Interface QRDecomposition
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- All Known Implementing Classes:
GramSchmidt
,HouseholderQR
,QR
public interface QRDecomposition
QR decomposition of a matrix decomposes an m x n matrix A so that A = Q * R.- Q is an m x n orthogonal matrix;
- R is a n x n upper triangular matrix.
- sqQ is a square m x m orthogonal matrix;
- tallR is a m x n matrix.
- See Also:
- Wikipedia: QR decomposition
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description PermutationMatrix
P()
Get P, the pivoting matrix in the QR decomposition.Matrix
Q()
Get the orthogonal Q matrix in the QR decomposition, A = QR.UpperTriangularMatrix
R()
Get the upper triangular matrix R in the QR decomposition, A = QR.int
rank()
Get the numerical rank of A as computed by the QR decomposition.Matrix
squareQ()
Get the square Q matrix.Matrix
tallR()
Get the tall R matrix.
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Method Detail
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P
PermutationMatrix P()
Get P, the pivoting matrix in the QR decomposition.- Returns:
- P
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Q
Matrix Q()
Get the orthogonal Q matrix in the QR decomposition, A = QR. The dimension of Q is m x n, the same as A, the matrix to be orthogonalized.- Returns:
- Q
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R
UpperTriangularMatrix R()
Get the upper triangular matrix R in the QR decomposition, A = QR. The dimension of R is n x n, a square matrix.- Returns:
- R
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rank
int rank()
Get the numerical rank of A as computed by the QR decomposition. Numerical determination of rank requires a criterion to decide when a value should be treated as zero, hence a precision parameter. This is a practical choice which depends on both the matrix and the application. For instance, for a matrix with a big first eigenvector, we should accordingly decrease the precision to compute the rank.- Returns:
- the rank of A
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squareQ
Matrix squareQ()
Get the square Q matrix. This is an arbitrary orthogonal completion of the Q matrix in the QR decomposition. The dimension is m x m (square). We have A = sqQ * tallR.- Returns:
- the square Q matrix
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tallR
Matrix tallR()
Get the tall R matrix. This is completed by binding zero rows beneath the square upper triangular matrix R in the QR decomposition. The dimension is m x n. It may not be square. We have A = sqQ * tallR.- Returns:
- the tall R matrix
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