slepc-main 2024-12-17

DSHSVD

Dense Hyperbolic 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. U is orthogonal with respect to a signature matrix, stored in D. V is orthogonal. Sigma is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, A is overwritten with Sigma, D is overwritten with the new signature.

The 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 DSHSVDSetDimensions().

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. 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_D	- diagonal matrix (signature)
	DS_MAT_U	- left singular vectors
	DS_MAT_V	- right singular vectors

Implemented methods

- Cross product A'*Omega*A

Level

beginner

Location