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symbfact

Symbolic factorization analysis

Syntax

count = symbfact(A)
count = symbfact(A,'sym')
数= symbfact (A,“上校”)
count = symbfact(A,'row')
count = symbfact(A,'lo')
[count,h,parent,post,R] = symbfact(...)
[count,h,parent,post,L] = symbfact(A,type,'lower')

Description

count = symbfact(A)returns the vector of row counts ofR =胆固醇(A).symbfactshould be much faster thanchol(A).

count = symbfact(A,'sym')is the same ascount = symbfact(A).

数= symbfact (A,“上校”)returns row counts ofR=chol(A'*A)(without forming it explicitly).

count = symbfact(A,'row')returns row counts ofR=chol(A*A').

count = symbfact(A,'lo')is the same ascount = symbfact(A)and usestril(A).

[count,h,parent,post,R] = symbfact(...)has several optional return values.

The flop count for a subsequent Cholesky factorization issum(count.^2)

Return Value Description
h

Height of the elimination tree
父

The elimination tree itself
post

Postordering of the elimination tree
R

0-1 matrix having the structure ofchol(A)for the symmetric case,chol(A'*A)for the'col'case, orchol(A*A')for the'row'case.

symbfact(A)andsymbfact(A,'sym')use the upper triangular part ofA (triu(A))and assume the lower triangular part is the transpose of the upper triangular part.symbfact(A,'lo')usestril(A)instead.

[count,h,parent,post,L] = symbfact(A,type,'lower')wheretypeis one of'sym','col','row', or'lo'returns a lower triangular symbolic factorL=R'. This form is quicker and requires less memory.

References

[1] Chen, Yanqing, Timothy A. Davis, William W. Hager, and Sivasankaran Rajamanickam. “Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate.”ACM Transactions on Mathematical Software35, no. 3 (October 2008): 1–14.https://doi.org/10.1145/1391989.1391995.

Extended Capabilities

Version History

Introduced before R2006a

See Also

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