matrix.csr.chol-class {SparseM} | R Documentation |
Class "matrix.csr.chol" (Block Sparse Cholesky Decomposition)
Description
A class of objects returned from Ng and Peyton's (1993) block sparse Cholesky algorithm.
Details
Note that the perm
and notably invp
maybe important to back
permute rows and columns of the decompositions, see the Examples, and our
chol
help page.
Objects from the Class
Objects may be created by calls of the form new("matrix.csr.chol",
...)
, but typically result from
chol(<matrix.csr>)
.
Slots
nrow
:an
integer
, the number of rows of the original matrix, or in the linear system of equations.nnzlindx
:Object of class
numeric
, number of non-zero elements inlindx
nsuper
:an
integer
, the number of supernodes of the decompositionlindx
:Object of class
integer
, vector of integer containing, in column major order, the row subscripts of the non-zero entries in the Cholesky factor in a compressed storage formatxlindx
:Object of class
integer
, vector of integer of pointers forlindx
nnzl
:of class
"numeric"
, an integer, the number of non-zero entries, including the diagonal entries, of the Cholesky factor stored inlnz
lnz
:a
numeric
vector of the entries of the Cholesky factorxlnz
:an
integer
vector, the column pointers for the Cholesky factor stored inlnz
invp
:inverse permutation vector,
integer
perm
:permutation vector,
integer
xsuper
:Object of class
integer
, array containing the supernode partioningdet
:numeric
, the determinant of the Cholesky factorlog.det
:numeric
, the log determinant of the Cholesky factorierr
:an
integer
, the error flag (from Fortran's ‘src/chol.f’)time
:numeric
, unused (always0.
) currently.
Methods
- as.matrix.csr
signature(x = "matrix.csr.chol", upper.tri=TRUE)
: to get the sparse ("matrix.csr"
) upper triangular matrix corresponding to the Cholesky decomposition.- backsolve
signature(r = "matrix.csr.chol")
: for computingR^{-1} b
when the Cholesky decomposition isA = R'R
.
See Also
Base R's chol
and SparseM's
chol
, notably for examples;
backsolve
Examples
x5g <- new("matrix.csr",
ra = c(300, 130, 5, 130, 330,
125, 10, 5, 125, 200, 70,
10, 70, 121.5, 1e30),
ja = c(1:3, 1:4, 1:4, 2:5),
ia = c(1L, 4L, 8L, 12L, 15L, 16L),
dimension = c(5L, 5L))
(m5g <- as.matrix(x5g)) # yes, is symmetric, and positive definite:
eigen(m5g, only.values=TRUE)$values # all positive (but close to singular)
ch5g <- chol(x5g)
str(ch5g) # --> the slots of the "matrix.csr.chol" class
mch5g <- as.matrix.csr(ch5g)
print.table(as.matrix(mch5g), zero.print=".") # indeed upper triagonal w/ positive diagonal
## x5 has even more extreme entry at [5,5]:
x5 <- x5g; x5[5,5] <- 2.9e32
m5 <- as.matrix(x5)
(c5 <- chol(m5))# still fine, w/ [5,5] entry = 1.7e16 and other diag.entries in (9.56, 17.32)
ch5 <- chol(x5) # --> warning "Replaced 3 tiny diagonal entries by 'Large'"
# gave error for a while
(mmc5 <- as.matrix(as.matrix.csr(ch5)))
# yes, these replacements were extreme, and the result is "strange'
## Solve the problem (here) specifying non-default singularity-tuning par 'tiny':
ch5. <- chol(x5, tiny = 1e-33)
(mmc5. <- as.matrix(as.matrix.csr(ch5.))) # looks much better.
## Indeed: R'R back-permuted *is* the original matrix x5, here m5:
(RtR <- crossprod(mmc5.)[ch5.@invp, ch5.@invp])
all.equal(m5, RtR, tolerance = 2^-52)
stopifnot(all.equal(m5, RtR, tolerance = 1e-14)) # on F38 Linux, only need tol = 1.25e-16