trait SVDecomp extends AnyRef
The SVDDecomp
trait specifies the major methods for Singular Value
Decomposition implementations:
------------------------------------------------------------------------------
SVD - Golub-Kahan-Reinsch Algorithm translated from Algol code
SVD2 - Compute 'a.t * a', 'a * a.t' and use Eigenvalue
and Eigenvector
SVD3 - Implicit Zero-Shift 'QR' Algorithm
SVD4 - Golub-Kahan-Reinsch Algorithm coded from psuedo-code in Matrix Computations
The last three are still under development.
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def
factor(): FactorType
Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.
Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero. Then return the vector of singular values (i.e., the main diagonal), along with the left and right singular matrices.
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def
flip(u: MatrixD, v: MatrixD): Unit
Flip negative main diagonal elements in the singular vectors to positive.
Flip negative main diagonal elements in the singular vectors to positive.
- u
the left orthongonal matrix
- v
the right orthongonal matrix
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def
flip(u: MatrixD, s: VectorD): Unit
Flip negative singular values to positive and set singular values close to zero to zero.
Flip negative singular values to positive and set singular values close to zero to zero.
- u
the left orthongonal matrix
- s
the vector of singular values
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def
reorder(ft: FactorType): Unit
Reorder the singular values to be in non-increasing order.
Reorder the singular values to be in non-increasing order. Must swap singular vectors in lock step with singular values. To minimize the number of swaps, selection sort is used.
- ft
the factored matrix (u, s, v)
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