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#### Toplevel ``virtual'' class "Matrix"


### Virtual coercions -- via smart "helpers" (-> ./Auxiliaries.R)

setAs("Matrix", "sparseMatrix", function(from) as_Csparse(from))
setAs("Matrix", "denseMatrix",  function(from) as_dense(from))

## ## probably not needed eventually:
## setAs(from = "ddenseMatrix", to = "matrix",
##       function(from) {
##    if(length(d <- dim(from)) != 2) stop("dim(.) has not length 2")
##    array(from@x, dim = d, dimnames = dimnames(from))
##       })

## should propagate to all subclasses:
setMethod("as.matrix", signature(x = "Matrix"), function(x) as(x, "matrix"))
## for 'Matrix' objects, as.array() should be equivalent:
setMethod("as.array",  signature(x = "Matrix"), function(x) as(x, "matrix"))

## head and tail apply to all Matrix objects for which subscripting is allowed:
## if(paste(R.version$major, R.version$minor, sep=".") < "2.4") {
    setMethod("head", signature(x = "Matrix"), utils:::head.matrix)
    setMethod("tail", signature(x = "Matrix"), utils:::tail.matrix)
## } else { # R 2.4.0 and newer
##     setMethod("head", signature(x = "Matrix"), utils::head.matrix)
##     setMethod("tail", signature(x = "Matrix"), utils::tail.matrix)
## }

## slow "fall back" method {subclasses should have faster ones}:
setMethod("as.vector", signature(x = "Matrix", mode = "missing"),
      function(x) as.vector(as(x, "matrix")))

## mainly need these for "dMatrix" or "lMatrix" respectively, but why not general:
setMethod("as.numeric", signature(x = "Matrix"),
      function(x, ...) as.numeric(as.vector(x)))
setMethod("as.logical", signature(x = "Matrix"),
      function(x, ...) as.logical(as.vector(x)))


## "base" has an isSymmetric() S3-generic since R 2.3.0
setMethod("isSymmetric", signature(object = "symmetricMatrix"),
          function(object,tol) TRUE)
setMethod("isSymmetric", signature(object = "triangularMatrix"),
          ## TRUE iff diagonal:
          function(object,tol) isDiagonal(object))

setMethod("isTriangular", signature(object = "triangularMatrix"),
          function(object, ...) TRUE)

setMethod("isTriangular", signature(object = "matrix"), isTriMat)

setMethod("isDiagonal", signature(object = "matrix"), .is.diagonal)



setMethod("dim", signature(x = "Matrix"),
      function(x) x@Dim, valueClass = "integer")
setMethod("dimnames", signature(x = "Matrix"), function(x) x@Dimnames)
## not exported but used more than once for "dimnames<-" method :
## -- or do only once for all "Matrix" classes ??
dimnamesGets <- function (x, value) {
    d <- dim(x)
    if (!is.list(value) || length(value) != 2 ||
    !(is.null(v1 <- value[[1]]) || length(v1) == d[1]) ||
    !(is.null(v2 <- value[[2]]) || length(v2) == d[2]))
    stop(sprintf("invalid dimnames given for '%s' object", class(x)))
    x@Dimnames <- list(if(!is.null(v1)) as.character(v1),
               if(!is.null(v2)) as.character(v2))
    x
}
setMethod("dimnames<-", signature(x = "Matrix", value = "list"),
      dimnamesGets)

setMethod("unname", signature("Matrix", force="missing"),
      function(obj) { obj@Dimnames <- list(NULL,NULL); obj})

Matrix <-
    function (data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL,
          sparse = NULL, forceCheck = FALSE)
{
    sparseDefault <- function(m)
    prod(dim(m)) > 2*sum(is.na(m <- as(m, "matrix")) | m != 0)

    i.M <- is(data, "Matrix")
    if(is.null(sparse) && (i.M || is(data, "matrix")))
    sparse <- sparseDefault(data)

    doDN <- TRUE
    if (i.M && !forceCheck) {
    sM <- is(data,"sparseMatrix")
    if((sparse && sM) || (!sparse && !sM))
        return(data)
    ## else : convert  dense <-> sparse -> at end
    }
    else if (!is.matrix(data)) { ## cut & paste from "base::matrix" :
    if (missing(nrow))
        nrow <- ceiling(length(data)/ncol)
    else if (missing(ncol))
        ncol <- ceiling(length(data)/nrow)
    if(length(data) == 1 && !is.na(data) && data == 0 &&
           !identical(sparse, FALSE)) {

        if(is.null(sparse)) sparse <- TRUE
        ## will be sparse: do NOT construct full matrix!
        data <- new(if(is.numeric(data)) "dgTMatrix" else
            if(is.logical(data)) "lgTMatrix" else
            stop("invalid 'data'"),
            Dim = as.integer(c(nrow,ncol)),
            Dimnames = if(is.null(dimnames)) list(NULL,NULL)
            else dimnames)
    } else { ## normal case
        data <- .Internal(matrix(data, nrow, ncol, byrow))
        if(is.null(sparse))
        sparse <- sparseDefault(data)
        dimnames(data) <- dimnames
    }
        doDN <- FALSE
    }
    ## 'data' is now a "matrix" or "Matrix"
    if (doDN && !is.null(dimnames))
    dimnames(data) <- dimnames

    ## check for symmetric / triangular / diagonal :
    isSym <- isSymmetric(data)
    if((isTri <- !isSym))
    isTri <- isTriangular(data)
    isDiag <- isSym # cannot be diagonal if it isn't symmetric
    if(isDiag)
    isDiag <- isDiagonal(data)

### TODO: Compare with as.Matrix() and its tests in ./dgeMatrix.R

    ## Find proper matrix class 'cl'
    cl <-
    if(isDiag)
        "diagonalMatrix" # -> will automatically check for type
    else {
        ## consider it's type
        ctype <-
        if(is(data,"Matrix")) class(data)
        else {
            if("complex" == (ctype <- typeof(data)))
            "z" else ctype
        }
        ctype <- substr(ctype, 1,1) # "d", "l", "i" or "z"
        if(ctype == "z")
        stop("complex matrices not yet implemented in Matrix package")
        if(ctype == "i") {
        warning("integer matrices not yet implemented in 'Matrix'; ",
            "using 'double' ones'")
        ctype <- "d"
        }
        paste(ctype,
          if(sparse) {
              if(isSym) "sCMatrix" else
              if(isTri) "tCMatrix" else "gCMatrix"
          } else { ## dense
              if(isSym) "syMatrix" else
              if(isTri) "trMatrix" else "geMatrix"
          }, sep="")
    }

    ## Now coerce and return
    as(data, cl)
}

## Methods for operations where one argument is numeric

## Using as.matrix() and rbind()
## in order to get dimnames from names {at least potentially}:

setMethod("%*%", signature(x = "Matrix", y = "numeric"),
      function(x, y) callGeneric(x, as.matrix(y)))

setMethod("%*%", signature(x = "numeric", y = "Matrix"),
      function(x, y) callGeneric(rbind(x), y))

setMethod("crossprod", signature(x = "Matrix", y = "numeric"),
      function(x, y = NULL) callGeneric(x, as.matrix(y)))
setMethod("crossprod", signature(x = "numeric", y = "Matrix"),
      function(x, y = NULL)  callGeneric(as.matrix(x), y))

## The as.matrix() promotion seems illogical to MM,
## but is according to help(tcrossprod, package = "base") :
setMethod("tcrossprod", signature(x = "Matrix", y = "numeric"),
      function(x, y = NULL) callGeneric(x, as.matrix(y)))
setMethod("tcrossprod", signature(x = "numeric", y = "Matrix"),
      function(x, y = NULL)  callGeneric(as.matrix(x), y))

setMethod("solve", signature(a = "Matrix", b = "numeric"),
      function(a, b, ...) callGeneric(a, as.matrix(b)))

## bail-out methods in order to get better error messages
setMethod("%*%", signature(x = "Matrix", y = "Matrix"),
      function (x, y)
          stop(gettextf('not-yet-implemented method for <%s> %%*%% <%s>',
                        class(x), class(y))))

setMethod("crossprod", signature(x = "Matrix", y = "ANY"),
      function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))
setMethod("crossprod", signature(x = "ANY", y = "Matrix"),
      function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))
setMethod("tcrossprod", signature(x = "Matrix", y = "ANY"),
      function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))
setMethod("tcrossprod", signature(x = "ANY", y = "Matrix"),
      function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))

## cheap fallbacks
setMethod("crossprod", signature(x = "Matrix", y = "Matrix"),
      function(x, y = NULL) t(x) %*% y)
setMethod("tcrossprod", signature(x = "Matrix", y = "Matrix"),
      function(x, y = NULL) x %*% t(y))

## There are special sparse methods; this is a "fall back":
setMethod("kronecker", signature(X = "Matrix", Y = "ANY",
                                 FUN = "ANY", make.dimnames = "ANY"),
          function(X, Y, FUN, make.dimnames, ...) {
              X <- as(X, "matrix") ; Matrix(callGeneric()) })
setMethod("kronecker", signature(X = "ANY", Y = "Matrix",
                                 FUN = "ANY", make.dimnames = "ANY"),
          function(X, Y, FUN, make.dimnames, ...) {
              Y <- as(Y, "matrix") ; Matrix(callGeneric()) })


setMethod("diag", signature(x = "Matrix"),
      function(x, nrow, ncol) .bail.out.1(.Generic, class(x)))
setMethod("t", signature(x = "Matrix"),
      function(x) .bail.out.1(.Generic, class(x)))

## Group Methods
setMethod("+", signature(e1 = "Matrix", e2 = "missing"), function(e1) e1)
## "fallback":
setMethod("-", signature(e1 = "Matrix", e2 = "missing"),
          function(e1) {
              warning("inefficient method used for \"- e1\"")
              0-e1
          })

## bail-outs:
setMethod("Compare", signature(e1 = "Matrix", e2 = "Matrix"),
          function(e1, e2) {
              d <- dimCheck(e1,e2)
              .bail.out.2(.Generic, class(e1), class(e2))
          })
setMethod("Compare", signature(e1 = "Matrix", e2 = "ANY"),
          function(e1, e2) .bail.out.2(.Generic, class(e1), class(e2)))
setMethod("Compare", signature(e1 = "ANY", e2 = "Matrix"),
          function(e1, e2) .bail.out.2(.Generic, class(e1), class(e2)))



### --------------------------------------------------------------------------
###
### Subsetting "["  and
### SubAssign  "[<-" : The "missing" cases can be dealt with here, "at the top":

## Using "index" for indices should allow
## integer (numeric), logical, or character (names!) indices :

## "x[]":
setMethod("[", signature(x = "Matrix",
             i = "missing", j = "missing", drop = "ANY"),
      function (x, i, j, drop) x)

## missing 'drop' --> 'drop = TRUE'
##                     -----------
## select rows
setMethod("[", signature(x = "Matrix", i = "index", j = "missing",
             drop = "missing"),
      function(x,i,j, drop) callGeneric(x, i=i, drop= TRUE))
## select columns
setMethod("[", signature(x = "Matrix", i = "missing", j = "index",
             drop = "missing"),
      function(x,i,j, drop) callGeneric(x, j=j, drop= TRUE))
setMethod("[", signature(x = "Matrix", i = "index", j = "index",
                         drop = "missing"),
      function(x,i,j, drop) callGeneric(x, i=i, j=j, drop= TRUE))

## bail out if any of (i,j,drop) is "non-sense"
setMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", drop = "ANY"),
      function(x,i,j, drop)
          stop("invalid or not-yet-implemented 'Matrix' subsetting"))

## logical indexing, such as M[ M >= 7 ] *BUT* also M[ M[,1] >= 3,],
## The following is *both* for    M [ <logical>   ]
##                 and also for   M [ <logical> , ]
.M.sub.i.logical <- function (x, i, j, drop)
{
    nA <- nargs()
    if(nA == 2) { ##  M [ M >= 7 ]
    as(x, geClass(x))@x[as.vector(i)]
    ## -> error when lengths don't match
    } else if(nA == 3) { ##  M [ M[,1, drop=FALSE] >= 7, ]
    stop("not-yet-implemented 'Matrix' subsetting") ## FIXME

    } else stop("nargs() = ", nA,
        " should never happen; please report.")
}
setMethod("[", signature(x = "Matrix", i = "lMatrix", j = "missing",
             drop = "ANY"),
      .M.sub.i.logical)
setMethod("[", signature(x = "Matrix", i = "logical", j = "missing",
             drop = "ANY"),
      .M.sub.i.logical)


## "FIXME:"
## ------ get at  A[ ij ]  where ij is (i,j) 2-column matrix?



### "[<-" : -----------------

## x[] <- value :
setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "missing",
                                value = "ANY"),## double/logical/...
      function (x, value) {
              x@x <- value
              validObject(x)# check if type and lengths above match
              x
          })

## Method for all 'Matrix' kinds (rather than incomprehensible error messages);
## (ANY,ANY,ANY) is used when no `real method' is implemented :
setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY",
                                value = "ANY"),
      function (x, i, j, value) {
              if(!is.atomic(value))
                  stop("RHS 'value' must match matrix class ", class(x))
              else stop("not-yet-implemented 'Matrix[<-' method")
          })


## The trivial methods :
setMethod("cbind2", signature(x = "Matrix", y = "NULL"),
          function(x, y) x)
setMethod("cbind2", signature(x = "Matrix", y = "missing"),
          function(x, y) x)
setMethod("cbind2", signature(x = "NULL", y="Matrix"),
          function(x, y) x)

setMethod("rbind2", signature(x = "Matrix", y = "NULL"),
          function(x, y) x)
setMethod("rbind2", signature(x = "Matrix", y = "missing"),
          function(x, y) x)
setMethod("rbind2", signature(x = "NULL", y="Matrix"),
          function(x, y) x)

## Makes sure one gets x decent error message for the unimplemented cases:
setMethod("cbind2", signature(x = "Matrix", y = "Matrix"),
          function(x, y) {
              rowCheck(x,y)
              stop(gettextf("cbind2() method for (%s,%s) not-yet defined",
                            class(x), class(y)))
          })

## Use a working fall back {particularly useful for sparse}:
## FIXME: implement rbind2 via "cholmod" for C* and Tsparse ones
setMethod("rbind2", signature(x = "Matrix", y = "Matrix"),
          function(x, y) {
              colCheck(x,y)
              t(cbind2(t(x), t(y)))
          })