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[matrix] Diff of /pkg/Matrix/R/diagMatrix.R
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Diff of /pkg/Matrix/R/diagMatrix.R

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revision 1805, Tue Mar 27 16:46:03 2007 UTC revision 2508, Thu Dec 24 09:47:57 2009 UTC
# Line 16  Line 16 
16      if(missing(x)) ## unit diagonal matrix      if(missing(x)) ## unit diagonal matrix
17          new("ddiMatrix", Dim = c(n,n), diag = "U")          new("ddiMatrix", Dim = c(n,n), diag = "U")
18      else {      else {
19          stopifnot(length(x) == n)          lx <- length(x)
20            stopifnot(lx == 1 || lx == n) # but keep 'x' short for now
21          if(is.logical(x))          if(is.logical(x))
22              cl <- "ldiMatrix"              cl <- "ldiMatrix"
23          else if(is.numeric(x)) {          else if(is.numeric(x)) {
# Line 26  Line 27 
27          else if(is.complex(x)) {          else if(is.complex(x)) {
28              cl <- "zdiMatrix"  # will not yet work              cl <- "zdiMatrix"  # will not yet work
29          } else stop("'x' has invalid data type")          } else stop("'x' has invalid data type")
30          new(cl, Dim = c(n,n), diag = "N", x = x)          new(cl, Dim = c(n,n), diag = "N",
31                x = if(lx == 1) rep.int(x,n) else x)
32      }      }
33  }  }
34    
35    .sparseDiagonal <- function(n, x = rep.int(1,m), uplo = "U",
36                                shape = if(missing(cols)) "t" else "g",
37                                kind, cols = if(n) 0:(n - 1L) else integer(0))
38    {
39        stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
40        if(!missing(cols))
41            stopifnot(0 <= (cols <- as.integer(cols)), cols < n)
42        m <- length(cols)
43        if(missing(kind))
44            kind <-
45                if(is.double(x)) "d"
46                else if(is.logical(x)) "l"
47                else { ## for now
48                    storage.mode(x) <- "double"
49                    "d"
50                }
51        else stopifnot(any(kind == c("d","l","n")))
52        if(kind != "n") {
53            if((lx <- length(x)) == 1) x <- rep.int(x, m)
54            else if(lx != m) stop("length(x) must be either 1 or #{cols}")
55        }
56        stopifnot(is.character(shape), nchar(shape) == 1,
57                  any(shape == c("t","s","g"))) # triangular / symmetric / general
58        if(kind == "n") {
59            if(shape == "g")
60                new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m)
61            else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
62                     i = cols, p = 0:m)
63        }
64        ## kind != "n" -- have x slot :
65        else if(shape == "g")
66            new(paste0(kind, "gCMatrix"), Dim = c(n,m),
67                x = x, i = cols, p = 0:m)
68        else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
69                 x = x, i = cols, p = 0:m)
70    }
71    
72    ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
73    .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
74        .sparseDiagonal(n, x, uplo, shape = "s")
75    
76    ## instead of   diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
77    .trDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
78        .sparseDiagonal(n, x, uplo, shape = "t")
79    
80    
81  ### This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.  ### This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.
82  ### Bert's code built on a post by Andy Liaw who most probably was influenced  ### Bert's code built on a post by Andy Liaw who most probably was influenced
83  ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002  ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
84  ### who posted his bdiag() function written in December 1995.  ### who posted his bdiag() function written in December 1995.
85    if(FALSE)##--- no longer used:
86  bdiag <- function(...) {  .bdiag <- function(lst) {
87      if(nargs() == 0) return(new("dgCMatrix"))      ### block-diagonal matrix [a dgTMatrix] from list of matrices
88      ## else :      stopifnot(is.list(lst), length(lst) >= 1)
89      mlist <- if (nargs() == 1) as.list(...) else list(...)      dims <- sapply(lst, dim, USE.NAMES=FALSE)
     dims <- sapply(mlist, dim)  
90      ## make sure we had all matrices:      ## make sure we had all matrices:
91      if(!(is.matrix(dims) && nrow(dims) == 2))      if(!(is.matrix(dims) && nrow(dims) == 2))
92          stop("some arguments are not matrices")          stop("some arguments are not matrices")
93      csdim <- rbind(rep.int(0:0, 2),      csdim <- rbind(rep.int(0L, 2),
94                     apply(sapply(mlist, dim), 1, cumsum))                     apply(dims, 1, cumsum))
95      ret <- new("dgTMatrix", Dim = as.integer(csdim[nrow(csdim),]))      r <- new("dgTMatrix")
96        r@Dim <- as.integer(csdim[nrow(csdim),])
97      add1 <- matrix(1:0, 2,2)      add1 <- matrix(1:0, 2,2)
98      for(i in seq_along(mlist)) {      for(i in seq_along(lst)) {
99          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])
100          if(is.null(dim(indx))) ## non-square matrix          if(is.null(dim(indx))) ## non-square matrix
101              ret[indx[[1]],indx[[2]]] <- mlist[[i]]              r[indx[[1]],indx[[2]]] <- lst[[i]]
102          else ## square matrix          else ## square matrix
103              ret[indx[,1],indx[,2]] <- mlist[[i]]              r[indx[,1], indx[,2]] <- lst[[i]]
104        }
105        r
106    }
107    ## expand(<mer>) needed something like bdiag() for lower-triangular
108    ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
109    ##  implementation for those; now extended and generalized:
110    .bdiag <- function(lst) {
111        ## block-diagonal matrix [a dgTMatrix] from list of matrices
112        stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
113    
114        Tlst <- lapply(lapply(lst, Matrix:::as_Csp2), # includes "diagU2N"
115                       as, "TsparseMatrix")
116        if(nl == 1) return(Tlst[[1]])
117        ## else
118        i_off <- c(0L, cumsum(sapply(Tlst, nrow)))
119        j_off <- c(0L, cumsum(sapply(Tlst, ncol)))
120    
121        clss <- sapply(Tlst, class)
122        knds <- substr(clss, 2, 2)
123        sym  <- knds == "s" # symmetric ones
124        tri  <- knds == "t" # triangular ones
125        use.n <- any(is.n <- substr(clss,1,1) == "n")
126        if(use.n && !(use.n <- all(is.n)))
127            Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
128        if(all(sym)) { ## result should be *symmetric*
129            uplos <- sapply(Tlst, slot, "uplo") ## either "U" or "L"
130            tLU <- table(uplos)# of length 1 or 2 ..
131            if(length(tLU) == 1) { ## all "U" or all "L"
132                useU <- uplos[1] == "U"
133            } else { ## length(tLU) == 2, counting "L" and "U"
134                useU <- diff(tLU) >= 0
135                if(useU && (hasL <- tLU[1] > 0))
136                    Tlst[hasL] <- lapply(Tlst[hasL], t)
137                else if(!useU && (hasU <- tLU[2] > 0))
138                    Tlst[hasU] <- lapply(Tlst[hasU], t)
139            }
140            if(use.n) { ## return nsparseMatrix :
141                r <- new("nsTMatrix")
142            } else {
143                r <- new("dsTMatrix")
144                r@x <- unlist(lapply(Tlst, slot, "x"))
145      }      }
146      ## slightly debatable if we really should return Csparse.. :          r@uplo <- if(useU) "U" else "L"
     as(ret, "CsparseMatrix")  
147  }  }
148        else if(all(tri) && { ULs <- sapply(Tlst, slot, "uplo")##  "U" or "L"
149                              all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
150           ){ ## *triangular* result
151    
152  diag2T <- function(from) {          if(use.n) { ## return nsparseMatrix :
153      i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1:1              r <- new("ntTMatrix")
154      new(paste(.M.kind(from), "tTMatrix", sep=''),          } else {
155                r <- new("dtTMatrix")
156                r@x <- unlist(lapply(Tlst, slot, "x"))
157            }
158            r@uplo <- ULs[1L]
159        }
160        else {
161            if(any(sym))
162                Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
163            if(use.n) { ## return nsparseMatrix :
164                r <- new("ngTMatrix")
165            } else {
166                r <- new("dgTMatrix")
167                r@x <- unlist(lapply(Tlst, slot, "x"))
168            }
169        }
170        r@Dim <- c(i_off[nl+1], j_off[nl + 1])
171        r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
172        r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
173        r
174    }
175    
176    bdiag <- function(...) {
177        if((nA <- nargs()) == 0) return(new("dgCMatrix"))
178        if(nA == 1 && !is.list(...))
179            return(as(..., "CsparseMatrix"))
180        alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
181        if(length(alis) == 1)
182            return(as(alis[[1]], "CsparseMatrix"))
183    
184        ## else : two or more arguments
185        as(.bdiag(alis), "CsparseMatrix")
186    }
187    
188    
189    .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
190        ## to triangular Tsparse
191        i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
192        new(paste(kind, "tTMatrix", sep=''),
193          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
194            uplo = uplo,
195          x = from@x, # <- ok for diag = "U" and "N" (!)          x = from@x, # <- ok for diag = "U" and "N" (!)
196          i = i, j = i)          i = i, j = i)
197  }  }
198    
199  setAs("diagonalMatrix", "triangularMatrix", diag2T)  .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
200  setAs("diagonalMatrix", "sparseMatrix", diag2T)      ## to symmetric Tsparse
201        n <- from@Dim[1]
202        i <- seq_len(n) - 1L
203        new(paste(kind, "sTMatrix", sep=''),
204            Dim = from@Dim, Dimnames = from@Dimnames,
205            i = i, j = i, uplo = uplo,
206            x = if(from@diag == "N") from@x else ## "U"-diag
207            rep.int(switch(kind,
208                           "d" = 1.,
209                           "l" =,
210                           "n" = TRUE,
211                           ## otherwise
212                           stop("'", kind,"' kind not yet implemented")), n))
213    }
214    
215    ## diagonal -> triangular,  upper / lower depending on "partner":
216    diag2tT.u <- function(d, x, kind = .M.kind(d))
217        .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
218    
219    ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
220    diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
221        clx <- getClassDef(class(x))
222        if(extends(clx, "symmetricMatrix"))
223            .diag2sT(d, uplo = x@uplo, kind)
224        else
225            .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
226    }
227    
228    
229    ## In order to evade method dispatch ambiguity warnings,
230    ## and because we can save a .M.kind() call, we use this explicit
231    ## "hack"  instead of signature  x = "diagonalMatrix" :
232    ##
233    ## ddi*:
234    diag2tT <- function(from) .diag2tT(from, "U", "d")
235    setAs("ddiMatrix", "triangularMatrix", diag2tT)
236    ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", diag2tT)
237    ## needed too (otherwise <dense> -> Tsparse is taken):
238    setAs("ddiMatrix", "TsparseMatrix", diag2tT)
239    setAs("ddiMatrix", "dsparseMatrix", diag2tT)
240    setAs("ddiMatrix", "CsparseMatrix",
241          function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
242    setAs("ddiMatrix", "symmetricMatrix",
243          function(from) .diag2sT(from, "U", "d"))
244    ##
245    ## ldi*:
246    diag2tT <- function(from) .diag2tT(from, "U", "l")
247    setAs("ldiMatrix", "triangularMatrix", diag2tT)
248    ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", diag2tT)
249  ## needed too (otherwise <dense> -> Tsparse is taken):  ## needed too (otherwise <dense> -> Tsparse is taken):
250  setAs("diagonalMatrix", "TsparseMatrix", diag2T)  setAs("ldiMatrix", "TsparseMatrix", diag2tT)
251  ## is better than this:  setAs("ldiMatrix", "lsparseMatrix", diag2tT)
252  ## setAs("diagonalMatrix", "sparseMatrix",  setAs("ldiMatrix", "CsparseMatrix",
253  ##       function(from)        function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
254  ##        as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix"))  setAs("ldiMatrix", "symmetricMatrix",
255  setAs("diagonalMatrix", "CsparseMatrix",        function(from) .diag2sT(from, "U", "l"))
       function(from) as(diag2T(from), "CsparseMatrix"))  
256    
257  setAs("diagonalMatrix", "matrix",  
258    setAs("diagonalMatrix", "nMatrix",
259        function(from) {        function(from) {
260            n <- from@Dim[1]            n <- from@Dim[1]
261            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
262                                       } else from@x,            new("ntTMatrix", i = i, j = i, diag = from@diag,
263                 nrow = n, ncol = n)                Dim = from@Dim, Dimnames = from@Dimnames)
264        })        })
265    
266  setAs("diagonalMatrix", "generalMatrix", # prefer sparse:  setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
       function(from) as(from, paste(.M.kind(from), "gCMatrix", sep='')))  
   
 .diag.x <- function(m) {  
     if(m@diag == "U")  
         rep.int(if(is.numeric(m@x)) 1. else TRUE,  
                 m@Dim[1])  
     else m@x  
 }  
267    
268  .diag.2N <- function(m) {  ## Cheap fast substitute for diag() which *does* preserve the mode of x :
269      if(m@diag == "U") m@diag <- "N"  mkDiag <- function(x, n) {
270      m      y <- matrix(as0(mod=mode(x)), n,n)
271        if (n > 0) y[1L + 0:(n - 1L) * (n + 1L)] <- x
272        y
273  }  }
274    
275  ## given the above, the following  4  coercions should be all unneeded;  setAs("diagonalMatrix", "matrix",
 ## we prefer triangular to general:  
 setAs("ddiMatrix", "dgTMatrix",  
276        function(from) {        function(from) {
277            .Deprecated("as(, \"sparseMatrix\")")            ## want "ldiMatrix" -> <logical> "matrix" :
278            n <- from@Dim[1]            mkDiag(if(from@diag == "U") as1(from@x) else from@x,
279            i <- seq_len(n) - 1:1                   n = from@Dim[1])
280            new("dgTMatrix", i = i, j = i, x = .diag.x(from),        })
               Dim = c(n,n), Dimnames = from@Dimnames) })  
281    
282  setAs("ddiMatrix", "dgCMatrix",  setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
283        function(from) as(as(from, "sparseMatrix"), "dgCMatrix"))            function(x, mode) {
284                  n <- x@Dim[1]
285                  mod.x <- mode(x@x)
286                  r <- vector(mod.x, length = n^2)
287                  if(n)
288                      r[1 + 0:(n - 1) * (n + 1)] <-
289                          if(x@diag == "U") as1(mod=mod.x) else x@x
290                  r
291              })
292    
293  setAs("ldiMatrix", "lgTMatrix",  setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
294        function(from) {        function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
           .Deprecated("as(, \"sparseMatrix\")")  
           n <- from@Dim[1]  
           if(from@diag == "U") { # unit-diagonal  
               x <- rep.int(TRUE, n)  
               i <- seq_len(n) - 1:1  
           } else { # "normal"  
               nz <- nz.NA(from@x, na. = TRUE)  
               x <- from@x[nz]  
               i <- which(nz) - 1:1  
           }  
           new("lgTMatrix", i = i, j = i, x = x,  
               Dim = c(n,n), Dimnames = from@Dimnames) })  
295    
296  setAs("ldiMatrix", "lgCMatrix",  setAs("diagonalMatrix", "denseMatrix",
297        function(from) as(as(from, "lgTMatrix"), "lgCMatrix"))        function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
298    
299    .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
300    
301    .diag.2N <- function(m) {
302        if(m@diag == "U") m@diag <- "N"
303        m
304    }
305    
 if(FALSE) # now have faster  "ddense" -> "dge"  
306  setAs("ddiMatrix", "dgeMatrix",  setAs("ddiMatrix", "dgeMatrix",
307        function(from) as(as(from, "matrix"), "dgeMatrix"))        function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
308    setAs("ddiMatrix", "ddenseMatrix",
309          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
310    setAs("ldiMatrix", "ldenseMatrix",
311          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
312    
313    
314  setAs("matrix", "diagonalMatrix",  setAs("matrix", "diagonalMatrix",
315        function(from) {        function(from) {
316            d <- dim(from)            d <- dim(from)
317            if(d[1] != (n <- d[2])) stop("non-square matrix")            if(d[1] != (n <- d[2])) stop("non-square matrix")
318            if(any(from[row(from) != col(from)] != 0))            if(any(from[row(from) != col(from)] != 0))
319                stop("has non-zero off-diagonal entries")                stop("matrix with non-zero off-diagonals cannot be coerced to diagonalMatrix")
320            x <- diag(from)            x <- diag(from)
321            if(is.logical(x)) {            if(is.logical(x)) {
322                cl <- "ldiMatrix"                cl <- "ldiMatrix"
323                uni <- all(x)                uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
324            } else {            } else {
325                cl <- "ddiMatrix"                cl <- "ddiMatrix"
326                uni <- all(x == 1)                uni <- allTrue(x == 1)
327                storage.mode(x) <- "double"                storage.mode(x) <- "double"
328            } ## TODO: complex            } ## TODO: complex
329            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 165  Line 340 
340            x <- diag(from)            x <- diag(from)
341            if(is.logical(x)) {            if(is.logical(x)) {
342                cl <- "ldiMatrix"                cl <- "ldiMatrix"
343                uni <- all(x)                uni <- allTrue(x)
344            } else {            } else {
345                cl <- "ddiMatrix"                cl <- "ddiMatrix"
346                uni <- all(x == 1)                uni <- allTrue(x == 1)
347                storage.mode(x) <- "double"                storage.mode(x) <- "double"
348            }            } ## TODO: complex
349            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",            new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
350                x = if(uni) x[FALSE] else x)                x = if(uni) x[FALSE] else x)
351        })        })
352    
353    
354  setMethod("diag", signature(x = "diagonalMatrix"),  setMethod("diag", signature(x = "diagonalMatrix"),
355            function(x = 1, nrow, ncol = n) .diag.x(x))            function(x = 1, nrow, ncol) .diag.x(x))
   
356    
357  subDiag <- function(x, i, j, drop) {  subDiag <- function(x, i, j, ..., drop) {
358      x <- as(x, "sparseMatrix")      x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
359      x <- if(missing(i))      x <- if(missing(i))
360          x[, j, drop=drop]          x[, j, drop=drop]
361      else if(missing(j))      else if(missing(j))
362          x[i, , drop=drop]          if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
363      else      else
364          x[i,j, drop=drop]          x[i,j, drop=drop]
365      if(isDiagonal(x)) as(x, "diagonalMatrix") else x      if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
366  }  }
367    
368  setMethod("[", signature(x = "diagonalMatrix", i = "index",  setMethod("[", signature(x = "diagonalMatrix", i = "index",
369                           j = "index", drop = "logical"), subDiag)                           j = "index", drop = "logical"), subDiag)
370  setMethod("[", signature(x = "diagonalMatrix", i = "index",  setMethod("[", signature(x = "diagonalMatrix", i = "index",
371                          j = "missing", drop = "logical"),                          j = "missing", drop = "logical"),
372            function(x, i, drop) subDiag(x, i=i, drop=drop))            function(x, i, j, ..., drop) {
373                  na <- nargs()
374                  Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
375                  if(na == 4)
376                       subDiag(x, i=i, , drop=drop)
377                  else subDiag(x, i=i,   drop=drop)
378              })
379  setMethod("[", signature(x = "diagonalMatrix", i = "missing",  setMethod("[", signature(x = "diagonalMatrix", i = "missing",
380                           j = "index", drop = "logical"),                           j = "index", drop = "logical"),
381            function(x, j, drop) subDiag(x, j=j, drop=drop))            function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
382    
383  ## When you assign to a diagonalMatrix, the result should be  ## When you assign to a diagonalMatrix, the result should be
384  ## diagonal or sparse ---  ## diagonal or sparse ---
385  ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch  ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
386  replDiag <- function(x, i, j, value) {  ## Only(?) current bug:  x[i] <- value  is wrong when  i is *vector*
387      x <- as(x, "sparseMatrix")  replDiag <- function(x, i, j, ..., value) {
388        x <- as(x, "TsparseMatrix")
389      if(missing(i))      if(missing(i))
390          x[, j] <- value          x[, j] <- value
391      else if(missing(j))      else if(missing(j)) { ##  x[i , ] <- v  *OR*   x[i] <- v
392            na <- nargs()
393    ##         message("diagnosing replDiag() -- nargs()= ", na)
394            if(na == 4)
395          x[i, ] <- value          x[i, ] <- value
396      else          else if(na == 3)
397                x[i] <- value
398            else stop("Internal bug: nargs()=",na,"; please report")
399        } else
400          x[i,j] <- value          x[i,j] <- value
401      if(isDiagonal(x)) as(x, "diagonalMatrix") else x      if(isDiagonal(x)) as(x, "diagonalMatrix") else x
402  }  }
403    
404  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
405                                  j = "index", value = "replValue"), replDiag)                                  j = "index", value = "replValue"), replDiag)
406    
407  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
408                                  j = "missing", value = "replValue"),                                  j = "missing", value = "replValue"),
409                   function(x, i, value) replDiag(x, i=i, value=value))                   function(x,i,j, ..., value) {
410                         ## message("before replDiag() -- nargs()= ", nargs())
411                         if(nargs() == 3)
412                             replDiag(x, i=i, value=value)
413                         else ## nargs() == 4 :
414                             replDiag(x, i=i, , value=value)
415                     })
416    
417    setReplaceMethod("[", signature(x = "diagonalMatrix",
418                                    i = "matrix", # 2-col.matrix
419                                    j = "missing", value = "replValue"),
420                     function(x,i,j, ..., value) {
421                         if(ncol(i) == 2) {
422                             if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
423                                 if(x@diag == "U") {
424                                     one <- as1(x@x)
425                                     if(any(value != one | is.na(value))) {
426                                         x@diag <- "N"
427                                         x@x <- rep.int(one, x@Dim[1])
428                                     }
429                                 }
430                                 x@x[ii] <- value
431                                 x
432                             } else { ## no longer diagonal, but remain sparse:
433                                 x <- as(x, "TsparseMatrix")
434                                 x[i] <- value
435                                 x
436                             }
437                         }
438                         else { # behave as "base R": use as if vector
439                             x <- as(x, "matrix")
440                             x[i] <- value
441                             Matrix(x)
442                         }
443                     })
444    
445  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",  setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
446                                  j = "index", value = "replValue"),                                  j = "index", value = "replValue"),
447                   function(x, j, value) replDiag(x, j=j, value=value))                   function(x,i,j, ..., value) replDiag(x, j=j, value=value))
448    
449    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
450                                    value = "sparseMatrix"),
451                     function (x, i, j, ..., value)
452                     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
453    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
454                                    value = "sparseMatrix"),
455                     function (x, i, j, ..., value)
456                     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
457    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
458                                    value = "sparseMatrix"),
459                     function (x, i, j, ..., value)
460                     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
461    
462    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
463                                    value = "sparseVector"),
464                     replDiag)
465    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
466                                    value = "sparseVector"),
467                     replDiag)
468    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
469                                    value = "sparseVector"),
470                     replDiag)
471    
472    
473  setMethod("t", signature(x = "diagonalMatrix"),  setMethod("t", signature(x = "diagonalMatrix"),
# Line 232  Line 478 
478  setMethod("isTriangular", signature(object = "diagonalMatrix"),  setMethod("isTriangular", signature(object = "diagonalMatrix"),
479            function(object) TRUE)            function(object) TRUE)
480  setMethod("isSymmetric", signature(object = "diagonalMatrix"),  setMethod("isSymmetric", signature(object = "diagonalMatrix"),
481            function(object) TRUE)            function(object, ...) TRUE)
482    
483  setMethod("chol", signature(x = "ddiMatrix"),# pivot = "ANY"  setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
484            function(x, pivot) {  setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
485                if(any(x@x < 0)) stop("chol() is undefined for diagonal matrix with negative entries")  
486    setMethod("chol", signature(x = "ddiMatrix"),
487              function(x, pivot, ...) {
488                  if(x@diag == "U") return(x)
489                  ## else
490                  if(any(x@x < 0))
491                      stop("chol() is undefined for diagonal matrix with negative entries")
492                x@x <- sqrt(x@x)                x@x <- sqrt(x@x)
493                x                x
494            })            })
495  ## chol(L) is L for logical diagonal:  ## chol(L) is L for logical diagonal:
496  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot) x)  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
497    
498  setMethod("!", "ldiMatrix", function(e1) {  setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
499      if(e1@diag == "N")            function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
500          e1@x <- !e1@x  
501      else { ## "U"  setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
502          e1@diag <- "N"            function(x, type, ...) {
503          e1@x <- rep.int(FALSE, e1@Dim[1])                if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
504                  type <- toupper(substr(type[1], 1, 1))
505                  isU <- (x@diag == "U") # unit-diagonal
506                  if(type == "F") sqrt(if(isU) n else sum(x@x^2))
507                  else { ## norm == "I","1","O","M" :
508                      if(isU) 1 else max(abs(x@x))
509      }      }
     e1  
510  })  })
511    
512    
513    
514  ## Basic Matrix Multiplication {many more to add}  ## Basic Matrix Multiplication {many more to add}
515  ##       ---------------------  ##       ---------------------
516  ## Note that "ldi" logical are treated as numeric  ## Note that "ldi" logical are treated as numeric
517  diagdiagprod <- function(x, y) {  diagdiagprod <- function(x, y) {
518      if(any(dim(x) != dim(y))) stop("non-matching dimensions")      n <- dimCheck(x,y)[1]
519      if(x@diag != "U") {      if(x@diag != "U") {
520          if(y@diag != "U") {          if(y@diag != "U") {
521              nx <- x@x * y@x              nx <- x@x * y@x
# Line 285  Line 543 
543    
544    
545  diagmatprod <- function(x, y) {  diagmatprod <- function(x, y) {
546        ## x is diagonalMatrix
547      dx <- dim(x)      dx <- dim(x)
548      dy <- dim(y)      dy <- dim(y)
549      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
550      n <- dx[1]      n <- dx[1]
551      as(if(x@diag == "U") y else x@x * y, "Matrix")      as(if(x@diag == "U") y else x@x * y, "Matrix")
552  }  }
   
553  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
554            diagmatprod)            diagmatprod)
555    ## sneaky .. :
556  formals(diagmatprod) <- alist(x=, y=NULL)  formals(diagmatprod) <- alist(x=, y=NULL)
557  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
558            diagmatprod)            diagmatprod)
 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"),  
           diagmatprod)  
559    
560  diagdgeprod <- function(x, y) {  diagGeprod <- function(x, y) {
561      dx <- dim(x)      dx <- dim(x)
562      dy <- dim(y)      dy <- dim(y)
563      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
# Line 308  Line 565 
565          y@x <- x@x * y@x          y@x <- x@x * y@x
566      y      y
567  }  }
568  setMethod("%*%", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
569            diagdgeprod, valueClass = "dgeMatrix")  setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
570  formals(diagdgeprod) <- alist(x=, y=NULL)  formals(diagGeprod) <- alist(x=, y=NULL)
571  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
572            diagdgeprod, valueClass = "dgeMatrix")            diagGeprod, valueClass = "dgeMatrix")
573    setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
574              diagGeprod)
575    
576  setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),  matdiagprod <- function(x, y) {
           function(x, y) {  
577                dx <- dim(x)                dx <- dim(x)
578                dy <- dim(y)                dy <- dim(y)
579                if(dx[2] != dy[1]) stop("non-matching dimensions")                if(dx[2] != dy[1]) stop("non-matching dimensions")
580                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]))
581            })  }
582    setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
583              matdiagprod)
584    formals(matdiagprod) <- alist(x=, y=NULL)
585    setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
586              matdiagprod)
587    
588  setMethod("%*%", signature(x = "dgeMatrix", y = "diagonalMatrix"),  gediagprod <- function(x, y) {
           function(x, y) {  
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")
592                if(y@diag == "N")                if(y@diag == "N")
593                    x@x <- x@x * rep(y@x, each = dx[1])                    x@x <- x@x * rep(y@x, each = dx[1])
594                x                x
595            })  }
596    setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
597    setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
598    formals(gediagprod) <- alist(x=, y=NULL)
599    setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
600              gediagprod)
601    setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
602              gediagprod)
603    
604  ## crossprod {more of these}  ## crossprod {more of these}
605    
606  ## tcrossprod --- all are not yet there: do the dense ones here:  ## tcrossprod --- all are not yet there: do the dense ones here:
607    
608    setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
609              function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
610    setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
611              function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
612    
613    
614  ## FIXME:  ## FIXME:
615  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
616  ##        function(x, y = NULL) {  ##        function(x, y = NULL) {
617  ##           })  ##           })
618    
619  ## setMethod("tcrossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),  Cspdiagprod <- function(x, y) {
620  ##        function(x, y = NULL) {      dx <- dim(x <- .Call(Csparse_diagU2N, x))
621  ##           })      dy <- dim(y)
622        if(dx[2] != dy[1]) stop("non-matching dimensions")
623        ind <- rep.int(seq_len(dx[2]), x@p[-1] - x@p[-dx[2]-1L])
624        if(y@diag == "N")
625            x@x <- x@x * y@x[ind]
626        x
627    }
628    
629    diagCspprod <- function(x, y) {
630        dx <- dim(x)
631        dy <- dim(y <- .Call(Csparse_diagU2N, y))
632        if(dx[2] != dy[1]) stop("non-matching dimensions")
633        if(x@diag == "N")
634            y@x <- y@x * x@x[y@i + 1L]
635        y
636    }
637    
638    setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
639              function(x, y = NULL) diagCspprod(x, y))
640    
641  setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
642            function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })            function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix")))
643    
644    ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
645    ##  x'y == (y'x)'
646    setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
647              function(x, y = NULL) t(diagCspprod(y, x)))
648    
649  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
650            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })            function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix"))))
651    
652    setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
653              function(x, y = NULL) diagCspprod(x, t(y)))
654    
655  setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
656            function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })            function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix"))))
657    
658    setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
659              function(x, y = NULL) Cspdiagprod(x, y))
660    
661  setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
662            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })            function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y))
663    
664    setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
665              function(x, y) diagCspprod(x, y))
666    
 ## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()  
667  setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
668            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)!  
669    
670  setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),  setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
671            function(x, y) x %*% as(y, "sparseMatrix"))            function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y))
672    
673    setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
674              function(x, y) Cspdiagprod(x, y))
675    
676    ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
677    ##       do indeed work by going through sparse (and *not* ddense)!
678    
679  setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),  setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
680            function(a, b, ...) {            function(a, b, ...) {
# Line 396  Line 696 
696  setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),  setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
697            solveDiag)            solveDiag)
698    
699    ## Schur()  ---> ./eigen.R
700    
701    
702    
703  ### ---------------- diagonal  o  sparse  -----------------------------  ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
   
704    
705  ## Use function for several signatures, in order to evade  ## Use function for several signatures, in order to evade
706  ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)  ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)
707  diagOdiag <- function(e1,e2) { # result should also be diagonal  diagOdiag <- function(e1,e2) {
708        ## result should also be diagonal _ if possible _
709      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
710        ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
711        r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
712                           if(is.numeric(e2@x)) 0 else FALSE)
713        if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* diagonal
714      if(is.numeric(r)) {      if(is.numeric(r)) {
715          if(is.numeric(e2@x)) {          if(is.numeric(e2@x)) {
716              e2@x <- r; return(.diag.2N(e2)) }              e2@x <- r; return(.diag.2N(e2)) }
# Line 419  Line 724 
724      e1@x <- r      e1@x <- r
725      .diag.2N(e1)      .diag.2N(e1)
726  }  }
727        else { ## result not diagonal, but at least symmetric:
728            ## e.g., m == m
729            isNum <- (is.numeric(r) || is.numeric(r00))
730            isLog <- (is.logical(r) || is.logical(r00))
731            Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
732            d <- e1@Dim
733            n <- d[1]
734            stopifnot(length(r) == n)
735            xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
736            newcl <-
737                paste(if(isNum) "d" else if(isLog) {
738                    if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
739                } else stop("not yet implemented .. please report")
740                      ,
741                      "syMatrix", sep='')
742    
743            new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
744        }
745    }
746    
747    ### This would be *the* way, but we get tons of "ambiguous method dispatch"
748    ## we use this hack instead of signature  x = "diagonalMatrix" :
749    diCls <- names(getClass("diagonalMatrix")@subclasses)
750    if(FALSE) {
751  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
752            diagOdiag)            diagOdiag)
753  ## These two are just for method disambiguation:  } else { ## These are just for method disambiguation:
754  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "diagonalMatrix"),      for(c1 in diCls)
755            diagOdiag)          for(c2 in diCls)
756  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ddiMatrix"),              setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
757            diagOdiag)  }
758    
759    ## diagonal  o  triangular  |-->  triangular
760    ## diagonal  o  symmetric   |-->  symmetric
761    ##    {also when other is sparse: do these "here" --
762    ##     before conversion to sparse, since that loses "diagonality"}
763    
764  ## For almost everything else, diag* shall be treated "as sparse" :  ## For almost everything else, diag* shall be treated "as sparse" :
765  ## These are cheap implementations via coercion  ## These are cheap implementations via coercion
766    
767  ## for disambiguation  ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
768  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "sparseMatrix"),  ## and because we can save an .M.kind() call, we use this explicit
769            function(e1,e2) callGeneric(as(e1, "sparseMatrix"), e2))  ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
770  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "diagonalMatrix"),  ##
771            function(e1,e2) callGeneric(e1, as(e2, "sparseMatrix")))  ## ddi*:
772  ## in general:  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
773  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ANY"),            function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
774            function(e1,e2) callGeneric(as(e1,"sparseMatrix"), e2))  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
775  setMethod("Ops", signature(e1 = "ANY", e2 = "diagonalMatrix"),            function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
776            function(e1,e2) callGeneric(e1, as(e2,"sparseMatrix")))  ## ldi*
777    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
778              function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
779    setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
780              function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
781    
782    ## Ops:  Arith  --> numeric : "dMatrix"
783    ##       Compare --> logical
784    ##       Logic   --> logical: "lMatrix"
785    
786    ##  other = "numeric" : stay diagonal if possible
787    ## ddi*: Arith: result numeric, potentially ddiMatrix
788    setMethod("Arith", signature(e1 = "ddiMatrix", e2 = "numeric"),
789              function(e1,e2) {
790                  n <- e1@Dim[1]; nsq <- n^2
791                  f0 <- callGeneric(0, e2)
792                  if(all(is0(f0))) { # remain diagonal
793                      L1 <- (le <- length(e2)) == 1L
794                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
795                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
796                          e1@diag <- "N"
797                          if(L1) r <- rep.int(r, n)
798                      } else
799                          r <- callGeneric(e1@x, e2)
800                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
801                      return(e1)
802                  }
803                  callGeneric(diag2tT.u(e1,e2, "d"), e2)
804              })
805    
806    setMethod("Arith", signature(e1 = "numeric", e2 = "ddiMatrix"),
807              function(e1,e2) {
808                  n <- e2@Dim[1]; nsq <- n^2
809                  f0 <- callGeneric(e1, 0)
810                  if(all(is0(f0))) { # remain diagonal
811                      L1 <- (le <- length(e1)) == 1L
812                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
813                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
814                          e2@diag <- "N"
815                          if(L1) r <- rep.int(r, n)
816                      } else
817                          r <- callGeneric(e1, e2@x)
818                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
819                      return(e2)
820                  }
821                  callGeneric(e1, diag2tT.u(e2,e1, "d"))
822              })
823    
824    ## ldi* Arith --> result numeric, potentially ddiMatrix
825    setMethod("Arith", signature(e1 = "ldiMatrix", e2 = "numeric"),
826              function(e1,e2) {
827                  n <- e1@Dim[1]; nsq <- n^2
828                  f0 <- callGeneric(0, e2)
829                  if(all(is0(f0))) { # remain diagonal
830                      L1 <- (le <- length(e2)) == 1L
831                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
832                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
833                          e1@diag <- "N"
834                          if(L1) r <- rep.int(r, n)
835                      } else
836                          r <- callGeneric(e1@x, e2)
837                      e1 <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))
838                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
839                      return(e1)
840                  }
841                  callGeneric(diag2tT.u(e1,e2, "d"), e2)
842              })
843    
844    setMethod("Arith", signature(e1 = "numeric", e2 = "ldiMatrix"),
845              function(e1,e2) {
846                  n <- e2@Dim[1]; nsq <- n^2
847                  f0 <- callGeneric(e1, 0)
848                  if(all(is0(f0))) { # remain diagonal
849                      L1 <- (le <- length(e1)) == 1L
850                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
851                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
852                          e2@diag <- "N"
853                          if(L1) r <- rep.int(r, n)
854                      } else
855                          r <- callGeneric(e1, e2@x)
856                      e2 <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))
857                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
858                      return(e2)
859                  }
860                  callGeneric(e1, diag2tT.u(e2,e1, "d"))
861              })
862    
863    ## ddi*: for "Ops" without Arith --> result logical, potentially ldi
864    setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "numeric"),
865              function(e1,e2) {
866                  n <- e1@Dim[1]; nsq <- n^2
867                  f0 <- callGeneric(0, e2)
868                  if(all(is0(f0))) { # remain diagonal
869                      L1 <- (le <- length(e2)) == 1L
870                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
871                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
872                          e1@diag <- "N"
873                          if(L1) r <- rep.int(r, n)
874                      } else
875                          r <- callGeneric(e1@x, e2)
876                      e1 <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))
877                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
878                      return(e1)
879                  }
880                  callGeneric(diag2tT.u(e1,e2, "l"), e2)
881              })
882    
883    setMethod("Ops", signature(e1 = "numeric", e2 = "ddiMatrix"),
884              function(e1,e2) {
885                  n <- e2@Dim[1]; nsq <- n^2
886                  f0 <- callGeneric(e1, 0)
887                  if(all(is0(f0))) { # remain diagonal
888                      L1 <- (le <- length(e1)) == 1L
889                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
890                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
891                          e2@diag <- "N"
892                          if(L1) r <- rep.int(r, n)
893                      } else
894                          r <- callGeneric(e1, e2@x)
895                      e2 <- copyClass(e2, "ldiMatrix", c("diag", "Dim", "Dimnames"))
896                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
897                      return(e2)
898                  }
899                  callGeneric(e1, diag2tT.u(e2,e1, "l"))
900              })
901    
902    ## ldi*: for "Ops" without Arith --> result logical, potentially ldi
903    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "numeric"),
904              function(e1,e2) {
905                  n <- e1@Dim[1]; nsq <- n^2
906                  f0 <- callGeneric(FALSE, e2)
907                  if(all(is0(f0))) { # remain diagonal
908                      L1 <- (le <- length(e2)) == 1L
909                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
910                      if(e1@diag == "U" && any((r <- callGeneric(TRUE, e2)) != 1)) {
911                          e1@diag <- "N"
912                          if(L1) r <- rep.int(r, n)
913                      } else
914                          r <- callGeneric(e1@x, e2)
915                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
916                      return(e1)
917                  }
918                  callGeneric(diag2tT.u(e1,e2, "l"), e2)
919              })
920    
921    setMethod("Ops", signature(e1 = "numeric", e2 = "ldiMatrix"),
922              function(e1,e2) {
923                  n <- e2@Dim[1]; nsq <- n^2
924                  f0 <- callGeneric(e1, FALSE)
925                  if(all(is0(f0))) { # remain diagonal
926                      L1 <- (le <- length(e1)) == 1L
927                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
928                      if(e2@diag == "U" && any((r <- callGeneric(e1, TRUE)) != 1)) {
929                          e2@diag <- "N"
930                          if(L1) r <- rep.int(r, n)
931                      } else
932                          r <- callGeneric(e1, e2@x)
933                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
934                      return(e2)
935                  }
936                  callGeneric(e1, diag2tT.u(e2,e1, "l"))
937              })
938    
939    
940    
941    ## Not {"sparseMatrix", "numeric} :  {"denseMatrix", "matrix", ... }
942    for(other in c("ANY", "Matrix", "dMatrix")) {
943        ## ddi*:
944        setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
945                  function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
946        setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
947                  function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
948        ## ldi*:
949        setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
950                  function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
951        setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
952                  function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
953    }
954    
955    ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
956    dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
957                           names(dM.scl)[sapply(dM.scl, slot, "distance") == 1] })
958    for(DI in diCls) {
959        for(c2 in c(dense.subCl, "Matrix")) {
960            for(Fun in c("*", "^", "&")) {
961                setMethod(Fun, signature(e1 = DI, e2 = c2),
962                          function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
963                setMethod(Fun, signature(e1 = c2, e2 = DI),
964                          function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
965            }
966            ## NB: This arguably implicitly uses  0/0 :== 0  to keep diagonality
967            for(Fun in c("%%", "%/%", "/")) {
968                setMethod(Fun, signature(e1 = DI, e2 = c2),
969                          function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
970            }
971        }
972    }
973    
974    
975    ### "Summary" : "max"   "min"   "range" "prod"  "sum"   "any"   "all"
976    ### ----------   the last 4: separately here
977    for(cl in diCls) {
978    setMethod("any", cl,
979              function (x, ..., na.rm) {
980                  if(any(x@Dim == 0)) FALSE
981                  else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
982              })
983    setMethod("all",  cl, function (x, ..., na.rm) {
984        n <- x@Dim[1]
985        if(n >= 2) FALSE
986        else if(n == 0 || x@diag == "U") TRUE
987        else all(x@x, ..., na.rm = na.rm)
988    })
989    setMethod("prod", cl, function (x, ..., na.rm) {
990        n <- x@Dim[1]
991        if(n >= 2) 0
992        else if(n == 0 || x@diag == "U") 1
993        else ## n == 1, diag = "N" :
994            prod(x@x, ..., na.rm = na.rm)
995    })
996    
997    setMethod("sum", cl,
998              function(x, ..., na.rm) {
999                  r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1000                  if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
1001              })
1002    }
1003    
1004    ## The remaining ones are  max, min, range :
1005    
1006    setMethod("Summary", "ddiMatrix",
1007              function(x, ..., na.rm) {
1008                  if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1009                  else if(x@diag == "U")
1010                      callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1011                  else callGeneric(x@x, 0, ..., na.rm=na.rm)
1012              })
1013    setMethod("Summary", "ldiMatrix",
1014              function(x, ..., na.rm) {
1015                  if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1016                  else if(x@diag == "U")
1017                      callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1018                  else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1019              })
1020    
1021    
1022    
# Line 455  Line 1031 
1031      invisible(x)      invisible(x)
1032  }  }
1033    
1034    ## somewhat consistent with "print" for sparseMatrix :
1035    setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1036    
1037  setMethod("show", signature(object = "diagonalMatrix"),  setMethod("show", signature(object = "diagonalMatrix"),
1038            function(object) {            function(object) {
1039                d <- dim(object)                d <- dim(object)
1040                cl <- class(object)                cl <- class(object)
1041                cat(sprintf('%d x %d diagonal matrix of class "%s"\n',                cat(sprintf('%d x %d diagonal matrix of class "%s"',
1042                            d[1], d[2], cl))                            d[1], d[2], cl))
1043                  if(d[1] < 50) {
1044                      cat("\n")
1045                prDiag(object)                prDiag(object)
1046                  } else {
1047                      cat(", with diagonal entries\n")
1048                      show(diag(object))
1049                      invisible(object)
1050                  }
1051            })            })

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