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Diff of /pkg/Matrix/R/diagMatrix.R

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pkg/R/diagMatrix.R revision 2052, Wed Aug 15 13:33:19 2007 UTC pkg/Matrix/R/diagMatrix.R revision 2891, Fri Aug 16 14:09:01 2013 UTC
# Line 5  Line 5 
5  ##          but *not* diag() extractor!  ##          but *not* diag() extractor!
6  Diagonal <- function(n, x = NULL)  Diagonal <- function(n, x = NULL)
7  {  {
8      ## Allow  Diagonal(4)  and  Diagonal(x=1:5)      ## Allow  Diagonal(4), Diagonal(x=1:5), and  Diagonal(4, TRUE)
9      if(missing(n))      n <- if(missing(n)) length(x) else {
         n <- length(x)  
     else {  
10          stopifnot(length(n) == 1, n == as.integer(n), n >= 0)          stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
11          n <- as.integer(n)          as.integer(n)
12      }      }
13    
14      if(missing(x)) ## unit diagonal matrix      if(missing(x)) ## unit diagonal matrix
15          new("ddiMatrix", Dim = c(n,n), diag = "U")          new("ddiMatrix", Dim = c(n,n), diag = "U")
16      else {      else {
17          stopifnot(length(x) == n)          lx <- length(x)
18            lx.1 <- lx == 1L
19            stopifnot(lx.1 || lx == n) # but keep 'x' short for now
20          if(is.logical(x))          if(is.logical(x))
21              cl <- "ldiMatrix"              cl <- "ldiMatrix"
22          else if(is.numeric(x)) {          else if(is.numeric(x)) {
# Line 26  Line 26 
26          else if(is.complex(x)) {          else if(is.complex(x)) {
27              cl <- "zdiMatrix"  # will not yet work              cl <- "zdiMatrix"  # will not yet work
28          } else stop("'x' has invalid data type")          } else stop("'x' has invalid data type")
29          new(cl, Dim = c(n,n), diag = "N", x = x)          if(lx.1 && !is.na(x) && x == 1) # cheap check for uni-diagonal..
30                new(cl, Dim = c(n,n), diag = "U")
31            else
32                new(cl, Dim = c(n,n), diag = "N",
33                    x = if(lx.1) rep.int(x,n) else x)
34      }      }
35  }  }
36    
37  ### This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.  .sparseDiagonal <- function(n, x = 1, uplo = "U",
38  ### Bert's code built on a post by Andy Liaw who most probably was influenced                              shape = if(missing(cols)) "t" else "g",
39  ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002                              unitri, kind,
40  ### who posted his bdiag() function written in December 1995.                              cols = if(n) 0:(n - 1L) else integer(0))
41    {
42        stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
43        if(!(mcols <- missing(cols)))
44            stopifnot(0 <= (cols <- as.integer(cols)), cols < n)
45        m <- length(cols)
46        if(missing(kind))
47            kind <-
48                if(is.double(x)) "d"
49                else if(is.logical(x)) "l"
50                else { ## for now
51                    storage.mode(x) <- "double"
52                    "d"
53                }
54        else stopifnot(any(kind == c("d","l","n")))
55        stopifnot(is.character(shape), nchar(shape) == 1,
56                  any(shape == c("t","s","g"))) # triangular / symmetric / general
57        if((missing(unitri) || unitri) && shape == "t" &&
58           (mcols || cols == 0:(n-1L)) &&
59           ((any(kind == c("l", "n")) && allTrue(x)) ||
60            (    kind == "d"          && allTrue(x == 1)))) { ## uni-triangular
61            new(paste0(kind,"tCMatrix"), Dim = c(n,n),
62                       uplo = uplo, diag = "U", p = rep.int(0L, n+1L))
63        }
64        else if(kind == "n") {
65            if(shape == "g")
66                new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m)
67            else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
68                     i = cols, p = 0:m)
69        }
70        else { ## kind != "n" -- have x slot :
71            if((lx <- length(x)) == 1) x <- rep.int(x, m)
72            else if(lx != m) stop("length(x) must be either 1 or #{cols}")
73            if(shape == "g")
74                new(paste0(kind, "gCMatrix"), Dim = c(n,m),
75                    x = x, i = cols, p = 0:m)
76            else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
77                     x = x, i = cols, p = 0:m)
78        }
79    }
80    
81  bdiag <- function(...) {  ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
82      if(nargs() == 0) return(new("dgCMatrix"))  .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
83      ## else :      .sparseDiagonal(n, x, uplo, shape = "s")
84      mlist <- if (nargs() == 1) as.list(...) else list(...)  
85      dims <- sapply(mlist, dim)  # instead of   diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
86    .trDiagonal <- function(n, x = 1, uplo = "U", unitri=TRUE)
87        .sparseDiagonal(n, x, uplo, shape = "t", unitri=unitri)
88    
89    
90    ## This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.
91    ## Bert's code built on a post by Andy Liaw who most probably was influenced
92    ## by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
93    ## who posted his bdiag() function written in December 1995.
94    if(FALSE)##--- no longer used:
95    .bdiag <- function(lst) {
96        ## block-diagonal matrix [a dgTMatrix] from list of matrices
97        stopifnot(is.list(lst), length(lst) >= 1)
98        dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE)
99      ## make sure we had all matrices:      ## make sure we had all matrices:
100      if(!(is.matrix(dims) && nrow(dims) == 2))      if(!(is.matrix(dims) && nrow(dims) == 2))
101          stop("some arguments are not matrices")          stop("some arguments are not matrices")
102      csdim <- rbind(rep.int(0L, 2),      csdim <- rbind(rep.int(0L, 2),
103                     apply(sapply(mlist, dim), 1, cumsum))                     apply(dims, 1, cumsum))
104      ret <- new("dgTMatrix", Dim = as.integer(csdim[nrow(csdim),]))      r <- new("dgTMatrix")
105        r@Dim <- as.integer(csdim[nrow(csdim),])
106      add1 <- matrix(1:0, 2,2)      add1 <- matrix(1:0, 2,2)
107      for(i in seq_along(mlist)) {      for(i in seq_along(lst)) {
108          indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])          indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
109          if(is.null(dim(indx))) ## non-square matrix          if(is.null(dim(indx))) ## non-square matrix
110              ret[indx[[1]],indx[[2]]] <- mlist[[i]]              r[indx[[1]],indx[[2]]] <- lst[[i]]
111          else ## square matrix          else ## square matrix
112              ret[indx[,1],indx[,2]] <- mlist[[i]]              r[indx[,1], indx[,2]] <- lst[[i]]
113        }
114        r
115    }
116    ## expand(<mer>) needed something like bdiag() for lower-triangular
117    ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
118    ##  implementation for those; now extended and generalized:
119    .bdiag <- function(lst) {
120        ## block-diagonal matrix [a dgTMatrix] from list of matrices
121        stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
122    
123        Tlst <- lapply(lapply(lst, as_Csp2), # includes "diagU2N"
124                       as, "TsparseMatrix")
125        if(nl == 1) return(Tlst[[1]])
126        ## else
127        i_off <- c(0L, cumsum(vapply(Tlst, nrow, 1L)))
128        j_off <- c(0L, cumsum(vapply(Tlst, ncol, 1L)))
129    
130        clss <- vapply(Tlst, class, "")
131        typ <- substr(clss, 2, 2)
132        knd <- substr(clss, 1, 1)
133        sym <- typ == "s" # symmetric ones
134        tri <- typ == "t" # triangular ones
135        use.n <- any(is.n <- knd == "n")
136        if(use.n && !(use.n <- all(is.n))) {
137            Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
138            knd [is.n] <- "l"
139        }
140        use.l <- !use.n && all(knd == "l")
141        if(all(sym)) { ## result should be *symmetric*
142            uplos <- vapply(Tlst, slot, ".", "uplo") ## either "U" or "L"
143            tLU <- table(uplos)# of length 1 or 2 ..
144            if(length(tLU) == 1) { ## all "U" or all "L"
145                useU <- uplos[1] == "U"
146            } else { ## length(tLU) == 2, counting "L" and "U"
147                useU <- diff(tLU) >= 0
148                if(useU && (hasL <- tLU[1] > 0))
149                    Tlst[hasL] <- lapply(Tlst[hasL], t)
150                else if(!useU && (hasU <- tLU[2] > 0))
151                    Tlst[hasU] <- lapply(Tlst[hasU], t)
152            }
153            if(use.n) { ## return nsparseMatrix :
154                r <- new("nsTMatrix")
155            } else {
156                r <- new(paste0(if(use.l) "l" else "d", "sTMatrix"))
157                r@x <- unlist(lapply(Tlst, slot, "x"))
158            }
159            r@uplo <- if(useU) "U" else "L"
160        }
161        else if(all(tri) && { ULs <- vapply(Tlst, slot, ".", "uplo")##  "U" or "L"
162                              all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
163           ){ ## *triangular* result
164    
165            if(use.n) { ## return nsparseMatrix :
166                r <- new("ntTMatrix")
167            } else {
168                r <- new(paste0(if(use.l) "l" else "d", "tTMatrix"))
169                r@x <- unlist(lapply(Tlst, slot, "x"))
170            }
171            r@uplo <- ULs[1L]
172        }
173        else {
174            if(any(sym))
175                Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
176            if(use.n) { ## return nsparseMatrix :
177                r <- new("ngTMatrix")
178            } else {
179                r <- new(paste0(if(use.l) "l" else "d", "gTMatrix"))
180                r@x <- unlist(lapply(Tlst, slot, "x"))
181            }
182        }
183        r@Dim <- c(i_off[nl+1], j_off[nl + 1])
184        r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
185        r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
186        r
187      }      }
188      ## slightly debatable if we really should return Csparse.. :  
189      as(ret, "CsparseMatrix")  bdiag <- function(...) {
190        if((nA <- nargs()) == 0) return(new("dgCMatrix"))
191        if(nA == 1 && !is.list(...))
192            return(as(..., "CsparseMatrix"))
193        alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
194        if(length(alis) == 1)
195            return(as(alis[[1]], "CsparseMatrix"))
196    
197        ## else : two or more arguments
198        as(.bdiag(alis), "CsparseMatrix")
199  }  }
200    
201  diag2tT <- function(from) {  
202    .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
203        ## to triangular Tsparse
204      i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L      i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
205      new(paste(.M.kind(from), "tTMatrix", sep=''),      new(paste0(kind, "tTMatrix"),
206          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
207            uplo = uplo,
208          x = from@x, # <- ok for diag = "U" and "N" (!)          x = from@x, # <- ok for diag = "U" and "N" (!)
209          i = i, j = i)          i = i, j = i)
210  }  }
211    
212  diag2sT <- function(from) { # to symmetric Tsparse  .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
213      i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L      ## to symmetric Tsparse
214      new(paste(.M.kind(from), "sTMatrix", sep=''),      n <- from@Dim[1]
215        i <- seq_len(n) - 1L
216        new(paste0(kind, "sTMatrix"),
217          Dim = from@Dim, Dimnames = from@Dimnames,          Dim = from@Dim, Dimnames = from@Dimnames,
218          x = from@x, i = i, j = i)          i = i, j = i, uplo = uplo,
219            x = if(from@diag == "N") from@x else ## "U"-diag
220            rep.int(switch(kind,
221                           "d" = 1.,
222                           "l" =,
223                           "n" = TRUE,
224                           ## otherwise
225                           stop(gettextf("%s kind not yet implemented",
226                                         sQuote(kind)), domain=NA)),
227                    n))
228    }
229    
230    ## diagonal -> triangular,  upper / lower depending on "partner":
231    diag2tT.u <- function(d, x, kind = .M.kind(d))
232        .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
233    
234    ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
235    diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
236        clx <- getClassDef(class(x))
237        if(extends(clx, "symmetricMatrix"))
238            .diag2sT(d, uplo = x@uplo, kind)
239        else
240            .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
241  }  }
242    
243  setAs("diagonalMatrix", "triangularMatrix", diag2tT)  ## FIXME: should not be needed {when ddi* is dsparse* etc}:
244  setAs("diagonalMatrix", "sparseMatrix", diag2tT)  setMethod("is.finite", signature(x = "diagonalMatrix"),
245              function(x) is.finite(.diag2tT(x)))
246    setMethod("is.infinite", signature(x = "diagonalMatrix"),
247              function(x) is.infinite(.diag2tT(x)))
248    
249    ## In order to evade method dispatch ambiguity warnings,
250    ## and because we can save a .M.kind() call, we use this explicit
251    ## "hack"  instead of signature  x = "diagonalMatrix" :
252    ##
253    ## ddi*:
254    diag2tT <- function(from) .diag2tT(from, "U", "d")
255    setAs("ddiMatrix", "triangularMatrix", diag2tT)
256    ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", diag2tT)
257    ## needed too (otherwise <dense> -> Tsparse is taken):
258    setAs("ddiMatrix", "TsparseMatrix", diag2tT)
259    setAs("ddiMatrix", "dsparseMatrix", diag2tT)
260    setAs("ddiMatrix", "CsparseMatrix",
261          function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
262    setAs("ddiMatrix", "symmetricMatrix",
263          function(from) .diag2sT(from, "U", "d"))
264    ##
265    ## ldi*:
266    diag2tT <- function(from) .diag2tT(from, "U", "l")
267    setAs("ldiMatrix", "triangularMatrix", diag2tT)
268    ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", diag2tT)
269  ## needed too (otherwise <dense> -> Tsparse is taken):  ## needed too (otherwise <dense> -> Tsparse is taken):
270  setAs("diagonalMatrix", "TsparseMatrix", diag2tT)  setAs("ldiMatrix", "TsparseMatrix", diag2tT)
271  ## is better than this:  setAs("ldiMatrix", "lsparseMatrix", diag2tT)
272  ## setAs("diagonalMatrix", "sparseMatrix",  setAs("ldiMatrix", "CsparseMatrix",
273  ##       function(from)        function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
274  ##        as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix"))  setAs("ldiMatrix", "symmetricMatrix",
275  setAs("diagonalMatrix", "CsparseMatrix",        function(from) .diag2sT(from, "U", "l"))
       function(from) as(diag2tT(from), "CsparseMatrix"))  
276    
 setAs("diagonalMatrix", "symmetricMatrix", diag2sT)  
277    
278  setAs("diagonalMatrix", "matrix",  setAs("diagonalMatrix", "nMatrix",
279        function(from) {        function(from) {
280            n <- from@Dim[1]            n <- from@Dim[1]
281            diag(x = if(from@diag == "U") { if(is.numeric(from@x)) 1. else TRUE            i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
282                                       } else from@x,            new("ntTMatrix", i = i, j = i, diag = from@diag,
283                 nrow = n, ncol = n)                Dim = from@Dim, Dimnames = from@Dimnames)
284        })        })
285    
286  setAs("diagonalMatrix", "generalMatrix", # prefer sparse:  setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
       function(from) as(from, paste(.M.kind(from), "gCMatrix", sep='')))  
287    
288  .diag.x <- function(m) {  ## Cheap fast substitute for diag() which *does* preserve the mode of x :
289      if(m@diag == "U")  mkDiag <- function(x, n) {
290          rep.int(if(is.numeric(m@x)) 1. else TRUE,      y <- matrix(as0(mod=mode(x)), n,n)
291                  m@Dim[1])      if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x
292      else m@x      y
 }  
   
 .diag.2N <- function(m) {  
     if(m@diag == "U") m@diag <- "N"  
     m  
293  }  }
294    
295  ## given the above, the following  4  coercions should be all unneeded;  setAs("diagonalMatrix", "matrix",
 ## we prefer triangular to general:  
 setAs("ddiMatrix", "dgTMatrix",  
296        function(from) {        function(from) {
297            .Deprecated("as(, \"sparseMatrix\")")            ## want "ldiMatrix" -> <logical> "matrix" :
298            n <- from@Dim[1]            mkDiag(if(from@diag == "U") as1(from@x) else from@x,
299            i <- seq_len(n) - 1L                   n = from@Dim[1])
300            new("dgTMatrix", i = i, j = i, x = .diag.x(from),        })
               Dim = c(n,n), Dimnames = from@Dimnames) })  
301    
302  setAs("ddiMatrix", "dgCMatrix",  setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
303        function(from) as(as(from, "sparseMatrix"), "dgCMatrix"))            function(x, mode) {
304                  n <- x@Dim[1]
305                  mod.x <- mode(x@x)
306                  r <- vector(mod.x, length = n^2)
307                  if(n)
308                      r[1 + 0:(n - 1L) * (n + 1)] <-
309                          if(x@diag == "U") as1(mod=mod.x) else x@x
310                  r
311              })
312    
313  setAs("ldiMatrix", "lgTMatrix",  setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
314        function(from) {        function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
315            .Deprecated("as(, \"sparseMatrix\")")  
316            n <- from@Dim[1]  setAs("diagonalMatrix", "denseMatrix",
317            if(from@diag == "U") { # unit-diagonal        function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
               x <- rep.int(TRUE, n)  
               i <- seq_len(n) - 1L  
           } else { # "normal"  
               nz <- nz.NA(from@x, na. = TRUE)  
               x <- from@x[nz]  
               i <- which(nz) - 1L  
           }  
           new("lgTMatrix", i = i, j = i, x = x,  
               Dim = c(n,n), Dimnames = from@Dimnames) })  
318    
319  setAs("ldiMatrix", "lgCMatrix",  ..diag.x <- function(m)                   rep.int(as1(m@x), m@Dim[1])
320        function(from) as(as(from, "lgTMatrix"), "lgCMatrix"))  .diag.x  <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
321    
322    .diag.2N <- function(m) {
323        if(m@diag == "U") m@diag <- "N"
324        m
325    }
326    
 if(FALSE) # now have faster  "ddense" -> "dge"  
327  setAs("ddiMatrix", "dgeMatrix",  setAs("ddiMatrix", "dgeMatrix",
328        function(from) as(as(from, "matrix"), "dgeMatrix"))        function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
329    setAs("ddiMatrix", "ddenseMatrix",
330          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
331    setAs("ldiMatrix", "ldenseMatrix",
332          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
333    
334    
335  setAs("matrix", "diagonalMatrix",  setAs("matrix", "diagonalMatrix",
336        function(from) {        function(from) {
337            d <- dim(from)            d <- dim(from)
338            if(d[1] != (n <- d[2])) stop("non-square matrix")            if(d[1] != (n <- d[2])) stop("non-square matrix")
339            if(any(from[row(from) != col(from)] != 0))            if(any(from[row(from) != col(from)] != 0))
340                stop("has non-zero off-diagonal entries")                stop("matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"")
341            x <- diag(from)            x <- diag(from)
342            if(is.logical(x)) {            if(is.logical(x)) {
343                cl <- "ldiMatrix"                cl <- "ldiMatrix"
344                uni <- all(x)                uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
345            } else {            } else {
346                cl <- "ddiMatrix"                cl <- "ddiMatrix"
347                uni <- all(x == 1)                uni <- allTrue(x == 1)
348                storage.mode(x) <- "double"                storage.mode(x) <- "double"
349            } ## TODO: complex            } ## TODO: complex
350            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
# Line 174  Line 361 
361            x <- diag(from)            x <- diag(from)
362            if(is.logical(x)) {            if(is.logical(x)) {
363                cl <- "ldiMatrix"                cl <- "ldiMatrix"
364                uni <- all(x)                uni <- allTrue(x)
365            } else {            } else {
366                cl <- "ddiMatrix"                cl <- "ddiMatrix"
367                uni <- all(x == 1)                uni <- allTrue(x == 1)
368                storage.mode(x) <- "double"                storage.mode(x) <- "double"
369            }            } ## TODO: complex
370            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
371                x = if(uni) x[FALSE] else x)                x = if(uni) x[FALSE] else x)
372        })        })
# Line 188  Line 375 
375  setMethod("diag", signature(x = "diagonalMatrix"),  setMethod("diag", signature(x = "diagonalMatrix"),
376            function(x = 1, nrow, ncol) .diag.x(x))            function(x = 1, nrow, ncol) .diag.x(x))
377    
378    subDiag <- function(x, i, j, ..., drop) {
379  subDiag <- function(x, i, j, drop) {      x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
     x <- as(x, "sparseMatrix")  
380      x <- if(missing(i))      x <- if(missing(i))
381          x[, j, drop=drop]          x[, j, drop=drop]
382      else if(missing(j))      else if(missing(j))
383          x[i, , drop=drop]          if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
384      else      else
385          x[i,j, drop=drop]          x[i,j, drop=drop]
386      if(isDiagonal(x)) as(x, "diagonalMatrix") else x      if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
387  }  }
388    
389  setMethod("[", signature(x = "diagonalMatrix", i = "index",  setMethod("[", signature(x = "diagonalMatrix", i = "index",
390                           j = "index", drop = "logical"), subDiag)                           j = "index", drop = "logical"), subDiag)
391  setMethod("[", signature(x = "diagonalMatrix", i = "index",  setMethod("[", signature(x = "diagonalMatrix", i = "index",
392                          j = "missing", drop = "logical"),                          j = "missing", drop = "logical"),
393            function(x, i, drop) subDiag(x, i=i, drop=drop))            function(x, i, j, ..., drop) {
394                  na <- nargs()
395                  Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
396                  if(na == 4)
397                       subDiag(x, i=i, , drop=drop)
398                  else subDiag(x, i=i,   drop=drop)
399              })
400  setMethod("[", signature(x = "diagonalMatrix", i = "missing",  setMethod("[", signature(x = "diagonalMatrix", i = "missing",
401                           j = "index", drop = "logical"),                           j = "index", drop = "logical"),
402            function(x, j, drop) subDiag(x, j=j, drop=drop))            function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
403    
404  ## When you assign to a diagonalMatrix, the result should be  ## When you assign to a diagonalMatrix, the result should be
405  ## diagonal or sparse ---  ## diagonal or sparse ---
406  ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch  ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
407  replDiag <- function(x, i, j, value) {  ## Only(?) current bug:  x[i] <- value  is wrong when  i is *vector*
408      x <- as(x, "sparseMatrix")  replDiag <- function(x, i, j, ..., value) {
409        x <- as(x, "CsparseMatrix")# was "Tsparse.." till 2012-07
410      if(missing(i))      if(missing(i))
411          x[, j] <- value          x[, j] <- value
412      else if(missing(j))      else if(missing(j)) { ##  x[i , ] <- v  *OR*   x[i] <- v
413            na <- nargs()
414    ##         message("diagnosing replDiag() -- nargs()= ", na)
415            if(na == 4)
416          x[i, ] <- value          x[i, ] <- value
417      else          else if(na == 3)
418                x[i] <- value
419            else stop(gettextf("Internal bug: nargs()=%d; please report",
420                               na), domain=NA)
421        } else
422          x[i,j] <- value          x[i,j] <- value
423      if(isDiagonal(x)) as(x, "diagonalMatrix") else x      if(isDiagonal(x)) as(x, "diagonalMatrix") else x
424  }  }
425    
426  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
427                                  j = "index", value = "replValue"), replDiag)                                  j = "index", value = "replValue"), replDiag)
428    
429  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
430                                  j = "missing", value = "replValue"),                                  j = "missing", value = "replValue"),
431                   function(x, i, value) replDiag(x, i=i, value=value))                   function(x,i,j, ..., value) {
432                         ## message("before replDiag() -- nargs()= ", nargs())
433                         if(nargs() == 3)
434                             replDiag(x, i=i, value=value)
435                         else ## nargs() == 4 :
436                             replDiag(x, i=i, , value=value)
437                     })
438    
439  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
440                                  j = "index", value = "replValue"),                                  j = "index", value = "replValue"),
441                   function(x, j, value) replDiag(x, j=j, value=value))                   function(x,i,j, ..., value) replDiag(x, j=j, value=value))
442    
443    ## x[] <- value :
444    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
445                                    j = "missing", value = "ANY"),
446                     function(x,i,j, ..., value)
447                 {
448                  if(all0(value)) { # be faster
449                      r <- new(paste0(.M.kindC(getClassDef(class(x))),"tTMatrix"))# of all "0"
450                      r@Dim <- x@Dim
451                      r@Dimnames <- x@Dimnames
452                      r
453                  } else { ## typically non-sense: assigning to full sparseMatrix
454                      x[TRUE] <- value
455                      x
456                  }
457              })
458    
459    
460    setReplaceMethod("[", signature(x = "diagonalMatrix",
461                                    i = "matrix", # 2-col.matrix
462                                    j = "missing", value = "replValue"),
463                     function(x,i,j, ..., value) {
464                         if(ncol(i) == 2) {
465                             if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
466                                 if(x@diag == "U") {
467                                     one <- as1(x@x)
468                                     if(any(value != one | is.na(value))) {
469                                         x@diag <- "N"
470                                         x@x <- rep.int(one, x@Dim[1])
471                                     } else return(x)
472                                 }
473                                 x@x[ii] <- value
474                                 x
475                             } else { ## no longer diagonal, but remain sparse:
476                                 x <- as(x, "TsparseMatrix")
477                                 x[i] <- value
478                                 x
479                             }
480                         }
481                         else { # behave as "base R": use as if vector
482                             x <- as(x, "matrix")
483                             x[i] <- value
484                             Matrix(x)
485                         }
486                     })
487    
488    
489    ## value = "sparseMatrix":
490    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
491                                    value = "sparseMatrix"),
492                     function (x, i, j, ..., value)
493                     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
494    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
495                                    value = "sparseMatrix"),
496                     function (x, i, j, ..., value)
497                     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
498    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
499                                    value = "sparseMatrix"),
500                     function (x, i, j, ..., value)
501                     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
502    
503    ## value = "sparseVector":
504    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
505                                    value = "sparseVector"),
506                     replDiag)
507    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
508                                    value = "sparseVector"),
509                     replDiag)
510    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
511                                    value = "sparseVector"),
512                     replDiag)
513    
514    
515  setMethod("t", signature(x = "diagonalMatrix"),  setMethod("t", signature(x = "diagonalMatrix"),
# Line 241  Line 520 
520  setMethod("isTriangular", signature(object = "diagonalMatrix"),  setMethod("isTriangular", signature(object = "diagonalMatrix"),
521            function(object) TRUE)            function(object) TRUE)
522  setMethod("isSymmetric", signature(object = "diagonalMatrix"),  setMethod("isSymmetric", signature(object = "diagonalMatrix"),
523            function(object) TRUE)            function(object, ...) TRUE)
524    
525    setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
526    setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
527    
528  setMethod("chol", signature(x = "ddiMatrix"),# pivot = "ANY"  setMethod("chol", signature(x = "ddiMatrix"),
529            function(x, pivot) {            function(x, pivot, ...) {
530                if(any(x@x < 0)) stop("chol() is undefined for diagonal matrix with negative entries")                if(x@diag == "U") return(x)
531                  ## else
532                  if(any(x@x < 0))
533                      stop("chol() is undefined for diagonal matrix with negative entries")
534                x@x <- sqrt(x@x)                x@x <- sqrt(x@x)
535                x                x
536            })            })
537  ## chol(L) is L for logical diagonal:  ## chol(L) is L for logical diagonal:
538  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot) x)  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
539    
540    setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
541              function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
542    
543    setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
544              function(x, type, ...) {
545                  if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
546                  type <- toupper(substr(type[1], 1, 1))
547                  isU <- (x@diag == "U") # unit-diagonal
548                  if(type == "F") sqrt(if(isU) n else sum(x@x^2))
549                  else { ## norm == "I","1","O","M" :
550                      if(isU) 1 else max(abs(x@x))
551                  }
552              })
553    
554    
555    
556  ## Basic Matrix Multiplication {many more to add}  ## Basic Matrix Multiplication {many more to add}
557  ##       ---------------------  ##       ---------------------
558  ## Note that "ldi" logical are treated as numeric  ## Note that "ldi" logical are treated as numeric
559  diagdiagprod <- function(x, y) {  diagdiagprod <- function(x, y) {
560      if(any(dim(x) != dim(y))) stop("non-matching dimensions")      dimCheck(x,y)
561      if(x@diag != "U") {      if(x@diag != "U") {
562          if(y@diag != "U") {          if(y@diag != "U") {
563              nx <- x@x * y@x              nx <- x@x * y@x
# Line 284  Line 585 
585    
586    
587  diagmatprod <- function(x, y) {  diagmatprod <- function(x, y) {
588        ## x is diagonalMatrix
589      dx <- dim(x)      dx <- dim(x)
590      dy <- dim(y)      dy <- dim(y)
591      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
     n <- dx[1]  
592      as(if(x@diag == "U") y else x@x * y, "Matrix")      as(if(x@diag == "U") y else x@x * y, "Matrix")
593  }  }
   
594  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
595            diagmatprod)            diagmatprod)
596    ## sneaky .. :
597  formals(diagmatprod) <- alist(x=, y=NULL)  formals(diagmatprod) <- alist(x=, y=NULL)
598  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
599            diagmatprod)            diagmatprod)
 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"),  
           diagmatprod)  
600    
601  diagdgeprod <- function(x, y) {  diagGeprod <- function(x, y) {
602      dx <- dim(x)      dx <- dim(x)
603      dy <- dim(y)      dy <- dim(y)
604      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
# Line 307  Line 606 
606          y@x <- x@x * y@x          y@x <- x@x * y@x
607      y      y
608  }  }
609  setMethod("%*%", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
610            diagdgeprod, valueClass = "dgeMatrix")  setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
611  formals(diagdgeprod) <- alist(x=, y=NULL)  formals(diagGeprod) <- alist(x=, y=NULL)
612  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
613            diagdgeprod, valueClass = "dgeMatrix")            diagGeprod, valueClass = "dgeMatrix")
614    setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
615              diagGeprod)
616    
617  setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),  matdiagprod <- function(x, y) {
           function(x, y) {  
618                dx <- dim(x)                dx <- dim(x)
619                dy <- dim(y)                dy <- dim(y)
620                if(dx[2] != dy[1]) stop("non-matching dimensions")                if(dx[2] != dy[1]) stop("non-matching dimensions")
621                as(if(y@diag == "U") x else x * rep(y@x, each = dx[1]), "Matrix")      Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
622            })  }
623    setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
624              matdiagprod)
625    formals(matdiagprod) <- alist(x=, y=NULL)
626    setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
627              matdiagprod)
628    
629  setMethod("%*%", signature(x = "dgeMatrix", y = "diagonalMatrix"),  gediagprod <- function(x, y) {
           function(x, y) {  
630                dx <- dim(x)                dx <- dim(x)
631                dy <- dim(y)                dy <- dim(y)
632                if(dx[2] != dy[1]) stop("non-matching dimensions")                if(dx[2] != dy[1]) stop("non-matching dimensions")
633                if(y@diag == "N")                if(y@diag == "N")
634                    x@x <- x@x * rep(y@x, each = dx[1])                    x@x <- x@x * rep(y@x, each = dx[1])
635                x                x
636            })  }
637    setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
638    setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
639    formals(gediagprod) <- alist(x=, y=NULL)
640    setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
641              gediagprod)
642    setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
643              gediagprod)
644    
645  ## crossprod {more of these}  ## crossprod {more of these}
646    
647  ## tcrossprod --- all are not yet there: do the dense ones here:  ## tcrossprod --- all are not yet there: do the dense ones here:
648    
649    setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
650              function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
651    setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
652              function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
653    
654    
655  ## FIXME:  ## FIXME:
656  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
657  ##        function(x, y = NULL) {  ##        function(x, y = NULL) {
658  ##           })  ##           })
659    
660  ## setMethod("tcrossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),  Cspdiagprod <- function(x, y) {
661  ##        function(x, y = NULL) {      dx <- dim(x <- .Call(Csparse_diagU2N, x))
662  ##           })      dy <- dim(y)
663        if(dx[2] != dy[1]) stop("non-matching dimensions")
664        if(y@diag == "N") {
665            if(!all(y@x[1L] == y@x[-1L]) && is(x, "symmetricMatrix"))
666                x <- as(x, "generalMatrix")
667            ind <- rep.int(seq_len(dx[2]), x@p[-1] - x@p[-dx[2]-1L])
668            x@x <- x@x * y@x[ind]
669        }
670        if(is(x, "compMatrix") && length(xf <- x@factors)) {
671            ## instead of dropping all factors, be smart about some
672            ## TODO ......
673            x@factors <- list()
674        }
675        x
676    }
677    
678    diagCspprod <- function(x, y) {
679        dx <- dim(x)
680        dy <- dim(y <- .Call(Csparse_diagU2N, y))
681        if(dx[2] != dy[1]) stop("non-matching dimensions")
682        if(x@diag == "N") {
683            if(!all(x@x[1L] == x@x[-1L]) && is(y, "symmetricMatrix"))
684                y <- as(y, "generalMatrix")
685            y@x <- y@x * x@x[y@i + 1L]
686        }
687        if(is(y, "compMatrix") && length(yf <- y@factors)) {
688            ## instead of dropping all factors, be smart about some
689            ## TODO
690            keep <- character()
691            if(iLU <- names(yf) == "LU") {
692                ## TODO keep <- "LU"
693            }
694            y@factors <- yf[keep]
695        }
696        y
697    }
698    
699    setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
700              function(x, y = NULL) diagCspprod(x, y))
701    
702  setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
703            function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })            function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix")))
704    
705    ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
706    ##  x'y == (y'x)'
707    setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
708              function(x, y = NULL) t(diagCspprod(y, x)))
709    
710  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
711            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })            function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix"))))
712    
713    setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
714              function(x, y = NULL) diagCspprod(x, t(y)))
715    
716  setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
717            function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })            function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix"))))
718    
719    setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
720              function(x, y = NULL) Cspdiagprod(x, y))
721    
722  setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
723            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })            function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y))
724    
725    setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
726              function(x, y) diagCspprod(x, y))
727    
 ## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()  
728  setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
729            function(x, y) as(x, "sparseMatrix") %*% y)            function(x, y) diagCspprod(as(x, "CsparseMatrix"), y))
 ## NB: The previous is *not* triggering for  "ddi" o "dgC" (= distance 3)  
 ##     since there's a "ddense" o "Csparse" at dist. 2 => triggers first.  
 ## ==> do this:  
 setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),  
           function(x, y) as(x, "CsparseMatrix") %*% y)  
 setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),  
           function(x, y) x %*% as(y, "CsparseMatrix"))  
 ## NB: this is *not* needed for Tsparse & Rsparse  
 ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*  
 ##       do indeed work by going through sparse (and *not* ddense)!  
730    
731  setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
732            function(x, y) x %*% as(y, "sparseMatrix"))            function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y))
733    
734    setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
735              function(x, y) Cspdiagprod(x, y))
736    
737    ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
738    ##       do indeed work by going through sparse (and *not* ddense)!
739    
740  setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),  setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
741            function(a, b, ...) {            function(a, b, ...) {
# Line 383  Line 745 
745            })            })
746    
747  solveDiag <- function(a, b, ...) {  solveDiag <- function(a, b, ...) {
748      if((n <- a@Dim[1]) != nrow(b))      if(a@Dim[1] != nrow(b))
749          stop("incompatible matrix dimensions")          stop("incompatible matrix dimensions")
750      ## trivially invert a 'in place' and multiply:      ## trivially invert a 'in place' and multiply:
751      a@x <- 1/ a@x      a@x <- 1/ a@x
# Line 395  Line 757 
757  setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),  setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
758            solveDiag)            solveDiag)
759    
760    ## Schur()  ---> ./eigen.R
761    
762    
763    
764  ### ---------------- diagonal  o  sparse  -----------------------------  ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
   
765    
766  ## Use function for several signatures, in order to evade  ## Use function for several signatures, in order to evade
767  ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)  diagOdiag <- function(e1,e2) {
768  diagOdiag <- function(e1,e2) { # result should also be diagonal      ## result should also be diagonal _ if possible _
769      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
770      if(is.numeric(r)) {      ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
771        r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
772                           if(is.numeric(e2@x)) 0 else FALSE)
773        if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* diagonal
774            if(is.numeric(r)) { # "double" *or* "integer"
775          if(is.numeric(e2@x)) {          if(is.numeric(e2@x)) {
776              e2@x <- r; return(.diag.2N(e2)) }              e2@x <- r; return(.diag.2N(e2)) }
777          if(!is.numeric(e1@x))          if(!is.numeric(e1@x))
778              ## e.g. e1, e2 are logical;              ## e.g. e1, e2 are logical;
779              e1 <- as(e1, "dMatrix")              e1 <- as(e1, "dMatrix")
780                if(!is.double(r)) r <- as.double(r)
781      }      }
782      else if(is.logical(r))      else if(is.logical(r))
783          e1 <- as(e1, "lMatrix")          e1 <- as(e1, "lMatrix")
784      else stop("intermediate 'r' is of type", typeof(r))          else stop(gettextf("intermediate 'r' is of type %s",
785                               typeof(r)), domain=NA)
786      e1@x <- r      e1@x <- r
787      .diag.2N(e1)      .diag.2N(e1)
788  }  }
789        else { ## result not diagonal, but at least symmetric:
790            ## e.g., m == m
791            isNum <- (is.numeric(r) || is.numeric(r00))
792            isLog <- (is.logical(r) || is.logical(r00))
793            Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
794            d <- e1@Dim
795            n <- d[1]
796            stopifnot(length(r) == n)
797            if(isNum && !is.double(r)) r <- as.double(r)
798            xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
799            newcl <-
800                paste0(if(isNum) "d" else if(isLog) {
801                    if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
802                } else stop("not yet implemented .. please report"), "syMatrix")
803    
804            new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
805        }
806    }
807    
808    ### This would be *the* way, but we get tons of "ambiguous method dispatch"
809    ## we use this hack instead of signature  x = "diagonalMatrix" :
810    diCls <- names(getClass("diagonalMatrix")@subclasses)
811    if(FALSE) {
812  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
813            diagOdiag)            diagOdiag)
814  ## These two are just for method disambiguation:  } else { ## These are just for method disambiguation:
815  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "diagonalMatrix"),      for(c1 in diCls)
816            diagOdiag)          for(c2 in diCls)
817  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ddiMatrix"),              setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
818            diagOdiag)  }
819    
820  ## FIXME:    diagonal  o  triangular  |-->  triangular  ## diagonal  o  triangular  |-->  triangular
821  ## -----     diagonal  o  symmetric   |-->  symmetric  ## diagonal  o  symmetric   |-->  symmetric
822  ##    {also when other is sparse: do these "here" --  ##    {also when other is sparse: do these "here" --
823  ##     before conversion to sparse, since that loses "diagonality"}  ##     before conversion to sparse, since that loses "diagonality"}
824    diagOtri <- function(e1,e2) {
825        ## result must be triangular
826        r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible"
827        ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
828        e1.0 <- if(.n1 <- is.numeric(d1   )) 0 else FALSE
829        r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0])) 0 else FALSE)
830        if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* triangular
831            diag(e2) <- r
832            ## check what happens "in the triangle"
833            e2.2 <- if(.n2) 2 else TRUE
834            if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change:
835                n <- dim(e2)[1L]
836                it <- indTri(n, upper = (e2@uplo == "U"))
837                e2[it] <- callGeneric(e1.0, e2[it])
838            }
839            e2
840        }
841        else { ## result not triangular ---> general
842            rr <- as(e2, "generalMatrix")
843            diag(rr) <- r
844            rr
845        }
846    }
847    
848    
849    setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"),
850              diagOtri)
851    ## For the reverse,  Ops == "Arith" | "Compare" | "Logic"
852    ##   'Arith'  :=  '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"'
853    setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
854              function(e1,e2)
855          { ## this must only trigger for *dense* e1
856              switch(.Generic,
857                     "+" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"),   .diag.x(e2)),
858                     "-" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), - .diag.x(e2)),
859                     "*" = {
860                         n <- e2@Dim[1L]
861                         d2 <- if(e2@diag == "U") { # unit-diagonal
862                             d <- rep.int(as1(e2@x), n)
863                             e2@x <- d
864                             e2@diag <- "N"
865                             d
866                         } else e2@x
867                         e2@x <- diag(e1) * d2
868                         e2
869                     },
870                     "^" = { ## will be dense ( as  <ANY> ^ 0 == 1 ):
871                         e1 ^ as(e2, "denseMatrix")
872                     },
873                     ## otherwise:
874                     callGeneric(e1, diag2Tsmart(e2,e1)))
875    })
876    
877    ## Compare --> 'swap' (e.g.   e1 < e2   <==>  e2 > e1 ):
878    setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
879              .Cmp.swap)
880    ## '&' and "|'  are commutative:
881    setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
882              function(e1,e2) callGeneric(e2, e1))
883    
884  ## For almost everything else, diag* shall be treated "as sparse" :  ## For almost everything else, diag* shall be treated "as sparse" :
885  ## These are cheap implementations via coercion  ## These are cheap implementations via coercion
886    
887  ## for disambiguation  ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
888  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "sparseMatrix"),  ## and because we can save an .M.kind() call, we use this explicit
889            function(e1,e2) callGeneric(as(e1, "sparseMatrix"), e2))  ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
890  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "diagonalMatrix"),  ##
891            function(e1,e2) callGeneric(e1, as(e2, "sparseMatrix")))  ## ddi*:
892  ## in general:  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
893  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ANY"),            function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
894            function(e1,e2) callGeneric(as(e1,"sparseMatrix"), e2))  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
895  setMethod("Ops", signature(e1 = "ANY", e2 = "diagonalMatrix"),            function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
896            function(e1,e2) callGeneric(e1, as(e2,"sparseMatrix")))  ## ldi*
897    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
898              function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
899    setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
900              function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
901    
902    ## Ops:  Arith  --> numeric : "dMatrix"
903    ##       Compare --> logical
904    ##       Logic   --> logical: "lMatrix"
905    
906    ## Other = "numeric" : stay diagonal if possible
907    ## ddi*: Arith: result numeric, potentially ddiMatrix
908    for(arg2 in c("numeric","logical"))
909    setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2),
910              function(e1,e2) {
911                  n <- e1@Dim[1]
912                  f0 <- callGeneric(0, e2)
913                  if(all(is0(f0))) { # remain diagonal
914                      L1 <- (le <- length(e2)) == 1L
915                      if(e1@diag == "U") {
916                          if(any((r <- callGeneric(1, e2)) != 1)) {
917                              e1@diag <- "N"
918                              e1@x[seq_len(n)] <- r # possibly recycling r
919                          } ## else: result = e1  (is "U" diag)
920                      } else {
921                          r <- callGeneric(e1@x, e2)
922                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
923                          e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
924                      }
925                      e1
926                  } else
927                      callGeneric(diag2tT.u(e1,e2, "d"), e2)
928              })
929    
930    for(arg1 in c("numeric","logical"))
931    setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"),
932              function(e1,e2) {
933                  n <- e2@Dim[1]
934                  f0 <- callGeneric(e1, 0)
935                  if(all(is0(f0))) { # remain diagonal
936                      L1 <- (le <- length(e1)) == 1L
937                      if(e2@diag == "U") {
938                          if(any((r <- callGeneric(e1, 1)) != 1)) {
939                              e2@diag <- "N"
940                              e2@x[seq_len(n)] <- r # possibly recycling r
941                          } ## else: result = e2  (is "U" diag)
942                      } else {
943                          r <- callGeneric(e1, e2@x)
944                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
945                          e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
946                      }
947                      e2
948                  } else
949                      callGeneric(e1, diag2tT.u(e2,e1, "d"))
950              })
951    
952    ## ldi* Arith --> result numeric, potentially ddiMatrix
953    for(arg2 in c("numeric","logical"))
954    setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2),
955              function(e1,e2) {
956                  n <- e1@Dim[1]
957                  f0 <- callGeneric(0, e2)
958                  if(all(is0(f0))) { # remain diagonal
959                      L1 <- (le <- length(e2)) == 1L
960                      E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
961                      ## E <- copyClass(e1, "ddiMatrix", check=FALSE)
962                      ## storage.mode(E@x) <- "double"
963                      if(e1@diag == "U") {
964                          if(any((r <- callGeneric(1, e2)) != 1)) {
965                              E@diag <- "N"
966                              E@x[seq_len(n)] <- r # possibly recycling r
967                          } ## else: result = E  (is "U" diag)
968                      } else {
969                          r <- callGeneric(e1@x, e2)
970                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
971                          E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
972                      }
973                      E
974                  } else
975                      callGeneric(diag2tT.u(e1,e2, "l"), e2)
976              })
977    
978    for(arg1 in c("numeric","logical"))
979    setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"),
980              function(e1,e2) {
981                  n <- e2@Dim[1]
982                  f0 <- callGeneric(e1, 0)
983                  if(all(is0(f0))) { # remain diagonal
984                      L1 <- (le <- length(e1)) == 1L
985                      E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
986                      ## E <- copyClass(e2, "ddiMatrix", check=FALSE)
987                      ## storage.mode(E@x) <- "double"
988                      if(e2@diag == "U") {
989                          if(any((r <- callGeneric(e1, 1)) != 1)) {
990                              E@diag <- "N"
991                              E@x[seq_len(n)] <- r # possibly recycling r
992                          } ## else: result = E  (is "U" diag)
993                      } else {
994                          r <- callGeneric(e1, e2@x)
995                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
996                          E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
997                      }
998                      E
999                  } else
1000                      callGeneric(e1, diag2tT.u(e2,e1, "l"))
1001              })
1002    
1003    ## ddi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1004    ##
1005    ## Note that  ("numeric", "ddiMatrix")  is simply swapped, e.g.,
1006    if(FALSE) {
1007        selectMethod("<", c("numeric","lMatrix"))# Compare
1008        selectMethod("&", c("numeric","lMatrix"))# Logic
1009    } ## so we don't need to define a method here :
1010    
1011    for(arg2 in c("numeric","logical"))
1012    setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2),
1013              function(e1,e2) {
1014                  n <- e1@Dim[1]
1015                  f0 <- callGeneric(0, e2)
1016                  if(all(is0(f0))) { # remain diagonal
1017                      L1 <- (le <- length(e2)) == 1L
1018                      E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))#FIXME: if ok, check=FALSE
1019                      ## E <- copyClass(e1, "ldiMatrix", check=FALSE)
1020                      ## storage.mode(E@x) <- "logical"
1021                      if(e1@diag == "U") {
1022                          if(any((r <- callGeneric(1, e2)) != 1)) {
1023                              E@diag <- "N"
1024                              E@x[seq_len(n)] <- r # possibly recycling r
1025                          } ## else: result = E  (is "U" diag)
1026                      } else {
1027                          r <- callGeneric(e1@x, e2)
1028                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1029                          E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1030                      }
1031                      E
1032                  } else
1033                      callGeneric(diag2tT.u(e1,e2, "d"), e2)
1034              })
1035    
1036    ## ldi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1037    for(arg2 in c("numeric","logical"))
1038    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2),
1039              function(e1,e2) {
1040                  n <- e1@Dim[1]
1041                  f0 <- callGeneric(FALSE, e2)
1042                  if(all(is0(f0))) { # remain diagonal
1043                      L1 <- (le <- length(e2)) == 1L
1044    
1045                      if(e1@diag == "U") {
1046                          if(any((r <- callGeneric(TRUE, e2)) != 1)) {
1047                              e1@diag <- "N"
1048                              e1@x[seq_len(n)] <- r # possibly recycling r
1049                          } ## else: result = e1  (is "U" diag)
1050                      } else {
1051                          r <- callGeneric(e1@x, e2)
1052                          ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1053                          e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1054                      }
1055                      e1
1056                  } else
1057                      callGeneric(diag2tT.u(e1,e2, "l"), e2)
1058              })
1059    
1060    
1061    ## Not {"sparseMatrix", "numeric} :  {"denseMatrix", "matrix", ... }
1062    for(other in c("ANY", "Matrix", "dMatrix")) {
1063        ## ddi*:
1064        setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
1065                  function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
1066        setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
1067                  function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
1068        ## ldi*:
1069        setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
1070                  function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
1071        setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
1072                  function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
1073    }
1074    
1075    ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
1076    dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
1077                           names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] })
1078    for(DI in diCls) {
1079        dMeth <- if(extends(DI, "dMatrix"))
1080            function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)
1081        else # "lMatrix", the only other kind for now
1082            function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)
1083        for(c2 in c(dense.subCl, "Matrix")) {
1084            for(Fun in c("*", "&")) {
1085                setMethod(Fun, signature(e1 = DI, e2 = c2),
1086                          function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
1087                setMethod(Fun, signature(e1 = c2, e2 = DI),
1088                          function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1089            }
1090            setMethod("^", signature(e1 = c2, e2 = DI),
1091                      function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1092            for(Fun in c("%%", "%/%", "/")) ## 0 <op> 0 |--> NaN  for these.
1093                setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth)
1094        }
1095    }
1096    
1097    
1098    ### "Summary" : "max"   "min"   "range" "prod"  "sum"   "any"   "all"
1099    ### ----------   the last 4: separately here
1100    for(cl in diCls) {
1101    setMethod("any", cl,
1102              function (x, ..., na.rm) {
1103                  if(any(x@Dim == 0)) FALSE
1104                  else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
1105              })
1106    setMethod("all",  cl, function (x, ..., na.rm) {
1107        n <- x@Dim[1]
1108        if(n >= 2) FALSE
1109        else if(n == 0 || x@diag == "U") TRUE
1110        else all(x@x, ..., na.rm = na.rm)
1111    })
1112    setMethod("prod", cl, function (x, ..., na.rm) {
1113        n <- x@Dim[1]
1114        if(n >= 2) 0
1115        else if(n == 0 || x@diag == "U") 1
1116        else ## n == 1, diag = "N" :
1117            prod(x@x, ..., na.rm = na.rm)
1118    })
1119    
1120    setMethod("sum", cl,
1121              function(x, ..., na.rm) {
1122                  r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1123                  if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
1124              })
1125    }
1126    
1127    ## The remaining ones are  max, min, range :
1128    
1129    setMethod("Summary", "ddiMatrix",
1130              function(x, ..., na.rm) {
1131                  if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1132                  else if(x@diag == "U")
1133                      callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1134                  else callGeneric(x@x, 0, ..., na.rm=na.rm)
1135              })
1136    setMethod("Summary", "ldiMatrix",
1137              function(x, ..., na.rm) {
1138                  if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1139                  else if(x@diag == "U")
1140                      callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1141                  else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1142              })
1143    
1144    
1145    
# Line 459  Line 1154 
1154      invisible(x)      invisible(x)
1155  }  }
1156    
1157    ## somewhat consistent with "print" for sparseMatrix :
1158    setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1159    
1160  setMethod("show", signature(object = "diagonalMatrix"),  setMethod("show", signature(object = "diagonalMatrix"),
1161            function(object) {            function(object) {
1162                d <- dim(object)                d <- dim(object)
1163                cl <- class(object)                cl <- class(object)
1164                cat(sprintf('%d x %d diagonal matrix of class "%s"\n',                cat(sprintf('%d x %d diagonal matrix of class "%s"',
1165                            d[1], d[2], cl))                            d[1], d[2], cl))
1166                  if(d[1] < 50) {
1167                      cat("\n")
1168                prDiag(object)                prDiag(object)
1169                  } else {
1170                      cat(", with diagonal entries\n")
1171                      show(diag(object))
1172                      invisible(object)
1173                  }
1174            })            })
1175    
1176    rm(dense.subCl, diCls)# not used elsewhere
1177    
1178    setMethod("summary", signature(object = "diagonalMatrix"),
1179              function(object, ...) {
1180                  d <- dim(object)
1181                  r <- summary(object@x, ...)
1182                  attr(r, "header") <-
1183                      sprintf('%d x %d diagonal Matrix of class "%s"',
1184                              d[1], d[2], class(object))
1185                  ## use ole' S3 technology for such a simple case
1186                  class(r) <- c("diagSummary", class(r))
1187                  r
1188              })
1189    
1190    print.diagSummary <- function (x, ...) {
1191        cat(attr(x, "header"),"\n")
1192        class(x) <- class(x)[-1]
1193        print(x, ...)
1194        invisible(x)
1195    }

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