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

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1 : maechler 1617 #### All methods for "diagonalMatrix" and its subclasses,
2 :     #### currently "ddiMatrix", "ldiMatrix"
3 :    
4 : maechler 1109 ## Purpose: Constructor of diagonal matrices -- ~= diag() ,
5 :     ## but *not* diag() extractor!
6 :     Diagonal <- function(n, x = NULL)
7 :     {
8 : mmaechler 2820 ## Allow Diagonal(4), Diagonal(x=1:5), and Diagonal(4, TRUE)
9 : mmaechler 2863 n <- if(missing(n)) length(x) else {
10 : maechler 1575 stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
11 : mmaechler 2863 as.integer(n)
12 : maechler 1109 }
13 :    
14 : maechler 1654 if(missing(x)) ## unit diagonal matrix
15 : maechler 1575 new("ddiMatrix", Dim = c(n,n), diag = "U")
16 : maechler 1109 else {
17 : maechler 2128 lx <- length(x)
18 : mmaechler 2820 lx.1 <- lx == 1L
19 :     stopifnot(lx.1 || lx == n) # but keep 'x' short for now
20 : maechler 1575 if(is.logical(x))
21 :     cl <- "ldiMatrix"
22 :     else if(is.numeric(x)) {
23 :     cl <- "ddiMatrix"
24 :     x <- as.numeric(x)
25 :     }
26 :     else if(is.complex(x)) {
27 :     cl <- "zdiMatrix" # will not yet work
28 :     } else stop("'x' has invalid data type")
29 : mmaechler 2820 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 : maechler 1109 }
35 :     }
36 :    
37 : mmaechler 2840 .sparseDiagonal <- function(n, x = 1, uplo = "U",
38 : mmaechler 2508 shape = if(missing(cols)) "t" else "g",
39 : mmaechler 2840 unitri, kind,
40 :     cols = if(n) 0:(n - 1L) else integer(0))
41 : mmaechler 2508 {
42 : mmaechler 3264 n <- if (missing(n)) length(x) else {
43 :     stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
44 :     as.integer(n)
45 :     }
46 : mmaechler 2840 if(!(mcols <- missing(cols)))
47 : mmaechler 2508 stopifnot(0 <= (cols <- as.integer(cols)), cols < n)
48 :     m <- length(cols)
49 :     if(missing(kind))
50 :     kind <-
51 :     if(is.double(x)) "d"
52 :     else if(is.logical(x)) "l"
53 :     else { ## for now
54 :     storage.mode(x) <- "double"
55 :     "d"
56 :     }
57 :     else stopifnot(any(kind == c("d","l","n")))
58 : mmaechler 2226 stopifnot(is.character(shape), nchar(shape) == 1,
59 :     any(shape == c("t","s","g"))) # triangular / symmetric / general
60 : mmaechler 2840 if((missing(unitri) || unitri) && shape == "t" &&
61 :     (mcols || cols == 0:(n-1L)) &&
62 :     ((any(kind == c("l", "n")) && allTrue(x)) ||
63 :     ( kind == "d" && allTrue(x == 1)))) { ## uni-triangular
64 :     new(paste0(kind,"tCMatrix"), Dim = c(n,n),
65 :     uplo = uplo, diag = "U", p = rep.int(0L, n+1L))
66 :     }
67 :     else if(kind == "n") {
68 : mmaechler 2508 if(shape == "g")
69 :     new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m)
70 :     else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
71 :     i = cols, p = 0:m)
72 :     }
73 : mmaechler 2840 else { ## kind != "n" -- have x slot :
74 :     if((lx <- length(x)) == 1) x <- rep.int(x, m)
75 :     else if(lx != m) stop("length(x) must be either 1 or #{cols}")
76 :     if(shape == "g")
77 :     new(paste0(kind, "gCMatrix"), Dim = c(n,m),
78 :     x = x, i = cols, p = 0:m)
79 :     else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
80 :     x = x, i = cols, p = 0:m)
81 :     }
82 : maechler 2144 }
83 :    
84 : mmaechler 2226 ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
85 : mmaechler 3264 .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U", kind)
86 : mmaechler 3222 .sparseDiagonal(n, x, uplo, shape = "s", kind = kind)
87 : mmaechler 2226
88 : mmaechler 3222 ## NOTA BENE: .triDiagonal() would be misleading (<=> banded tri-diagonal matrix !)
89 : mmaechler 2608 # instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
90 : mmaechler 3264 .trDiagonal <- function(n, x = 1, uplo = "U", unitri = TRUE, kind)
91 : mmaechler 3222 .sparseDiagonal(n, x, uplo, shape = "t", unitri=unitri, kind=kind)
92 : mmaechler 2226
93 :    
94 : mmaechler 2764 ## This is modified from a post of Bert Gunter to R-help on 1 Sep 2005.
95 :     ## Bert's code built on a post by Andy Liaw who most probably was influenced
96 :     ## by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
97 :     ## who posted his bdiag() function written in December 1995.
98 : mmaechler 2209 if(FALSE)##--- no longer used:
99 : mmaechler 2206 .bdiag <- function(lst) {
100 : mmaechler 2764 ## block-diagonal matrix [a dgTMatrix] from list of matrices
101 : mmaechler 2206 stopifnot(is.list(lst), length(lst) >= 1)
102 : mmaechler 2813 dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE)
103 : maechler 1617 ## make sure we had all matrices:
104 :     if(!(is.matrix(dims) && nrow(dims) == 2))
105 :     stop("some arguments are not matrices")
106 : maechler 1845 csdim <- rbind(rep.int(0L, 2),
107 : mmaechler 2206 apply(dims, 1, cumsum))
108 :     r <- new("dgTMatrix")
109 :     r@Dim <- as.integer(csdim[nrow(csdim),])
110 : maechler 1617 add1 <- matrix(1:0, 2,2)
111 : mmaechler 2206 for(i in seq_along(lst)) {
112 : maechler 1617 indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
113 :     if(is.null(dim(indx))) ## non-square matrix
114 : mmaechler 2206 r[indx[[1]],indx[[2]]] <- lst[[i]]
115 : maechler 1617 else ## square matrix
116 : mmaechler 2206 r[indx[,1], indx[,2]] <- lst[[i]]
117 : maechler 1617 }
118 : mmaechler 2206 r
119 : maechler 1617 }
120 : mmaechler 2209 ## expand(<mer>) needed something like bdiag() for lower-triangular
121 :     ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
122 :     ## implementation for those; now extended and generalized:
123 : mmaechler 2206 .bdiag <- function(lst) {
124 : mmaechler 2209 ## block-diagonal matrix [a dgTMatrix] from list of matrices
125 : mmaechler 2206 stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
126 : maechler 1617
127 : mmaechler 3192 ### FIXME: next line is *slow* when lst = list of 75'000 dense 3x3 matrices
128 : mmaechler 2891 Tlst <- lapply(lapply(lst, as_Csp2), # includes "diagU2N"
129 : mmaechler 2209 as, "TsparseMatrix")
130 : mmaechler 2206 if(nl == 1) return(Tlst[[1]])
131 :     ## else
132 : mmaechler 2813 i_off <- c(0L, cumsum(vapply(Tlst, nrow, 1L)))
133 :     j_off <- c(0L, cumsum(vapply(Tlst, ncol, 1L)))
134 : mmaechler 2209
135 : mmaechler 2813 clss <- vapply(Tlst, class, "")
136 : mmaechler 3158 ## NB ("FIXME"): this requires the component classes to be *called*
137 :     ## -- "dgTMatrix" | "dnTMatrix" etc (and not just *extend* those)!
138 : mmaechler 2741 typ <- substr(clss, 2, 2)
139 :     knd <- substr(clss, 1, 1)
140 :     sym <- typ == "s" # symmetric ones
141 :     tri <- typ == "t" # triangular ones
142 :     use.n <- any(is.n <- knd == "n")
143 :     if(use.n && !(use.n <- all(is.n))) {
144 : mmaechler 2209 Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
145 : mmaechler 2741 knd [is.n] <- "l"
146 :     }
147 :     use.l <- !use.n && all(knd == "l")
148 : mmaechler 2209 if(all(sym)) { ## result should be *symmetric*
149 : mmaechler 2813 uplos <- vapply(Tlst, slot, ".", "uplo") ## either "U" or "L"
150 : mmaechler 2209 tLU <- table(uplos)# of length 1 or 2 ..
151 :     if(length(tLU) == 1) { ## all "U" or all "L"
152 :     useU <- uplos[1] == "U"
153 :     } else { ## length(tLU) == 2, counting "L" and "U"
154 :     useU <- diff(tLU) >= 0
155 :     if(useU && (hasL <- tLU[1] > 0))
156 :     Tlst[hasL] <- lapply(Tlst[hasL], t)
157 :     else if(!useU && (hasU <- tLU[2] > 0))
158 :     Tlst[hasU] <- lapply(Tlst[hasU], t)
159 :     }
160 :     if(use.n) { ## return nsparseMatrix :
161 :     r <- new("nsTMatrix")
162 :     } else {
163 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "sTMatrix"))
164 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
165 :     }
166 :     r@uplo <- if(useU) "U" else "L"
167 :     }
168 : mmaechler 2813 else if(all(tri) && { ULs <- vapply(Tlst, slot, ".", "uplo")## "U" or "L"
169 : mmaechler 2209 all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
170 :     ){ ## *triangular* result
171 :    
172 :     if(use.n) { ## return nsparseMatrix :
173 :     r <- new("ntTMatrix")
174 :     } else {
175 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "tTMatrix"))
176 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
177 :     }
178 :     r@uplo <- ULs[1L]
179 :     }
180 :     else {
181 :     if(any(sym))
182 :     Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
183 :     if(use.n) { ## return nsparseMatrix :
184 :     r <- new("ngTMatrix")
185 :     } else {
186 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "gTMatrix"))
187 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
188 :     }
189 :     }
190 :     r@Dim <- c(i_off[nl+1], j_off[nl + 1])
191 :     r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
192 :     r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
193 :     r
194 : mmaechler 2206 }
195 :    
196 :     bdiag <- function(...) {
197 :     if((nA <- nargs()) == 0) return(new("dgCMatrix"))
198 :     if(nA == 1 && !is.list(...))
199 :     return(as(..., "CsparseMatrix"))
200 :     alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
201 :     if(length(alis) == 1)
202 :     return(as(alis[[1]], "CsparseMatrix"))
203 :    
204 :     ## else : two or more arguments
205 :     as(.bdiag(alis), "CsparseMatrix")
206 :     }
207 :    
208 : mmaechler 3023 setMethod("tril", "diagonalMatrix", function(x, k = 0, ...)
209 :     if(k >= 0) x else .setZero(x, paste0(.M.kind(x), "tCMatrix")))
210 : mmaechler 2206
211 : mmaechler 3023 setMethod("triu", "diagonalMatrix", function(x, k = 0, ...)
212 :     if(k <= 0) x else .setZero(x, paste0(.M.kind(x), "tCMatrix")))
213 :    
214 :    
215 :    
216 : maechler 2136 .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
217 :     ## to triangular Tsparse
218 : maechler 1845 i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
219 : mmaechler 2778 new(paste0(kind, "tTMatrix"),
220 : maechler 1654 diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
221 : maechler 2128 uplo = uplo,
222 : maechler 1654 x = from@x, # <- ok for diag = "U" and "N" (!)
223 :     i = i, j = i)
224 :     }
225 : maechler 1109
226 : maechler 2136 .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
227 :     ## to symmetric Tsparse
228 : maechler 2128 n <- from@Dim[1]
229 :     i <- seq_len(n) - 1L
230 : mmaechler 2778 new(paste0(kind, "sTMatrix"),
231 : maechler 1845 Dim = from@Dim, Dimnames = from@Dimnames,
232 : maechler 2128 i = i, j = i, uplo = uplo,
233 :     x = if(from@diag == "N") from@x else ## "U"-diag
234 :     rep.int(switch(kind,
235 :     "d" = 1.,
236 :     "l" =,
237 :     "n" = TRUE,
238 :     ## otherwise
239 : mmaechler 2863 stop(gettextf("%s kind not yet implemented",
240 :     sQuote(kind)), domain=NA)),
241 :     n))
242 : maechler 1845 }
243 :    
244 : mmaechler 2998 ## diagonal -> triangular, upper / lower depending on "partner" 'x':
245 : maechler 2144 diag2tT.u <- function(d, x, kind = .M.kind(d))
246 :     .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
247 : maechler 2128
248 : mmaechler 2175 ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
249 :     diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
250 :     clx <- getClassDef(class(x))
251 :     if(extends(clx, "symmetricMatrix"))
252 :     .diag2sT(d, uplo = x@uplo, kind)
253 :     else
254 :     .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
255 :     }
256 : maechler 2136
257 : mmaechler 2814 ## FIXME: should not be needed {when ddi* is dsparse* etc}:
258 :     setMethod("is.finite", signature(x = "diagonalMatrix"),
259 :     function(x) is.finite(.diag2tT(x)))
260 :     setMethod("is.infinite", signature(x = "diagonalMatrix"),
261 :     function(x) is.infinite(.diag2tT(x)))
262 : mmaechler 2175
263 : maechler 2136 ## In order to evade method dispatch ambiguity warnings,
264 :     ## and because we can save a .M.kind() call, we use this explicit
265 :     ## "hack" instead of signature x = "diagonalMatrix" :
266 :     ##
267 :     ## ddi*:
268 : mmaechler 2922 di2tT <- function(from) .diag2tT(from, "U", "d")
269 :     setAs("ddiMatrix", "triangularMatrix", di2tT)
270 :     ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", di2tT)
271 : maechler 1805 ## needed too (otherwise <dense> -> Tsparse is taken):
272 : mmaechler 2922 setAs("ddiMatrix", "TsparseMatrix", di2tT)
273 :     setAs("ddiMatrix", "dsparseMatrix", di2tT)
274 : maechler 2136 setAs("ddiMatrix", "CsparseMatrix",
275 :     function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
276 : mmaechler 2998 setAs("ddiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "d"))
277 : maechler 2136 ##
278 :     ## ldi*:
279 : mmaechler 2922 di2tT <- function(from) .diag2tT(from, "U", "l")
280 :     setAs("ldiMatrix", "triangularMatrix", di2tT)
281 :     ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", di2tT)
282 : maechler 2136 ## needed too (otherwise <dense> -> Tsparse is taken):
283 : mmaechler 2922 setAs("ldiMatrix", "TsparseMatrix", di2tT)
284 :     setAs("ldiMatrix", "lsparseMatrix", di2tT)
285 : maechler 2136 setAs("ldiMatrix", "CsparseMatrix",
286 :     function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
287 : mmaechler 2998 setAs("ldiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "l"))
288 : mmaechler 2922 rm(di2tT)
289 : maechler 1654
290 : maechler 2128 setAs("diagonalMatrix", "nMatrix",
291 : mmaechler 3092 di2nMat <- function(from) {
292 : maechler 2128 i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
293 :     new("ntTMatrix", i = i, j = i, diag = from@diag,
294 :     Dim = from@Dim, Dimnames = from@Dimnames)
295 :     })
296 :    
297 : mmaechler 2237 setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
298 : maechler 2128
299 : mmaechler 2998 ##' A version of diag(x,n) which *does* preserve the mode of x, where diag() "fails"
300 : mmaechler 2175 mkDiag <- function(x, n) {
301 :     y <- matrix(as0(mod=mode(x)), n,n)
302 : mmaechler 2820 if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x
303 : mmaechler 2175 y
304 :     }
305 : mmaechler 2998 ## NB: diag(x,n) is really faster for n >= 20, and even more for large n
306 :     ## --> using diag() where possible, ==> .ddi2mat()
307 : mmaechler 2175
308 : mmaechler 2998 .diag2mat <- function(from)
309 :     ## want "ldiMatrix" -> <logical> "matrix" (but integer -> <double> for now)
310 :     mkDiag(if(from@diag == "U") as1(from@x) else from@x, n = from@Dim[1])
311 : maechler 1109
312 : mmaechler 2998 .ddi2mat <- function(from)
313 :     base::diag(if(from@diag == "U") as1(from@x) else from@x, nrow = from@Dim[1])
314 :    
315 :     setAs("ddiMatrix", "matrix", .ddi2mat)
316 :     ## the non-ddi diagonalMatrix -- only "ldiMatrix" currently:
317 :     setAs("diagonalMatrix", "matrix", .diag2mat)
318 :    
319 : mmaechler 3154 setMethod("as.vector", "diagonalMatrix",
320 : maechler 2098 function(x, mode) {
321 :     n <- x@Dim[1]
322 : mmaechler 2175 mod.x <- mode(x@x)
323 :     r <- vector(mod.x, length = n^2)
324 : maechler 2098 if(n)
325 : mmaechler 2820 r[1 + 0:(n - 1L) * (n + 1)] <-
326 : mmaechler 2175 if(x@diag == "U") as1(mod=mod.x) else x@x
327 : mmaechler 3154 as.vector(r, mode)
328 : maechler 2098 })
329 :    
330 : maechler 1654 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
331 : maechler 2128 function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
332 : maechler 1174
333 : mmaechler 2268 setAs("diagonalMatrix", "denseMatrix",
334 :     function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
335 :    
336 : mmaechler 2877 ..diag.x <- function(m) rep.int(as1(m@x), m@Dim[1])
337 :     .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
338 : maechler 1655
339 :     .diag.2N <- function(m) {
340 :     if(m@diag == "U") m@diag <- "N"
341 :     m
342 :     }
343 :    
344 : mmaechler 3092 setAs("ddiMatrix", "dgeMatrix", ..2dge)
345 :    
346 :     setAs("ddiMatrix", "ddenseMatrix", #-> "dtr"
347 : mmaechler 2183 function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
348 : mmaechler 3092 setAs("ldiMatrix", "ldenseMatrix", #-> "ltr"
349 : mmaechler 2183 function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
350 : maechler 1174
351 : mmaechler 2183
352 : maechler 1109 setAs("matrix", "diagonalMatrix",
353 :     function(from) {
354 : maechler 1295 d <- dim(from)
355 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
356 :     if(any(from[row(from) != col(from)] != 0))
357 : mmaechler 2863 stop("matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"")
358 : mmaechler 3204 x <- diag(from); names(x) <- NULL # don't want them in 'x' slot
359 : maechler 1295 if(is.logical(x)) {
360 :     cl <- "ldiMatrix"
361 : mmaechler 2341 uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
362 : maechler 1295 } else {
363 :     cl <- "ddiMatrix"
364 : mmaechler 2341 uni <- allTrue(x == 1)
365 : maechler 1295 storage.mode(x) <- "double"
366 : maechler 1575 } ## TODO: complex
367 : maechler 1295 new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
368 : mmaechler 3120 x = if(uni) x[FALSE] else x, Dimnames = .M.DN(from))
369 : maechler 1109 })
370 :    
371 :     ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag()
372 :     setAs("Matrix", "diagonalMatrix",
373 :     function(from) {
374 : mmaechler 2341 d <- dim(from)
375 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
376 : mmaechler 2341 if(!isDiagonal(from)) stop("matrix is not diagonal")
377 :     ## else:
378 : mmaechler 3204 x <- diag(from); names(x) <- NULL # don't want them in 'x' slot
379 : mmaechler 2341 if(is.logical(x)) {
380 :     cl <- "ldiMatrix"
381 :     uni <- allTrue(x)
382 :     } else {
383 :     cl <- "ddiMatrix"
384 :     uni <- allTrue(x == 1)
385 :     storage.mode(x) <- "double"
386 :     } ## TODO: complex
387 :     new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
388 : mmaechler 3120 x = if(uni) x[FALSE] else x, Dimnames = from@Dimnames)
389 : maechler 1109 })
390 :    
391 : maechler 1708
392 : mmaechler 2185 setMethod("diag", signature(x = "diagonalMatrix"),
393 :     function(x = 1, nrow, ncol) .diag.x(x))
394 : maechler 1708
395 : maechler 2098 subDiag <- function(x, i, j, ..., drop) {
396 : mmaechler 2508 x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
397 : maechler 1799 x <- if(missing(i))
398 :     x[, j, drop=drop]
399 :     else if(missing(j))
400 : mmaechler 2363 if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
401 : maechler 1799 else
402 :     x[i,j, drop=drop]
403 : maechler 2120 if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
404 : maechler 1799 }
405 :    
406 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
407 :     j = "index", drop = "logical"), subDiag)
408 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
409 : mmaechler 2363 j = "missing", drop = "logical"),
410 :     function(x, i, j, ..., drop) {
411 :     na <- nargs()
412 :     Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
413 :     if(na == 4)
414 :     subDiag(x, i=i, , drop=drop)
415 :     else subDiag(x, i=i, drop=drop)
416 :     })
417 : maechler 1799 setMethod("[", signature(x = "diagonalMatrix", i = "missing",
418 :     j = "index", drop = "logical"),
419 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
420 : maechler 1799
421 : maechler 1617 ## When you assign to a diagonalMatrix, the result should be
422 : maechler 1708 ## diagonal or sparse ---
423 :     ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
424 : maechler 2098 ## Only(?) current bug: x[i] <- value is wrong when i is *vector*
425 :     replDiag <- function(x, i, j, ..., value) {
426 : mmaechler 3303 ## FIXME: if (i == j) && isSymmetric(value) then -- want symmetricMatrix result! -- or diagMatrix
427 : mmaechler 2811 x <- as(x, "CsparseMatrix")# was "Tsparse.." till 2012-07
428 : maechler 1710 if(missing(i))
429 :     x[, j] <- value
430 : maechler 2098 else if(missing(j)) { ## x[i , ] <- v *OR* x[i] <- v
431 :     na <- nargs()
432 :     ## message("diagnosing replDiag() -- nargs()= ", na)
433 :     if(na == 4)
434 :     x[i, ] <- value
435 :     else if(na == 3)
436 :     x[i] <- value
437 : mmaechler 2863 else stop(gettextf("Internal bug: nargs()=%d; please report",
438 :     na), domain=NA)
439 : maechler 2098 } else
440 : maechler 1710 x[i,j] <- value
441 : mmaechler 3303 if(isDiagonal(x)) as(x, "diagonalMatrix") else
442 :     if(isTriangular(x)) as(x, "triangularMatrix") else
443 :     if(isSymmetric(x)) as(x, "symmetricMatrix") else x
444 : maechler 1710 }
445 : maechler 1617
446 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
447 :     j = "index", value = "replValue"), replDiag)
448 : maechler 2098
449 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
450 :     j = "missing", value = "replValue"),
451 : maechler 2098 function(x,i,j, ..., value) {
452 :     ## message("before replDiag() -- nargs()= ", nargs())
453 :     if(nargs() == 3)
454 :     replDiag(x, i=i, value=value)
455 :     else ## nargs() == 4 :
456 :     replDiag(x, i=i, , value=value)
457 :     })
458 :    
459 : mmaechler 2877 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
460 :     j = "index", value = "replValue"),
461 :     function(x,i,j, ..., value) replDiag(x, j=j, value=value))
462 :    
463 :     ## x[] <- value :
464 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
465 :     j = "missing", value = "ANY"),
466 :     function(x,i,j, ..., value)
467 :     {
468 :     if(all0(value)) { # be faster
469 :     r <- new(paste0(.M.kindC(getClassDef(class(x))),"tTMatrix"))# of all "0"
470 :     r@Dim <- x@Dim
471 :     r@Dimnames <- x@Dimnames
472 :     r
473 :     } else { ## typically non-sense: assigning to full sparseMatrix
474 :     x[TRUE] <- value
475 :     x
476 :     }
477 :     })
478 :    
479 :    
480 : mmaechler 2192 setReplaceMethod("[", signature(x = "diagonalMatrix",
481 :     i = "matrix", # 2-col.matrix
482 : maechler 2096 j = "missing", value = "replValue"),
483 : maechler 2098 function(x,i,j, ..., value) {
484 : maechler 2096 if(ncol(i) == 2) {
485 :     if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
486 : mmaechler 2192 if(x@diag == "U") {
487 :     one <- as1(x@x)
488 :     if(any(value != one | is.na(value))) {
489 :     x@diag <- "N"
490 :     x@x <- rep.int(one, x@Dim[1])
491 : mmaechler 2811 } else return(x)
492 : mmaechler 2192 }
493 : maechler 2096 x@x[ii] <- value
494 :     x
495 :     } else { ## no longer diagonal, but remain sparse:
496 : mmaechler 3303 x <- as(x, "triangularMatrix") # was "TsparseMatrix"
497 : maechler 2096 x[i] <- value
498 :     x
499 :     }
500 :     }
501 :     else { # behave as "base R": use as if vector
502 :     x <- as(x, "matrix")
503 :     x[i] <- value
504 :     Matrix(x)
505 :     }
506 :     })
507 :    
508 : maechler 1710
509 : mmaechler 2877 ## value = "sparseMatrix":
510 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
511 : mmaechler 2239 value = "sparseMatrix"),
512 : mmaechler 2207 function (x, i, j, ..., value)
513 :     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
514 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
515 : mmaechler 2239 value = "sparseMatrix"),
516 : mmaechler 2207 function (x, i, j, ..., value)
517 :     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
518 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
519 : mmaechler 2239 value = "sparseMatrix"),
520 : mmaechler 2207 function (x, i, j, ..., value)
521 :     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
522 : maechler 1710
523 : mmaechler 2877 ## value = "sparseVector":
524 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
525 :     value = "sparseVector"),
526 :     replDiag)
527 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
528 :     value = "sparseVector"),
529 :     replDiag)
530 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
531 :     value = "sparseVector"),
532 :     replDiag)
533 :    
534 :    
535 : maechler 1109 setMethod("t", signature(x = "diagonalMatrix"),
536 :     function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
537 :    
538 : mmaechler 2904 setMethod("isDiagonal", "diagonalMatrix", function(object) TRUE)
539 : mmaechler 3015 setMethod("isTriangular", "diagonalMatrix", function(object, upper=NA, ...) TRUE)
540 : mmaechler 2904 setMethod("isSymmetric", "diagonalMatrix", function(object, ...) TRUE)
541 : maechler 1109
542 : maechler 2112 setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
543 : mmaechler 3023 setMethod("skewpart", signature(x = "diagonalMatrix"), function(x) .setZero(x))
544 : maechler 2112
545 : maechler 2133 setMethod("chol", signature(x = "ddiMatrix"),
546 :     function(x, pivot, ...) {
547 : mmaechler 2183 if(x@diag == "U") return(x)
548 :     ## else
549 : maechler 2133 if(any(x@x < 0))
550 :     stop("chol() is undefined for diagonal matrix with negative entries")
551 : maechler 1654 x@x <- sqrt(x@x)
552 :     x
553 :     })
554 :     ## chol(L) is L for logical diagonal:
555 : maechler 2133 setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
556 : maechler 1654
557 : mmaechler 2175 setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
558 : mmaechler 2185 function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
559 : mmaechler 2175
560 : mmaechler 2183 setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
561 :     function(x, type, ...) {
562 :     if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
563 :     type <- toupper(substr(type[1], 1, 1))
564 :     isU <- (x@diag == "U") # unit-diagonal
565 :     if(type == "F") sqrt(if(isU) n else sum(x@x^2))
566 : mmaechler 3206 else { ## norm == "I","1","O","M","2" :
567 : mmaechler 2183 if(isU) 1 else max(abs(x@x))
568 :     }
569 :     })
570 :    
571 :    
572 :    
573 : maechler 1109 ## Basic Matrix Multiplication {many more to add}
574 : maechler 1654 ## ---------------------
575 :     ## Note that "ldi" logical are treated as numeric
576 : maechler 1109 diagdiagprod <- function(x, y) {
577 : mmaechler 2633 dimCheck(x,y)
578 : maechler 1109 if(x@diag != "U") {
579 : maechler 1654 if(y@diag != "U") {
580 :     nx <- x@x * y@x
581 :     if(is.numeric(nx) && !is.numeric(x@x))
582 :     x <- as(x, "dMatrix")
583 :     x@x <- as.numeric(nx)
584 :     }
585 : mmaechler 3120 x
586 : maechler 1109 } else ## x is unit diagonal
587 : mmaechler 3120 y
588 : maechler 1109 }
589 :    
590 : mmaechler 3069 ##' Boolean Algebra/Arithmetic Product of Diagonal Matrices
591 :     ##' %&%
592 :     diagdiagprodBool <- function(x, y) {
593 :     dimCheck(x,y)
594 :     if(x@diag != "U") {
595 :     if(!is.logical(x@x)) x <- as(x, "lMatrix")
596 :     if(y@diag != "U") {
597 :     nx <- x@x & y@x
598 :     x@x <- as.logical(nx)
599 :     }
600 :     x
601 :     } else { ## x is unit diagonal: return y
602 :     if(!is.logical(y@x)) y <- as(y, "lMatrix")
603 :     y
604 :     }
605 :     }
606 :    
607 : maechler 1654 setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
608 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
609 :    
610 : mmaechler 3069 setMethod("%&%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
611 :     diagdiagprodBool, valueClass = "ldiMatrix")# do *not* have "ndiMatrix" !
612 :    
613 : mmaechler 3072 ##' Both Numeric or Boolean Algebra/Arithmetic Product of Diagonal Matrices
614 :     diagdiagprodFlexi <- function(x, y=NULL, boolArith = NA, ...)
615 :     {
616 :     dimCheck(x,y)
617 :     bool <- isTRUE(boolArith)
618 :     if(x@diag != "U") {
619 :     if(bool && !is.logical(x@x)) x <- as(x, "lMatrix")
620 :     if(y@diag != "U") {
621 :     if(bool) {
622 :     nx <- x@x & y@x
623 :     x@x <- as.logical(nx)
624 :     } else { ## boolArith is NA or FALSE: ==> numeric, as have *no* "diagMatrix" patter[n]:
625 :     nx <- x@x * y@x
626 :     if(is.numeric(nx) && !is.numeric(x@x))
627 :     x <- as(x, "dMatrix")
628 :     x@x <- as.numeric(nx)
629 :     }
630 :     }
631 :     x
632 :     } else { ## x is unit diagonal: return y
633 :     if(bool && !is.logical(y@x)) y <- as(y, "lMatrix")
634 :     y
635 :     }
636 :     }
637 : maechler 1654 setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
638 : mmaechler 3072 diagdiagprodFlexi)
639 : maechler 1654 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
640 : mmaechler 3072 diagdiagprodFlexi)
641 : mmaechler 3069
642 :     ##' crossprod(x) := x'x
643 : mmaechler 3072 diagprod <- function(x, y = NULL, boolArith = NA, ...) {
644 :     bool <- isTRUE(boolArith)
645 :     if(bool && !is.logical(x@x)) x <- as(x, "lMatrix")
646 : mmaechler 3069 if(x@diag != "U") {
647 : mmaechler 3072 if(bool) {
648 :     nx <- x@x & y@x
649 :     x@x <- as.logical(nx)
650 :     } else { ## boolArith is NA or FALSE: ==> numeric, as have *no* "diagMatrix" patter[n]:
651 :     nx <- x@x * x@x
652 :     if(is.numeric(nx) && !is.numeric(x@x))
653 :     x <- as(x, "dMatrix")
654 :     x@x <- as.numeric(nx)
655 :     }
656 : mmaechler 3069 }
657 :     x
658 :     }
659 : mmaechler 3072 setMethod( "crossprod", signature(x = "diagonalMatrix", y = "missing"), diagprod)
660 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"), diagprod)
661 : maechler 1109
662 :    
663 : mmaechler 2998 ## analogous to matdiagprod() below:
664 : maechler 1109 diagmatprod <- function(x, y) {
665 : mmaechler 2183 ## x is diagonalMatrix
666 : mmaechler 3167 dy <- dim(y)
667 :     if(x@Dim[2L] != dy[1L]) stop("non-matching dimensions")
668 : mmaechler 3174 if(prod(dy))
669 :     Matrix(if(x@diag == "U") y else x@x * y)
670 :     else
671 :     Matrix(if(x@diag == "U") y else x@x * y, nrow=dy[1L], ncol=dy[2L])
672 : maechler 1109 }
673 : mmaechler 3072 setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"), diagmatprod)
674 : mmaechler 3069
675 : mmaechler 3120 ##formals(diagmatprod) <- alist(x=, y=NULL, boolArith = NA, ...=) ## FIXME boolArith
676 : mmaechler 3079 diagmatprod2 <- function(x, y=NULL, boolArith = NA, ...) {
677 :     ## x is diagonalMatrix
678 : mmaechler 3167 dy <- dim(y)
679 :     if(x@Dim[2L] != dy[1L]) stop("non-matching dimensions")
680 : mmaechler 3174 if(prod(dy))
681 :     Matrix(if(x@diag == "U") y else x@x * y)
682 :     else
683 :     Matrix(if(x@diag == "U") y else x@x * y, nrow=dy[1L], ncol=dy[2L])
684 : mmaechler 3079 }
685 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"), diagmatprod2)
686 : maechler 1109
687 : mmaechler 2183 diagGeprod <- function(x, y) {
688 : mmaechler 3167 if(x@Dim[2L] != y@Dim[1L]) stop("non-matching dimensions")
689 :     if(x@diag != "U") {
690 :     if(!is.numeric(y@x)) y <- as(y, "dMatrix")
691 : maechler 1109 y@x <- x@x * y@x
692 : mmaechler 3167 }
693 : maechler 1109 y
694 :     }
695 : mmaechler 2183 setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
696 :     setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
697 : maechler 1109
698 : mmaechler 3069 diagGeprodBool <- function(x, y) {
699 : mmaechler 3167 if(x@Dim[2L] != y@Dim[1L]) stop("non-matching dimensions")
700 : mmaechler 3069 if(!is.logical(y@x)) y <- as(y, "lMatrix")
701 :     if(x@diag != "U")
702 :     y@x <- x@x & y@x
703 :     y
704 :     }
705 :     setMethod("%&%", signature(x= "diagonalMatrix", y= "geMatrix"), diagGeprodBool)
706 :    
707 : mmaechler 3072 diagGeprod2 <- function(x, y=NULL, boolArith = NA, ...) {
708 : mmaechler 3167 if(x@Dim[2L] != y@Dim[1L]) stop("non-matching dimensions")
709 : mmaechler 3072 bool <- isTRUE(boolArith)
710 :     if(bool && !is.logical(y@x)) y <- as(y, "lMatrix")
711 : mmaechler 3167 else if(!bool && !is.numeric(y@x)) y <- as(y, "dMatrix")
712 : mmaechler 3072 if(x@diag != "U")
713 :     y@x <- if(bool) x@x & y@x else x@x * y@x
714 :     y
715 :     }
716 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"), diagGeprod2)
717 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"), diagGeprod2)
718 : mmaechler 3069
719 : mmaechler 3072
720 : mmaechler 2998 ## analogous to diagmatprod() above:
721 : mmaechler 2183 matdiagprod <- function(x, y) {
722 :     dx <- dim(x)
723 : mmaechler 3167 if(dx[2L] != y@Dim[1L]) stop("non-matching dimensions")
724 :     Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1L]))
725 : mmaechler 2183 }
726 : mmaechler 2998 setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"), matdiagprod)
727 : maechler 1109
728 : mmaechler 2183 gediagprod <- function(x, y) {
729 :     dx <- dim(x)
730 : mmaechler 3167 if(dx[2L] != y@Dim[1L]) stop("non-matching dimensions")
731 :     if(y@diag == "N") {
732 :     if(!is.numeric(x@x)) x <- as(x, "dMatrix")
733 :     x@x <- x@x * rep(y@x, each = dx[1L])
734 :     }
735 : mmaechler 2183 x
736 :     }
737 :     setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
738 :     setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
739 : maechler 1109
740 : mmaechler 3069 gediagprodBool <- function(x, y) {
741 :     dx <- dim(x)
742 : mmaechler 3167 if(dx[2L] != y@Dim[1L]) stop("non-matching dimensions")
743 : mmaechler 3069 if(!is.logical(x@x)) x <- as(x, "lMatrix")
744 :     if(y@diag == "N")
745 : mmaechler 3167 x@x <- x@x & rep(y@x, each = dx[1L])
746 : mmaechler 3069 x
747 :     }
748 :     setMethod("%&%", signature(x= "geMatrix", y= "diagonalMatrix"), gediagprodBool)
749 :    
750 : mmaechler 3072 setMethod("tcrossprod",signature(x = "matrix", y = "diagonalMatrix"),
751 :     function(x, y=NULL, boolArith = NA, ...) {
752 :     dx <- dim(x)
753 : mmaechler 3167 if(dx[2L] != y@Dim[1L]) stop("non-matching dimensions")
754 : mmaechler 3072 bool <- isTRUE(boolArith)
755 :     if(bool && !is.logical(y@x)) y <- as(y, "lMatrix")
756 :     Matrix(if(y@diag == "U") x else
757 : mmaechler 3167 if(bool) x & rep(y@x, each = dx[1L])
758 :     else x * rep(y@x, each = dx[1L]))
759 : mmaechler 3072 })
760 :    
761 :     setMethod("crossprod", signature(x = "matrix", y = "diagonalMatrix"),
762 :     function(x, y=NULL, boolArith = NA, ...) {
763 :     dx <- dim(x)
764 : mmaechler 3167 if(dx[1L] != y@Dim[1L]) stop("non-matching dimensions")
765 : mmaechler 3072 bool <- isTRUE(boolArith)
766 :     if(bool && !is.logical(y@x)) y <- as(y, "lMatrix")
767 : mmaechler 3120 Matrix(if(y@diag == "U") t(x) else
768 : mmaechler 3167 if(bool) t(rep.int(y@x, dx[2L]) & x)
769 :     else t(rep.int(y@x, dx[2L]) * x))
770 : mmaechler 3072 })
771 :    
772 :    
773 :     gediagprod2 <- function(x, y=NULL, boolArith = NA, ...) {
774 :     dx <- dim(x)
775 : mmaechler 3167 if(dx[2L] != y@Dim[1L]) stop("non-matching dimensions")
776 : mmaechler 3072 bool <- isTRUE(boolArith)
777 :     if(bool && !is.logical(x@x)) x <- as(x, "lMatrix")
778 : mmaechler 3167 else if(!bool && !is.numeric(x@x)) x <- as(x, "dMatrix")
779 : mmaechler 3072 if(y@diag == "N")
780 : mmaechler 3167 x@x <- if(bool) x@x & rep(y@x, each = dx[1L])
781 :     else x@x * rep(y@x, each = dx[1L])
782 : mmaechler 3072 x
783 :     }
784 :     setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"), gediagprod2)
785 :     setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"), gediagprod2)
786 :    
787 :    
788 : maechler 1295 ## crossprod {more of these}
789 : maechler 1109
790 : maechler 1295 ## tcrossprod --- all are not yet there: do the dense ones here:
791 : maechler 1109
792 : mmaechler 2183 setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
793 :     function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
794 :     setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
795 :     function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
796 :    
797 :    
798 : maechler 1295 ## FIXME:
799 :     ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
800 :     ## function(x, y = NULL) {
801 :     ## })
802 : maechler 1109
803 : mmaechler 2912 ##' @param x CsparseMatrix
804 :     ##' @param y diagonalMatrix
805 :     ##' @return x %*% y
806 : mmaechler 3072 Cspdiagprod <- function(x, y, boolArith = NA, ...) {
807 : mmaechler 3167 if((m <- ncol(x)) != y@Dim[1L]) stop("non-matching dimensions")
808 : mmaechler 2912 if(y@diag == "N") { ## otherwise: y == Diagonal(n) : multiplication is identity
809 : mmaechler 3069 x <- .Call(Csparse_diagU2N, x)
810 :     cx <- getClass(class(x))
811 :     if(!all(y@x[1L] == y@x[-1L]) && extends(cx, "symmetricMatrix"))
812 : mmaechler 2674 x <- as(x, "generalMatrix")
813 : mmaechler 2998 ind <- rep.int(seq_len(m), x@p[-1] - x@p[-m-1L])
814 : mmaechler 3069 if(isTRUE(boolArith)) {
815 :     if(extends(cx, "nMatrix")) x <- as(x, "lMatrix") # so, has y@x
816 : mmaechler 3079 x@x <- r <- x@x & y@x[x@i + 1L]
817 :     if(!anyNA(r) && !extends(cx, "diagonalMatrix")) x <- as(drop0(x), "nMatrix")
818 : mmaechler 3069 } else {
819 :     if(!extends(cx, "dMatrix")) x <- as(x, "dMatrix") # <- FIXME if we have zMatrix
820 :     x@x <- x@x * y@x[ind]
821 :     }
822 : mmaechler 2978 if(.hasSlot(x, "factors") && length(x@factors)) {# drop cashed ones
823 : mmaechler 2912 ## instead of dropping all factors, be smart about some
824 :     ## TODO ......
825 :     x@factors <- list()
826 :     }
827 : mmaechler 3079 x
828 :     } else { # y is unit-diagonal ==> "return x"
829 :     cx <- getClass(class(x))
830 :     if(isTRUE(boolArith)) {
831 :     is.l <- if(extends(cx, "dMatrix")) { ## <- FIXME: extend once we have iMatrix, zMatrix
832 :     x <- as(x, "lMatrix"); TRUE } else extends(cx, "lMatrix")
833 :     if(is.l && !anyNA(x@x)) as(drop0(x), "nMatrix")
834 :     else if(is.l) x else # defensive:
835 :     as(x, "lMatrix")
836 :     } else {
837 :     ## else boolArith is NA or FALSE {which are equivalent here, das diagonal = "numLike"}
838 :     if(extends(cx, "nMatrix") || extends(cx, "lMatrix"))
839 :     as(x, "dMatrix") else x
840 :     }
841 : mmaechler 2674 }
842 : dmbates 2417 }
843 : maechler 1109
844 : mmaechler 2912 ##' @param x diagonalMatrix
845 :     ##' @param y CsparseMatrix
846 :     ##' @return x %*% y
847 : mmaechler 3072 diagCspprod <- function(x, y, boolArith = NA, ...) {
848 : mmaechler 3167 if(x@Dim[2L] != y@Dim[1L]) stop("non-matching dimensions")
849 : mmaechler 2984 if(x@diag == "N") {
850 : mmaechler 3069 y <- .Call(Csparse_diagU2N, y)
851 :     cy <- getClass(class(y))
852 :     if(!all(x@x[1L] == x@x[-1L]) && extends(cy, "symmetricMatrix"))
853 : mmaechler 2674 y <- as(y, "generalMatrix")
854 : mmaechler 3069 if(isTRUE(boolArith)) {
855 :     if(extends(cy, "nMatrix")) y <- as(y, "lMatrix") # so, has y@x
856 : mmaechler 3079 y@x <- r <- y@x & x@x[y@i + 1L]
857 :     if(!anyNA(r) && !extends(cy, "diagonalMatrix")) y <- as(drop0(y), "nMatrix")
858 : mmaechler 3069 } else {
859 :     if(!extends(cy, "dMatrix")) y <- as(y, "dMatrix") # <- FIXME if we have zMatrix
860 :     y@x <- y@x * x@x[y@i + 1L]
861 :     }
862 : mmaechler 3046 if(.hasSlot(y, "factors") && length(y@factors)) {
863 :     ## if(.hasSlot(y, "factors") && length(yf <- y@factors)) { ## -- TODO? --
864 :     ## instead of dropping all factors, be smart about some
865 :     ## keep <- character()
866 :     ## if(any(names(yf) == "LU")) { ## <- not easy: y = P'LUQ, x y = xP'LUQ => LU ???
867 :     ## keep <- "LU"
868 :     ## }
869 :     ## y@factors <- yf[keep]
870 :     y@factors <- list()
871 : mmaechler 2912 }
872 : mmaechler 3079 y
873 :     } else { ## x @ diag == "U"
874 :     cy <- getClass(class(y))
875 :     if(isTRUE(boolArith)) {
876 :     is.l <- if(extends(cy, "dMatrix")) { ## <- FIXME: extend once we have iMatrix, zMatrix
877 :     y <- as(y, "lMatrix"); TRUE } else extends(cy, "lMatrix")
878 :     if(is.l && !anyNA(y@x)) as(drop0(y), "nMatrix")
879 :     else if(is.l) y else # defensive:
880 :     as(y, "lMatrix")
881 :     } else {
882 :     ## else boolArith is NA or FALSE {which are equivalent here, das diagonal = "numLike"}
883 :     if(extends(cy, "nMatrix") || extends(cy, "lMatrix"))
884 :     as(y, "dMatrix") else y
885 :     }
886 : mmaechler 2674 }
887 : dmbates 2417 }
888 :    
889 : mmaechler 3069 ## + 'boolArith' argument { ==> .local() is used in any case; keep formals simple :}
890 : dmbates 2417 setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
891 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) diagCspprod(x, y, boolArith=boolArith))
892 : dmbates 2417
893 : maechler 1799 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
894 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...)
895 : mmaechler 3069 diagCspprod(x, as(y, "CsparseMatrix"), boolArith=boolArith))
896 : maechler 1295
897 : dmbates 2417 ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
898 :     ## x'y == (y'x)'
899 :     setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
900 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) t(diagCspprod(y, x, boolArith=boolArith)))
901 : dmbates 2417
902 : maechler 1799 setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
903 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) t(diagCspprod(y, as(x, "Csparsematrix"), boolArith=boolArith)))
904 : maechler 1799
905 : dmbates 2417 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
906 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) diagCspprod(x, t(y), boolArith=boolArith))
907 : dmbates 2417
908 : maechler 1799 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
909 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) diagCspprod(x, t(as(y, "CsparseMatrix")), boolArith=boolArith))
910 : maechler 1799
911 : dmbates 2417 setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
912 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) Cspdiagprod(x, y, boolArith=boolArith))
913 : dmbates 2417
914 : maechler 1799 setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
915 : mmaechler 3072 function(x, y=NULL, boolArith=NA, ...) Cspdiagprod(as(x, "CsparseMatrix"), y, boolArith=boolArith))
916 : mmaechler 2472
917 : dmbates 2417 setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
918 : mmaechler 3069 function(x, y) diagCspprod(x, y, boolArith=NA))
919 :     setMethod("%&%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
920 :     function(x, y) diagCspprod(x, y, boolArith=TRUE))
921 : maechler 1799
922 : mmaechler 2912 ## instead of "sparseMatrix", use: [RT]sparse.. ("closer" in method dispatch)
923 :     for(cl in c("TsparseMatrix", "RsparseMatrix")) {
924 :    
925 : maechler 1799 setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
926 : mmaechler 3069 function(x, y) diagCspprod(as(x, "CsparseMatrix"), y, boolArith=NA))
927 : mmaechler 2472
928 : mmaechler 2183 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
929 : mmaechler 3069 function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y, boolArith=NA))
930 :    
931 :     setMethod("%&%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
932 :     function(x, y) diagCspprod(as(x, "CsparseMatrix"), y, boolArith=TRUE))
933 :    
934 :     setMethod("%&%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
935 :     function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y, boolArith=TRUE))
936 :    
937 : mmaechler 2912 }
938 : dmbates 2417
939 : maechler 1799 setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
940 : mmaechler 3069 function(x, y) Cspdiagprod(x, y, boolArith=NA))
941 :     setMethod("%&%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
942 :     function(x, y) Cspdiagprod(x, y, boolArith=TRUE))
943 : dmbates 2417
944 : maechler 1799 ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
945 :     ## do indeed work by going through sparse (and *not* ddense)!
946 :    
947 :     setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
948 :     function(a, b, ...) {
949 :     a@x <- 1/ a@x
950 :     a@Dimnames <- a@Dimnames[2:1]
951 :     a
952 :     })
953 :    
954 :     solveDiag <- function(a, b, ...) {
955 : mmaechler 3167 if(a@Dim[1L] != nrow(b))
956 : maechler 1799 stop("incompatible matrix dimensions")
957 :     ## trivially invert a 'in place' and multiply:
958 :     a@x <- 1/ a@x
959 :     a@Dimnames <- a@Dimnames[2:1]
960 :     a %*% b
961 :     }
962 :     setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
963 :     solveDiag)
964 :     setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
965 :     solveDiag)
966 :    
967 : maechler 2106 ## Schur() ---> ./eigen.R
968 : maechler 1799
969 :    
970 :    
971 : mmaechler 2175 ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
972 : maechler 1295
973 : maechler 1655 ## Use function for several signatures, in order to evade
974 : mmaechler 2175 diagOdiag <- function(e1,e2) {
975 :     ## result should also be diagonal _ if possible _
976 : maechler 1655 r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
977 : mmaechler 2175 ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
978 :     r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
979 :     if(is.numeric(e2@x)) 0 else FALSE)
980 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal
981 : mmaechler 2814 if(is.numeric(r)) { # "double" *or* "integer"
982 : mmaechler 2175 if(is.numeric(e2@x)) {
983 :     e2@x <- r; return(.diag.2N(e2)) }
984 :     if(!is.numeric(e1@x))
985 :     ## e.g. e1, e2 are logical;
986 :     e1 <- as(e1, "dMatrix")
987 : mmaechler 2814 if(!is.double(r)) r <- as.double(r)
988 : mmaechler 2175 }
989 :     else if(is.logical(r))
990 :     e1 <- as(e1, "lMatrix")
991 : mmaechler 2863 else stop(gettextf("intermediate 'r' is of type %s",
992 :     typeof(r)), domain=NA)
993 : mmaechler 2175 e1@x <- r
994 :     .diag.2N(e1)
995 : maechler 1655 }
996 : mmaechler 2175 else { ## result not diagonal, but at least symmetric:
997 : mmaechler 2496 ## e.g., m == m
998 : mmaechler 2175 isNum <- (is.numeric(r) || is.numeric(r00))
999 :     isLog <- (is.logical(r) || is.logical(r00))
1000 : mmaechler 2496 Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
1001 : mmaechler 2175 d <- e1@Dim
1002 : mmaechler 3167 n <- d[1L]
1003 : mmaechler 2175 stopifnot(length(r) == n)
1004 : mmaechler 2814 if(isNum && !is.double(r)) r <- as.double(r)
1005 : mmaechler 2175 xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
1006 :     newcl <-
1007 : mmaechler 2811 paste0(if(isNum) "d" else if(isLog) {
1008 : mmaechler 3092 if(!anyNA(r) && !anyNA(r00)) "n" else "l"
1009 : mmaechler 2811 } else stop("not yet implemented .. please report"), "syMatrix")
1010 : mmaechler 2175
1011 :     new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
1012 :     }
1013 : maechler 1655 }
1014 :    
1015 : mmaechler 2175 ### This would be *the* way, but we get tons of "ambiguous method dispatch"
1016 : mmaechler 2185 ## we use this hack instead of signature x = "diagonalMatrix" :
1017 :     diCls <- names(getClass("diagonalMatrix")@subclasses)
1018 : mmaechler 2175 if(FALSE) {
1019 : maechler 1655 setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
1020 :     diagOdiag)
1021 : mmaechler 2175 } else { ## These are just for method disambiguation:
1022 :     for(c1 in diCls)
1023 :     for(c2 in diCls)
1024 :     setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
1025 :     }
1026 : maechler 1655
1027 : mmaechler 2493 ## diagonal o triangular |--> triangular
1028 :     ## diagonal o symmetric |--> symmetric
1029 : maechler 1845 ## {also when other is sparse: do these "here" --
1030 :     ## before conversion to sparse, since that loses "diagonality"}
1031 : mmaechler 2811 diagOtri <- function(e1,e2) {
1032 :     ## result must be triangular
1033 :     r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible"
1034 :     ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
1035 : mmaechler 3046 e1.0 <- if(is.numeric(d1)) 0 else FALSE
1036 : mmaechler 3167 r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0L])) 0 else FALSE)
1037 : mmaechler 2811 if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* triangular
1038 :     diag(e2) <- r
1039 :     ## check what happens "in the triangle"
1040 :     e2.2 <- if(.n2) 2 else TRUE
1041 :     if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change:
1042 :     n <- dim(e2)[1L]
1043 :     it <- indTri(n, upper = (e2@uplo == "U"))
1044 :     e2[it] <- callGeneric(e1.0, e2[it])
1045 :     }
1046 :     e2
1047 :     }
1048 :     else { ## result not triangular ---> general
1049 :     rr <- as(e2, "generalMatrix")
1050 :     diag(rr) <- r
1051 :     rr
1052 :     }
1053 :     }
1054 : maechler 1845
1055 : mmaechler 2811
1056 :     setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"),
1057 :     diagOtri)
1058 :     ## For the reverse, Ops == "Arith" | "Compare" | "Logic"
1059 :     ## 'Arith' := '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"'
1060 :     setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
1061 :     function(e1,e2)
1062 :     { ## this must only trigger for *dense* e1
1063 :     switch(.Generic,
1064 :     "+" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), .diag.x(e2)),
1065 :     "-" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), - .diag.x(e2)),
1066 :     "*" = {
1067 :     n <- e2@Dim[1L]
1068 :     d2 <- if(e2@diag == "U") { # unit-diagonal
1069 :     d <- rep.int(as1(e2@x), n)
1070 :     e2@x <- d
1071 :     e2@diag <- "N"
1072 :     d
1073 :     } else e2@x
1074 :     e2@x <- diag(e1) * d2
1075 :     e2
1076 :     },
1077 :     "^" = { ## will be dense ( as <ANY> ^ 0 == 1 ):
1078 :     e1 ^ as(e2, "denseMatrix")
1079 :     },
1080 :     ## otherwise:
1081 :     callGeneric(e1, diag2Tsmart(e2,e1)))
1082 :     })
1083 :    
1084 :     ## Compare --> 'swap' (e.g. e1 < e2 <==> e2 > e1 ):
1085 :     setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
1086 :     .Cmp.swap)
1087 :     ## '&' and "|' are commutative:
1088 :     setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
1089 :     function(e1,e2) callGeneric(e2, e1))
1090 :    
1091 : maechler 1655 ## For almost everything else, diag* shall be treated "as sparse" :
1092 : maechler 1295 ## These are cheap implementations via coercion
1093 :    
1094 : maechler 2144 ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
1095 :     ## and because we can save an .M.kind() call, we use this explicit
1096 :     ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
1097 :     ##
1098 :     ## ddi*:
1099 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
1100 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
1101 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
1102 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
1103 : maechler 2144 ## ldi*
1104 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
1105 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
1106 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
1107 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
1108 : maechler 1654
1109 : mmaechler 2820 ## Ops: Arith --> numeric : "dMatrix"
1110 :     ## Compare --> logical
1111 :     ## Logic --> logical: "lMatrix"
1112 : mmaechler 2175
1113 : mmaechler 2820 ## Other = "numeric" : stay diagonal if possible
1114 : mmaechler 2175 ## ddi*: Arith: result numeric, potentially ddiMatrix
1115 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1116 :     setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2),
1117 : maechler 2144 function(e1,e2) {
1118 : mmaechler 3167 n <- e1@Dim[1L]
1119 : mmaechler 3287 if(length(e2) == 0L)
1120 :     return(if(n) numeric() else e1)
1121 : maechler 2144 f0 <- callGeneric(0, e2)
1122 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1123 : maechler 2157 L1 <- (le <- length(e2)) == 1L
1124 : mmaechler 2820 if(e1@diag == "U") {
1125 :     if(any((r <- callGeneric(1, e2)) != 1)) {
1126 :     e1@diag <- "N"
1127 :     e1@x[seq_len(n)] <- r # possibly recycling r
1128 :     } ## else: result = e1 (is "U" diag)
1129 :     } else {
1130 : maechler 2144 r <- callGeneric(e1@x, e2)
1131 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1132 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1133 :     }
1134 :     e1
1135 :     } else
1136 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
1137 : maechler 2144 })
1138 : maechler 1655
1139 : mmaechler 2813 for(arg1 in c("numeric","logical"))
1140 :     setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"),
1141 : maechler 2144 function(e1,e2) {
1142 : mmaechler 3167 n <- e2@Dim[1L]
1143 : mmaechler 3287 if(length(e1) == 0L)
1144 :     return(if(n) numeric() else e2)
1145 : maechler 2144 f0 <- callGeneric(e1, 0)
1146 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1147 : maechler 2157 L1 <- (le <- length(e1)) == 1L
1148 : mmaechler 2820 if(e2@diag == "U") {
1149 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
1150 :     e2@diag <- "N"
1151 :     e2@x[seq_len(n)] <- r # possibly recycling r
1152 :     } ## else: result = e2 (is "U" diag)
1153 :     } else {
1154 : maechler 2144 r <- callGeneric(e1, e2@x)
1155 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1156 :     e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1157 :     }
1158 :     e2
1159 :     } else
1160 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
1161 : maechler 2144 })
1162 : mmaechler 2175
1163 :     ## ldi* Arith --> result numeric, potentially ddiMatrix
1164 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1165 :     setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2),
1166 : mmaechler 2175 function(e1,e2) {
1167 : mmaechler 3167 n <- e1@Dim[1L]
1168 : mmaechler 3287 if(length(e2) == 0L)
1169 :     return(if(n) numeric()
1170 :     else copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
1171 : mmaechler 2175 f0 <- callGeneric(0, e2)
1172 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1173 : mmaechler 2175 L1 <- (le <- length(e2)) == 1L
1174 : mmaechler 2984 E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
1175 : mmaechler 2820 ## storage.mode(E@x) <- "double"
1176 :     if(e1@diag == "U") {
1177 :     if(any((r <- callGeneric(1, e2)) != 1)) {
1178 :     E@diag <- "N"
1179 :     E@x[seq_len(n)] <- r # possibly recycling r
1180 :     } ## else: result = E (is "U" diag)
1181 :     } else {
1182 : mmaechler 2175 r <- callGeneric(e1@x, e2)
1183 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1184 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1185 : mmaechler 2814 }
1186 : mmaechler 2820 E
1187 :     } else
1188 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
1189 : mmaechler 2175 })
1190 :    
1191 : mmaechler 2813 for(arg1 in c("numeric","logical"))
1192 :     setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"),
1193 : mmaechler 2175 function(e1,e2) {
1194 : mmaechler 3167 n <- e2@Dim[1L]
1195 : mmaechler 3287 if(length(e1) == 0L)
1196 :     return(if(n) numeric()
1197 :     else copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
1198 : mmaechler 2175 f0 <- callGeneric(e1, 0)
1199 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1200 : mmaechler 2175 L1 <- (le <- length(e1)) == 1L
1201 : mmaechler 2984 E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
1202 : mmaechler 2820 ## storage.mode(E@x) <- "double"
1203 :     if(e2@diag == "U") {
1204 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
1205 :     E@diag <- "N"
1206 :     E@x[seq_len(n)] <- r # possibly recycling r
1207 :     } ## else: result = E (is "U" diag)
1208 :     } else {
1209 : mmaechler 2175 r <- callGeneric(e1, e2@x)
1210 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1211 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1212 : mmaechler 2814 }
1213 : mmaechler 2820 E
1214 :     } else
1215 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
1216 : mmaechler 2175 })
1217 :    
1218 : mmaechler 2820 ## ddi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1219 :     ##
1220 :     ## Note that ("numeric", "ddiMatrix") is simply swapped, e.g.,
1221 :     if(FALSE) {
1222 :     selectMethod("<", c("numeric","lMatrix"))# Compare
1223 :     selectMethod("&", c("numeric","lMatrix"))# Logic
1224 :     } ## so we don't need to define a method here :
1225 :    
1226 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1227 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2),
1228 : mmaechler 2175 function(e1,e2) {
1229 : mmaechler 3167 n <- e1@Dim[1L]
1230 : mmaechler 3287 if(length(e2) == 0L)
1231 :     return(if(n) logical()
1232 :     else copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
1233 : mmaechler 2175 f0 <- callGeneric(0, e2)
1234 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1235 : mmaechler 2175 L1 <- (le <- length(e2)) == 1L
1236 : mmaechler 2984 E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
1237 : mmaechler 2820 ## storage.mode(E@x) <- "logical"
1238 :     if(e1@diag == "U") {
1239 :     if(any((r <- callGeneric(1, e2)) != 1)) {
1240 :     E@diag <- "N"
1241 :     E@x[seq_len(n)] <- r # possibly recycling r
1242 :     } ## else: result = E (is "U" diag)
1243 :     } else {
1244 : mmaechler 2175 r <- callGeneric(e1@x, e2)
1245 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1246 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1247 : mmaechler 2814 }
1248 : mmaechler 2820 E
1249 :     } else
1250 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
1251 : mmaechler 2175 })
1252 :    
1253 : mmaechler 2820 ## ldi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1254 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1255 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2),
1256 : maechler 2144 function(e1,e2) {
1257 : mmaechler 3167 n <- e1@Dim[1L]
1258 : mmaechler 3287 if(length(e2) == 0L)
1259 :     return(if(n) logical() else e1)
1260 : maechler 2144 f0 <- callGeneric(FALSE, e2)
1261 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1262 : maechler 2157 L1 <- (le <- length(e2)) == 1L
1263 : mmaechler 2820
1264 :     if(e1@diag == "U") {
1265 :     if(any((r <- callGeneric(TRUE, e2)) != 1)) {
1266 :     e1@diag <- "N"
1267 :     e1@x[seq_len(n)] <- r # possibly recycling r
1268 :     } ## else: result = e1 (is "U" diag)
1269 :     } else {
1270 : maechler 2144 r <- callGeneric(e1@x, e2)
1271 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1272 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1273 :     }
1274 :     e1
1275 :     } else
1276 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
1277 : maechler 2144 })
1278 : maechler 1655
1279 : maechler 2144
1280 :     ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... }
1281 : mmaechler 2196 for(other in c("ANY", "Matrix", "dMatrix")) {
1282 :     ## ddi*:
1283 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
1284 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
1285 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
1286 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
1287 : mmaechler 2196 ## ldi*:
1288 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
1289 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
1290 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
1291 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
1292 : mmaechler 2196 }
1293 : mmaechler 2331
1294 :     ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
1295 : mmaechler 3069 if(FALSE) # now also contains "geMatrix"
1296 : mmaechler 2331 dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
1297 : mmaechler 2813 names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] })
1298 : mmaechler 3069 dense.subCl <- paste0(c("d","l","n"), "denseMatrix")
1299 : mmaechler 2268 for(DI in diCls) {
1300 : mmaechler 2814 dMeth <- if(extends(DI, "dMatrix"))
1301 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)
1302 :     else # "lMatrix", the only other kind for now
1303 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)
1304 : mmaechler 2331 for(c2 in c(dense.subCl, "Matrix")) {
1305 : mmaechler 2814 for(Fun in c("*", "&")) {
1306 : mmaechler 2268 setMethod(Fun, signature(e1 = DI, e2 = c2),
1307 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
1308 :     setMethod(Fun, signature(e1 = c2, e2 = DI),
1309 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1310 :     }
1311 : mmaechler 2814 setMethod("^", signature(e1 = c2, e2 = DI),
1312 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1313 :     for(Fun in c("%%", "%/%", "/")) ## 0 <op> 0 |--> NaN for these.
1314 :     setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth)
1315 : mmaechler 2175 }
1316 :     }
1317 : maechler 2144
1318 : mmaechler 3002 ## Group methods "Math", "Math2" in --> ./Math.R
1319 :    
1320 : mmaechler 2175 ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all"
1321 : mmaechler 2345 ### ---------- the last 4: separately here
1322 : mmaechler 2175 for(cl in diCls) {
1323 :     setMethod("any", cl,
1324 :     function (x, ..., na.rm) {
1325 :     if(any(x@Dim == 0)) FALSE
1326 :     else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
1327 :     })
1328 : mmaechler 2341 setMethod("all", cl, function (x, ..., na.rm) {
1329 : mmaechler 3167 n <- x@Dim[1L]
1330 : mmaechler 2341 if(n >= 2) FALSE
1331 :     else if(n == 0 || x@diag == "U") TRUE
1332 :     else all(x@x, ..., na.rm = na.rm)
1333 :     })
1334 :     setMethod("prod", cl, function (x, ..., na.rm) {
1335 : mmaechler 3167 n <- x@Dim[1L]
1336 : mmaechler 2341 if(n >= 2) 0
1337 :     else if(n == 0 || x@diag == "U") 1
1338 :     else ## n == 1, diag = "N" :
1339 :     prod(x@x, ..., na.rm = na.rm)
1340 :     })
1341 : mmaechler 2175
1342 :     setMethod("sum", cl,
1343 :     function(x, ..., na.rm) {
1344 :     r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1345 : mmaechler 3167 if(x@diag == "U" && !is.na(r)) r + x@Dim[1L] else r
1346 : mmaechler 2175 })
1347 :     }
1348 :    
1349 :     ## The remaining ones are max, min, range :
1350 :    
1351 :     setMethod("Summary", "ddiMatrix",
1352 :     function(x, ..., na.rm) {
1353 :     if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1354 :     else if(x@diag == "U")
1355 :     callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1356 :     else callGeneric(x@x, 0, ..., na.rm=na.rm)
1357 :     })
1358 :     setMethod("Summary", "ldiMatrix",
1359 :     function(x, ..., na.rm) {
1360 :     if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1361 :     else if(x@diag == "U")
1362 :     callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1363 :     else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1364 :     })
1365 :    
1366 :    
1367 :    
1368 : maechler 1109 ## similar to prTriang() in ./Auxiliaries.R :
1369 :     prDiag <-
1370 :     function(x, digits = getOption("digits"), justify = "none", right = TRUE)
1371 :     {
1372 :     cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
1373 :     cf[row(cf) == col(cf)] <-
1374 : mmaechler 3120 vapply(diag(x), format, "", digits = digits, justify = justify)
1375 : maechler 1109 print(cf, quote = FALSE, right = right)
1376 :     invisible(x)
1377 :     }
1378 :    
1379 : mmaechler 2237 ## somewhat consistent with "print" for sparseMatrix :
1380 :     setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1381 :    
1382 : maechler 1109 setMethod("show", signature(object = "diagonalMatrix"),
1383 : maechler 1592 function(object) {
1384 :     d <- dim(object)
1385 :     cl <- class(object)
1386 : mmaechler 2203 cat(sprintf('%d x %d diagonal matrix of class "%s"',
1387 : mmaechler 3167 d[1L], d[2L], cl))
1388 :     if(d[1L] < 50) {
1389 : mmaechler 2203 cat("\n")
1390 :     prDiag(object)
1391 :     } else {
1392 :     cat(", with diagonal entries\n")
1393 :     show(diag(object))
1394 :     invisible(object)
1395 :     }
1396 : maechler 1592 })
1397 : mmaechler 2813
1398 : mmaechler 2998 rm(arg1, arg2, other, DI, Fun, cl, c1, c2,
1399 : mmaechler 2898 dense.subCl, diCls)# not used elsewhere
1400 : mmaechler 2820
1401 :     setMethod("summary", signature(object = "diagonalMatrix"),
1402 :     function(object, ...) {
1403 :     d <- dim(object)
1404 :     r <- summary(object@x, ...)
1405 :     attr(r, "header") <-
1406 :     sprintf('%d x %d diagonal Matrix of class "%s"',
1407 : mmaechler 3167 d[1L], d[2L], class(object))
1408 : mmaechler 2820 ## use ole' S3 technology for such a simple case
1409 :     class(r) <- c("diagSummary", class(r))
1410 :     r
1411 :     })
1412 :    
1413 :     print.diagSummary <- function (x, ...) {
1414 :     cat(attr(x, "header"),"\n")
1415 :     class(x) <- class(x)[-1]
1416 :     print(x, ...)
1417 :     invisible(x)
1418 :     }

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