove,0,m-remove-1,n);


        QRDecomposition decomp = new QRDecompositionHouseholderColumn();


        // now compute the results by removing elements from A
        decomp.decompose(A);
        Q.reshape(m,m, false);
        decomp.getQ(Q,false);
        decomp.getR(R,false);


        QrUpdate update = new QrUpdate(m,n);


        update.deleteRow(Q,R,remove,true);

        DenseMatrix64F A_e = RandomMatrices.createRandom(m+1,n,rand);
        SubmatrixOps.setSubMatrix(A,A_e,0,0,0,0,insert,n);
        System.arraycopy(row, 0, A_e.data, insert * n, n);
        SubmatrixOps.setSubMatrix(A,A_e,insert,0,insert+1,0,m-insert,n);


        QRDecomposition decomp = new QRDecompositionHouseholderColumn();


        decomp.decompose(A);
        Q.reshape(m,m, false);
        decomp.getQ(Q,false);
        R.reshape(m,n,false);
        decomp.getR(R,false);


        DenseMatrix64F Qmod = createQMod(Q,insert);


        QrUpdate update = new QrUpdate(m+1,n);

Examples of org.ejml.factory.QRDecomposition

Related Classes of org.ejml.factory.QRDecomposition