DSSVD

Dense Singular Value Decomposition.

Notes

The problem is expressed as \(A = U\Sigma V^*\), where \(A\) is rectangular in general, with \(n\) rows and \(m\) columns. \(\Sigma\) is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, \(A\) is overwritten with \(\Sigma\).

The orthogonal (or unitary) matrices of left and right singular vectors, \(U\) and \(V\), have size \(n\) and \(m\), respectively. The number of columns \(m\) must be specified via DSSVDSetDimensions().

If the DS object is in the intermediate state, \(A\) is assumed to be in upper bidiagonal form (possibly with an arrow) and is stored in compact format on matrix \(T\). Otherwise, no particular structure is assumed. The compact storage is implemented for the square case only, \(m=n\). The extra row should be interpreted in this case as an extra column.

Used DS matrices

• DS_MAT_A - problem matrix (used only if compact=PETSC_FALSE)

• DS_MAT_T - upper bidiagonal matrix

• DS_MAT_U - left singular vectors

• DS_MAT_V - right singular vectors

Implemented methods

• 0 - Implicit zero-shift QR for bidiagonals (_bdsqr)

• 1 - Divide and Conquer (_bdsdc or _gesdd)

See Also

DS: Direct Solver (or Dense System), DSCreate(), DSSetType(), DSType, DSSVDSetDimensions(), DSSetCompact()

Level

beginner

Location

src/sys/classes/ds/impls/svd/dssvd.c

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