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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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Revision 2268 - (view) (download)
Original Path: pkg/R/diagMatrix.R

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 2226 .sparseDiagonal <- function(n, x = rep.int(1,n), uplo = "U", shape = "t") {
36 : maechler 2144 stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
37 :     if((lx <- length(x)) == 1) x <- rep.int(x, n)
38 :     else if(lx != n) stop("length(x) must be 1 or n")
39 : mmaechler 2226 stopifnot(is.character(shape), nchar(shape) == 1,
40 :     any(shape == c("t","s","g"))) # triangular / symmetric / general
41 :     kind <-
42 :     if(is.double(x)) "d"
43 :     else if(is.logical(x)) "l"
44 :     else { ## for now
45 :     storage.mode(x) <- "double"
46 :     "d"
47 :     }
48 :     new(paste(kind, shape, "CMatrix", sep=''),
49 :     Dim = c(n,n), x = x, uplo = uplo,
50 :     i = if(n) 0:(n - 1L) else integer(0), p = 0:n)
51 : maechler 2144 }
52 :    
53 : mmaechler 2226 ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
54 :     .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
55 :     .sparseDiagonal(n, x, uplo, shape = "s")
56 :    
57 :     ## instead of diagU2N(as(Diagonal(n), "CsparseMatrix")), diag = "N" in any case:
58 :     .trDiagonal <- function(n, x = rep.int(1,n), uplo = "U")
59 :     .sparseDiagonal(n, x, uplo, shape = "t")
60 :    
61 :    
62 : maechler 1617 ### This is modified from a post of Bert Gunter to R-help on 1 Sep 2005.
63 :     ### Bert's code built on a post by Andy Liaw who most probably was influenced
64 :     ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
65 :     ### who posted his bdiag() function written in December 1995.
66 : mmaechler 2209 if(FALSE)##--- no longer used:
67 : mmaechler 2206 .bdiag <- function(lst) {
68 :     ### block-diagonal matrix [a dgTMatrix] from list of matrices
69 :     stopifnot(is.list(lst), length(lst) >= 1)
70 :     dims <- sapply(lst, dim, USE.NAMES=FALSE)
71 : maechler 1617 ## make sure we had all matrices:
72 :     if(!(is.matrix(dims) && nrow(dims) == 2))
73 :     stop("some arguments are not matrices")
74 : maechler 1845 csdim <- rbind(rep.int(0L, 2),
75 : mmaechler 2206 apply(dims, 1, cumsum))
76 :     r <- new("dgTMatrix")
77 :     r@Dim <- as.integer(csdim[nrow(csdim),])
78 : maechler 1617 add1 <- matrix(1:0, 2,2)
79 : mmaechler 2206 for(i in seq_along(lst)) {
80 : maechler 1617 indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
81 :     if(is.null(dim(indx))) ## non-square matrix
82 : mmaechler 2206 r[indx[[1]],indx[[2]]] <- lst[[i]]
83 : maechler 1617 else ## square matrix
84 : mmaechler 2206 r[indx[,1], indx[,2]] <- lst[[i]]
85 : maechler 1617 }
86 : mmaechler 2206 r
87 : maechler 1617 }
88 : mmaechler 2209 ## expand(<mer>) needed something like bdiag() for lower-triangular
89 :     ## (Tsparse) Matrices; hence Doug Bates provided a much more efficient
90 :     ## implementation for those; now extended and generalized:
91 : mmaechler 2206 .bdiag <- function(lst) {
92 : mmaechler 2209 ## block-diagonal matrix [a dgTMatrix] from list of matrices
93 : mmaechler 2206 stopifnot(is.list(lst), (nl <- length(lst)) >= 1)
94 : maechler 1617
95 : mmaechler 2206 Tlst <- lapply(lapply(lst, Matrix:::as_Csp2), # includes "diagU2N"
96 : mmaechler 2209 as, "TsparseMatrix")
97 : mmaechler 2206 if(nl == 1) return(Tlst[[1]])
98 :     ## else
99 :     i_off <- c(0L, cumsum(sapply(Tlst, nrow)))
100 :     j_off <- c(0L, cumsum(sapply(Tlst, ncol)))
101 : mmaechler 2209
102 :     clss <- sapply(Tlst, class)
103 :     knds <- substr(clss, 2, 2)
104 :     sym <- knds == "s" # symmetric ones
105 :     tri <- knds == "t" # triangular ones
106 :     use.n <- any(is.n <- substr(clss,1,1) == "n")
107 :     if(use.n && !(use.n <- all(is.n)))
108 :     Tlst[is.n] <- lapply(Tlst[is.n], as, "lMatrix")
109 :     if(all(sym)) { ## result should be *symmetric*
110 :     uplos <- sapply(Tlst, slot, "uplo") ## either "U" or "L"
111 :     tLU <- table(uplos)# of length 1 or 2 ..
112 :     if(length(tLU) == 1) { ## all "U" or all "L"
113 :     useU <- uplos[1] == "U"
114 :     } else { ## length(tLU) == 2, counting "L" and "U"
115 :     useU <- diff(tLU) >= 0
116 :     if(useU && (hasL <- tLU[1] > 0))
117 :     Tlst[hasL] <- lapply(Tlst[hasL], t)
118 :     else if(!useU && (hasU <- tLU[2] > 0))
119 :     Tlst[hasU] <- lapply(Tlst[hasU], t)
120 :     }
121 :     if(use.n) { ## return nsparseMatrix :
122 :     r <- new("nsTMatrix")
123 :     } else {
124 :     r <- new("dsTMatrix")
125 :     r@x <- unlist(lapply(Tlst, slot, "x"))
126 :     }
127 :     r@uplo <- if(useU) "U" else "L"
128 :     }
129 :     else if(all(tri) && { ULs <- sapply(Tlst, slot, "uplo")## "U" or "L"
130 :     all(ULs[1L] == ULs[-1L]) } ## all upper or all lower
131 :     ){ ## *triangular* result
132 :    
133 :     if(use.n) { ## return nsparseMatrix :
134 :     r <- new("ntTMatrix")
135 :     } else {
136 :     r <- new("dtTMatrix")
137 :     r@x <- unlist(lapply(Tlst, slot, "x"))
138 :     }
139 :     r@uplo <- ULs[1L]
140 :     }
141 :     else {
142 :     if(any(sym))
143 :     Tlst[sym] <- lapply(Tlst[sym], as, "generalMatrix")
144 :     if(use.n) { ## return nsparseMatrix :
145 :     r <- new("ngTMatrix")
146 :     } else {
147 :     r <- new("dgTMatrix")
148 :     r@x <- unlist(lapply(Tlst, slot, "x"))
149 :     }
150 :     }
151 :     r@Dim <- c(i_off[nl+1], j_off[nl + 1])
152 :     r@i <- unlist(lapply(1:nl, function(k) Tlst[[k]]@i + i_off[k]))
153 :     r@j <- unlist(lapply(1:nl, function(k) Tlst[[k]]@j + j_off[k]))
154 :     r
155 : mmaechler 2206 }
156 :    
157 :     bdiag <- function(...) {
158 :     if((nA <- nargs()) == 0) return(new("dgCMatrix"))
159 :     if(nA == 1 && !is.list(...))
160 :     return(as(..., "CsparseMatrix"))
161 :     alis <- if(nA == 1 && is.list(..1)) ..1 else list(...)
162 :     if(length(alis) == 1)
163 :     return(as(alis[[1]], "CsparseMatrix"))
164 :    
165 :     ## else : two or more arguments
166 :     as(.bdiag(alis), "CsparseMatrix")
167 :     }
168 :    
169 :    
170 : maechler 2136 .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
171 :     ## to triangular Tsparse
172 : maechler 1845 i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
173 : maechler 2136 new(paste(kind, "tTMatrix", sep=''),
174 : maechler 1654 diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
175 : maechler 2128 uplo = uplo,
176 : maechler 1654 x = from@x, # <- ok for diag = "U" and "N" (!)
177 :     i = i, j = i)
178 :     }
179 : maechler 1109
180 : maechler 2136 .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
181 :     ## to symmetric Tsparse
182 : maechler 2128 n <- from@Dim[1]
183 :     i <- seq_len(n) - 1L
184 :     new(paste(kind, "sTMatrix", sep=''),
185 : maechler 1845 Dim = from@Dim, Dimnames = from@Dimnames,
186 : maechler 2128 i = i, j = i, uplo = uplo,
187 :     x = if(from@diag == "N") from@x else ## "U"-diag
188 :     rep.int(switch(kind,
189 :     "d" = 1.,
190 :     "l" =,
191 :     "n" = TRUE,
192 :     ## otherwise
193 :     stop("'", kind,"' kind not yet implemented")), n))
194 : maechler 1845 }
195 :    
196 : maechler 2128 ## diagonal -> triangular, upper / lower depending on "partner":
197 : maechler 2144 diag2tT.u <- function(d, x, kind = .M.kind(d))
198 :     .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
199 : maechler 2128
200 : mmaechler 2175 ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
201 :     diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
202 :     clx <- getClassDef(class(x))
203 :     if(extends(clx, "symmetricMatrix"))
204 :     .diag2sT(d, uplo = x@uplo, kind)
205 :     else
206 :     .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
207 :     }
208 : maechler 2136
209 : mmaechler 2175
210 : maechler 2136 ## In order to evade method dispatch ambiguity warnings,
211 :     ## and because we can save a .M.kind() call, we use this explicit
212 :     ## "hack" instead of signature x = "diagonalMatrix" :
213 :     ##
214 :     ## ddi*:
215 :     diag2tT <- function(from) .diag2tT(from, "U", "d")
216 :     setAs("ddiMatrix", "triangularMatrix", diag2tT)
217 : mmaechler 2239 ##_no_longer_ setAs("ddiMatrix", "sparseMatrix", diag2tT)
218 : maechler 1805 ## needed too (otherwise <dense> -> Tsparse is taken):
219 : maechler 2136 setAs("ddiMatrix", "TsparseMatrix", diag2tT)
220 :     setAs("ddiMatrix", "CsparseMatrix",
221 :     function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
222 :     setAs("ddiMatrix", "symmetricMatrix",
223 :     function(from) .diag2sT(from, "U", "d"))
224 :     ##
225 :     ## ldi*:
226 :     diag2tT <- function(from) .diag2tT(from, "U", "l")
227 :     setAs("ldiMatrix", "triangularMatrix", diag2tT)
228 : mmaechler 2239 ##_no_longer_ setAs("ldiMatrix", "sparseMatrix", diag2tT)
229 : maechler 2136 ## needed too (otherwise <dense> -> Tsparse is taken):
230 :     setAs("ldiMatrix", "TsparseMatrix", diag2tT)
231 :     setAs("ldiMatrix", "CsparseMatrix",
232 :     function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
233 :     setAs("ldiMatrix", "symmetricMatrix",
234 :     function(from) .diag2sT(from, "U", "l"))
235 : maechler 1654
236 : maechler 1845
237 : maechler 2128 setAs("diagonalMatrix", "nMatrix",
238 :     function(from) {
239 :     n <- from@Dim[1]
240 :     i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
241 :     new("ntTMatrix", i = i, j = i, diag = from@diag,
242 :     Dim = from@Dim, Dimnames = from@Dimnames)
243 :     })
244 :    
245 : mmaechler 2237 setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))
246 : maechler 2128
247 : mmaechler 2175 ## Cheap fast substitute for diag() which *does* preserve the mode of x :
248 :     mkDiag <- function(x, n) {
249 :     y <- matrix(as0(mod=mode(x)), n,n)
250 :     if (n > 0) y[1L + 0:(n - 1L) * (n + 1L)] <- x
251 :     y
252 :     }
253 :    
254 : maechler 1109 setAs("diagonalMatrix", "matrix",
255 :     function(from) {
256 : mmaechler 2175 ## want "ldiMatrix" -> <logical> "matrix" :
257 :     mkDiag(if(from@diag == "U") as1(from@x) else from@x,
258 :     n = from@Dim[1])
259 : maechler 1109 })
260 :    
261 : maechler 2098 setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
262 :     function(x, mode) {
263 :     n <- x@Dim[1]
264 : mmaechler 2175 mod.x <- mode(x@x)
265 :     r <- vector(mod.x, length = n^2)
266 : maechler 2098 if(n)
267 :     r[1 + 0:(n - 1) * (n + 1)] <-
268 : mmaechler 2175 if(x@diag == "U") as1(mod=mod.x) else x@x
269 : maechler 2098 r
270 :     })
271 :    
272 : maechler 1654 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
273 : maechler 2128 function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
274 : maechler 1174
275 : mmaechler 2268 setAs("diagonalMatrix", "denseMatrix",
276 :     function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))
277 :    
278 : mmaechler 2185 .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
279 : maechler 1655
280 :     .diag.2N <- function(m) {
281 :     if(m@diag == "U") m@diag <- "N"
282 :     m
283 :     }
284 :    
285 : maechler 1174 setAs("ddiMatrix", "dgeMatrix",
286 : mmaechler 2183 function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
287 :     setAs("ddiMatrix", "ddenseMatrix",
288 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
289 :     setAs("ldiMatrix", "ldenseMatrix",
290 :     function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
291 : maechler 1174
292 : mmaechler 2183
293 : maechler 1109 setAs("matrix", "diagonalMatrix",
294 :     function(from) {
295 : maechler 1295 d <- dim(from)
296 : maechler 1109 if(d[1] != (n <- d[2])) stop("non-square matrix")
297 :     if(any(from[row(from) != col(from)] != 0))
298 :     stop("has non-zero off-diagonal entries")
299 : maechler 1295 x <- diag(from)
300 :     if(is.logical(x)) {
301 :     cl <- "ldiMatrix"
302 :     uni <- all(x)
303 :     } else {
304 :     cl <- "ddiMatrix"
305 :     uni <- all(x == 1)
306 :     storage.mode(x) <- "double"
307 : maechler 1575 } ## TODO: complex
308 : maechler 1295 new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
309 :     x = if(uni) x[FALSE] else x)
310 : maechler 1109 })
311 :    
312 :     ## ``generic'' coercion to diagonalMatrix : build on isDiagonal() and diag()
313 :     setAs("Matrix", "diagonalMatrix",
314 :     function(from) {
315 :     d <- dim(from)
316 :     if(d[1] != (n <- d[2])) stop("non-square matrix")
317 :     if(!isDiagonal(from)) stop("matrix is not diagonal")
318 :     ## else:
319 :     x <- diag(from)
320 :     if(is.logical(x)) {
321 :     cl <- "ldiMatrix"
322 :     uni <- all(x)
323 :     } else {
324 :     cl <- "ddiMatrix"
325 :     uni <- all(x == 1)
326 :     storage.mode(x) <- "double"
327 :     }
328 :     new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
329 :     x = if(uni) x[FALSE] else x)
330 :     })
331 :    
332 : maechler 1708
333 : mmaechler 2185 setMethod("diag", signature(x = "diagonalMatrix"),
334 :     function(x = 1, nrow, ncol) .diag.x(x))
335 : maechler 1708
336 : maechler 2098 subDiag <- function(x, i, j, ..., drop) {
337 : mmaechler 2239 x <- as(x, "TsparseMatrix")
338 : maechler 1799 x <- if(missing(i))
339 :     x[, j, drop=drop]
340 :     else if(missing(j))
341 :     x[i, , drop=drop]
342 :     else
343 :     x[i,j, drop=drop]
344 : maechler 2120 if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
345 : maechler 1799 }
346 :    
347 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
348 :     j = "index", drop = "logical"), subDiag)
349 :     setMethod("[", signature(x = "diagonalMatrix", i = "index",
350 :     j = "missing", drop = "logical"),
351 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, i=i, drop=drop))
352 : maechler 1799 setMethod("[", signature(x = "diagonalMatrix", i = "missing",
353 :     j = "index", drop = "logical"),
354 : maechler 2098 function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
355 : maechler 1799
356 : maechler 1617 ## When you assign to a diagonalMatrix, the result should be
357 : maechler 1708 ## diagonal or sparse ---
358 :     ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
359 : maechler 2098 ## Only(?) current bug: x[i] <- value is wrong when i is *vector*
360 :     replDiag <- function(x, i, j, ..., value) {
361 : mmaechler 2239 x <- as(x, "TsparseMatrix")
362 : maechler 1710 if(missing(i))
363 :     x[, j] <- value
364 : maechler 2098 else if(missing(j)) { ## x[i , ] <- v *OR* x[i] <- v
365 :     na <- nargs()
366 :     ## message("diagnosing replDiag() -- nargs()= ", na)
367 :     if(na == 4)
368 :     x[i, ] <- value
369 :     else if(na == 3)
370 :     x[i] <- value
371 :     else stop("Internal bug: nargs()=",na,"; please report")
372 :     } else
373 : maechler 1710 x[i,j] <- value
374 :     if(isDiagonal(x)) as(x, "diagonalMatrix") else x
375 :     }
376 : maechler 1617
377 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
378 :     j = "index", value = "replValue"), replDiag)
379 : maechler 2098
380 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
381 :     j = "missing", value = "replValue"),
382 : maechler 2098 function(x,i,j, ..., value) {
383 :     ## message("before replDiag() -- nargs()= ", nargs())
384 :     if(nargs() == 3)
385 :     replDiag(x, i=i, value=value)
386 :     else ## nargs() == 4 :
387 :     replDiag(x, i=i, , value=value)
388 :     })
389 :    
390 : mmaechler 2192 setReplaceMethod("[", signature(x = "diagonalMatrix",
391 :     i = "matrix", # 2-col.matrix
392 : maechler 2096 j = "missing", value = "replValue"),
393 : maechler 2098 function(x,i,j, ..., value) {
394 : maechler 2096 if(ncol(i) == 2) {
395 :     if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
396 : mmaechler 2192 if(x@diag == "U") {
397 :     one <- as1(x@x)
398 :     if(any(value != one | is.na(value))) {
399 :     x@diag <- "N"
400 :     x@x <- rep.int(one, x@Dim[1])
401 :     }
402 :     }
403 : maechler 2096 x@x[ii] <- value
404 :     x
405 :     } else { ## no longer diagonal, but remain sparse:
406 : mmaechler 2239 x <- as(x, "TsparseMatrix")
407 : maechler 2096 x[i] <- value
408 :     x
409 :     }
410 :     }
411 :     else { # behave as "base R": use as if vector
412 :     x <- as(x, "matrix")
413 :     x[i] <- value
414 :     Matrix(x)
415 :     }
416 :     })
417 :    
418 : maechler 1710 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
419 :     j = "index", value = "replValue"),
420 : maechler 2098 function(x,i,j, ..., value) replDiag(x, j=j, value=value))
421 : maechler 1710
422 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
423 : mmaechler 2239 value = "sparseMatrix"),
424 : mmaechler 2207 function (x, i, j, ..., value)
425 :     callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
426 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
427 : mmaechler 2239 value = "sparseMatrix"),
428 : mmaechler 2207 function (x, i, j, ..., value)
429 :     callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
430 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
431 : mmaechler 2239 value = "sparseMatrix"),
432 : mmaechler 2207 function (x, i, j, ..., value)
433 :     callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))
434 : maechler 1710
435 : mmaechler 2207 setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
436 :     value = "sparseVector"),
437 :     replDiag)
438 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
439 :     value = "sparseVector"),
440 :     replDiag)
441 :     setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
442 :     value = "sparseVector"),
443 :     replDiag)
444 :    
445 :    
446 : maechler 1109 setMethod("t", signature(x = "diagonalMatrix"),
447 :     function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
448 :    
449 : maechler 1331 setMethod("isDiagonal", signature(object = "diagonalMatrix"),
450 :     function(object) TRUE)
451 :     setMethod("isTriangular", signature(object = "diagonalMatrix"),
452 :     function(object) TRUE)
453 : maechler 1109 setMethod("isSymmetric", signature(object = "diagonalMatrix"),
454 : maechler 2112 function(object, ...) TRUE)
455 : maechler 1109
456 : maechler 2112 setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
457 :     setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
458 :    
459 : maechler 2133 setMethod("chol", signature(x = "ddiMatrix"),
460 :     function(x, pivot, ...) {
461 : mmaechler 2183 if(x@diag == "U") return(x)
462 :     ## else
463 : maechler 2133 if(any(x@x < 0))
464 :     stop("chol() is undefined for diagonal matrix with negative entries")
465 : maechler 1654 x@x <- sqrt(x@x)
466 :     x
467 :     })
468 :     ## chol(L) is L for logical diagonal:
469 : maechler 2133 setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
470 : maechler 1654
471 : mmaechler 2175 setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
472 : mmaechler 2185 function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
473 : mmaechler 2175
474 : mmaechler 2183 setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
475 :     function(x, type, ...) {
476 :     if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
477 :     type <- toupper(substr(type[1], 1, 1))
478 :     isU <- (x@diag == "U") # unit-diagonal
479 :     if(type == "F") sqrt(if(isU) n else sum(x@x^2))
480 :     else { ## norm == "I","1","O","M" :
481 :     if(isU) 1 else max(abs(x@x))
482 :     }
483 :     })
484 :    
485 :    
486 :    
487 : maechler 1109 ## Basic Matrix Multiplication {many more to add}
488 : maechler 1654 ## ---------------------
489 :     ## Note that "ldi" logical are treated as numeric
490 : maechler 1109 diagdiagprod <- function(x, y) {
491 : mmaechler 2183 n <- dimCheck(x,y)[1]
492 : maechler 1109 if(x@diag != "U") {
493 : maechler 1654 if(y@diag != "U") {
494 :     nx <- x@x * y@x
495 :     if(is.numeric(nx) && !is.numeric(x@x))
496 :     x <- as(x, "dMatrix")
497 :     x@x <- as.numeric(nx)
498 :     }
499 :     return(x)
500 : maechler 1109 } else ## x is unit diagonal
501 :     return(y)
502 :     }
503 :    
504 : maechler 1654 setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
505 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
506 :    
507 : maechler 1654 formals(diagdiagprod) <- alist(x=, y=x)
508 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
509 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
510 : maechler 1654 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
511 : maechler 1109 diagdiagprod, valueClass = "ddiMatrix")
512 : maechler 1654 setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"),
513 :     diagdiagprod, valueClass = "ddiMatrix")
514 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
515 :     diagdiagprod, valueClass = "ddiMatrix")
516 : maechler 1109
517 :    
518 :     diagmatprod <- function(x, y) {
519 : mmaechler 2183 ## x is diagonalMatrix
520 : maechler 1109 dx <- dim(x)
521 :     dy <- dim(y)
522 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
523 :     n <- dx[1]
524 :     as(if(x@diag == "U") y else x@x * y, "Matrix")
525 :     }
526 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
527 : maechler 1654 diagmatprod)
528 : mmaechler 2183 ## sneaky .. :
529 : maechler 1109 formals(diagmatprod) <- alist(x=, y=NULL)
530 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
531 : maechler 1654 diagmatprod)
532 : maechler 1109
533 : mmaechler 2183 diagGeprod <- function(x, y) {
534 : maechler 1109 dx <- dim(x)
535 :     dy <- dim(y)
536 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
537 :     if(x@diag != "U")
538 :     y@x <- x@x * y@x
539 :     y
540 :     }
541 : mmaechler 2183 setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
542 :     setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
543 :     formals(diagGeprod) <- alist(x=, y=NULL)
544 : maechler 1109 setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
545 : mmaechler 2183 diagGeprod, valueClass = "dgeMatrix")
546 :     setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
547 :     diagGeprod)
548 : maechler 1109
549 : mmaechler 2183 matdiagprod <- function(x, y) {
550 :     dx <- dim(x)
551 :     dy <- dim(y)
552 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
553 :     Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
554 :     }
555 : maechler 1109 setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
556 : mmaechler 2183 matdiagprod)
557 :     formals(matdiagprod) <- alist(x=, y=NULL)
558 :     setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
559 :     matdiagprod)
560 : maechler 1109
561 : mmaechler 2183 gediagprod <- function(x, y) {
562 :     dx <- dim(x)
563 :     dy <- dim(y)
564 :     if(dx[2] != dy[1]) stop("non-matching dimensions")
565 :     if(y@diag == "N")
566 :     x@x <- x@x * rep(y@x, each = dx[1])
567 :     x
568 :     }
569 :     setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
570 :     setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
571 :     formals(gediagprod) <- alist(x=, y=NULL)
572 :     setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
573 :     gediagprod)
574 :     setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
575 :     gediagprod)
576 : maechler 1109
577 : maechler 1295 ## crossprod {more of these}
578 : maechler 1109
579 : maechler 1295 ## tcrossprod --- all are not yet there: do the dense ones here:
580 : maechler 1109
581 : mmaechler 2183 setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
582 :     function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
583 :     setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
584 :     function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
585 :    
586 :    
587 : maechler 1295 ## FIXME:
588 :     ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
589 :     ## function(x, y = NULL) {
590 :     ## })
591 : maechler 1109
592 : maechler 1295 ## setMethod("tcrossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),
593 :     ## function(x, y = NULL) {
594 :     ## })
595 : maechler 1109
596 : maechler 1799 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
597 : mmaechler 2239 function(x, y = NULL) crossprod(as(x, "TsparseMatrix"), y))
598 : maechler 1295
599 : maechler 1799 setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
600 : mmaechler 2239 function(x, y = NULL) crossprod(x, as(y, "TsparseMatrix")))
601 : maechler 1799
602 :     setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
603 : mmaechler 2239 function(x, y = NULL) tcrossprod(as(x, "TsparseMatrix"), y))
604 : maechler 1799
605 :     setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
606 : mmaechler 2239 function(x, y = NULL) tcrossprod(x, as(y, "TsparseMatrix")))
607 : maechler 1799
608 :    
609 :     ## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()
610 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
611 : mmaechler 2239 function(x, y) as(x, "TsparseMatrix") %*% y)
612 : mmaechler 2183 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
613 : mmaechler 2239 function(x, y) x %*% as(y, "TsparseMatrix"))
614 : maechler 1799 ## NB: The previous is *not* triggering for "ddi" o "dgC" (= distance 3)
615 :     ## since there's a "ddense" o "Csparse" at dist. 2 => triggers first.
616 :     ## ==> do this:
617 :     setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
618 :     function(x, y) as(x, "CsparseMatrix") %*% y)
619 :     setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
620 :     function(x, y) x %*% as(y, "CsparseMatrix"))
621 :     ## NB: this is *not* needed for Tsparse & Rsparse
622 :     ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
623 :     ## do indeed work by going through sparse (and *not* ddense)!
624 :    
625 :    
626 :    
627 :     setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
628 :     function(a, b, ...) {
629 :     a@x <- 1/ a@x
630 :     a@Dimnames <- a@Dimnames[2:1]
631 :     a
632 :     })
633 :    
634 :     solveDiag <- function(a, b, ...) {
635 :     if((n <- a@Dim[1]) != nrow(b))
636 :     stop("incompatible matrix dimensions")
637 :     ## trivially invert a 'in place' and multiply:
638 :     a@x <- 1/ a@x
639 :     a@Dimnames <- a@Dimnames[2:1]
640 :     a %*% b
641 :     }
642 :     setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
643 :     solveDiag)
644 :     setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
645 :     solveDiag)
646 :    
647 : maechler 2106 ## Schur() ---> ./eigen.R
648 : maechler 1799
649 :    
650 :    
651 : mmaechler 2175 ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
652 : maechler 1295
653 : maechler 1655 ## Use function for several signatures, in order to evade
654 :     ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)
655 : mmaechler 2175 diagOdiag <- function(e1,e2) {
656 :     ## result should also be diagonal _ if possible _
657 : maechler 1655 r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
658 : mmaechler 2175 ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
659 :     r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
660 :     if(is.numeric(e2@x)) 0 else FALSE)
661 :     if(is0(r00)) { ## r00 == 0 or FALSE --- result *is* diagonal
662 :     if(is.numeric(r)) {
663 :     if(is.numeric(e2@x)) {
664 :     e2@x <- r; return(.diag.2N(e2)) }
665 :     if(!is.numeric(e1@x))
666 :     ## e.g. e1, e2 are logical;
667 :     e1 <- as(e1, "dMatrix")
668 :     }
669 :     else if(is.logical(r))
670 :     e1 <- as(e1, "lMatrix")
671 :     else stop("intermediate 'r' is of type", typeof(r))
672 :     e1@x <- r
673 :     .diag.2N(e1)
674 : maechler 1655 }
675 : mmaechler 2175 else { ## result not diagonal, but at least symmetric:
676 :     isNum <- (is.numeric(r) || is.numeric(r00))
677 :     isLog <- (is.logical(r) || is.logical(r00))
678 :    
679 :     if(getOption("verbose"))
680 :     message("exploding <diag> o <diag> into dense matrix")
681 :     d <- e1@Dim
682 :     n <- d[1]
683 :     stopifnot(length(r) == n)
684 :     xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
685 :     newcl <-
686 :     paste(if(isNum) "d" else if(isLog) {
687 :     if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
688 :     } else stop("not yet implemented .. please report")
689 :     ,
690 :     "syMatrix", sep='')
691 :    
692 :     new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
693 :     }
694 : maechler 1655 }
695 :    
696 : mmaechler 2175 ### This would be *the* way, but we get tons of "ambiguous method dispatch"
697 : mmaechler 2185 ## we use this hack instead of signature x = "diagonalMatrix" :
698 :     diCls <- names(getClass("diagonalMatrix")@subclasses)
699 : mmaechler 2175 if(FALSE) {
700 : maechler 1655 setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
701 :     diagOdiag)
702 : mmaechler 2175 } else { ## These are just for method disambiguation:
703 :     for(c1 in diCls)
704 :     for(c2 in diCls)
705 :     setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
706 :     }
707 : maechler 1655
708 : maechler 1845 ## FIXME: diagonal o triangular |--> triangular
709 :     ## ----- diagonal o symmetric |--> symmetric
710 :     ## {also when other is sparse: do these "here" --
711 :     ## before conversion to sparse, since that loses "diagonality"}
712 :    
713 : maechler 1655 ## For almost everything else, diag* shall be treated "as sparse" :
714 : maechler 1295 ## These are cheap implementations via coercion
715 :    
716 : maechler 2144 ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
717 :     ## and because we can save an .M.kind() call, we use this explicit
718 :     ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
719 :     ##
720 :     ## ddi*:
721 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
722 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
723 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
724 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
725 : maechler 2144 ## ldi*
726 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
727 : mmaechler 2175 function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
728 : maechler 2144 setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
729 : mmaechler 2175 function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
730 : maechler 1654
731 : mmaechler 2175 ## Ops: Arith --> numeric : "dMatrix"
732 :     ## Compare --> logical
733 :     ## Logic --> logical: "lMatrix"
734 :    
735 : maechler 2144 ## other = "numeric" : stay diagonal if possible
736 : mmaechler 2175 ## ddi*: Arith: result numeric, potentially ddiMatrix
737 :     setMethod("Arith", signature(e1 = "ddiMatrix", e2 = "numeric"),
738 : maechler 2144 function(e1,e2) {
739 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
740 : maechler 2144 f0 <- callGeneric(0, e2)
741 :     if(all(is0(f0))) { # remain diagonal
742 : maechler 2157 L1 <- (le <- length(e2)) == 1L
743 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
744 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
745 : maechler 2144 e1@diag <- "N"
746 : maechler 2157 if(L1) r <- rep.int(r, n)
747 :     } else
748 : maechler 2144 r <- callGeneric(e1@x, e2)
749 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
750 : maechler 2144 return(e1)
751 :     }
752 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
753 :     })
754 : maechler 1655
755 : mmaechler 2175 setMethod("Arith", signature(e1 = "numeric", e2 = "ddiMatrix"),
756 : maechler 2144 function(e1,e2) {
757 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
758 : maechler 2144 f0 <- callGeneric(e1, 0)
759 :     if(all(is0(f0))) { # remain diagonal
760 : maechler 2157 L1 <- (le <- length(e1)) == 1L
761 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
762 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
763 : maechler 2144 e2@diag <- "N"
764 : maechler 2157 if(L1) r <- rep.int(r, n)
765 :     } else
766 : maechler 2144 r <- callGeneric(e1, e2@x)
767 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
768 : maechler 2144 return(e2)
769 :     }
770 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
771 :     })
772 : mmaechler 2175
773 :     ## ldi* Arith --> result numeric, potentially ddiMatrix
774 :     setMethod("Arith", signature(e1 = "ldiMatrix", e2 = "numeric"),
775 :     function(e1,e2) {
776 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
777 : mmaechler 2175 f0 <- callGeneric(0, e2)
778 :     if(all(is0(f0))) { # remain diagonal
779 :     L1 <- (le <- length(e2)) == 1L
780 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
781 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
782 :     e1@diag <- "N"
783 :     if(L1) r <- rep.int(r, n)
784 :     } else
785 :     r <- callGeneric(e1@x, e2)
786 :     e1 <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))
787 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
788 : mmaechler 2175 return(e1)
789 :     }
790 :     callGeneric(diag2tT.u(e1,e2, "d"), e2)
791 :     })
792 :    
793 :     setMethod("Arith", signature(e1 = "numeric", e2 = "ldiMatrix"),
794 :     function(e1,e2) {
795 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
796 : mmaechler 2175 f0 <- callGeneric(e1, 0)
797 :     if(all(is0(f0))) { # remain diagonal
798 :     L1 <- (le <- length(e1)) == 1L
799 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
800 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
801 :     e2@diag <- "N"
802 :     if(L1) r <- rep.int(r, n)
803 :     } else
804 :     r <- callGeneric(e1, e2@x)
805 :     e2 <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))
806 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
807 : mmaechler 2175 return(e2)
808 :     }
809 :     callGeneric(e1, diag2tT.u(e2,e1, "d"))
810 :     })
811 :    
812 :     ## ddi*: for "Ops" without Arith --> result logical, potentially ldi
813 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "numeric"),
814 :     function(e1,e2) {
815 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
816 : mmaechler 2175 f0 <- callGeneric(0, e2)
817 :     if(all(is0(f0))) { # remain diagonal
818 :     L1 <- (le <- length(e2)) == 1L
819 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
820 :     if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
821 :     e1@diag <- "N"
822 :     if(L1) r <- rep.int(r, n)
823 :     } else
824 :     r <- callGeneric(e1@x, e2)
825 :     e1 <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))
826 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
827 : mmaechler 2175 return(e1)
828 :     }
829 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
830 :     })
831 :    
832 :     setMethod("Ops", signature(e1 = "numeric", e2 = "ddiMatrix"),
833 :     function(e1,e2) {
834 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
835 : mmaechler 2175 f0 <- callGeneric(e1, 0)
836 :     if(all(is0(f0))) { # remain diagonal
837 :     L1 <- (le <- length(e1)) == 1L
838 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
839 :     if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
840 :     e2@diag <- "N"
841 :     if(L1) r <- rep.int(r, n)
842 :     } else
843 :     r <- callGeneric(e1, e2@x)
844 :     e2 <- copyClass(e2, "ldiMatrix", c("diag", "Dim", "Dimnames"))
845 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
846 : mmaechler 2175 return(e2)
847 :     }
848 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
849 :     })
850 :    
851 :     ## ldi*: for "Ops" without Arith --> result logical, potentially ldi
852 : maechler 2144 setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "numeric"),
853 :     function(e1,e2) {
854 : mmaechler 2203 n <- e1@Dim[1]; nsq <- n^2
855 : maechler 2144 f0 <- callGeneric(FALSE, e2)
856 :     if(all(is0(f0))) { # remain diagonal
857 : maechler 2157 L1 <- (le <- length(e2)) == 1L
858 :     if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
859 :     if(e1@diag == "U" && any((r <- callGeneric(TRUE, e2)) != 1)) {
860 : maechler 2144 e1@diag <- "N"
861 : maechler 2157 if(L1) r <- rep.int(r, n)
862 :     } else
863 : maechler 2144 r <- callGeneric(e1@x, e2)
864 : mmaechler 2197 e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
865 : maechler 2144 return(e1)
866 :     }
867 :     callGeneric(diag2tT.u(e1,e2, "l"), e2)
868 :     })
869 : maechler 1655
870 : maechler 2144 setMethod("Ops", signature(e1 = "numeric", e2 = "ldiMatrix"),
871 :     function(e1,e2) {
872 : mmaechler 2203 n <- e2@Dim[1]; nsq <- n^2
873 : maechler 2144 f0 <- callGeneric(e1, FALSE)
874 :     if(all(is0(f0))) { # remain diagonal
875 : maechler 2157 L1 <- (le <- length(e1)) == 1L
876 :     if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
877 :     if(e2@diag == "U" && any((r <- callGeneric(e1, TRUE)) != 1)) {
878 : maechler 2144 e2@diag <- "N"
879 : maechler 2157 if(L1) r <- rep.int(r, n)
880 :     } else
881 : maechler 2144 r <- callGeneric(e1, e2@x)
882 : mmaechler 2197 e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
883 : maechler 2144 return(e2)
884 :     }
885 :     callGeneric(e1, diag2tT.u(e2,e1, "l"))
886 :     })
887 :    
888 :    
889 :    
890 :     ## Not {"sparseMatrix", "numeric} : {"denseMatrix", "matrix", ... }
891 : mmaechler 2196 for(other in c("ANY", "Matrix", "dMatrix")) {
892 :     ## ddi*:
893 :     setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
894 :     function(e1,e2) callGeneric(diag2tT.u(e1,e2, "d"), e2))
895 :     setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
896 :     function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1, "d")))
897 :     ## ldi*:
898 :     setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
899 :     function(e1,e2) callGeneric(diag2tT.u(e1,e2, "l"), e2))
900 :     setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
901 :     function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1, "l")))
902 :     }
903 : mmaechler 2268 for(DI in diCls) {
904 : mmaechler 2175 for(c2 in c("denseMatrix", "Matrix")) {
905 : mmaechler 2268 for(Fun in c("*", "^", "&")) {
906 :     setMethod(Fun, signature(e1 = DI, e2 = c2),
907 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
908 :     setMethod(Fun, signature(e1 = c2, e2 = DI),
909 :     function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
910 :     }
911 :     ## NB: This arguably implicitly uses 0/0 :== 0 to keep diagonality
912 :     for(Fun in c("%%", "%/%", "/")) {
913 :     setMethod(Fun, signature(e1 = DI, e2 = c2),
914 :     function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
915 :     }
916 : mmaechler 2175 }
917 :     }
918 : maechler 2144
919 :    
920 : mmaechler 2175 ### "Summary" : "max" "min" "range" "prod" "sum" "any" "all"
921 :     ### ---------- any, all: separately here
922 :     for(cl in diCls) {
923 :     setMethod("any", cl,
924 :     function (x, ..., na.rm) {
925 :     if(any(x@Dim == 0)) FALSE
926 :     else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
927 :     })
928 :     setMethod("all", cl, function (x, ..., na.rm) any(x@Dim == 0))
929 :     setMethod("prod", cl, function (x, ..., na.rm) as.numeric(any(x@Dim == 0)))
930 :    
931 :     setMethod("sum", cl,
932 :     function(x, ..., na.rm) {
933 :     r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
934 :     if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
935 :     })
936 :     }
937 :    
938 :     ## The remaining ones are max, min, range :
939 :    
940 :     setMethod("Summary", "ddiMatrix",
941 :     function(x, ..., na.rm) {
942 :     if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
943 :     else if(x@diag == "U")
944 :     callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
945 :     else callGeneric(x@x, 0, ..., na.rm=na.rm)
946 :     })
947 :     setMethod("Summary", "ldiMatrix",
948 :     function(x, ..., na.rm) {
949 :     if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
950 :     else if(x@diag == "U")
951 :     callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
952 :     else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
953 :     })
954 :    
955 :    
956 :    
957 : maechler 1109 ## similar to prTriang() in ./Auxiliaries.R :
958 :     prDiag <-
959 :     function(x, digits = getOption("digits"), justify = "none", right = TRUE)
960 :     {
961 :     cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
962 :     cf[row(cf) == col(cf)] <-
963 :     sapply(diag(x), format, digits = digits, justify = justify)
964 :     print(cf, quote = FALSE, right = right)
965 :     invisible(x)
966 :     }
967 :    
968 : mmaechler 2237 ## somewhat consistent with "print" for sparseMatrix :
969 :     setMethod("print", signature(x = "diagonalMatrix"), prDiag)
970 :    
971 : maechler 1109 setMethod("show", signature(object = "diagonalMatrix"),
972 : maechler 1592 function(object) {
973 :     d <- dim(object)
974 :     cl <- class(object)
975 : mmaechler 2203 cat(sprintf('%d x %d diagonal matrix of class "%s"',
976 : maechler 1592 d[1], d[2], cl))
977 : mmaechler 2203 if(d[1] < 50) {
978 :     cat("\n")
979 :     prDiag(object)
980 :     } else {
981 :     cat(", with diagonal entries\n")
982 :     show(diag(object))
983 :     invisible(object)
984 :     }
985 : maechler 1592 })

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