public class GramSchmidt extends Object implements QRDecomposition
Householder reflection
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the result for the orthogonal complement may differ because the kernel basis is not unique.Constructor and Description |
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GramSchmidt(Matrix A)
Run the Gram-Schmidt process to orthogonalize a matrix.
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GramSchmidt(Matrix A,
boolean pad0Cols,
double epsilon)
Run the Gram-Schmidt process to orthogonalize a matrix.
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Modifier and Type | Method and Description |
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PermutationMatrix |
P()
Get P, the pivoting matrix in the QR decomposition.
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Matrix |
Q()
Get the orthogonal Q matrix in the QR decomposition, A = QR.
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UpperTriangularMatrix |
R()
Get the upper triangular matrix R in the QR decomposition, A = QR.
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int |
rank()
Get the numerical rank of A as computed by the QR decomposition.
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Matrix |
squareQ()
Get the square Q matrix.
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Matrix |
tallR()
Get the tall R matrix.
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public GramSchmidt(Matrix A, boolean pad0Cols, double epsilon)
A
- a matrixpad0Cols
- when a column is linearly dependent on the previous columns, there is no orthogonal vector. We pad the basis with a 0-vector.epsilon
- a precision parameter: when a number |x| ≤ ε, it is considered 0public GramSchmidt(Matrix A)
A
- a matrixpublic Matrix Q()
QRDecomposition
Q
in interface QRDecomposition
public UpperTriangularMatrix R()
QRDecomposition
R
in interface QRDecomposition
public PermutationMatrix P()
QRDecomposition
P
in interface QRDecomposition
public int rank()
QRDecomposition
rank
in interface QRDecomposition
public Matrix squareQ()
squareQ
in interface QRDecomposition
public Matrix tallR()
QRDecomposition
tallR
in interface QRDecomposition
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