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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 : maechler 2144 stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
43 : mmaechler 2840 if(!(mcols <- missing(cols)))
44 : mmaechler 2508 stopifnot(0 <= (cols <- as.integer(cols)), cols < n)
45 :     m <- length(cols)
46 :     if(missing(kind))
47 :     kind <-
48 :     if(is.double(x)) "d"
49 :     else if(is.logical(x)) "l"
50 :     else { ## for now
51 :     storage.mode(x) <- "double"
52 :     "d"
53 :     }
54 :     else stopifnot(any(kind == c("d","l","n")))
55 : mmaechler 2226 stopifnot(is.character(shape), nchar(shape) == 1,
56 :     any(shape == c("t","s","g"))) # triangular / symmetric / general
57 : mmaechler 2840 if((missing(unitri) || unitri) && shape == "t" &&
58 :     (mcols || cols == 0:(n-1L)) &&
59 :     ((any(kind == c("l", "n")) && allTrue(x)) ||
60 :     ( kind == "d" && allTrue(x == 1)))) { ## uni-triangular
61 :     new(paste0(kind,"tCMatrix"), Dim = c(n,n),
62 :     uplo = uplo, diag = "U", p = rep.int(0L, n+1L))
63 :     }
64 :     else if(kind == "n") {
65 : mmaechler 2508 if(shape == "g")
66 :     new("ngCMatrix", Dim = c(n,m), i = cols, p = 0:m)
67 :     else new(paste0("n", shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
68 :     i = cols, p = 0:m)
69 :     }
70 : mmaechler 2840 else { ## kind != "n" -- have x slot :
71 :     if((lx <- length(x)) == 1) x <- rep.int(x, m)
72 :     else if(lx != m) stop("length(x) must be either 1 or #{cols}")
73 :     if(shape == "g")
74 :     new(paste0(kind, "gCMatrix"), Dim = c(n,m),
75 :     x = x, i = cols, p = 0:m)
76 :     else new(paste0(kind, shape, "CMatrix"), Dim = c(n,m), uplo = uplo,
77 :     x = x, i = cols, p = 0:m)
78 :     }
79 : maechler 2144 }
80 :    
81 : mmaechler 2226 ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
82 :     .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
83 :     .sparseDiagonal(n, x, uplo, shape = "s")
84 :    
85 : mmaechler 2608 # instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
86 : mmaechler 2840 .trDiagonal <- function(n, x = 1, uplo = "U", unitri=TRUE)
87 :     .sparseDiagonal(n, x, uplo, shape = "t", unitri=unitri)
88 : mmaechler 2226
89 :    
90 : mmaechler 2764 ## This is modified from a post of Bert Gunter to R-help on 1 Sep 2005.
91 :     ## Bert's code built on a post by Andy Liaw who most probably was influenced
92 :     ## by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
93 :     ## who posted his bdiag() function written in December 1995.
94 : mmaechler 2209 if(FALSE)##--- no longer used:
95 : mmaechler 2206 .bdiag <- function(lst) {
96 : mmaechler 2764 ## block-diagonal matrix [a dgTMatrix] from list of matrices
97 : mmaechler 2206 stopifnot(is.list(lst), length(lst) >= 1)
98 : mmaechler 2813 dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE)
99 : maechler 1617 ## make sure we had all matrices:
100 :     if(!(is.matrix(dims) && nrow(dims) == 2))
101 :     stop("some arguments are not matrices")
102 : maechler 1845 csdim <- rbind(rep.int(0L, 2),
103 : mmaechler 2206 apply(dims, 1, cumsum))
104 :     r <- new("dgTMatrix")
105 :     r@Dim <- as.integer(csdim[nrow(csdim),])
106 : maechler 1617 add1 <- matrix(1:0, 2,2)
107 : mmaechler 2206 for(i in seq_along(lst)) {
108 : maechler 1617 indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
109 :     if(is.null(dim(indx))) ## non-square matrix
110 : mmaechler 2206 r[indx[[1]],indx[[2]]] <- lst[[i]]
111 : maechler 1617 else ## square matrix
112 : mmaechler 2206 r[indx[,1], indx[,2]] <- lst[[i]]
113 : maechler 1617 }
114 : mmaechler 2206 r
115 : maechler 1617 }
116 : mmaechler 2209 ## expand(<mer>) needed something like bdiag() for lower-triangular
117 :     ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
118 :     ## implementation for those; now extended and generalized:
119 : mmaechler 2206 .bdiag <- function(lst) {
120 : mmaechler 2209 ## block-diagonal matrix [a dgTMatrix] from list of matrices
121 : mmaechler 2206 stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
122 : maechler 1617
123 : mmaechler 2891 Tlst <- lapply(lapply(lst, as_Csp2), # includes "diagU2N"
124 : mmaechler 2209 as, "TsparseMatrix")
125 : mmaechler 2206 if(nl == 1) return(Tlst[[1]])
126 :     ## else
127 : mmaechler 2813 i_off <- c(0L, cumsum(vapply(Tlst, nrow, 1L)))
128 :     j_off <- c(0L, cumsum(vapply(Tlst, ncol, 1L)))
129 : mmaechler 2209
130 : mmaechler 2813 clss <- vapply(Tlst, class, "")
131 : mmaechler 2741 typ <- substr(clss, 2, 2)
132 :     knd <- substr(clss, 1, 1)
133 :     sym <- typ == "s" # symmetric ones
134 :     tri <- typ == "t" # triangular ones
135 :     use.n <- any(is.n <- knd == "n")
136 :     if(use.n && !(use.n <- all(is.n))) {
137 : mmaechler 2209 Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
138 : mmaechler 2741 knd [is.n] <- "l"
139 :     }
140 :     use.l <- !use.n && all(knd == "l")
141 : mmaechler 2209 if(all(sym)) { ## result should be *symmetric*
142 : mmaechler 2813 uplos <- vapply(Tlst, slot, ".", "uplo") ## either "U" or "L"
143 : mmaechler 2209 tLU <- table(uplos)# of length 1 or 2 ..
144 :     if(length(tLU) == 1) { ## all "U" or all "L"
145 :     useU <- uplos[1] == "U"
146 :     } else { ## length(tLU) == 2, counting "L" and "U"
147 :     useU <- diff(tLU) >= 0
148 :     if(useU && (hasL <- tLU[1] > 0))
149 :     Tlst[hasL] <- lapply(Tlst[hasL], t)
150 :     else if(!useU && (hasU <- tLU[2] > 0))
151 :     Tlst[hasU] <- lapply(Tlst[hasU], t)
152 :     }
153 :     if(use.n) { ## return nsparseMatrix :
154 :     r <- new("nsTMatrix")
155 :     } else {
156 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "sTMatrix"))
157 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
158 :     }
159 :     r@uplo <- if(useU) "U" else "L"
160 :     }
161 : mmaechler 2813 else if(all(tri) && { ULs <- vapply(Tlst, slot, ".", "uplo")## "U" or "L"
162 : mmaechler 2209 all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
163 :     ){ ## *triangular* result
164 :    
165 :     if(use.n) { ## return nsparseMatrix :
166 :     r <- new("ntTMatrix")
167 :     } else {
168 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "tTMatrix"))
169 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
170 :     }
171 :     r@uplo <- ULs[1L]
172 :     }
173 :     else {
174 :     if(any(sym))
175 :     Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
176 :     if(use.n) { ## return nsparseMatrix :
177 :     r <- new("ngTMatrix")
178 :     } else {
179 : mmaechler 2741 r <- new(paste0(if(use.l) "l" else "d", "gTMatrix"))
180 : mmaechler 2209 r@x <- unlist(lapply(Tlst, slot, "x"))
181 :     }
182 :     }
183 :     r@Dim <- c(i_off[nl+1], j_off[nl + 1])
184 :     r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
185 :     r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
186 :     r
187 : mmaechler 2206 }
188 :    
189 :     bdiag <- function(...) {
190 :     if((nA <- nargs()) == 0) return(new("dgCMatrix"))
191 :     if(nA == 1 && !is.list(...))
192 :     return(as(..., "CsparseMatrix"))
193 :     alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
194 :     if(length(alis) == 1)
195 :     return(as(alis[[1]], "CsparseMatrix"))
196 :    
197 :     ## else : two or more arguments
198 :     as(.bdiag(alis), "CsparseMatrix")
199 :     }
200 :    
201 :    
202 : maechler 2136 .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
203 :     ## to triangular Tsparse
204 : maechler 1845 i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
205 : mmaechler 2778 new(paste0(kind, "tTMatrix"),
206 : maechler 1654 diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
207 : maechler 2128 uplo = uplo,
208 : maechler 1654 x = from@x, # <- ok for diag = "U" and "N" (!)
209 :     i = i, j = i)
210 :     }
211 : maechler 1109
212 : maechler 2136 .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
213 :     ## to symmetric Tsparse
214 : maechler 2128 n <- from@Dim[1]
215 :     i <- seq_len(n) - 1L
216 : mmaechler 2778 new(paste0(kind, "sTMatrix"),
217 : maechler 1845 Dim = from@Dim, Dimnames = from@Dimnames,
218 : maechler 2128 i = i, j = i, uplo = uplo,
219 :     x = if(from@diag == "N") from@x else ## "U"-diag
220 :     rep.int(switch(kind,
221 :     "d" = 1.,
222 :     "l" =,
223 :     "n" = TRUE,
224 :     ## otherwise
225 : mmaechler 2863 stop(gettextf("%s kind not yet implemented",
226 :     sQuote(kind)), domain=NA)),
227 :     n))
228 : maechler 1845 }
229 :    
230 : mmaechler 2998 ## diagonal -> triangular, upper / lower depending on "partner" 'x':
231 : maechler 2144 diag2tT.u <- function(d, x, kind = .M.kind(d))
232 :     .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
233 : maechler 2128
234 : mmaechler 2175 ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
235 :     diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
236 :     clx <- getClassDef(class(x))
237 :     if(extends(clx, "symmetricMatrix"))
238 :     .diag2sT(d, uplo = x@uplo, kind)
239 :     else
240 :     .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
241 :     }
242 : maechler 2136
243 : mmaechler 2814 ## FIXME: should not be needed {when ddi* is dsparse* etc}:
244 :     setMethod("is.finite", signature(x = "diagonalMatrix"),
245 :     function(x) is.finite(.diag2tT(x)))
246 :     setMethod("is.infinite", signature(x = "diagonalMatrix"),
247 :     function(x) is.infinite(.diag2tT(x)))
248 : mmaechler 2175
249 : maechler 2136 ## In order to evade method dispatch ambiguity warnings,
250 :     ## and because we can save a .M.kind() call, we use this explicit
251 :     ## "hack" instead of signature x = "diagonalMatrix" :
252 :     ##
253 :     ## ddi*:
254 : mmaechler 2922 di2tT <- function(from) .diag2tT(from, "U", "d")
255 :     setAs("ddiMatrix", "triangularMatrix", di2tT)
256 :     ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", di2tT)
257 : maechler 1805 ## needed too (otherwise <dense> -> Tsparse is taken):
258 : mmaechler 2922 setAs("ddiMatrix", "TsparseMatrix", di2tT)
259 :     setAs("ddiMatrix", "dsparseMatrix", di2tT)
260 : maechler 2136 setAs("ddiMatrix", "CsparseMatrix",
261 :     function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
262 : mmaechler 2998 setAs("ddiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "d"))
263 : maechler 2136 ##
264 :     ## ldi*:
265 : mmaechler 2922 di2tT <- function(from) .diag2tT(from, "U", "l")
266 :     setAs("ldiMatrix", "triangularMatrix", di2tT)
267 :     ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", di2tT)
268 : maechler 2136 ## needed too (otherwise <dense> -> Tsparse is taken):
269 : mmaechler 2922 setAs("ldiMatrix", "TsparseMatrix", di2tT)
270 :     setAs("ldiMatrix", "lsparseMatrix", di2tT)
271 : maechler 2136 setAs("ldiMatrix", "CsparseMatrix",
272 :     function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
273 : mmaechler 2998 setAs("ldiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "l"))
274 : mmaechler 2922 rm(di2tT)
275 : maechler 1654
276 : maechler 2128 setAs("diagonalMatrix", "nMatrix",
277 :     function(from) {
278 :     n <- from@Dim[1]
279 :     i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
280 :     new("ntTMatrix", i = i, j = i, diag = from@diag,
281 :     Dim = from@Dim, Dimnames = from@Dimnames)
282 :     })
283 :    
284 : mmaechler 2237 setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
285 : maechler 2128
286 : mmaechler 2998 ##' A version of diag(x,n) which *does* preserve the mode of x, where diag() "fails"
287 : mmaechler 2175 mkDiag <- function(x, n) {
288 :     y <- matrix(as0(mod=mode(x)), n,n)
289 : mmaechler 2820 if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x
290 : mmaechler 2175 y
291 :     }
292 : mmaechler 2998 ## NB: diag(x,n) is really faster for n >= 20, and even more for large n
293 :     ## --> using diag() where possible, ==> .ddi2mat()
294 : mmaechler 2175
295 : mmaechler 2998 .diag2mat <- function(from)
296 :     ## want "ldiMatrix" -> <logical> "matrix" (but integer -> <double> for now)
297 :     mkDiag(if(from@diag == "U") as1(from@x) else from@x, n = from@Dim[1])
298 : maechler 1109
299 : mmaechler 2998 .ddi2mat <- function(from)
300 :     base::diag(if(from@diag == "U") as1(from@x) else from@x, nrow = from@Dim[1])
301 :    
302 :     setAs("ddiMatrix", "matrix", .ddi2mat)
303 :     ## the non-ddi diagonalMatrix -- only "ldiMatrix" currently:
304 :     setAs("diagonalMatrix", "matrix", .diag2mat)
305 :    
306 : maechler 2098 setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
307 :     function(x, mode) {
308 :     n <- x@Dim[1]
309 : mmaechler 2175 mod.x <- mode(x@x)
310 :     r <- vector(mod.x, length = n^2)
311 : maechler 2098 if(n)
312 : mmaechler 2820 r[1 + 0:(n - 1L) * (n + 1)] <-
313 : mmaechler 2175 if(x@diag == "U") as1(mod=mod.x) else x@x
314 : maechler 2098 r
315 :     })
316 :    
317 : maechler 1654 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
318 : maechler 2128 function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
319 : maechler 1174
320 : mmaechler 2268 setAs("diagonalMatrix", "denseMatrix",
321 :     function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
322 :    
323 : mmaechler 2877 ..diag.x <- function(m) rep.int(as1(m@x), m@Dim[1])
324 :     .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
325 : maechler 1655
326 :     .diag.2N <- function(m) {
327 :     if(m@diag == "U") m@diag <- "N"
328 :     m
329 :     }
330 :    
331 : maechler 1174 setAs("ddiMatrix", "dgeMatrix",
332 : mmaechler 2183 function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
333 :     setAs("ddiMatrix", "ddenseMatrix",
334 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
335 :     setAs("ldiMatrix", "ldenseMatrix",
336 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
337 : maechler 1174
338 : mmaechler 2183
339 : maechler 1109 setAs("matrix", "diagonalMatrix",
340 :     function(from) {
341 : maechler 1295 d <- dim(from)
342 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
343 :     if(any(from[row(from) != col(from)] != 0))
344 : mmaechler 2863 stop("matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"")
345 : maechler 1295 x <- diag(from)
346 :     if(is.logical(x)) {
347 :     cl <- "ldiMatrix"
348 : mmaechler 2341 uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
349 : maechler 1295 } else {
350 :     cl <- "ddiMatrix"
351 : mmaechler 2341 uni <- allTrue(x == 1)
352 : maechler 1295 storage.mode(x) <- "double"
353 : maechler 1575 } ## TODO: complex
354 : maechler 1295 new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
355 :     x = if(uni) x[FALSE] else x)
356 : maechler 1109 })
357 :    
358 :     ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag()
359 :     setAs("Matrix", "diagonalMatrix",
360 :     function(from) {
361 : mmaechler 2341 d <- dim(from)
362 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
363 : mmaechler 2341 if(!isDiagonal(from)) stop("matrix is not diagonal")
364 :     ## else:
365 :     x <- diag(from)
366 :     if(is.logical(x)) {
367 :     cl <- "ldiMatrix"
368 :     uni <- allTrue(x)
369 :     } else {
370 :     cl <- "ddiMatrix"
371 :     uni <- allTrue(x == 1)
372 :     storage.mode(x) <- "double"
373 :     } ## TODO: complex
374 :     new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
375 :     x = if(uni) x[FALSE] else x)
376 : maechler 1109 })
377 :    
378 : maechler 1708
379 : mmaechler 2185 setMethod("diag", signature(x = "diagonalMatrix"),
380 :     function(x = 1, nrow, ncol) .diag.x(x))
381 : maechler 1708
382 : maechler 2098 subDiag <- function(x, i, j, ..., drop) {
383 : mmaechler 2508 x <- as(x, "CsparseMatrix") ## << was "TsparseMatrix" (Csparse is faster now)
384 : maechler 1799 x <- if(missing(i))
385 :     x[, j, drop=drop]
386 :     else if(missing(j))
387 : mmaechler 2363 if(nargs() == 4) x[i, , drop=drop] else x[i, drop=drop]
388 : maechler 1799 else
389 :     x[i,j, drop=drop]
390 : maechler 2120 if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
391 : maechler 1799 }
392 :    
393 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
394 :     j = "index", drop = "logical"), subDiag)
395 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
396 : mmaechler 2363 j = "missing", drop = "logical"),
397 :     function(x, i, j, ..., drop) {
398 :     na <- nargs()
399 :     Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
400 :     if(na == 4)
401 :     subDiag(x, i=i, , drop=drop)
402 :     else subDiag(x, i=i, drop=drop)
403 :     })
404 : maechler 1799 setMethod("[", signature(x = "diagonalMatrix", i = "missing",
405 :     j = "index", drop = "logical"),
406 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
407 : maechler 1799
408 : maechler 1617 ## When you assign to a diagonalMatrix, the result should be
409 : maechler 1708 ## diagonal or sparse ---
410 :     ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
411 : maechler 2098 ## Only(?) current bug: x[i] <- value is wrong when i is *vector*
412 :     replDiag <- function(x, i, j, ..., value) {
413 : mmaechler 2811 x <- as(x, "CsparseMatrix")# was "Tsparse.." till 2012-07
414 : maechler 1710 if(missing(i))
415 :     x[, j] <- value
416 : maechler 2098 else if(missing(j)) { ## x[i , ] <- v *OR* x[i] <- v
417 :     na <- nargs()
418 :     ## message("diagnosing replDiag() -- nargs()= ", na)
419 :     if(na == 4)
420 :     x[i, ] <- value
421 :     else if(na == 3)
422 :     x[i] <- value
423 : mmaechler 2863 else stop(gettextf("Internal bug: nargs()=%d; please report",
424 :     na), domain=NA)
425 : maechler 2098 } else
426 : maechler 1710 x[i,j] <- value
427 :     if(isDiagonal(x)) as(x, "diagonalMatrix") else x
428 :     }
429 : maechler 1617
430 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
431 :     j = "index", value = "replValue"), replDiag)
432 : maechler 2098
433 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
434 :     j = "missing", value = "replValue"),
435 : maechler 2098 function(x,i,j, ..., value) {
436 :     ## message("before replDiag() -- nargs()= ", nargs())
437 :     if(nargs() == 3)
438 :     replDiag(x, i=i, value=value)
439 :     else ## nargs() == 4 :
440 :     replDiag(x, i=i, , value=value)
441 :     })
442 :    
443 : mmaechler 2877 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
444 :     j = "index", value = "replValue"),
445 :     function(x,i,j, ..., value) replDiag(x, j=j, value=value))
446 :    
447 :     ## x[] <- value :
448 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
449 :     j = "missing", value = "ANY"),
450 :     function(x,i,j, ..., value)
451 :     {
452 :     if(all0(value)) { # be faster
453 :     r <- new(paste0(.M.kindC(getClassDef(class(x))),"tTMatrix"))# of all "0"
454 :     r@Dim <- x@Dim
455 :     r@Dimnames <- x@Dimnames
456 :     r
457 :     } else { ## typically non-sense: assigning to full sparseMatrix
458 :     x[TRUE] <- value
459 :     x
460 :     }
461 :     })
462 :    
463 :    
464 : mmaechler 2192 setReplaceMethod("[", signature(x = "diagonalMatrix",
465 :     i = "matrix", # 2-col.matrix
466 : maechler 2096 j = "missing", value = "replValue"),
467 : maechler 2098 function(x,i,j, ..., value) {
468 : maechler 2096 if(ncol(i) == 2) {
469 :     if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
470 : mmaechler 2192 if(x@diag == "U") {
471 :     one <- as1(x@x)
472 :     if(any(value != one | is.na(value))) {
473 :     x@diag <- "N"
474 :     x@x <- rep.int(one, x@Dim[1])
475 : mmaechler 2811 } else return(x)
476 : mmaechler 2192 }
477 : maechler 2096 x@x[ii] <- value
478 :     x
479 :     } else { ## no longer diagonal, but remain sparse:
480 : mmaechler 2239 x <- as(x, "TsparseMatrix")
481 : maechler 2096 x[i] <- value
482 :     x
483 :     }
484 :     }
485 :     else { # behave as "base R": use as if vector
486 :     x <- as(x, "matrix")
487 :     x[i] <- value
488 :     Matrix(x)
489 :     }
490 :     })
491 :    
492 : maechler 1710
493 : mmaechler 2877 ## value = "sparseMatrix":
494 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
495 : mmaechler 2239 value = "sparseMatrix"),
496 : mmaechler 2207 function (x, i, j, ..., value)
497 :     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
498 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
499 : mmaechler 2239 value = "sparseMatrix"),
500 : mmaechler 2207 function (x, i, j, ..., value)
501 :     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
502 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
503 : mmaechler 2239 value = "sparseMatrix"),
504 : mmaechler 2207 function (x, i, j, ..., value)
505 :     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
506 : maechler 1710
507 : mmaechler 2877 ## value = "sparseVector":
508 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
509 :     value = "sparseVector"),
510 :     replDiag)
511 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
512 :     value = "sparseVector"),
513 :     replDiag)
514 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
515 :     value = "sparseVector"),
516 :     replDiag)
517 :    
518 :    
519 : maechler 1109 setMethod("t", signature(x = "diagonalMatrix"),
520 :     function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
521 :    
522 : mmaechler 2904 setMethod("isDiagonal", "diagonalMatrix", function(object) TRUE)
523 : mmaechler 3015 setMethod("isTriangular", "diagonalMatrix", function(object, upper=NA, ...) TRUE)
524 : mmaechler 2904 setMethod("isSymmetric", "diagonalMatrix", function(object, ...) TRUE)
525 : maechler 1109
526 : maechler 2112 setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
527 :     setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
528 :    
529 : maechler 2133 setMethod("chol", signature(x = "ddiMatrix"),
530 :     function(x, pivot, ...) {
531 : mmaechler 2183 if(x@diag == "U") return(x)
532 :     ## else
533 : maechler 2133 if(any(x@x < 0))
534 :     stop("chol() is undefined for diagonal matrix with negative entries")
535 : maechler 1654 x@x <- sqrt(x@x)
536 :     x
537 :     })
538 :     ## chol(L) is L for logical diagonal:
539 : maechler 2133 setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
540 : maechler 1654
541 : mmaechler 2175 setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
542 : mmaechler 2185 function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
543 : mmaechler 2175
544 : mmaechler 2183 setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
545 :     function(x, type, ...) {
546 :     if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
547 :     type <- toupper(substr(type[1], 1, 1))
548 :     isU <- (x@diag == "U") # unit-diagonal
549 :     if(type == "F") sqrt(if(isU) n else sum(x@x^2))
550 :     else { ## norm == "I","1","O","M" :
551 :     if(isU) 1 else max(abs(x@x))
552 :     }
553 :     })
554 :    
555 :    
556 :    
557 : maechler 1109 ## Basic Matrix Multiplication {many more to add}
558 : maechler 1654 ## ---------------------
559 :     ## Note that "ldi" logical are treated as numeric
560 : maechler 1109 diagdiagprod <- function(x, y) {
561 : mmaechler 2633 dimCheck(x,y)
562 : maechler 1109 if(x@diag != "U") {
563 : maechler 1654 if(y@diag != "U") {
564 :     nx <- x@x * y@x
565 :     if(is.numeric(nx) && !is.numeric(x@x))
566 :     x <- as(x, "dMatrix")
567 :     x@x <- as.numeric(nx)
568 :     }
569 :     return(x)
570 : maechler 1109 } else ## x is unit diagonal
571 : mmaechler 2912 return(y)
572 : maechler 1109 }
573 :    
574 : maechler 1654 setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
575 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
576 :    
577 : maechler 1654 formals(diagdiagprod) <- alist(x=, y=x)
578 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
579 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
580 : maechler 1654 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
581 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
582 : maechler 1654 setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"),
583 :     diagdiagprod, valueClass = "ddiMatrix")
584 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
585 :     diagdiagprod, valueClass = "ddiMatrix")
586 : maechler 1109
587 :    
588 : mmaechler 2998 ## analogous to matdiagprod() below:
589 : maechler 1109 diagmatprod <- function(x, y) {
590 : mmaechler 2183 ## x is diagonalMatrix
591 : mmaechler 2998 if(x@Dim[2] != nrow(y)) stop("non-matching dimensions")
592 :     Matrix(if(x@diag == "U") y else x@x * y)
593 : maechler 1109 }
594 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
595 : maechler 1654 diagmatprod)
596 : mmaechler 2183 ## sneaky .. :
597 : maechler 1109 formals(diagmatprod) <- alist(x=, y=NULL)
598 : mmaechler 2998 setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"), diagmatprod)
599 : maechler 1109
600 : mmaechler 2183 diagGeprod <- function(x, y) {
601 : mmaechler 2998 if(x@Dim[2] != y@Dim[1]) stop("non-matching dimensions")
602 : maechler 1109 if(x@diag != "U")
603 :     y@x <- x@x * y@x
604 :     y
605 :     }
606 : mmaechler 2183 setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
607 :     setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
608 :     formals(diagGeprod) <- alist(x=, y=NULL)
609 : maechler 1109 setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
610 : mmaechler 2183 diagGeprod, valueClass = "dgeMatrix")
611 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
612 :     diagGeprod)
613 : maechler 1109
614 : mmaechler 2998 ## analogous to diagmatprod() above:
615 : mmaechler 2183 matdiagprod <- function(x, y) {
616 :     dx <- dim(x)
617 : mmaechler 2998 if(dx[2] != y@Dim[1]) stop("non-matching dimensions")
618 : mmaechler 2183 Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
619 :     }
620 : mmaechler 2998 setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"), matdiagprod)
621 : mmaechler 2183 formals(matdiagprod) <- alist(x=, y=NULL)
622 : mmaechler 2998 setMethod("tcrossprod",signature(x = "matrix", y = "diagonalMatrix"), matdiagprod)
623 :     setMethod("crossprod", signature(x = "matrix", y = "diagonalMatrix"),
624 :     function(x, y=NULL) {
625 :     dx <- dim(x)
626 :     if(dx[1] != y@Dim[1]) stop("non-matching dimensions")
627 :     Matrix(t(rep.int(y@x, dx[2]) * x))
628 :     })
629 : maechler 1109
630 : mmaechler 2183 gediagprod <- function(x, y) {
631 :     dx <- dim(x)
632 : mmaechler 2998 if(dx[2] != y@Dim[1]) stop("non-matching dimensions")
633 : mmaechler 2183 if(y@diag == "N")
634 :     x@x <- x@x * rep(y@x, each = dx[1])
635 :     x
636 :     }
637 :     setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
638 :     setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
639 :     formals(gediagprod) <- alist(x=, y=NULL)
640 :     setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
641 :     gediagprod)
642 :     setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
643 :     gediagprod)
644 : maechler 1109
645 : maechler 1295 ## crossprod {more of these}
646 : maechler 1109
647 : maechler 1295 ## tcrossprod --- all are not yet there: do the dense ones here:
648 : maechler 1109
649 : mmaechler 2183 setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
650 :     function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
651 :     setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
652 :     function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
653 :    
654 :    
655 : maechler 1295 ## FIXME:
656 :     ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
657 :     ## function(x, y = NULL) {
658 :     ## })
659 : maechler 1109
660 : mmaechler 2912 ##' @param x CsparseMatrix
661 :     ##' @param y diagonalMatrix
662 :     ##' @return x %*% y
663 : dmbates 2417 Cspdiagprod <- function(x, y) {
664 : mmaechler 2998 m <- ncol(x <- .Call(Csparse_diagU2N, x))
665 :     if(m != y@Dim[1]) stop("non-matching dimensions")
666 : mmaechler 2912 if(y@diag == "N") { ## otherwise: y == Diagonal(n) : multiplication is identity
667 : mmaechler 2674 if(!all(y@x[1L] == y@x[-1L]) && is(x, "symmetricMatrix"))
668 :     x <- as(x, "generalMatrix")
669 : mmaechler 2998 ind <- rep.int(seq_len(m), x@p[-1] - x@p[-m-1L])
670 : mmaechler 2674 x@x <- x@x * y@x[ind]
671 : mmaechler 2978 if(.hasSlot(x, "factors") && length(x@factors)) {# drop cashed ones
672 : mmaechler 2912 ## instead of dropping all factors, be smart about some
673 :     ## TODO ......
674 :     x@factors <- list()
675 :     }
676 : mmaechler 2674 }
677 : dmbates 2417 x
678 :     }
679 : maechler 1109
680 : mmaechler 2912 ##' @param x diagonalMatrix
681 :     ##' @param y CsparseMatrix
682 :     ##' @return x %*% y
683 : dmbates 2417 diagCspprod <- function(x, y) {
684 : mmaechler 2998 y <- .Call(Csparse_diagU2N, y)
685 :     if(x@Dim[2] != y@Dim[1]) stop("non-matching dimensions")
686 : mmaechler 2984 if(x@diag == "N") {
687 : mmaechler 2674 if(!all(x@x[1L] == x@x[-1L]) && is(y, "symmetricMatrix"))
688 :     y <- as(y, "generalMatrix")
689 :     y@x <- y@x * x@x[y@i + 1L]
690 : mmaechler 2978 if(.hasSlot(y, "factors") && length(yf <- y@factors)) {
691 : mmaechler 2912 ## TODO
692 :     if(FALSE) { ## instead of dropping all factors, be smart about some
693 :     keep <- character()
694 :     if(any(iLU <- names(yf) == "LU")) {
695 :     keep <- "LU"
696 :     }
697 :     y@factors <- yf[keep]
698 :     } else y@factors <- list() ## for now
699 :     }
700 : mmaechler 2674 }
701 : dmbates 2417 y
702 :     }
703 :    
704 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
705 :     function(x, y = NULL) diagCspprod(x, y))
706 :    
707 : maechler 1799 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
708 : dmbates 2417 function(x, y = NULL) diagCspprod(x, as(y, "CsparseMatrix")))
709 : maechler 1295
710 : dmbates 2417 ## Prefer calling diagCspprod to Cspdiagprod if going to transpose anyway
711 :     ## x'y == (y'x)'
712 :     setMethod("crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
713 :     function(x, y = NULL) t(diagCspprod(y, x)))
714 :    
715 : maechler 1799 setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
716 : dmbates 2417 function(x, y = NULL) t(diagCspprod(y, as(x, "Csparsematrix"))))
717 : maechler 1799
718 : dmbates 2417 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
719 :     function(x, y = NULL) diagCspprod(x, t(y)))
720 :    
721 : maechler 1799 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
722 : dmbates 2417 function(x, y = NULL) diagCspprod(x, t(as(y, "CsparseMatrix"))))
723 : maechler 1799
724 : dmbates 2417 setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
725 :     function(x, y = NULL) Cspdiagprod(x, y))
726 :    
727 : maechler 1799 setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
728 : dmbates 2417 function(x, y = NULL) Cspdiagprod(as(x, "CsparseMatrix"), y))
729 : mmaechler 2472
730 : dmbates 2417 setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
731 :     function(x, y) diagCspprod(x, y))
732 : maechler 1799
733 : mmaechler 2912 ## instead of "sparseMatrix", use: [RT]sparse.. ("closer" in method dispatch)
734 :     for(cl in c("TsparseMatrix", "RsparseMatrix")) {
735 :    
736 : maechler 1799 setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
737 : dmbates 2417 function(x, y) diagCspprod(as(x, "CsparseMatrix"), y))
738 : mmaechler 2472
739 : mmaechler 2183 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
740 : dmbates 2417 function(x, y) Cspdiagprod(as(x, "CsparseMatrix"), y))
741 : mmaechler 2912 }
742 : dmbates 2417
743 : maechler 1799 setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
744 : dmbates 2417 function(x, y) Cspdiagprod(x, y))
745 :    
746 : maechler 1799 ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
747 :     ## do indeed work by going through sparse (and *not* ddense)!
748 :    
749 :     setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
750 :     function(a, b, ...) {
751 :     a@x <- 1/ a@x
752 :     a@Dimnames <- a@Dimnames[2:1]
753 :     a
754 :     })
755 :    
756 :     solveDiag <- function(a, b, ...) {
757 : mmaechler 2633 if(a@Dim[1] != nrow(b))
758 : maechler 1799 stop("incompatible matrix dimensions")
759 :     ## trivially invert a 'in place' and multiply:
760 :     a@x <- 1/ a@x
761 :     a@Dimnames <- a@Dimnames[2:1]
762 :     a %*% b
763 :     }
764 :     setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
765 :     solveDiag)
766 :     setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
767 :     solveDiag)
768 :    
769 : maechler 2106 ## Schur() ---> ./eigen.R
770 : maechler 1799
771 :    
772 :    
773 : mmaechler 2175 ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
774 : maechler 1295
775 : maechler 1655 ## Use function for several signatures, in order to evade
776 : mmaechler 2175 diagOdiag <- function(e1,e2) {
777 :     ## result should also be diagonal _ if possible _
778 : maechler 1655 r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
779 : mmaechler 2175 ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
780 :     r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
781 :     if(is.numeric(e2@x)) 0 else FALSE)
782 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal
783 : mmaechler 2814 if(is.numeric(r)) { # "double" *or* "integer"
784 : mmaechler 2175 if(is.numeric(e2@x)) {
785 :     e2@x <- r; return(.diag.2N(e2)) }
786 :     if(!is.numeric(e1@x))
787 :     ## e.g. e1, e2 are logical;
788 :     e1 <- as(e1, "dMatrix")
789 : mmaechler 2814 if(!is.double(r)) r <- as.double(r)
790 : mmaechler 2175 }
791 :     else if(is.logical(r))
792 :     e1 <- as(e1, "lMatrix")
793 : mmaechler 2863 else stop(gettextf("intermediate 'r' is of type %s",
794 :     typeof(r)), domain=NA)
795 : mmaechler 2175 e1@x <- r
796 :     .diag.2N(e1)
797 : maechler 1655 }
798 : mmaechler 2175 else { ## result not diagonal, but at least symmetric:
799 : mmaechler 2496 ## e.g., m == m
800 : mmaechler 2175 isNum <- (is.numeric(r) || is.numeric(r00))
801 :     isLog <- (is.logical(r) || is.logical(r00))
802 : mmaechler 2496 Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
803 : mmaechler 2175 d <- e1@Dim
804 :     n <- d[1]
805 :     stopifnot(length(r) == n)
806 : mmaechler 2814 if(isNum && !is.double(r)) r <- as.double(r)
807 : mmaechler 2175 xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
808 :     newcl <-
809 : mmaechler 2811 paste0(if(isNum) "d" else if(isLog) {
810 : mmaechler 2175 if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
811 : mmaechler 2811 } else stop("not yet implemented .. please report"), "syMatrix")
812 : mmaechler 2175
813 :     new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
814 :     }
815 : maechler 1655 }
816 :    
817 : mmaechler 2175 ### This would be *the* way, but we get tons of "ambiguous method dispatch"
818 : mmaechler 2185 ## we use this hack instead of signature x = "diagonalMatrix" :
819 :     diCls <- names(getClass("diagonalMatrix")@subclasses)
820 : mmaechler 2175 if(FALSE) {
821 : maechler 1655 setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
822 :     diagOdiag)
823 : mmaechler 2175 } else { ## These are just for method disambiguation:
824 :     for(c1 in diCls)
825 :     for(c2 in diCls)
826 :     setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
827 :     }
828 : maechler 1655
829 : mmaechler 2493 ## diagonal o triangular |--> triangular
830 :     ## diagonal o symmetric |--> symmetric
831 : maechler 1845 ## {also when other is sparse: do these "here" --
832 :     ## before conversion to sparse, since that loses "diagonality"}
833 : mmaechler 2811 diagOtri <- function(e1,e2) {
834 :     ## result must be triangular
835 :     r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible"
836 :     ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
837 :     e1.0 <- if(.n1 <- is.numeric(d1 )) 0 else FALSE
838 :     r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0])) 0 else FALSE)
839 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* triangular
840 :     diag(e2) <- r
841 :     ## check what happens "in the triangle"
842 :     e2.2 <- if(.n2) 2 else TRUE
843 :     if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change:
844 :     n <- dim(e2)[1L]
845 :     it <- indTri(n, upper = (e2@uplo == "U"))
846 :     e2[it] <- callGeneric(e1.0, e2[it])
847 :     }
848 :     e2
849 :     }
850 :     else { ## result not triangular ---> general
851 :     rr <- as(e2, "generalMatrix")
852 :     diag(rr) <- r
853 :     rr
854 :     }
855 :     }
856 : maechler 1845
857 : mmaechler 2811
858 :     setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"),
859 :     diagOtri)
860 :     ## For the reverse, Ops == "Arith" | "Compare" | "Logic"
861 :     ## 'Arith' := '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"'
862 :     setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
863 :     function(e1,e2)
864 :     { ## this must only trigger for *dense* e1
865 :     switch(.Generic,
866 :     "+" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), .diag.x(e2)),
867 :     "-" = .Call(dtrMatrix_addDiag, as(e1,"dtrMatrix"), - .diag.x(e2)),
868 :     "*" = {
869 :     n <- e2@Dim[1L]
870 :     d2 <- if(e2@diag == "U") { # unit-diagonal
871 :     d <- rep.int(as1(e2@x), n)
872 :     e2@x <- d
873 :     e2@diag <- "N"
874 :     d
875 :     } else e2@x
876 :     e2@x <- diag(e1) * d2
877 :     e2
878 :     },
879 :     "^" = { ## will be dense ( as <ANY> ^ 0 == 1 ):
880 :     e1 ^ as(e2, "denseMatrix")
881 :     },
882 :     ## otherwise:
883 :     callGeneric(e1, diag2Tsmart(e2,e1)))
884 :     })
885 :    
886 :     ## Compare --> 'swap' (e.g. e1 < e2 <==> e2 > e1 ):
887 :     setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
888 :     .Cmp.swap)
889 :     ## '&' and "|' are commutative:
890 :     setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
891 :     function(e1,e2) callGeneric(e2, e1))
892 :    
893 : maechler 1655 ## For almost everything else, diag* shall be treated "as sparse" :
894 : maechler 1295 ## These are cheap implementations via coercion
895 :    
896 : maechler 2144 ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
897 :     ## and because we can save an .M.kind() call, we use this explicit
898 :     ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
899 :     ##
900 :     ## ddi*:
901 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
902 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
903 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
904 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
905 : maechler 2144 ## ldi*
906 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
907 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
908 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
909 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
910 : maechler 1654
911 : mmaechler 2820 ## Ops: Arith --> numeric : "dMatrix"
912 :     ## Compare --> logical
913 :     ## Logic --> logical: "lMatrix"
914 : mmaechler 2175
915 : mmaechler 2820 ## Other = "numeric" : stay diagonal if possible
916 : mmaechler 2175 ## ddi*: Arith: result numeric, potentially ddiMatrix
917 : mmaechler 2813 for(arg2 in c("numeric","logical"))
918 :     setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2),
919 : maechler 2144 function(e1,e2) {
920 : mmaechler 2820 n <- e1@Dim[1]
921 : maechler 2144 f0 <- callGeneric(0, e2)
922 : mmaechler 2945 if(all0(f0)) { # remain diagonal
923 : maechler 2157 L1 <- (le <- length(e2)) == 1L
924 : mmaechler 2820 if(e1@diag == "U") {
925 :     if(any((r <- callGeneric(1, e2)) != 1)) {
926 :     e1@diag <- "N"
927 :     e1@x[seq_len(n)] <- r # possibly recycling r
928 :     } ## else: result = e1 (is "U" diag)
929 :     } else {
930 : maechler 2144 r <- callGeneric(e1@x, e2)
931 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
932 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
933 :     }
934 :     e1
935 :     } else
936 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
937 : maechler 2144 })
938 : maechler 1655
939 : mmaechler 2813 for(arg1 in c("numeric","logical"))
940 :     setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"),
941 : maechler 2144 function(e1,e2) {
942 : mmaechler 2820 n <- e2@Dim[1]
943 : maechler 2144 f0 <- callGeneric(e1, 0)
944 : mmaechler 2945 if(all0(f0)) { # remain diagonal
945 : maechler 2157 L1 <- (le <- length(e1)) == 1L
946 : mmaechler 2820 if(e2@diag == "U") {
947 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
948 :     e2@diag <- "N"
949 :     e2@x[seq_len(n)] <- r # possibly recycling r
950 :     } ## else: result = e2 (is "U" diag)
951 :     } else {
952 : maechler 2144 r <- callGeneric(e1, e2@x)
953 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
954 :     e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
955 :     }
956 :     e2
957 :     } else
958 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
959 : maechler 2144 })
960 : mmaechler 2175
961 :     ## ldi* Arith --> result numeric, potentially ddiMatrix
962 : mmaechler 2813 for(arg2 in c("numeric","logical"))
963 :     setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2),
964 : mmaechler 2175 function(e1,e2) {
965 : mmaechler 2820 n <- e1@Dim[1]
966 : mmaechler 2175 f0 <- callGeneric(0, e2)
967 : mmaechler 2945 if(all0(f0)) { # remain diagonal
968 : mmaechler 2175 L1 <- (le <- length(e2)) == 1L
969 : mmaechler 2984 E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
970 : mmaechler 2820 ## storage.mode(E@x) <- "double"
971 :     if(e1@diag == "U") {
972 :     if(any((r <- callGeneric(1, e2)) != 1)) {
973 :     E@diag <- "N"
974 :     E@x[seq_len(n)] <- r # possibly recycling r
975 :     } ## else: result = E (is "U" diag)
976 :     } else {
977 : mmaechler 2175 r <- callGeneric(e1@x, e2)
978 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
979 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
980 : mmaechler 2814 }
981 : mmaechler 2820 E
982 :     } else
983 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
984 : mmaechler 2175 })
985 :    
986 : mmaechler 2813 for(arg1 in c("numeric","logical"))
987 :     setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"),
988 : mmaechler 2175 function(e1,e2) {
989 : mmaechler 2820 n <- e2@Dim[1]
990 : mmaechler 2175 f0 <- callGeneric(e1, 0)
991 : mmaechler 2945 if(all0(f0)) { # remain diagonal
992 : mmaechler 2175 L1 <- (le <- length(e1)) == 1L
993 : mmaechler 2984 E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
994 : mmaechler 2820 ## storage.mode(E@x) <- "double"
995 :     if(e2@diag == "U") {
996 :     if(any((r <- callGeneric(e1, 1)) != 1)) {
997 :     E@diag <- "N"
998 :     E@x[seq_len(n)] <- r # possibly recycling r
999 :     } ## else: result = E (is "U" diag)
1000 :     } else {
1001 : mmaechler 2175 r <- callGeneric(e1, e2@x)
1002 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1003 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1004 : mmaechler 2814 }
1005 : mmaechler 2820 E
1006 :     } else
1007 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
1008 : mmaechler 2175 })
1009 :    
1010 : mmaechler 2820 ## ddi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1011 :     ##
1012 :     ## Note that ("numeric", "ddiMatrix") is simply swapped, e.g.,
1013 :     if(FALSE) {
1014 :     selectMethod("<", c("numeric","lMatrix"))# Compare
1015 :     selectMethod("&", c("numeric","lMatrix"))# Logic
1016 :     } ## so we don't need to define a method here :
1017 :    
1018 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1019 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2),
1020 : mmaechler 2175 function(e1,e2) {
1021 : mmaechler 2820 n <- e1@Dim[1]
1022 : mmaechler 2175 f0 <- callGeneric(0, e2)
1023 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1024 : mmaechler 2175 L1 <- (le <- length(e2)) == 1L
1025 : mmaechler 2984 E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
1026 : mmaechler 2820 ## storage.mode(E@x) <- "logical"
1027 :     if(e1@diag == "U") {
1028 :     if(any((r <- callGeneric(1, e2)) != 1)) {
1029 :     E@diag <- "N"
1030 :     E@x[seq_len(n)] <- r # possibly recycling r
1031 :     } ## else: result = E (is "U" diag)
1032 :     } else {
1033 : mmaechler 2175 r <- callGeneric(e1@x, e2)
1034 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1035 :     E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1036 : mmaechler 2814 }
1037 : mmaechler 2820 E
1038 :     } else
1039 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
1040 : mmaechler 2175 })
1041 :    
1042 : mmaechler 2820 ## ldi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
1043 : mmaechler 2813 for(arg2 in c("numeric","logical"))
1044 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2),
1045 : maechler 2144 function(e1,e2) {
1046 : mmaechler 2820 n <- e1@Dim[1]
1047 : maechler 2144 f0 <- callGeneric(FALSE, e2)
1048 : mmaechler 2945 if(all0(f0)) { # remain diagonal
1049 : maechler 2157 L1 <- (le <- length(e2)) == 1L
1050 : mmaechler 2820
1051 :     if(e1@diag == "U") {
1052 :     if(any((r <- callGeneric(TRUE, e2)) != 1)) {
1053 :     e1@diag <- "N"
1054 :     e1@x[seq_len(n)] <- r # possibly recycling r
1055 :     } ## else: result = e1 (is "U" diag)
1056 :     } else {
1057 : maechler 2144 r <- callGeneric(e1@x, e2)
1058 : mmaechler 2820 ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
1059 :     e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
1060 :     }
1061 :     e1
1062 :     } else
1063 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
1064 : maechler 2144 })
1065 : maechler 1655
1066 : maechler 2144
1067 :     ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... }
1068 : mmaechler 2196 for(other in c("ANY", "Matrix", "dMatrix")) {
1069 :     ## ddi*:
1070 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
1071 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
1072 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
1073 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
1074 : mmaechler 2196 ## ldi*:
1075 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
1076 : mmaechler 2493 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
1077 : mmaechler 2196 setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
1078 : mmaechler 2493 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
1079 : mmaechler 2196 }
1080 : mmaechler 2331
1081 :     ## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
1082 :     dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
1083 : mmaechler 2813 names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] })
1084 : mmaechler 2268 for(DI in diCls) {
1085 : mmaechler 2814 dMeth <- if(extends(DI, "dMatrix"))
1086 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2)
1087 :     else # "lMatrix", the only other kind for now
1088 :     function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2)
1089 : mmaechler 2331 for(c2 in c(dense.subCl, "Matrix")) {
1090 : mmaechler 2814 for(Fun in c("*", "&")) {
1091 : mmaechler 2268 setMethod(Fun, signature(e1 = DI, e2 = c2),
1092 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
1093 :     setMethod(Fun, signature(e1 = c2, e2 = DI),
1094 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1095 :     }
1096 : mmaechler 2814 setMethod("^", signature(e1 = c2, e2 = DI),
1097 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
1098 :     for(Fun in c("%%", "%/%", "/")) ## 0 <op> 0 |--> NaN for these.
1099 :     setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth)
1100 : mmaechler 2175 }
1101 :     }
1102 : maechler 2144
1103 : mmaechler 3002 ## Group methods "Math", "Math2" in --> ./Math.R
1104 :    
1105 : mmaechler 2175 ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all"
1106 : mmaechler 2345 ### ---------- the last 4: separately here
1107 : mmaechler 2175 for(cl in diCls) {
1108 :     setMethod("any", cl,
1109 :     function (x, ..., na.rm) {
1110 :     if(any(x@Dim == 0)) FALSE
1111 :     else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
1112 :     })
1113 : mmaechler 2341 setMethod("all", cl, function (x, ..., na.rm) {
1114 :     n <- x@Dim[1]
1115 :     if(n >= 2) FALSE
1116 :     else if(n == 0 || x@diag == "U") TRUE
1117 :     else all(x@x, ..., na.rm = na.rm)
1118 :     })
1119 :     setMethod("prod", cl, function (x, ..., na.rm) {
1120 :     n <- x@Dim[1]
1121 :     if(n >= 2) 0
1122 :     else if(n == 0 || x@diag == "U") 1
1123 :     else ## n == 1, diag = "N" :
1124 :     prod(x@x, ..., na.rm = na.rm)
1125 :     })
1126 : mmaechler 2175
1127 :     setMethod("sum", cl,
1128 :     function(x, ..., na.rm) {
1129 :     r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
1130 :     if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
1131 :     })
1132 :     }
1133 :    
1134 :     ## The remaining ones are max, min, range :
1135 :    
1136 :     setMethod("Summary", "ddiMatrix",
1137 :     function(x, ..., na.rm) {
1138 :     if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
1139 :     else if(x@diag == "U")
1140 :     callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
1141 :     else callGeneric(x@x, 0, ..., na.rm=na.rm)
1142 :     })
1143 :     setMethod("Summary", "ldiMatrix",
1144 :     function(x, ..., na.rm) {
1145 :     if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
1146 :     else if(x@diag == "U")
1147 :     callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
1148 :     else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
1149 :     })
1150 :    
1151 :    
1152 :    
1153 : maechler 1109 ## similar to prTriang() in ./Auxiliaries.R :
1154 :     prDiag <-
1155 :     function(x, digits = getOption("digits"), justify = "none", right = TRUE)
1156 :     {
1157 :     cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
1158 :     cf[row(cf) == col(cf)] <-
1159 :     sapply(diag(x), format, digits = digits, justify = justify)
1160 :     print(cf, quote = FALSE, right = right)
1161 :     invisible(x)
1162 :     }
1163 :    
1164 : mmaechler 2237 ## somewhat consistent with "print" for sparseMatrix :
1165 :     setMethod("print", signature(x = "diagonalMatrix"), prDiag)
1166 :    
1167 : maechler 1109 setMethod("show", signature(object = "diagonalMatrix"),
1168 : maechler 1592 function(object) {
1169 :     d <- dim(object)
1170 :     cl <- class(object)
1171 : mmaechler 2203 cat(sprintf('%d x %d diagonal matrix of class "%s"',
1172 : maechler 1592 d[1], d[2], cl))
1173 : mmaechler 2203 if(d[1] < 50) {
1174 :     cat("\n")
1175 :     prDiag(object)
1176 :     } else {
1177 :     cat(", with diagonal entries\n")
1178 :     show(diag(object))
1179 :     invisible(object)
1180 :     }
1181 : maechler 1592 })
1182 : mmaechler 2813
1183 : mmaechler 2998 rm(arg1, arg2, other, DI, Fun, cl, c1, c2,
1184 : mmaechler 2898 dense.subCl, diCls)# not used elsewhere
1185 : mmaechler 2820
1186 :     setMethod("summary", signature(object = "diagonalMatrix"),
1187 :     function(object, ...) {
1188 :     d <- dim(object)
1189 :     r <- summary(object@x, ...)
1190 :     attr(r, "header") <-
1191 :     sprintf('%d x %d diagonal Matrix of class "%s"',
1192 :     d[1], d[2], class(object))
1193 :     ## use ole' S3 technology for such a simple case
1194 :     class(r) <- c("diagSummary", class(r))
1195 :     r
1196 :     })
1197 :    
1198 :     print.diagSummary <- function (x, ...) {
1199 :     cat(attr(x, "header"),"\n")
1200 :     class(x) <- class(x)[-1]
1201 :     print(x, ...)
1202 :     invisible(x)
1203 :     }

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