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**2105**- (**download**) (**annotate**)*Tue Jan 15 10:16:29 2008 UTC*(11 years, 7 months ago) by*maechler*File size: 8236 byte(s)

solve(<CHMfactor>, <numeric>) and related

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. - [,] indexing: for sparse "works", but not yet for negative indices! - consider moving alloc3Darray from ./src/Mutils.c to $(RSRC)/src/base/array.c ------ - 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>) - 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 - (A + tr(A))/2 := the symmetric part of A, is needed in several circumstances; unfortunately it's not "smart" (preserving symmetry, ...) --> define a generic and methods for it! Names: symPart(A) or symMat(A) or symmetrize(A) or ... ? Googling around I found that Nick Higham has a GPL contributed Matlab toolbox where he uses symmpart(A) := (A + A') /. 2 {and skewpart(A) := (A - A') /. 2} - 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 New generic for "chol" does not agree with implicit generic from package "base"; a new generic will be assigned with package "Matrix" New generic for "qr" does not agree with implicit generic from package "base"; a new generic will be assigned with package "Matrix" 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..

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