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

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revision 1655, Mon Oct 30 17:16:27 2006 UTC revision 2197, Mon Jun 2 14:34:42 2008 UTC
# Line 16  Line 16 
16      if(missing(x)) ## unit diagonal matrix      if(missing(x)) ## unit diagonal matrix
17          new("ddiMatrix", Dim = c(n,n), diag = "U")          new("ddiMatrix", Dim = c(n,n), diag = "U")
18      else {      else {
19          stopifnot(length(x) == n)          lx <- length(x)
20            stopifnot(lx == 1 || lx == n) # but keep 'x' short for now
21          if(is.logical(x))          if(is.logical(x))
22              cl <- "ldiMatrix"              cl <- "ldiMatrix"
23          else if(is.numeric(x)) {          else if(is.numeric(x)) {
# Line 26  Line 27 
27          else if(is.complex(x)) {          else if(is.complex(x)) {
28              cl <- "zdiMatrix"  # will not yet work              cl <- "zdiMatrix"  # will not yet work
29          } else stop("'x' has invalid data type")          } else stop("'x' has invalid data type")
30          new(cl, Dim = c(n,n), diag = "N", x = x)          new(cl, Dim = c(n,n), diag = "N",
31                x = if(lx == 1) rep.int(x,n) else x)
32      }      }
33  }  }
34    
35    ## Pkg 'spdep' had (relatively slow) versions of this as_dsCMatrix_I()
36    .symDiagonal <- function(n, x = rep.int(1,n), uplo = "U") {
37        stopifnot(n == (n. <- as.integer(n)), (n <- n.) >= 0)
38        if((lx <- length(x)) == 1) x <- rep.int(x, n)
39        else if(lx != n) stop("length(x) must be 1 or n")
40        cls <-
41            if(is.double(x)) "dsCMatrix"
42            else if(is.logical(x)) "lsCMatrix"
43            else { ## for now
44                storage.mode(x) <- "double"
45                "dsCMatrix"
46            }
47        new(cls, Dim = c(n,n), x = x, uplo = uplo,
48            i = if(n) 0:(n - 1L) else integer(0), p = 0:n)
49    }
50    
51  ### This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.  ### This is modified from a post of Bert Gunter to R-help on  1 Sep 2005.
52  ### Bert's code built on a post by Andy Liaw who most probably was influenced  ### Bert's code built on a post by Andy Liaw who most probably was influenced
53  ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002  ### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
# Line 43  Line 61 
61      ## make sure we had all matrices:      ## make sure we had all matrices:
62      if(!(is.matrix(dims) && nrow(dims) == 2))      if(!(is.matrix(dims) && nrow(dims) == 2))
63          stop("some arguments are not matrices")          stop("some arguments are not matrices")
64      csdim <- rbind(rep.int(0:0, 2),      csdim <- rbind(rep.int(0L, 2),
65                     apply(sapply(mlist, dim), 1, cumsum))                     apply(sapply(mlist, dim), 1, cumsum))
66      ret <- new("dgTMatrix", Dim = as.integer(csdim[nrow(csdim),]))      ret <- new("dgTMatrix", Dim = as.integer(csdim[nrow(csdim),]))
67      add1 <- matrix(1:0, 2,2)      add1 <- matrix(1:0, 2,2)
# Line 58  Line 76 
76      as(ret, "CsparseMatrix")      as(ret, "CsparseMatrix")
77  }  }
78    
79  diag2T <- function(from) {  
80      i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1:1  .diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
81      new(paste(.M.kind(from), "tTMatrix", sep=''),      ## to triangular Tsparse
82        i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
83        new(paste(kind, "tTMatrix", sep=''),
84          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,          diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
85            uplo = uplo,
86          x = from@x, # <- ok for diag = "U" and "N" (!)          x = from@x, # <- ok for diag = "U" and "N" (!)
87          i = i, j = i)          i = i, j = i)
88  }  }
89    
90  setAs("diagonalMatrix", "triangularMatrix", diag2T)  .diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
91  setAs("diagonalMatrix", "sparseMatrix", diag2T)      ## to symmetric Tsparse
92  ## is better than this:      n <- from@Dim[1]
93  ## setAs("diagonalMatrix", "sparseMatrix",      i <- seq_len(n) - 1L
94  ##       function(from)      new(paste(kind, "sTMatrix", sep=''),
95  ##        as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix"))          Dim = from@Dim, Dimnames = from@Dimnames,
96  setAs("diagonalMatrix", "CsparseMatrix",          i = i, j = i, uplo = uplo,
97        function(from) as(diag2T(from), "CsparseMatrix"))          x = if(from@diag == "N") from@x else ## "U"-diag
98            rep.int(switch(kind,
99                           "d" = 1.,
100                           "l" =,
101                           "n" = TRUE,
102                           ## otherwise
103                           stop("'", kind,"' kind not yet implemented")), n))
104    }
105    
106    ## diagonal -> triangular,  upper / lower depending on "partner":
107    diag2tT.u <- function(d, x, kind = .M.kind(d))
108        .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind)
109    
110    ## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
111    diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
112        clx <- getClassDef(class(x))
113        if(extends(clx, "symmetricMatrix"))
114            .diag2sT(d, uplo = x@uplo, kind)
115        else
116            .diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
117    }
118    
119  setAs("diagonalMatrix", "matrix",  
120    ## In order to evade method dispatch ambiguity warnings,
121    ## and because we can save a .M.kind() call, we use this explicit
122    ## "hack"  instead of signature  x = "diagonalMatrix" :
123    ##
124    ## ddi*:
125    diag2tT <- function(from) .diag2tT(from, "U", "d")
126    setAs("ddiMatrix", "triangularMatrix", diag2tT)
127    setAs("ddiMatrix", "sparseMatrix", diag2tT)
128    ## needed too (otherwise <dense> -> Tsparse is taken):
129    setAs("ddiMatrix", "TsparseMatrix", diag2tT)
130    setAs("ddiMatrix", "CsparseMatrix",
131          function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
132    setAs("ddiMatrix", "symmetricMatrix",
133          function(from) .diag2sT(from, "U", "d"))
134    ##
135    ## ldi*:
136    diag2tT <- function(from) .diag2tT(from, "U", "l")
137    setAs("ldiMatrix", "triangularMatrix", diag2tT)
138    setAs("ldiMatrix", "sparseMatrix", diag2tT)
139    ## needed too (otherwise <dense> -> Tsparse is taken):
140    setAs("ldiMatrix", "TsparseMatrix", diag2tT)
141    setAs("ldiMatrix", "CsparseMatrix",
142          function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
143    setAs("ldiMatrix", "symmetricMatrix",
144          function(from) .diag2sT(from, "U", "l"))
145    
146    
147    setAs("diagonalMatrix", "nMatrix",
148        function(from) {        function(from) {
149            n <- from@Dim[1]            n <- from@Dim[1]
150            diag(x = if(from@diag == "U") { if(is.numeric(from@x)) 1. else TRUE            i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
151                                       } else from@x,            new("ntTMatrix", i = i, j = i, diag = from@diag,
152                 nrow = n, ncol = n)                Dim = from@Dim, Dimnames = from@Dimnames)
153        })        })
154    
 setAs("diagonalMatrix", "generalMatrix", # prefer sparse:  
       function(from) as(from, paste(.M.kind(from), "gCMatrix", sep='')))  
   
 .diag.x <- function(m) {  
     if(m@diag == "U")  
         rep.int(if(is.numeric(m@x)) 1. else TRUE,  
                 m@Dim[1])  
     else m@x  
 }  
155    
156  .diag.2N <- function(m) {  ## Cheap fast substitute for diag() which *does* preserve the mode of x :
157      if(m@diag == "U") m@diag <- "N"  mkDiag <- function(x, n) {
158      m      y <- matrix(as0(mod=mode(x)), n,n)
159        if (n > 0) y[1L + 0:(n - 1L) * (n + 1L)] <- x
160        y
161  }  }
162    
163  ## given the above, the following  4  coercions should be all unneeded;  setAs("diagonalMatrix", "matrix",
 ## we prefer triangular to general:  
 setAs("ddiMatrix", "dgTMatrix",  
164        function(from) {        function(from) {
165            .Deprecated("as(, \"sparseMatrix\")")            ## want "ldiMatrix" -> <logical> "matrix" :
166            n <- from@Dim[1]            mkDiag(if(from@diag == "U") as1(from@x) else from@x,
167            i <- seq_len(n) - 1:1                   n = from@Dim[1])
168            new("dgTMatrix", i = i, j = i, x = .diag.x(from),        })
               Dim = c(n,n), Dimnames = from@Dimnames) })  
169    
170  setAs("ddiMatrix", "dgCMatrix",  setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
171        function(from) as(as(from, "sparseMatrix"), "dgCMatrix"))            function(x, mode) {
172                  n <- x@Dim[1]
173                  mod.x <- mode(x@x)
174                  r <- vector(mod.x, length = n^2)
175                  if(n)
176                      r[1 + 0:(n - 1) * (n + 1)] <-
177                          if(x@diag == "U") as1(mod=mod.x) else x@x
178                  r
179              })
180    
181  setAs("ldiMatrix", "lgTMatrix",  setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
182        function(from) {        function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))
           .Deprecated("as(, \"sparseMatrix\")")  
           n <- from@Dim[1]  
           if(from@diag == "U") { # unit-diagonal  
               x <- rep.int(TRUE, n)  
               i <- seq_len(n) - 1:1  
           } else { # "normal"  
               nz <- nz.NA(from@x, na. = TRUE)  
               x <- from@x[nz]  
               i <- which(nz) - 1:1  
           }  
           new("lgTMatrix", i = i, j = i, x = x,  
               Dim = c(n,n), Dimnames = from@Dimnames) })  
183    
184  setAs("ldiMatrix", "lgCMatrix",  .diag.x <- function(m) if(m@diag == "U") rep.int(as1(m@x), m@Dim[1]) else m@x
       function(from) as(as(from, "lgTMatrix"), "lgCMatrix"))  
185    
186    .diag.2N <- function(m) {
187        if(m@diag == "U") m@diag <- "N"
188        m
189    }
190    
 if(FALSE) # now have faster  "ddense" -> "dge"  
191  setAs("ddiMatrix", "dgeMatrix",  setAs("ddiMatrix", "dgeMatrix",
192        function(from) as(as(from, "matrix"), "dgeMatrix"))        function(from) .Call(dup_mMatrix_as_dgeMatrix, from))
193    setAs("ddiMatrix", "ddenseMatrix",
194          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
195    setAs("ldiMatrix", "ldenseMatrix",
196          function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
197    
198    
199  setAs("matrix", "diagonalMatrix",  setAs("matrix", "diagonalMatrix",
200        function(from) {        function(from) {
# Line 173  Line 235 
235                x = if(uni) x[FALSE] else x)                x = if(uni) x[FALSE] else x)
236        })        })
237    
238    
239    setMethod("diag", signature(x = "diagonalMatrix"),
240              function(x = 1, nrow, ncol) .diag.x(x))
241    
242    subDiag <- function(x, i, j, ..., drop) {
243        x <- as(x, "sparseMatrix")
244        x <- if(missing(i))
245            x[, j, drop=drop]
246        else if(missing(j))
247            x[i, , drop=drop]
248        else
249            x[i,j, drop=drop]
250        if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
251    }
252    
253    setMethod("[", signature(x = "diagonalMatrix", i = "index",
254                             j = "index", drop = "logical"), subDiag)
255    setMethod("[", signature(x = "diagonalMatrix", i = "index",
256                            j = "missing", drop = "logical"),
257              function(x, i, j, ..., drop) subDiag(x, i=i, drop=drop))
258    setMethod("[", signature(x = "diagonalMatrix", i = "missing",
259                             j = "index", drop = "logical"),
260              function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))
261    
262  ## When you assign to a diagonalMatrix, the result should be  ## When you assign to a diagonalMatrix, the result should be
263  ## diagonal or sparse  ## diagonal or sparse ---
264    ## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
265    ## Only(?) current bug:  x[i] <- value  is wrong when  i is *vector*
266    replDiag <- function(x, i, j, ..., value) {
267        x <- as(x, "sparseMatrix")
268        if(missing(i))
269            x[, j] <- value
270        else if(missing(j)) { ##  x[i , ] <- v  *OR*   x[i] <- v
271            na <- nargs()
272    ##         message("diagnosing replDiag() -- nargs()= ", na)
273            if(na == 4)
274                x[i, ] <- value
275            else if(na == 3)
276                x[i] <- value
277            else stop("Internal bug: nargs()=",na,"; please report")
278        } else
279            x[i,j] <- value
280        if(isDiagonal(x)) as(x, "diagonalMatrix") else x
281    }
282    
283    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
284                                    j = "index", value = "replValue"), replDiag)
285    
286    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
287                                    j = "missing", value = "replValue"),
288                     function(x,i,j, ..., value) {
289                         ## message("before replDiag() -- nargs()= ", nargs())
290                         if(nargs() == 3)
291                             replDiag(x, i=i, value=value)
292                         else ## nargs() == 4 :
293                             replDiag(x, i=i, , value=value)
294                     })
295    
296  setReplaceMethod("[", signature(x = "diagonalMatrix",  setReplaceMethod("[", signature(x = "diagonalMatrix",
297                                  i = "ANY", j = "ANY", value = "ANY"),                                  i = "matrix", # 2-col.matrix
298                   function(x, i, j, value) {                                  j = "missing", value = "replValue"),
299                       r <- callGeneric(x = as(x,"sparseMatrix"),                   function(x,i,j, ..., value) {
300                                        i=i, j=j, value=value)                       if(ncol(i) == 2) {
301                       if(isDiagonal(r)) as(r, "diagonalMatrix") else r                           if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
302                                 if(x@diag == "U") {
303                                     one <- as1(x@x)
304                                     if(any(value != one | is.na(value))) {
305                                         x@diag <- "N"
306                                         x@x <- rep.int(one, x@Dim[1])
307                                     }
308                                 }
309                                 x@x[ii] <- value
310                                 x
311                             } else { ## no longer diagonal, but remain sparse:
312                                 x <- as(x, "sparseMatrix")
313                                 x[i] <- value
314                                 x
315                             }
316                         }
317                         else { # behave as "base R": use as if vector
318                             x <- as(x, "matrix")
319                             x[i] <- value
320                             Matrix(x)
321                         }
322                   })                   })
323    
324    setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
325                                    j = "index", value = "replValue"),
326                     function(x,i,j, ..., value) replDiag(x, j=j, value=value))
327    
328    
329  setMethod("t", signature(x = "diagonalMatrix"),  setMethod("t", signature(x = "diagonalMatrix"),
330            function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })            function(x) { x@Dimnames <- x@Dimnames[2:1] ; x })
# Line 192  Line 334 
334  setMethod("isTriangular", signature(object = "diagonalMatrix"),  setMethod("isTriangular", signature(object = "diagonalMatrix"),
335            function(object) TRUE)            function(object) TRUE)
336  setMethod("isSymmetric", signature(object = "diagonalMatrix"),  setMethod("isSymmetric", signature(object = "diagonalMatrix"),
337            function(object) TRUE)            function(object, ...) TRUE)
338    
339    setMethod("symmpart", signature(x = "diagonalMatrix"), function(x) x)
340    setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)
341    
342  setMethod("chol", signature(x = "ddiMatrix"),# pivot = "ANY"  setMethod("chol", signature(x = "ddiMatrix"),
343            function(x, pivot) {            function(x, pivot, ...) {
344                if(any(x@x < 0)) stop("chol() is undefined for diagonal matrix with negative entries")                if(x@diag == "U") return(x)
345                  ## else
346                  if(any(x@x < 0))
347                      stop("chol() is undefined for diagonal matrix with negative entries")
348                x@x <- sqrt(x@x)                x@x <- sqrt(x@x)
349                x                x
350            })            })
351  ## chol(L) is L for logical diagonal:  ## chol(L) is L for logical diagonal:
352  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot) x)  setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot, ...) x)
353    
354    setMethod("determinant", signature(x = "diagonalMatrix", logarithm = "logical"),
355              function(x, logarithm, ...) mkDet(.diag.x(x), logarithm))
356    
357  setMethod("diag", signature(x = "diagonalMatrix"),  setMethod("norm", signature(x = "diagonalMatrix", type = "character"),
358            function(x = 1, nrow, ncol = n) {            function(x, type, ...) {
359               if(x@diag == "U")                if((n <- x@Dim[1]) == 0) return(0) # as for "sparseMatrix"
360                   rep.int(if(is.logical(x@x)) TRUE else 1, x@Dim[1])                type <- toupper(substr(type[1], 1, 1))
361               else x@x                isU <- (x@diag == "U") # unit-diagonal
362            })                if(type == "F") sqrt(if(isU) n else sum(x@x^2))
363                  else { ## norm == "I","1","O","M" :
364  setMethod("!", "ldiMatrix", function(e1) {                    if(isU) 1 else max(abs(x@x))
     if(e1@diag == "N")  
         e1@x <- !e1@x  
     else { ## "U"  
         e1@diag <- "N"  
         e1@x <- rep.int(FALSE, e1@Dim[1])  
365      }      }
     x  
366  })  })
367    
368    
369    
370  ## Basic Matrix Multiplication {many more to add}  ## Basic Matrix Multiplication {many more to add}
371  ##       ---------------------  ##       ---------------------
372  ## Note that "ldi" logical are treated as numeric  ## Note that "ldi" logical are treated as numeric
373  diagdiagprod <- function(x, y) {  diagdiagprod <- function(x, y) {
374      if(any(dim(x) != dim(y))) stop("non-matching dimensions")      n <- dimCheck(x,y)[1]
375      if(x@diag != "U") {      if(x@diag != "U") {
376          if(y@diag != "U") {          if(y@diag != "U") {
377              nx <- x@x * y@x              nx <- x@x * y@x
# Line 253  Line 399 
399    
400    
401  diagmatprod <- function(x, y) {  diagmatprod <- function(x, y) {
402        ## x is diagonalMatrix
403      dx <- dim(x)      dx <- dim(x)
404      dy <- dim(y)      dy <- dim(y)
405      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
406      n <- dx[1]      n <- dx[1]
407      as(if(x@diag == "U") y else x@x * y, "Matrix")      as(if(x@diag == "U") y else x@x * y, "Matrix")
408  }  }
   
409  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
410            diagmatprod)            diagmatprod)
411    ## sneaky .. :
412  formals(diagmatprod) <- alist(x=, y=NULL)  formals(diagmatprod) <- alist(x=, y=NULL)
413  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
414            diagmatprod)            diagmatprod)
 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"),  
           diagmatprod)  
415    
416  diagdgeprod <- function(x, y) {  diagGeprod <- function(x, y) {
417      dx <- dim(x)      dx <- dim(x)
418      dy <- dim(y)      dy <- dim(y)
419      if(dx[2] != dy[1]) stop("non-matching dimensions")      if(dx[2] != dy[1]) stop("non-matching dimensions")
# Line 276  Line 421 
421          y@x <- x@x * y@x          y@x <- x@x * y@x
422      y      y
423  }  }
424  setMethod("%*%", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("%*%", signature(x= "diagonalMatrix", y= "dgeMatrix"), diagGeprod)
425            diagdgeprod, valueClass = "dgeMatrix")  setMethod("%*%", signature(x= "diagonalMatrix", y= "lgeMatrix"), diagGeprod)
426  formals(diagdgeprod) <- alist(x=, y=NULL)  formals(diagGeprod) <- alist(x=, y=NULL)
427  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),  setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
428            diagdgeprod, valueClass = "dgeMatrix")            diagGeprod, valueClass = "dgeMatrix")
429    setMethod("crossprod", signature(x = "diagonalMatrix", y = "lgeMatrix"),
430              diagGeprod)
431    
432  setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),  matdiagprod <- function(x, y) {
           function(x, y) {  
433                dx <- dim(x)                dx <- dim(x)
434                dy <- dim(y)                dy <- dim(y)
435                if(dx[2] != dy[1]) stop("non-matching dimensions")                if(dx[2] != dy[1]) stop("non-matching dimensions")
436                as(if(y@diag == "U") x else x * rep(y@x, each = dx[1]), "Matrix")      Matrix(if(y@diag == "U") x else x * rep(y@x, each = dx[1]))
437            })  }
438    setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
439              matdiagprod)
440    formals(matdiagprod) <- alist(x=, y=NULL)
441    setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
442              matdiagprod)
443    
444  setMethod("%*%", signature(x = "dgeMatrix", y = "diagonalMatrix"),  gediagprod <- function(x, y) {
           function(x, y) {  
445                dx <- dim(x)                dx <- dim(x)
446                dy <- dim(y)                dy <- dim(y)
447                if(dx[2] != dy[1]) stop("non-matching dimensions")                if(dx[2] != dy[1]) stop("non-matching dimensions")
448                if(y@diag == "N")                if(y@diag == "N")
449                    x@x <- x@x * rep(y@x, each = dx[1])                    x@x <- x@x * rep(y@x, each = dx[1])
450                x                x
451            })  }
452    setMethod("%*%", signature(x= "dgeMatrix", y= "diagonalMatrix"), gediagprod)
453    setMethod("%*%", signature(x= "lgeMatrix", y= "diagonalMatrix"), gediagprod)
454    formals(gediagprod) <- alist(x=, y=NULL)
455    setMethod("tcrossprod", signature(x = "dgeMatrix", y = "diagonalMatrix"),
456              gediagprod)
457    setMethod("tcrossprod", signature(x = "lgeMatrix", y = "diagonalMatrix"),
458              gediagprod)
459    
460  ## crossprod {more of these}  ## crossprod {more of these}
461    
462  ## tcrossprod --- all are not yet there: do the dense ones here:  ## tcrossprod --- all are not yet there: do the dense ones here:
463    
464    setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
465              function(x, y) if(x@diag == "U") y else x %*% as(y, "generalMatrix"))
466    setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
467              function(x, y) if(y@diag == "U") x else as(x, "generalMatrix") %*% y)
468    
469    
470  ## FIXME:  ## FIXME:
471  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),  ## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
472  ##        function(x, y = NULL) {  ##        function(x, y = NULL) {
# Line 313  Line 476 
476  ##        function(x, y = NULL) {  ##        function(x, y = NULL) {
477  ##           })  ##           })
478    
479    setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
480              function(x, y = NULL) crossprod(as(x, "sparseMatrix"), y))
481    
482  ### ---------------- diagonal  o  sparse  -----------------------------  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
483              function(x, y = NULL) crossprod(x, as(y, "sparseMatrix")))
484    
485    setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
486              function(x, y = NULL) tcrossprod(as(x, "sparseMatrix"), y))
487    
488    setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
489              function(x, y = NULL) tcrossprod(x, as(y, "sparseMatrix")))
490    
491    
492    ## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()
493    setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
494              function(x, y) as(x, "sparseMatrix") %*% y)
495    setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
496              function(x, y) x %*% as(y, "sparseMatrix"))
497    ## NB: The previous is *not* triggering for  "ddi" o "dgC" (= distance 3)
498    ##     since there's a "ddense" o "Csparse" at dist. 2 => triggers first.
499    ## ==> do this:
500    setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
501              function(x, y) as(x, "CsparseMatrix") %*% y)
502    setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
503              function(x, y) x %*% as(y, "CsparseMatrix"))
504    ## NB: this is *not* needed for Tsparse & Rsparse
505    ## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
506    ##       do indeed work by going through sparse (and *not* ddense)!
507    
508    
509    
510    setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
511              function(a, b, ...) {
512                  a@x <- 1/ a@x
513                  a@Dimnames <- a@Dimnames[2:1]
514                  a
515              })
516    
517    solveDiag <- function(a, b, ...) {
518        if((n <- a@Dim[1]) != nrow(b))
519            stop("incompatible matrix dimensions")
520        ## trivially invert a 'in place' and multiply:
521        a@x <- 1/ a@x
522        a@Dimnames <- a@Dimnames[2:1]
523        a %*% b
524    }
525    setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
526              solveDiag)
527    setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
528              solveDiag)
529    
530    ## Schur()  ---> ./eigen.R
531    
532    
533    
534    ###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------
535    
536  ## Use function for several signatures, in order to evade  ## Use function for several signatures, in order to evade
537  ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)  ## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)
538  diagOdiag <- function(e1,e2) { # result should also be diagonal  diagOdiag <- function(e1,e2) {
539        ## result should also be diagonal _ if possible _
540      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"      r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
541        ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
542        r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
543                           if(is.numeric(e2@x)) 0 else FALSE)
544        if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* diagonal
545      if(is.numeric(r)) {      if(is.numeric(r)) {
546          if(is.numeric(e2@x)) {          if(is.numeric(e2@x)) {
547              e2@x <- r; return(.diag.2N(e2)) }              e2@x <- r; return(.diag.2N(e2)) }
# Line 334  Line 555 
555      e1@x <- r      e1@x <- r
556      .diag.2N(e1)      .diag.2N(e1)
557  }  }
558        else { ## result not diagonal, but at least symmetric:
559            isNum <- (is.numeric(r) || is.numeric(r00))
560            isLog <- (is.logical(r) || is.logical(r00))
561    
562            if(getOption("verbose"))
563                message("exploding  <diag>  o  <diag>  into dense matrix")
564            d <- e1@Dim
565            n <- d[1]
566            stopifnot(length(r) == n)
567            xx <- as.vector(matrix(rbind(r, matrix(r00,n,n)), n,n))
568            newcl <-
569                paste(if(isNum) "d" else if(isLog) {
570                    if(!any(is.na(r)) && !any(is.na(r00))) "n" else "l"
571                } else stop("not yet implemented .. please report")
572                      ,
573                      "syMatrix", sep='')
574    
575            new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
576        }
577    }
578    
579    ### This would be *the* way, but we get tons of "ambiguous method dispatch"
580    ## we use this hack instead of signature  x = "diagonalMatrix" :
581    diCls <- names(getClass("diagonalMatrix")@subclasses)
582    if(FALSE) {
583  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
584            diagOdiag)            diagOdiag)
585  ## These two are just for method disambiguation:  } else { ## These are just for method disambiguation:
586  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "diagonalMatrix"),      for(c1 in diCls)
587            diagOdiag)          for(c2 in diCls)
588  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ddiMatrix"),              setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
589            diagOdiag)  }
590    
591    ## FIXME:    diagonal  o  triangular  |-->  triangular
592    ## -----     diagonal  o  symmetric   |-->  symmetric
593    ##    {also when other is sparse: do these "here" --
594    ##     before conversion to sparse, since that loses "diagonality"}
595    
596  ## For almost everything else, diag* shall be treated "as sparse" :  ## For almost everything else, diag* shall be treated "as sparse" :
597  ## These are cheap implementations via coercion  ## These are cheap implementations via coercion
598    
599  ## for disambiguation  ## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
600  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "sparseMatrix"),  ## and because we can save an .M.kind() call, we use this explicit
601            function(e1,e2) callGeneric(as(e1, "sparseMatrix"), e2))  ## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
602  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "diagonalMatrix"),  ##
603            function(e1,e2) callGeneric(e1, as(e2, "sparseMatrix")))  ## ddi*:
604  ## in general:  setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
605  setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ANY"),            function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "d"), e2))
606            function(e1,e2) callGeneric(as(e1,"sparseMatrix"), e2))  setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
607  setMethod("Ops", signature(e1 = "ANY", e2 = "diagonalMatrix"),            function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "d")))
608            function(e1,e2) callGeneric(e1, as(e2,"sparseMatrix")))  ## ldi*
609    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
610              function(e1,e2) callGeneric(diag2Tsmart(e1,e2, "l"), e2))
611    setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
612              function(e1,e2) callGeneric(e1, diag2Tsmart(e2,e1, "l")))
613    
614    ## Ops:  Arith  --> numeric : "dMatrix"
615    ##       Compare --> logical
616    ##       Logic   --> logical: "lMatrix"
617    
618    ##  other = "numeric" : stay diagonal if possible
619    ## ddi*: Arith: result numeric, potentially ddiMatrix
620    setMethod("Arith", signature(e1 = "ddiMatrix", e2 = "numeric"),
621              function(e1,e2) {
622                  n <- e1@Dim[1]; nsq <- n*n
623                  f0 <- callGeneric(0, e2)
624                  if(all(is0(f0))) { # remain diagonal
625                      L1 <- (le <- length(e2)) == 1L
626                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
627                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
628                          e1@diag <- "N"
629                          if(L1) r <- rep.int(r, n)
630                      } else
631                          r <- callGeneric(e1@x, e2)
632                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
633                      return(e1)
634                  }
635                  callGeneric(diag2tT.u(e1,e2, "d"), e2)
636              })
637    
638    setMethod("Arith", signature(e1 = "numeric", e2 = "ddiMatrix"),
639              function(e1,e2) {
640                  n <- e2@Dim[1]; nsq <- n*n
641                  f0 <- callGeneric(e1, 0)
642                  if(all(is0(f0))) { # remain diagonal
643                      L1 <- (le <- length(e1)) == 1L
644                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
645                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
646                          e2@diag <- "N"
647                          if(L1) r <- rep.int(r, n)
648                      } else
649                          r <- callGeneric(e1, e2@x)
650                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
651                      return(e2)
652                  }
653                  callGeneric(e1, diag2tT.u(e2,e1, "d"))
654              })
655    
656    ## ldi* Arith --> result numeric, potentially ddiMatrix
657    setMethod("Arith", signature(e1 = "ldiMatrix", e2 = "numeric"),
658              function(e1,e2) {
659                  n <- e1@Dim[1]; nsq <- n*n
660                  f0 <- callGeneric(0, e2)
661                  if(all(is0(f0))) { # remain diagonal
662                      L1 <- (le <- length(e2)) == 1L
663                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
664                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
665                          e1@diag <- "N"
666                          if(L1) r <- rep.int(r, n)
667                      } else
668                          r <- callGeneric(e1@x, e2)
669                      e1 <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"))
670                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
671                      return(e1)
672                  }
673                  callGeneric(diag2tT.u(e1,e2, "d"), e2)
674              })
675    
676    setMethod("Arith", signature(e1 = "numeric", e2 = "ldiMatrix"),
677              function(e1,e2) {
678                  n <- e2@Dim[1]; nsq <- n*n
679                  f0 <- callGeneric(e1, 0)
680                  if(all(is0(f0))) { # remain diagonal
681                      L1 <- (le <- length(e1)) == 1L
682                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
683                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
684                          e2@diag <- "N"
685                          if(L1) r <- rep.int(r, n)
686                      } else
687                          r <- callGeneric(e1, e2@x)
688                      e2 <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"))
689                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
690                      return(e2)
691                  }
692                  callGeneric(e1, diag2tT.u(e2,e1, "d"))
693              })
694    
695    ## ddi*: for "Ops" without Arith --> result logical, potentially ldi
696    setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "numeric"),
697              function(e1,e2) {
698                  n <- e1@Dim[1]; nsq <- n*n
699                  f0 <- callGeneric(0, e2)
700                  if(all(is0(f0))) { # remain diagonal
701                      L1 <- (le <- length(e2)) == 1L
702                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
703                      if(e1@diag == "U" && any((r <- callGeneric(1, e2)) != 1)) {
704                          e1@diag <- "N"
705                          if(L1) r <- rep.int(r, n)
706                      } else
707                          r <- callGeneric(e1@x, e2)
708                      e1 <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"))
709                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
710                      return(e1)
711                  }
712                  callGeneric(diag2tT.u(e1,e2, "l"), e2)
713              })
714    
715    setMethod("Ops", signature(e1 = "numeric", e2 = "ddiMatrix"),
716              function(e1,e2) {
717                  n <- e2@Dim[1]; nsq <- n*n
718                  f0 <- callGeneric(e1, 0)
719                  if(all(is0(f0))) { # remain diagonal
720                      L1 <- (le <- length(e1)) == 1L
721                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
722                      if(e2@diag == "U" && any((r <- callGeneric(e1, 1)) != 1)) {
723                          e2@diag <- "N"
724                          if(L1) r <- rep.int(r, n)
725                      } else
726                          r <- callGeneric(e1, e2@x)
727                      e2 <- copyClass(e2, "ldiMatrix", c("diag", "Dim", "Dimnames"))
728                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
729                      return(e2)
730                  }
731                  callGeneric(e1, diag2tT.u(e2,e1, "l"))
732              })
733    
734  ## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()  ## ldi*: for "Ops" without Arith --> result logical, potentially ldi
735    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "numeric"),
736              function(e1,e2) {
737                  n <- e1@Dim[1]; nsq <- n*n
738                  f0 <- callGeneric(FALSE, e2)
739                  if(all(is0(f0))) { # remain diagonal
740                      L1 <- (le <- length(e2)) == 1L
741                      if(!L1 && le != nsq) e2 <- rep(e2, length.out = nsq)
742                      if(e1@diag == "U" && any((r <- callGeneric(TRUE, e2)) != 1)) {
743                          e1@diag <- "N"
744                          if(L1) r <- rep.int(r, n)
745                      } else
746                          r <- callGeneric(e1@x, e2)
747                      e1@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
748                      return(e1)
749                  }
750                  callGeneric(diag2tT.u(e1,e2, "l"), e2)
751              })
752    
753  setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),  setMethod("Ops", signature(e1 = "numeric", e2 = "ldiMatrix"),
754            function(x, y) as(x, "sparseMatrix") %*% y)            function(e1,e2) {
755                  n <- e2@Dim[1]; nsq <- n*n
756                  f0 <- callGeneric(e1, FALSE)
757                  if(all(is0(f0))) { # remain diagonal
758                      L1 <- (le <- length(e1)) == 1L
759                      if(!L1 && le != nsq) e1 <- rep(e1, length.out = nsq)
760                      if(e2@diag == "U" && any((r <- callGeneric(e1, TRUE)) != 1)) {
761                          e2@diag <- "N"
762                          if(L1) r <- rep.int(r, n)
763                      } else
764                          r <- callGeneric(e1, e2@x)
765                      e2@x <- if(L1) r else r[1L + (n+1L)*(0:(n-1L))]
766                      return(e2)
767                  }
768                  callGeneric(e1, diag2tT.u(e2,e1, "l"))
769              })
770    
 setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),  
           function(x, y) x %*% as(y, "sparseMatrix"))  
771    
 setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  
           function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })  
772    
773  setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  ## Not {"sparseMatrix", "numeric} :  {"denseMatrix", "matrix", ... }
774            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })  for(other in c("ANY", "Matrix", "dMatrix")) {
775        ## ddi*:
776        setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
777                  function(e1,e2) callGeneric(diag2tT.u(e1,e2, "d"), e2))
778        setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
779                  function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1, "d")))
780        ## ldi*:
781        setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
782                  function(e1,e2) callGeneric(diag2tT.u(e1,e2, "l"), e2))
783        setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
784                  function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1, "l")))
785    }
786    ## This should *not* dispatch to <dense> methods (in ./Ops.R ), as
787    ##  FALSE & <anything> |-> FALSE : hence result should be diagonal:
788    for(cl in diCls) {
789        setMethod("&", signature(e1 = cl, e2 = "ANY"),
790                  function(e1,e2) e1 & as(e2,"Matrix"))
791        setMethod("&", signature(e1 = "ANY", e2 = cl),
792                  function(e1,e2) as(e1,"Matrix") & e2)
793        for(c2 in c("denseMatrix", "Matrix")) {
794            setMethod("&", signature(e1 = cl, e2 = c2),
795                      function(e1,e2) e1 & Diagonal(x = diag(e2)))
796            setMethod("&", signature(e1 = c2, e2 = cl),
797                      function(e1,e2) Diagonal(x = diag(e1)) & e2)
798        }
799    }
800    
 setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),  
           function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })  
801    
802  setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),  ### "Summary" : "max"   "min"   "range" "prod"  "sum"   "any"   "all"
803            function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })  ### ----------  any, all: separately here
804    for(cl in diCls) {
805    setMethod("any", cl,
806              function (x, ..., na.rm) {
807                  if(any(x@Dim == 0)) FALSE
808                  else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
809              })
810    setMethod("all",  cl, function (x, ..., na.rm) any(x@Dim == 0))
811    setMethod("prod", cl, function (x, ..., na.rm) as.numeric(any(x@Dim == 0)))
812    
813    setMethod("sum", cl,
814              function(x, ..., na.rm) {
815                  r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
816                  if(x@diag == "U" && !is.na(r)) r + x@Dim[1] else r
817              })
818    }
819    
820    ## The remaining ones are  max, min, range :
821    
822    setMethod("Summary", "ddiMatrix",
823              function(x, ..., na.rm) {
824                  if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
825                  else if(x@diag == "U")
826                      callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
827                  else callGeneric(x@x, 0, ..., na.rm=na.rm)
828              })
829    setMethod("Summary", "ldiMatrix",
830              function(x, ..., na.rm) {
831                  if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
832                  else if(x@diag == "U")
833                      callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
834                  else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
835              })
836    
837    
838    

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