Miscellaneous

<symbfact> - Symbolic factorization analysis.

SYMBFACT Symbolic factorization analysis.

Analyzes the Cholesky factorization of A, A'*A, or A*A'.

count = SYMBFACT(A) returns row counts of R = CHOL(A)

count = SYMBFACT(A,'sym') same as SYMBFACT(A)

count = SYMBFACT(A,'col') returns row counts of R = CHOL(A'*A)

count = SYMBFACT(A,'row') returns row counts of R = CHOL(A*A')

count = SYMBFACT(A,'lo') same as SYMBFACT(A'), uses TRIL(A)

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

[count,h,parent,post,R] = SYMBFACT(...) returns:

h: height of the elimination tree

parent: the elimination tree itself

post: postordering of the elimination tree

R: a 0-1 matrix whose structure is that of CHOL(A) for the

symmetric case, CHOL(A'*A) for the 'col' case, or

CHOL(A*A') for the 'row' case.

SYMBFACT(A) and SYMBFACT(A,'sym') uses the upper triangular part of A

(TRIU(A)) and assumes the lower triangular part is the transpose of

the upper triangular part. SYMBFACT(A,'lo') uses TRIL(A) instead.

[count, h, parent, post, L] = SYMBFACT(A,TYPE,'lower'), where TYPE is

one of 'sym', 'col', 'row', or 'lo' returns a lower triangular symbolic

factor L = R'. This form is quicker and requires less memory.

See also chol, etree, treelayout.

Reference page in Help browser

doc symbfact

<spparms> - Set parameters for sparse matrix routines.

SPPARMS Set parameters for sparse matrix routines.

SPPARMS('key',value) sets one or more of the "tunable" parameters

used in the sparse routines, particularly sparse / and \.

SPPARMS, by itself, prints a description of the current settings.

If no input argument is present, values = SPPARMS returns a

vector whose components give the current settings.

[keys,values] = SPPARMS returns that vector, and also returns

a character matrix whose rows are the keywords for the parameters.

SPPARMS(values), with no output argument, sets all the parameters

to the values specified by the argument vector.

value = SPPARMS('key') returns the current setting of one parameter.

SPPARMS('default') sets all the parameters to their default settings.

SPPARMS('tight') sets the minimum degree ordering parameters to their

"tight" settings, which may lead to orderings with less fill-in, but

which makes the ordering functions themselves use more execution time.

The parameters with the default and "tight" values are:

keyword default tight

values(1) 'spumoni' 0

values(2) 'thr_rel' 1.1 1.0

values(3) 'thr_abs' 1.0 0.0

values(4) 'exact_d' 0 1

values(5) 'supernd' 3 1

values(6) 'rreduce' 3 1

values(7) 'wh_frac' 0.5 0.5

values(8) 'autommd' 1

values(9) 'autoamd' 1

values(10) 'piv_tol' 0.1

values(11) 'bandden' 0.5

values(12) 'umfpack' 1

values(13) 'sym_tol' 0.001

values(14) 'ldl_tol' 0.01

The meanings of the parameters are

spumoni: The Sparse Monitor Flag controls diagnostic output;

0 means none, 1 means some, 2 means too much.

thr_rel,

thr_abs: Minimum degree threshold is thr_rel*mindegree + thr_abs.

exact_d: Nonzero to use exact degrees in minimum degree,

Zero to use approximate degrees.

supernd: If > 0, MMD amalgamates supernodes every supernd stages.

rreduce: If > 0, MMD does row reduction every rreduce stages.

wh_frac: Rows with density > wh_frac are ignored in COLMMD.

autommd: Nonzero to use SYMMMD and COLMMD orderings with \ and /.

autoamd: Nonzero to use AMD or COLAMD ordering with CHOLMOD, UMFPACK, and SuiteSparseQR in \ and /.

piv_tol: Pivot tolerance used by LU-based (UMFPACK) \ and /.

bandden: Backslash uses band solver if band density is > bandden.

If bandden = 1.0, never use band solver.

If bandden = 0.0, always use band solver.

umfpack: Nonzero to use UMFPACK instead of the v4 LU-based solver

in \ and /.

sym_tol: Symmetric pivot tolerance used by UMFPACK. See LU for

more information about the role of the symmetric pivot

tolerance.

ldl_tol: Pivot tolerance used by LDL-based (MA57) \ and /.

Note:

Solving symmetric positive definite matrices within \ and /:

The CHOLMOD CHOL-based solver uses AMD.

Solving general square matrices within \ and /:

The UMFPACK LU-based solver uses either AMD or a modified COLAMD.

The v4 LU-based solver uses COLMMD.

Solving rectangular matrices within \ and /:

The SuiteSparseQR QR-based solver uses COLAMD.

All of these algorithms respond to SPPARMS('autoamd') except for the

v4 LU-based, which responds to SPPARMS('autommd').

See also amd, colamd, symamd.

Reference page in Help browser

doc spparms

<spaugment> - Form least squares augmented system.

SPAUGMENT Form least squares augmented system.

S = SPAUGMENT(A,c) creates the sparse, square, symmetric indefinite

matrix S = [c*I A; A' 0]. This matrix is related to the least

squares problem

min norm(b - A*x)

by

r = b - A*x

S * [r/c; x] = [b; 0].

The optimum value of the residual scaling factor c, involves

min(svd(A)) and norm(r), which are usually too expensive to compute.

S = SPAUGMENT(A), without a specified value of c, uses

max(max(abs(A)))/1000.