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Revision 2137 - (download) (annotate)
Mon Mar 17 22:21:24 2008 UTC (11 years, 6 months ago) by maechler
File size: 8016 byte(s)
my fast determinant(<dsC..>) versions
- Check for DimNames propagation in coercion and other operations.

- Report the problem in the Linux ldexp manual page.  The second and
  third calls in the Synopsis should be to ldexpf and ldexpl.

- provide methods for "dspMatrix" and "dppMatrix"!

- implement (more) methods for supporting "packed" (symmetric / triangular)
  matrices; particularly something like pack() and unpack()  [to/from our
  classes from/to "numeric"] --- have already man/unpack.Rd but no method yet!

  (have some dtr* <-> dtp*)

- combine the C functions for multiplication by special forms and
  solution wrt special forms by using a 'right' argument and a
  'classed' argument.
   [done with dgeMatrix_matrix_mm();  not yet for other classes;
    and for _crossprod()]

-----

- "Math2" , "Math", "Arith":
   keep triangular and symmetric Matrices when appropriate:
   particularly desirable for  "Math2": round(), signif()

  For triangular matrices, more specifically make sure the four rules of
  "triangular matrix algebra" (Golub+Van Loan 1996, 3.1.8, p.93) are
  fulfilled; now(2008-03-06) ok for Csparse; not yet for <dtr> %*% <dtr>

- "d" <-> "l" coercion for all "[TCR]" sparse matrices is really trivial:
  "d" -> "l" : drops the 'x' slot
  "l" -> "d" : construct an 'x' slot of all '1'
  We currently have many of these conversions explicitly, e.g.
   setAs("dsTMatrix", "lsTMatrix",
      function(from) new("lsTMatrix", i = from@i, j = from@j, uplo = from@uplo,
                         Dim = from@Dim, Dimnames = from@Dimnames))
  but I would rather want to automatically construct all these coercion
  methods at once by a ``method constructor'', i.e.,
  for all  "dsparse*" -> "lsparse*" and vice versa.
  How can one do this {in a documented way} ?

- Think of constructing  setAs(...) calls automatically in order to
  basically enable all ``sensible'' as(fromMatrix, toMatrix)  calls,
  possibly using canCoerce(.)

- setAs(<Mcl>,  "[dln]Matrix") for <Mcl> in {Matrix or denseMatrix + sparseMatrix}

- When we have a packed matrix, it's a waste to go through "full" to "sparse":
  ==> implement
	setAs("dspMatrix", "sparseMatrix")
	setAs("dppMatrix", "sparseMatrix")
	setAs("dtpMatrix", "sparseMatrix")
  and the same for "lsp" , "ltp"  and  "nsp" , "ntp" !

- tcrossprod(x, y) : do provide methods for y != NULL
  calling Lapack's DGEMM for "dense"
  [2005-12-xx: done for dgeMatrix at least]

- BUGlet:  Shouldn't lose factorization here:
  h6 <- Hilbert(6); chol(h6) ; str(h6) # has factor
  str(H6 <- as(h6, "dspMatrix"))       # has lost factor
  ## and the same in a similar situation involving  "dpo", "dpp"

- Factorizations: LU done; also Schur()  for  *sparse*  Matrices.

- is.na() method for all our matrices [ ==> which(*, arr.ind=TRUE) might work ]

- use  .Call(Csparse_drop, M, tol) in more places,
  both with 'tol = 0.' to drop "values that happen to be 0" and for
  zapsmall() methods for Csparse*

- implement .Call(Csparse_scale, ....) interfacing to cholmod_scale()
  in src/CHOLMOD/Include/cholmod_matrixops.h : for another function
  specifically for multiplying a cholmod_sparse object by a diagonal matrix.
  Use it in %*% and [t]crossprod methods.

- chol() and determinant() should ``work'': proper result or "good" error
  message.

- make sure *all* group methods have (maybe "bail-out") setMethod for "Matrix".
  e.g. zapsmall(<pMatrix>) fails "badly"

- sum(): implement methods which work for *all* our matrices.

- Implement  expand(.) for the Cholesky() results
  "dCHMsimpl" and  "dCHMsuper"  -- currently have no *decent* way to get at
  the matrix factors of the corresponding matrix factorization !!

- rbind2(<sparse>, <dense>) does not work  (e.g. <dgC>, <dge>)

- <sparse> %*% <dense>  {also in crossprod/tcrossprod}  currently always
  returns <dense>, since --> Csparse_dense_prod --> cholmod_sdmult
  and that does only return dense.
  When the sparse matrix is very sparse, i.e. has many rows with only zero
  entries, it would make much sense to return sparse.

- sparse-symmetric + diagonal should stay sparse-symmetric
  (only stays sparse): Matrix(0, 4, 4) + Diagonal(4, 1:4)
  --> R/diagMatrix.R ('FIXME')
  but also R/Ops.R  to ensure  sp-sym. + sp-sym. |-> sp-sym.  etc

- Diagonal(n) %*% A ---  too slow!! --> ~/R/MM/Pkg-ex/Matrix/diag-Tamas-ex.R

- ! <symmetricMatrix>  loses symmetry, both for dense and sparse matrices.
  !M  where M is "sparseMatrix", currently always gives dense. This only
  makes sense when M is ``really sparse''.

- msy <- as(matrix(c(2:1,1:2),2), "dsyMatrix"); str(msy)

  shows that the Cholesky factorization is computed ``too quickly''.
  Can be a big pain for largish matrices, when it is unneeded.

- example(Cholesky, echo=FALSE) ; cm <- chol(mtm); str(cm); str(mtm)

  shows that chol() does not seems to make use of an already
  present factorization and rather uses one with more '0' in x slot.

- diag(m) <- val    currently automatically works via  m[cbind(i,i)] <- val
  This (`[<-` method) is now "smart" for diagonalMatrix, but needs also to
  be for triangularMatrix, and probably also "dense*general*Matrix" since the
  above currently goes via "matrix" and back instead of using the 'x' slot
  directly; in particular, the triangular* "class property" is lost!

- image(M, ..): Think about an optional smart option which keeps
   "0 |-> transparent" and allows colors to differentiate negative and
   positive entries.

- examples for solve( Cholesky(.), b, system = c("A", "LDLt"....))
  probably rather in man/CHMfactor-class.Rd than man/Cholesky.Rd

- LDL(<CHMsimpl>) looks relatively easy; via  "tCsparse_diag()"
   {diagonal entries of *triangular* Csparse}
  --> see comment in determinant(<dsC>) in R/dsCMatrix.R, will give
  faster determinant

- Cholesky() generalized: provide R interface cholmod_factorize_p()
  which factorizes |A + beta*I| ==> R interface to fast det|A + b*I|

- tr(A %*% B) {and even  tr(A %*% B %*% C) ...} are also needed
  frequently in some computations {conditional normal distr. ...}.
  Since this can be done faster than by
    sum(diag(A %*% B))  even for traditional matrices, e.g.
    	       sum(A * t(B)) or {even faster for "full" mat}
	       crossprod(as.vector(A), as.vector(B))
  and even more so for, e.g.  <sparse> %*% <dense>
  {used in Soeren's 'gR' computations},
  we should also provide a generic and methods.

- qr.R(qr(x)) may differ for the "same" matrix, depending on it being
  sparse or dense:
    "qr.R(<sparse>) may differ from qr.R(<dense>) because of permutations"

  This is not really acceptable and currently influences  rcond() as well.

- chol() and qr() generic:  currently have *two* arguments, and give the msg

  >  New generic for "chol" does not agree with implicit generic from package
  >  "base"; a new generic will be assigned with package "Matrix"

  (and ditto for "qr")

  It was mentioned by an R-core member that he thought it did not make
  sense to also dispatch on 'tol' or 'pivot' ...  --> maybe change that..

- eigen() should become generic, and get a method at least for diagonal,
  but also for symmetric -> dsyMatrix  [LAPACK dsyev() uses UPLO !],
  but also simply for dgeMatrix (without going via tradition matrices).
  What about Sparse?  There's fill-in, but it may still be sensible, e.g.
  mlist <- list(1, 2:3, diag(x=5:3), 27, cbind(1,3:6), 100:101)
  ee <- eigen(tcrossprod(bdiag(lapply(mlist, as.matrix))))
  Matrix( signif(ee$vectors, 3) )

- facmul() has no single method defined;  it looks like a good idea though
  (instead of the infamous qr.qy, qr.qty,.... functions)

- symmpart() and skewpart()  for *sparse* matrices still use (x +/- t(x))/2
  and could be made more efficient.
  Consider going via  asTuniq() or something very close to
  .Arith.Csparse() in R/Ops.R

- many setAs(*, "[dl]..Matrix") are still needed, as long as e.g.
  replCmat() uses as_CspClass() and drop0(.) which itself call
  as_CspClass() quite a bit.  --> try to replace these by
  as(*, "CsparseMatrix"); forceSymmetric, etc.

root@r-forge.r-project.org
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