Interface BiDiagonalization
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- All Known Implementing Classes:
BiDiagonalizationByGolubKahanLanczos
,BiDiagonalizationByHouseholder
public interface BiDiagonalization
Given a tall (m x n) matrix A, where m ≥ n, find orthogonal matrices U and V such that U' * A * V = B. B is an upper bi-diagonal matrix. That is, \[ U'AV = \begin{bmatrix} d_1 & f_1 & ... & & & \\ 0 & d_2 & f_2 & ... & & \\ 0 & ... & & & & \\ ... & & & & d_{n-1} & f_{n-1} \\ ... & & & & & d_n \\ 0 & ... & & & & 0 \\ & ... & & & & ... \\ 0 & ... & & & & 0 \end{bmatrix} \]
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description BidiagonalMatrix
B()
Gets B, which is the square upper part ofU.t().multiply(A).multiply(V)
.Matrix
U()
Gets U, where U' = Uk * ...Matrix
V()
Gets V, where V' = Vk * ...
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Method Detail
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B
BidiagonalMatrix B()
Gets B, which is the square upper part ofU.t().multiply(A).multiply(V)
. The dimension of B is n x n.- Returns:
- B
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U
Matrix U()
Gets U, where U' = Uk * ... * U1,k = A.nCols()
. The dimension of U is m x m.- Returns:
- U
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V
Matrix V()
Gets V, where V' = Vk * ... * V1,k = A.nCols() - 2
. The dimension of V is n x n.- Returns:
- V
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