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[matrix] View of /pkg/TODO
 [matrix] / pkg / TODO View of /pkg/TODO

Tue Aug 14 15:09:10 2007 UTC (12 years, 2 months ago) by maechler
File size: 6696 byte(s)
new nearPD() {from Jens` nearcor()}; some TODO cleanup
Check for DimNames propagation in coercion and other operations.
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- Report the problem in the Linux ldexp manual page.  The second and
third calls in the Synopsis should be to ldexpf and ldexpl.

- [,] indexing: for sparse "works", but not yet for negative indices!

- consider moving alloc3Darray from ./src/Mutils.c to
\$(RSRC)/src/base/array.c
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- 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()]

- add more comprehensive examples / tests for Schur decomposition

- arithmetic for sparse matrices:
<sparseMatrix>  o  <same-dim-sparseMatrix>
should return a sparse matrix  for at least "+" and "*" , also %%,
and "/" and "%/%" at least when the RHS is non-zero a scalar.
Challenge: nice implementation (``common non-0''; but Tsparse* is not uniq).

-----

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

- "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"

- Things like  M[upper.tri(M)] are not really most useful for  sparse
matrices.  --> provide generic functions
upperTriMatrix(), lowerTriMatrix()  both with argument  'diag = TRUE'
(which can be set to FALSE of course) which are used to extract a
triangle from an arbitrary sparse matrix and  return a  "dtCMatrix".

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

- band(), triu(), tril() for *all* including "matrix", not just 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"

- speedup: pass class definition to non0ind() [check all calls ..]

- 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 !!

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

- ensure that  M, M[FALSE], M[1:2]  works as for traditional Matrices

- make sure  M[FALSE, FALSE]  works for all Matrices
{e.g. fails for M <- Diagonal(4)}

- <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

- For a square sparse matrix 'b' {typically dgCMatrix or dgTMatrix},
we'd want a function  "Mat_plus_t_Mat" <- function(b) {....}
which computes the symmetric sparse matrix   b + t(b)
in way that never works with size-doubled vectors from  b@i etc..

- ! <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
However,
we need methods for 'diag<-' at least for diagonalMatrix,
triangularMatrix, and probably also "dense*general*Matrix" since the
above currently goes via "matrix" and back instead of using the 'x' slot
directly.

- 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

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