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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 : maechler 1575 ## Allow Diagonal(4) and Diagonal(x=1:5)
9 : maechler 1109 if(missing(n))
10 : maechler 1575 n <- length(x)
11 : maechler 1109 else {
12 : maechler 1575 stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
13 :     n <- as.integer(n)
14 : maechler 1109 }
15 :    
16 : maechler 1654 if(missing(x)) ## unit diagonal matrix
17 : maechler 1575 new("ddiMatrix", Dim = c(n,n), diag = "U")
18 : maechler 1109 else {
19 : maechler 2128 lx <- length(x)
20 :     stopifnot(lx == 1 || lx == n) # but keep 'x' short for now
21 : maechler 1575 if(is.logical(x))
22 :     cl <- "ldiMatrix"
23 :     else if(is.numeric(x)) {
24 :     cl <- "ddiMatrix"
25 :     x <- as.numeric(x)
26 :     }
27 :     else if(is.complex(x)) {
28 :     cl <- "zdiMatrix" # will not yet work
29 :     } else stop("'x' has invalid data type")
30 : maechler 2128 new(cl, Dim = c(n,n), diag = "N",
31 :     x = if(lx == 1) rep.int(x,n) else x)
32 : maechler 1109 }
33 :     }
34 :    
35 : mmaechler 2508 .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 : maechler 2144 stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
40 : mmaechler 2508 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 : mmaechler 2226 stopifnot(is.character(shape), nchar(shape) == 1,
57 :     any(shape == c("t","s","g"))) # triangular / symmetric / general
58 : mmaechler 2508 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 : maechler 2144 }
71 :    
72 : mmaechler 2226 ## 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 : mmaechler 2608 # instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
77 : mmaechler 2226 .trDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
78 :     .sparseDiagonal(n, x, uplo, shape = "t")
79 :    
80 :    
81 : maechler 1617 ### 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
83 :     ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
84 :     ### who posted his bdiag() function written in December 1995.
85 : mmaechler 2209 if(FALSE)##--- no longer used:
86 : mmaechler 2206 .bdiag <- function(lst) {
87 :     ### block-diagonal matrix [a dgTMatrix] from list of matrices
88 :     stopifnot(is.list(lst), length(lst) >= 1)
89 :     dims <- sapply(lst, dim, USE.NAMES=FALSE)
90 : maechler 1617 ## make sure we had all matrices:
91 :     if(!(is.matrix(dims) && nrow(dims) == 2))
92 :     stop("some arguments are not matrices")
93 : maechler 1845 csdim <- rbind(rep.int(0L, 2),
94 : mmaechler 2206 apply(dims, 1, cumsum))
95 :     r <- new("dgTMatrix")
96 :     r@Dim <- as.integer(csdim[nrow(csdim),])
97 : maechler 1617 add1 <- matrix(1:0, 2,2)
98 : mmaechler 2206 for(i in seq_along(lst)) {
99 : maechler 1617 indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
100 :     if(is.null(dim(indx))) ## non-square matrix
101 : mmaechler 2206 r[indx[[1]],indx[[2]]] <- lst[[i]]
102 : maechler 1617 else ## square matrix
103 : mmaechler 2206 r[indx[,1], indx[,2]] <- lst[[i]]
104 : maechler 1617 }
105 : mmaechler 2206 r
106 : maechler 1617 }
107 : mmaechler 2209 ## 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 : mmaechler 2206 .bdiag <- function(lst) {
111 : mmaechler 2209 ## block-diagonal matrix [a dgTMatrix] from list of matrices
112 : mmaechler 2206 stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
113 : maechler 1617
114 : mmaechler 2206 Tlst <- lapply(lapply(lst, Matrix:::as_Csp2), # includes "diagU2N"
115 : mmaechler 2209 as, "TsparseMatrix")
116 : mmaechler 2206 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 : mmaechler 2209
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 :     r@uplo <- if(useU) "U" else "L"
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 :     if(use.n) { ## return nsparseMatrix :
153 :     r <- new("ntTMatrix")
154 :     } 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 : mmaechler 2206 }
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 : maechler 2136 .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
190 :     ## to triangular Tsparse
191 : maechler 1845 i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
192 : maechler 2136 new(paste(kind, "tTMatrix", sep=''),
193 : maechler 1654 diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
194 : maechler 2128 uplo = uplo,
195 : maechler 1654 x = from@x, # <- ok for diag = "U" and "N" (!)
196 :     i = i, j = i)
197 :     }
198 : maechler 1109
199 : maechler 2136 .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
200 :     ## to symmetric Tsparse
201 : maechler 2128 n <- from@Dim[1]
202 :     i <- seq_len(n) - 1L
203 :     new(paste(kind, "sTMatrix", sep=''),
204 : maechler 1845 Dim = from@Dim, Dimnames = from@Dimnames,
205 : maechler 2128 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 : maechler 1845 }
214 :    
215 : maechler 2128 ## diagonal -> triangular, upper / lower depending on "partner":
216 : maechler 2144 diag2tT.u <- function(d, x, kind = .M.kind(d))
217 :     .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
218 : maechler 2128
219 : mmaechler 2175 ## 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 : maechler 2136
228 : mmaechler 2175
229 : maechler 2136 ## 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 : mmaechler 2239 ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", diag2tT)
237 : maechler 1805 ## needed too (otherwise <dense> -> Tsparse is taken):
238 : maechler 2136 setAs("ddiMatrix", "TsparseMatrix", diag2tT)
239 : mmaechler 2482 setAs("ddiMatrix", "dsparseMatrix", diag2tT)
240 : maechler 2136 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 : mmaechler 2239 ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", diag2tT)
249 : maechler 2136 ## needed too (otherwise <dense> -> Tsparse is taken):
250 :     setAs("ldiMatrix", "TsparseMatrix", diag2tT)
251 : mmaechler 2482 setAs("ldiMatrix", "lsparseMatrix", diag2tT)
252 : maechler 2136 setAs("ldiMatrix", "CsparseMatrix",
253 :     function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
254 :     setAs("ldiMatrix", "symmetricMatrix",
255 :     function(from) .diag2sT(from, "U", "l"))
256 : maechler 1654
257 : maechler 1845
258 : maechler 2128 setAs("diagonalMatrix", "nMatrix",
259 :     function(from) {
260 :     n <- from@Dim[1]
261 :     i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
262 :     new("ntTMatrix", i = i, j = i, diag = from@diag,
263 :     Dim = from@Dim, Dimnames = from@Dimnames)
264 :     })
265 :    
266 : mmaechler 2237 setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
267 : maechler 2128
268 : mmaechler 2175 ## Cheap fast substitute for diag() which *does* preserve the mode of x :
269 :     mkDiag <- function(x, n) {
270 :     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 : maechler 1109 setAs("diagonalMatrix", "matrix",
276 :     function(from) {
277 : mmaechler 2175 ## want "ldiMatrix" -> <logical> "matrix" :
278 :     mkDiag(if(from@diag == "U") as1(from@x) else from@x,
279 :     n = from@Dim[1])
280 : maechler 1109 })
281 :    
282 : maechler 2098 setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
283 :     function(x, mode) {
284 :     n <- x@Dim[1]
285 : mmaechler 2175 mod.x <- mode(x@x)
286 :     r <- vector(mod.x, length = n^2)
287 : maechler 2098 if(n)
288 :     r[1 + 0:(n - 1) * (n + 1)] <-
289 : mmaechler 2175 if(x@diag == "U") as1(mod=mod.x) else x@x
290 : maechler 2098 r
291 :     })
292 :    
293 : maechler 1654 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
294 : maechler 2128 function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
295 : maechler 1174
296 : mmaechler 2268 setAs("diagonalMatrix", "denseMatrix",
297 :     function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
298 :    
299 : mmaechler 2185 .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
300 : maechler 1655
301 :     .diag.2N <- function(m) {
302 :     if(m@diag == "U") m@diag <- "N"
303 :     m
304 :     }
305 :    
306 : maechler 1174 setAs("ddiMatrix", "dgeMatrix",
307 : mmaechler 2183 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 : maechler 1174
313 : mmaechler 2183
314 : maechler 1109 setAs("matrix", "diagonalMatrix",
315 :     function(from) {
316 : maechler 1295 d <- dim(from)
317 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
318 :     if(any(from[row(from) != col(from)] != 0))
319 : mmaechler 2341 stop("matrix with non-zero off-diagonals cannot be coerced to diagonalMatrix")
320 : maechler 1295 x <- diag(from)
321 :     if(is.logical(x)) {
322 :     cl <- "ldiMatrix"
323 : mmaechler 2341 uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
324 : maechler 1295 } else {
325 :     cl <- "ddiMatrix"
326 : mmaechler 2341 uni <- allTrue(x == 1)
327 : maechler 1295 storage.mode(x) <- "double"
328 : maechler 1575 } ## TODO: complex
329 : maechler 1295 new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
330 :     x = if(uni) x[FALSE] else x)
331 : maechler 1109 })
332 :    
333 :     ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag()
334 :     setAs("Matrix", "diagonalMatrix",
335 :     function(from) {
336 : mmaechler 2341 d <- dim(from)
337 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
338 : mmaechler 2341 if(!isDiagonal(from)) stop("matrix is not diagonal")
339 :     ## else:
340 :     x <- diag(from)
341 :     if(is.logical(x)) {
342 :     cl <- "ldiMatrix"
343 :     uni <- allTrue(x)
344 :     } else {
345 :     cl <- "ddiMatrix"
346 :     uni <- allTrue(x == 1)
347 :     storage.mode(x) <- "double"
348 :     } ## TODO: complex
349 :     new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
350 :     x = if(uni) x[FALSE] else x)
351 : maechler 1109 })
352 :    
353 : maechler 1708
354 : mmaechler 2185 setMethod("diag", signature(x = "diagonalMatrix"),
355 :     function(x = 1, nrow, ncol) .diag.x(x))
356 : maechler 1708
357 : maechler 2098 subDiag <- function(x, i, j, ..., drop) {
358 : mmaechler 2508 x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
359 : maechler 1799 x <- if(missing(i))
360 :     x[, j, drop=drop]
361 :     else if(missing(j))
362 : mmaechler 2363 if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
363 : maechler 1799 else
364 :     x[i,j, drop=drop]
365 : maechler 2120 if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
366 : maechler 1799 }
367 :    
368 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
369 :     j = "index", drop = "logical"), subDiag)
370 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
371 : mmaechler 2363 j = "missing", drop = "logical"),
372 :     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 : maechler 1799 setMethod("[", signature(x = "diagonalMatrix", i = "missing",
380 :     j = "index", drop = "logical"),
381 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
382 : maechler 1799
383 : maechler 1617 ## When you assign to a diagonalMatrix, the result should be
384 : maechler 1708 ## diagonal or sparse ---
385 :     ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
386 : maechler 2098 ## Only(?) current bug: x[i] <- value is wrong when i is *vector*
387 :     replDiag <- function(x, i, j, ..., value) {
388 : mmaechler 2239 x <- as(x, "TsparseMatrix")
389 : maechler 1710 if(missing(i))
390 :     x[, j] <- value
391 : maechler 2098 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
396 :     else if(na == 3)
397 :     x[i] <- value
398 :     else stop("Internal bug: nargs()=",na,"; please report")
399 :     } else
400 : maechler 1710 x[i,j] <- value
401 :     if(isDiagonal(x)) as(x, "diagonalMatrix") else x
402 :     }
403 : maechler 1617
404 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
405 :     j = "index", value = "replValue"), replDiag)
406 : maechler 2098
407 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
408 :     j = "missing", value = "replValue"),
409 : maechler 2098 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 : mmaechler 2192 setReplaceMethod("[", signature(x = "diagonalMatrix",
418 :     i = "matrix", # 2-col.matrix
419 : maechler 2096 j = "missing", value = "replValue"),
420 : maechler 2098 function(x,i,j, ..., value) {
421 : maechler 2096 if(ncol(i) == 2) {
422 :     if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
423 : mmaechler 2192 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 : maechler 2096 x@x[ii] <- value
431 :     x
432 :     } else { ## no longer diagonal, but remain sparse:
433 : mmaechler 2239 x <- as(x, "TsparseMatrix")
434 : maechler 2096 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 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
446 :     j = "index", value = "replValue"),
447 : maechler 2098 function(x,i,j, ..., value) replDiag(x, j=j, value=value))
448 : maechler 1710
449 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
450 : mmaechler 2239 value = "sparseMatrix"),
451 : mmaechler 2207 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 : mmaechler 2239 value = "sparseMatrix"),
455 : mmaechler 2207 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 : mmaechler 2239 value = "sparseMatrix"),
459 : mmaechler 2207 function (x, i, j, ..., value)
460 :     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
461 : maechler 1710
462 : mmaechler 2207 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 : maechler 1109 setMethod("t", signature(x = "diagonalMatrix"),
474 :     function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
475 :    
476 : maechler 1331 setMethod("isDiagonal", signature(object = "diagonalMatrix"),
477 :     function(object) TRUE)
478 :     setMethod("isTriangular", signature(object = "diagonalMatrix"),
479 :     function(object) TRUE)
480 : maechler 1109 setMethod("isSymmetric", signature(object = "diagonalMatrix"),
481 : maechler 2112 function(object, ...) TRUE)
482 : maechler 1109
483 : maechler 2112 setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
484 :     setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
485 :    
486 : maechler 2133 setMethod("chol", signature(x = "ddiMatrix"),
487 :     function(x, pivot, ...) {
488 : mmaechler 2183 if(x@diag == "U") return(x)
489 :     ## else
490 : maechler 2133 if(any(x@x < 0))
491 :     stop("chol() is undefined for diagonal matrix with negative entries")
492 : maechler 1654 x@x <- sqrt(x@x)
493 :     x
494 :     })
495 :     ## chol(L) is L for logical diagonal:
496 : maechler 2133 setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
497 : maechler 1654
498 : mmaechler 2175 setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
499 : mmaechler 2185 function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
500 : mmaechler 2175
501 : mmaechler 2183 setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
502 :     function(x, type, ...) {
503 :     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 :     }
510 :     })
511 :    
512 :    
513 :    
514 : maechler 1109 ## Basic Matrix Multiplication {many more to add}
515 : maechler 1654 ## ---------------------
516 :     ## Note that "ldi" logical are treated as numeric
517 : maechler 1109 diagdiagprod <- function(x, y) {
518 : mmaechler 2183 n <- dimCheck(x,y)[1]
519 : maechler 1109 if(x@diag != "U") {
520 : maechler 1654 if(y@diag != "U") {
521 :     nx <- x@x * y@x
522 :     if(is.numeric(nx) && !is.numeric(x@x))
523 :     x <- as(x, "dMatrix")
524 :     x@x <- as.numeric(nx)
525 :     }
526 :     return(x)
527 : maechler 1109 } else ## x is unit diagonal
528 :     return(y)
529 :     }
530 :    
531 : maechler 1654 setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
532 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
533 :    
534 : maechler 1654 formals(diagdiagprod) <- alist(x=, y=x)
535 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
536 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
537 : maechler 1654 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
538 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
539 : maechler 1654 setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"),
540 :     diagdiagprod, valueClass = "ddiMatrix")
541 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
542 :     diagdiagprod, valueClass = "ddiMatrix")
543 : maechler 1109
544 :    
545 :     diagmatprod <- function(x, y) {
546 : mmaechler 2183 ## x is diagonalMatrix
547 : maechler 1109 dx <- dim(x)
548 :     dy <- dim(y)
549 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
550 :     n <- dx[1]
551 :     as(if(x@diag == "U") y else x@x * y, "Matrix")
552 :     }
553 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
554 : maechler 1654 diagmatprod)
555 : mmaechler 2183 ## sneaky .. :
556 : maechler 1109 formals(diagmatprod) <- alist(x=, y=NULL)
557 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
558 : maechler 1654 diagmatprod)
559 : maechler 1109
560 : mmaechler 2183 diagGeprod <- function(x, y) {
561 : maechler 1109 dx <- dim(x)
562 :     dy <- dim(y)
563 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
564 :     if(x@diag != "U")
565 :     y@x <- x@x * y@x
566 :     y
567 :     }
568 : mmaechler 2183 setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
569 :     setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
570 :     formals(diagGeprod) <- alist(x=, y=NULL)
571 : maechler 1109 setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
572 : mmaechler 2183 diagGeprod, valueClass = "dgeMatrix")
573 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
574 :     diagGeprod)
575 : maechler 1109
576 : mmaechler 2183 matdiagprod <- function(x, y) {
577 :     dx <- dim(x)
578 :     dy <- dim(y)
579 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
580 :     Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
581 :     }
582 : maechler 1109 setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
583 : mmaechler 2183 matdiagprod)
584 :     formals(matdiagprod) <- alist(x=, y=NULL)
585 :     setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
586 :     matdiagprod)
587 : maechler 1109
588 : mmaechler 2183 gediagprod <- function(x, y) {
589 :     dx <- dim(x)
590 :     dy <- dim(y)
591 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
592 :     if(y@diag == "N")
593 :     x@x <- x@x * rep(y@x, each = dx[1])
594 :     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 : maechler 1109
604 : maechler 1295 ## crossprod {more of these}
605 : maechler 1109
606 : maechler 1295 ## tcrossprod --- all are not yet there: do the dense ones here:
607 : maechler 1109
608 : mmaechler 2183 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 : maechler 1295 ## FIXME:
615 :     ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
616 :     ## function(x, y = NULL) {
617 :     ## })
618 : maechler 1109
619 : dmbates 2417 Cspdiagprod <- function(x, y) {
620 : dmbates 2458 dx <- dim(x <- .Call(Csparse_diagU2N, x))
621 : dmbates 2417 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 : mmaechler 2608 if(is(x, "compMatrix") && length(xf <- x@factors)) {
627 :     ## instead of dropping all factors, be smart about some
628 :     ## TODO ......
629 :     x@factors <- list()
630 :     }
631 : dmbates 2417 x
632 :     }
633 : maechler 1109
634 : dmbates 2417 diagCspprod <- function(x, y) {
635 :     dx <- dim(x)
636 : dmbates 2458 dy <- dim(y <- .Call(Csparse_diagU2N, y))
637 : dmbates 2417 if(dx[2] != dy[1]) stop("non-matching dimensions")
638 :     if(x@diag == "N")
639 :     y@x <- y@x * x@x[y@i + 1L]
640 : mmaechler 2608 if(is(y, "compMatrix") && length(yf <- y@factors)) {
641 :     ## instead of dropping all factors, be smart about some
642 :     ## TODO
643 :     keep <- character()
644 :     if(iLU <- names(yf) == "LU") {
645 :     ## TODO keep <- "LU"
646 :     }
647 :     y@factors <- yf[keep]
648 :     }
649 : dmbates 2417 y
650 :     }
651 :    
652 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
653 :     function(x, y = NULL) diagCspprod(x, y))
654 :    
655 : maechler 1799 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
656 : dmbates 2417 function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix")))
657 : maechler 1295
658 : dmbates 2417 ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
659 :     ## x'y == (y'x)'
660 :     setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
661 :     function(x, y = NULL) t(diagCspprod(y, x)))
662 :    
663 : maechler 1799 setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
664 : dmbates 2417 function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix"))))
665 : maechler 1799
666 : dmbates 2417 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
667 :     function(x, y = NULL) diagCspprod(x, t(y)))
668 :    
669 : maechler 1799 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
670 : dmbates 2417 function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix"))))
671 : maechler 1799
672 : dmbates 2417 setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
673 :     function(x, y = NULL) Cspdiagprod(x, y))
674 :    
675 : maechler 1799 setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
676 : dmbates 2417 function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y))
677 : mmaechler 2472
678 : dmbates 2417 setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
679 :     function(x, y) diagCspprod(x, y))
680 : maechler 1799
681 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
682 : dmbates 2417 function(x, y) diagCspprod(as(x, "CsparseMatrix"), y))
683 : mmaechler 2472
684 : mmaechler 2183 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
685 : dmbates 2417 function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y))
686 :    
687 : maechler 1799 setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
688 : dmbates 2417 function(x, y) Cspdiagprod(x, y))
689 :    
690 : maechler 1799 ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
691 :     ## do indeed work by going through sparse (and *not* ddense)!
692 :    
693 :     setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
694 :     function(a, b, ...) {
695 :     a@x <- 1/ a@x
696 :     a@Dimnames <- a@Dimnames[2:1]
697 :     a
698 :     })
699 :    
700 :     solveDiag <- function(a, b, ...) {
701 :     if((n <- a@Dim[1]) != nrow(b))
702 :     stop("incompatible matrix dimensions")
703 :     ## trivially invert a 'in place' and multiply:
704 :     a@x <- 1/ a@x
705 :     a@Dimnames <- a@Dimnames[2:1]
706 :     a %*% b
707 :     }
708 :     setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
709 :     solveDiag)
710 :     setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
711 :     solveDiag)
712 :    
713 : maechler 2106 ## Schur() ---> ./eigen.R
714 : maechler 1799
715 :    
716 :    
717 : mmaechler 2175 ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
718 : maechler 1295
719 : maechler 1655 ## Use function for several signatures, in order to evade
720 :     ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)
721 : mmaechler 2175 diagOdiag <- function(e1,e2) {
722 :     ## result should also be diagonal _ if possible _
723 : maechler 1655 r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
724 : mmaechler 2175 ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
725 :     r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
726 :     if(is.numeric(e2@x)) 0 else FALSE)
727 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal
728 :     if(is.numeric(r)) {
729 :     if(is.numeric(e2@x)) {
730 :     e2@x <- r; return(.diag.2N(e2)) }
731 :     if(!is.numeric(e1@x))
732 :     ## e.g. e1, e2 are logical;
733 :     e1 <- as(e1, "dMatrix")
734 :     }
735 :     else if(is.logical(r))
736 :     e1 <- as(e1, "lMatrix")
737 :     else stop("intermediate 'r' is of type", typeof(r))
738 :     e1@x <- r
739 :     .diag.2N(e1)
740 : maechler 1655 }
741 : mmaechler 2175 else { ## result not diagonal, but at least symmetric:
742 : mmaechler 2496 ## e.g., m == m
743 : mmaechler 2175 isNum <- (is.numeric(r) || is.numeric(r00))
744 :     isLog <- (is.logical(r) || is.logical(r00))
745 : mmaechler 2496 Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
746 : mmaechler 2175 d <- e1@Dim
747 :     n <- d[1]
748 :     stopifnot(length(r) == n)
749 :     xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
750 :     newcl <-
751 :     paste(if(isNum) "d" else if(isLog) {
752 :     if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
753 :     } else stop("not yet implemented .. please report")
754 :     ,
755 :     "syMatrix", sep='')
756 :    
757 :     new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
758 :     }
759 : maechler 1655 }
760 :    
761 : mmaechler 2175 ### This would be *the* way, but we get tons of "ambiguous method dispatch"
762 : mmaechler 2185 ## we use this hack instead of signature x = "diagonalMatrix" :
763 :     diCls <- names(getClass("diagonalMatrix")@subclasses)
764 : mmaechler 2175 if(FALSE) {
765 : maechler 1655 setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
766 :     diagOdiag)
767 : mmaechler 2175 } else { ## These are just for method disambiguation:
768 :     for(c1 in diCls)
769 :     for(c2 in diCls)
770 :     setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
771 :     }
772 : maechler 1655
773 : mmaechler 2493 ## diagonal o triangular |--> triangular
774 :     ## diagonal o symmetric |--> symmetric
775 : maechler 1845 ## {also when other is sparse: do these "here" --
776 :     ## before conversion to sparse, since that loses "diagonality"}
777 :    
778 : maechler 1655 ## For almost everything else, diag* shall be treated "as sparse" :
779 : maechler 1295 ## These are cheap implementations via coercion
780 :    
781 : maechler 2144 ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
782 :     ## and because we can save an .M.kind() call, we use this explicit
783 :     ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
784 :     ##
785 :     ## ddi*:
786 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
787 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
788 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
789 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
790 : maechler 2144 ## ldi*
791 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
792 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
793 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
794 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
795 : maechler 1654
796 : mmaechler 2175 ## Ops: Arith --> numeric : "dMatrix"
797 :     ## Compare --> logical
798 :     ## Logic --> logical: "lMatrix"
799 :    
800 : maechler 2144 ## other = "numeric" : stay diagonal if possible
801 : mmaechler 2175 ## ddi*: Arith: result numeric, potentially ddiMatrix
802 :     setMethod("Arith", signature(e1 = "ddiMatrix", e2 = "numeric"),
803 : maechler 2144 function(e1,e2) {
804 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
805 : maechler 2144 f0 <- callGeneric(0, e2)
806 :     if(all(is0(f0))) { # remain diagonal
807 : maechler 2157 L1 <- (le <- length(e2)) == 1L
808 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
809 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
810 : maechler 2144 e1@diag <- "N"
811 : maechler 2157 if(L1) r <- rep.int(r, n)
812 :     } else
813 : maechler 2144 r <- callGeneric(e1@x, e2)
814 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
815 : maechler 2144 return(e1)
816 :     }
817 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
818 :     })
819 : maechler 1655
820 : mmaechler 2175 setMethod("Arith", signature(e1 = "numeric", e2 = "ddiMatrix"),
821 : maechler 2144 function(e1,e2) {
822 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
823 : maechler 2144 f0 <- callGeneric(e1, 0)
824 :     if(all(is0(f0))) { # remain diagonal
825 : maechler 2157 L1 <- (le <- length(e1)) == 1L
826 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
827 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
828 : maechler 2144 e2@diag <- "N"
829 : maechler 2157 if(L1) r <- rep.int(r, n)
830 :     } else
831 : maechler 2144 r <- callGeneric(e1, e2@x)
832 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
833 : maechler 2144 return(e2)
834 :     }
835 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
836 :     })
837 : mmaechler 2175
838 :     ## ldi* Arith --> result numeric, potentially ddiMatrix
839 :     setMethod("Arith", signature(e1 = "ldiMatrix", e2 = "numeric"),
840 :     function(e1,e2) {
841 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
842 : mmaechler 2175 f0 <- callGeneric(0, e2)
843 :     if(all(is0(f0))) { # remain diagonal
844 :     L1 <- (le <- length(e2)) == 1L
845 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
846 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
847 :     e1@diag <- "N"
848 :     if(L1) r <- rep.int(r, n)
849 :     } else
850 :     r <- callGeneric(e1@x, e2)
851 :     e1 <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))
852 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
853 : mmaechler 2175 return(e1)
854 :     }
855 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
856 :     })
857 :    
858 :     setMethod("Arith", signature(e1 = "numeric", e2 = "ldiMatrix"),
859 :     function(e1,e2) {
860 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
861 : mmaechler 2175 f0 <- callGeneric(e1, 0)
862 :     if(all(is0(f0))) { # remain diagonal
863 :     L1 <- (le <- length(e1)) == 1L
864 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
865 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
866 :     e2@diag <- "N"
867 :     if(L1) r <- rep.int(r, n)
868 :     } else
869 :     r <- callGeneric(e1, e2@x)
870 :     e2 <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))
871 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
872 : mmaechler 2175 return(e2)
873 :     }
874 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
875 :     })
876 :    
877 :     ## ddi*: for "Ops" without Arith --> result logical, potentially ldi
878 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "numeric"),
879 :     function(e1,e2) {
880 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
881 : mmaechler 2175 f0 <- callGeneric(0, e2)
882 :     if(all(is0(f0))) { # remain diagonal
883 :     L1 <- (le <- length(e2)) == 1L
884 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
885 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
886 :     e1@diag <- "N"
887 :     if(L1) r <- rep.int(r, n)
888 :     } else
889 :     r <- callGeneric(e1@x, e2)
890 :     e1 <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))
891 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
892 : mmaechler 2175 return(e1)
893 :     }
894 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
895 :     })
896 :    
897 :     setMethod("Ops", signature(e1 = "numeric", e2 = "ddiMatrix"),
898 :     function(e1,e2) {
899 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
900 : mmaechler 2175 f0 <- callGeneric(e1, 0)
901 :     if(all(is0(f0))) { # remain diagonal
902 :     L1 <- (le <- length(e1)) == 1L
903 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
904 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
905 :     e2@diag <- "N"
906 :     if(L1) r <- rep.int(r, n)
907 :     } else
908 :     r <- callGeneric(e1, e2@x)
909 :     e2 <- copyClass(e2, "ldiMatrix", c("diag", "Dim", "Dimnames"))
910 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
911 : mmaechler 2175 return(e2)
912 :     }
913 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
914 :     })
915 :    
916 :     ## ldi*: for "Ops" without Arith --> result logical, potentially ldi
917 : maechler 2144 setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "numeric"),
918 :     function(e1,e2) {
919 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
920 : maechler 2144 f0 <- callGeneric(FALSE, e2)
921 :     if(all(is0(f0))) { # remain diagonal
922 : maechler 2157 L1 <- (le <- length(e2)) == 1L
923 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
924 :     if(e1@diag == "U" && any((r <- callGeneric(TRUE, e2)) != 1)) {
925 : maechler 2144 e1@diag <- "N"
926 : maechler 2157 if(L1) r <- rep.int(r, n)
927 :     } else
928 : maechler 2144 r <- callGeneric(e1@x, e2)
929 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
930 : maechler 2144 return(e1)
931 :     }
932 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
933 :     })
934 : maechler 1655
935 : maechler 2144 setMethod("Ops", signature(e1 = "numeric", e2 = "ldiMatrix"),
936 :     function(e1,e2) {
937 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
938 : maechler 2144 f0 <- callGeneric(e1, FALSE)
939 :     if(all(is0(f0))) { # remain diagonal
940 : maechler 2157 L1 <- (le <- length(e1)) == 1L
941 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
942 :     if(e2@diag == "U" && any((r <- callGeneric(e1, TRUE)) != 1)) {
943 : maechler 2144 e2@diag <- "N"
944 : maechler 2157 if(L1) r <- rep.int(r, n)
945 :     } else
946 : maechler 2144 r <- callGeneric(e1, e2@x)
947 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
948 : maechler 2144 return(e2)
949 :     }
950 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
951 :     })
952 :    
953 :    
954 :    
955 :     ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... }
956 : mmaechler 2196 for(other in c("ANY", "Matrix", "dMatrix")) {
957 :     ## ddi*:
958 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
959 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
960 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
961 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
962 : mmaechler 2196 ## ldi*:
963 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
964 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
965 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
966 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
967 : mmaechler 2196 }
968 : mmaechler 2331
969 :     ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
970 : mmaechler 2544 if(FALSE)## too general, would contain denseModelMatrix:
971 : mmaechler 2331 dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
972 :     names(dM.scl)[sapply(dM.scl, slot, "distance") == 1] })
973 : mmaechler 2544 dense.subCl <- paste(c("d","l","n"), "denseMatrix", sep="")
974 : mmaechler 2268 for(DI in diCls) {
975 : mmaechler 2331 for(c2 in c(dense.subCl, "Matrix")) {
976 : mmaechler 2268 for(Fun in c("*", "^", "&")) {
977 :     setMethod(Fun, signature(e1 = DI, e2 = c2),
978 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
979 :     setMethod(Fun, signature(e1 = c2, e2 = DI),
980 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
981 :     }
982 :     ## NB: This arguably implicitly uses 0/0 :== 0 to keep diagonality
983 :     for(Fun in c("%%", "%/%", "/")) {
984 :     setMethod(Fun, signature(e1 = DI, e2 = c2),
985 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
986 :     }
987 : mmaechler 2175 }
988 :     }
989 : maechler 2144
990 :    
991 : mmaechler 2175 ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all"
992 : mmaechler 2345 ### ---------- the last 4: separately here
993 : mmaechler 2175 for(cl in diCls) {
994 :     setMethod("any", cl,
995 :     function (x, ..., na.rm) {
996 :     if(any(x@Dim == 0)) FALSE
997 :     else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
998 :     })
999 : mmaechler 2341 setMethod("all", cl, function (x, ..., na.rm) {
1000 :     n <- x@Dim[1]
1001 :     if(n >= 2) FALSE
1002 :     else if(n == 0 || x@diag == "U") TRUE
1003 :     else all(x@x, ..., na.rm = na.rm)
1004 :     })
1005 :     setMethod("prod", cl, function (x, ..., na.rm) {
1006 :     n <- x@Dim[1]
1007 :     if(n >= 2) 0
1008 :     else if(n == 0 || x@diag == "U") 1
1009 :     else ## n == 1, diag = "N" :
1010 :     prod(x@x, ..., na.rm = na.rm)
1011 :     })
1012 : mmaechler 2175
1013 :     setMethod("sum", cl,
1014 :     function(x, ..., na.rm) {
1015 :     r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1016 :     if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
1017 :     })
1018 :     }
1019 :    
1020 :     ## The remaining ones are max, min, range :
1021 :    
1022 :     setMethod("Summary", "ddiMatrix",
1023 :     function(x, ..., na.rm) {
1024 :     if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1025 :     else if(x@diag == "U")
1026 :     callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1027 :     else callGeneric(x@x, 0, ..., na.rm=na.rm)
1028 :     })
1029 :     setMethod("Summary", "ldiMatrix",
1030 :     function(x, ..., na.rm) {
1031 :     if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1032 :     else if(x@diag == "U")
1033 :     callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1034 :     else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1035 :     })
1036 :    
1037 :    
1038 :    
1039 : maechler 1109 ## similar to prTriang() in ./Auxiliaries.R :
1040 :     prDiag <-
1041 :     function(x, digits = getOption("digits"), justify = "none", right = TRUE)
1042 :     {
1043 :     cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
1044 :     cf[row(cf) == col(cf)] <-
1045 :     sapply(diag(x), format, digits = digits, justify = justify)
1046 :     print(cf, quote = FALSE, right = right)
1047 :     invisible(x)
1048 :     }
1049 :    
1050 : mmaechler 2237 ## somewhat consistent with "print" for sparseMatrix :
1051 :     setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1052 :    
1053 : maechler 1109 setMethod("show", signature(object = "diagonalMatrix"),
1054 : maechler 1592 function(object) {
1055 :     d <- dim(object)
1056 :     cl <- class(object)
1057 : mmaechler 2203 cat(sprintf('%d x %d diagonal matrix of class "%s"',
1058 : maechler 1592 d[1], d[2], cl))
1059 : mmaechler 2203 if(d[1] < 50) {
1060 :     cat("\n")
1061 :     prDiag(object)
1062 :     } else {
1063 :     cat(", with diagonal entries\n")
1064 :     show(diag(object))
1065 :     invisible(object)
1066 :     }
1067 : maechler 1592 })

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