Examples of org.ejml.alg.dense.decomposition.bidiagonal.BidiagonalDecompositionTall

org.ejml.alg.dense.decomposition.bidiagonal.BidiagonalDecompositionTall

{@link BidiagonalDecomposition} specifically designed for tall matrices.First step is to perform QR decomposition on the input matrix. Then R is decomposed using a bidiagonal decomposition. By performing the bidiagonal decomposition on the smaller matrix computations can be saved if m/n > 5/3 and if U is NOT needed.

A = [Q₁ Q₂][U1 0; 0 I] [B1;0] V^T
U=[Q₁*U1 Q₂]
B=[B1;0]
A = U*B*V^T

A QRP decomposition is used internally. That decomposition relies an a fixed threshold for selecting singular values and is known to be less stable than SVD. There is the potential for a degregation of stability by using BidiagonalDecompositionTall instead of BidiagonalDecomposition. A few simple tests have shown that loss in stability to be insignificant.

See page 404 in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.

@author Peter Abeles

        }


        // if it is a tall matrix and U is not needed then there is faster decomposition algorithm
        if( canUseTallBidiagonal && numRows > numCols * 2 && !computeU ) {
            if( bidiag == null || !(bidiag instanceof BidiagonalDecompositionTall) ) {
                bidiag = new BidiagonalDecompositionTall();
            }
        } else if( bidiag == null || !(bidiag instanceof BidiagonalDecompositionRow) ) {
            bidiag = new BidiagonalDecompositionRow();
        }
    }

Related Classes of org.ejml.alg.dense.decomposition.bidiagonal.BidiagonalDecompositionTall

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