DSSVD#

Dense Singular Value Decomposition.

Notes#

The problem is expressed as A = USigmaV’, 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=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#

DSCreate(), DSSetType(), DSType, DSSVDSetDimensions()

Level#

beginner

Location#

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

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