# inst/test-tools-Matrix.R In Matrix: Sparse and Dense Matrix Classes and Methods

#### Tools for Package Testing --- in Matrix, sourced by ./test-tools.R
#### -------------------------

### ------- Part III --  "Matrix" (classes) specific ----------------------

## lower.tri() and upper.tri()  -- masking  base definitions
##	R/src/library/base/R/lower.tri.R
##	R/src/library/base/R/upper.tri.R
## but we do __not__ want to coerce to "base R" 'matrix' via as.matrix():
##
lower.tri <- function(x, diag = FALSE) if(diag) row(x) >= col(x) else row(x) > col(x)
upper.tri <- function(x, diag = FALSE) if(diag) row(x) <= col(x) else row(x) < col(x)

lsM <- function(...) {
for(n in ls(..., envir=parent.frame()))
if(is((. <- get(n)),"Matrix"))
cat(sprintf("%5s: '%s' [%d x %d]\n",n,class(.), nrow(.),ncol(.)))
}

asD <- function(m) { ## as "Dense"
if(canCoerce(m, "denseMatrix")) as(m, "denseMatrix")
else if(canCoerce(m, (cl <- paste(.M.kind(m), "denseMatrix", sep=''))))
as(m, cl)
else if(canCoerce(m, "dgeMatrix")) as(m, "dgeMatrix")
else stop("cannot coerce to a typical dense Matrix")
}

## "normal" sparse Matrix: Csparse, no diag="U"
asCsp <- function(x) diagU2N(as(x, "CsparseMatrix"))

##' @title quasi-identical dimnames
Qidentical.DN <- function(dx, dy) {

stopifnot(is.list(dx) || is.null(dx),
is.list(dy) || is.null(dy))
## "empty"
(is.null.DN(dx) && is.null.DN(dy)) || identical(dx, dy)
}

##' quasi-identical()  for 'Matrix' matrices
Qidentical <- function(x,y, strictClass = TRUE) {
if(!identical(class(x), cy <- class(y))) {
if(strictClass || !is(x, cy))
return(FALSE)
## else try further
}
slts <- slotNames(x) ## MJ: should be slotNames(y), since is(x, class(y)) ??
if("Dimnames" %in% slts) { ## always (or we have no 'Matrix')
slts <- slts[slts != "Dimnames"]
if(!Qidentical.DN(x@Dimnames, y@Dimnames) &&
## allow for "completion" of (NULL, <names>) dimnames of symmetricMatrix:
!Qidentical.DN(dimnames(x), dimnames(y)))
return(FALSE)
}
if("factors" %in% slts) { ## allow one empty and one non-empty 'factors'
slts <- slts[slts != "factors"]
## if both are not empty, they must be the same:
if(length(xf <- x@factors) && length(yf <- y@factors))
if(!identical(xf, yf)) return(FALSE)
}
for(sl in slts)
if(!identical(slot(x,sl), slot(y,sl)))
return(FALSE)
TRUE
}

## MJ: It seems intuitive to allow either of is(x, class(y))
##     and is(y, class(x)) when strictClass=FALSE ...
.MJ.Qidentical <- function(x, y, strictClass = TRUE, skipSlots = NULL) {
isxy <- identical(cx <- class(x), cy <- class(y))
if (!isxy) {
if (strictClass)
return(FALSE)
isxy <- is(x, cy)
if (!(isxy || is(y, cx)))
return(FALSE)
## else try further
}
slts <- slotNames(if (isxy) y else x)
if (length(skipSlots))
slts <- setdiff(slts, skipSlots)
if ("Dimnames" %in% slts) { ## always, or we have no "Matrix"
## allow symmetrization of 'Dimnames' for "symmetricMatrix" :
slts <- slts[slts != "Dimnames"]
if(!Qidentical.DN(x@Dimnames, y@Dimnames) &&
!Qidentical.DN(dimnames(x), dimnames(y)))
return(FALSE)
}
if ("factors" %in% slts) {
## allow one empty and one non-empty 'factors' :
slts <- slts[slts != "factors"]
## if both are not empty, they must be the same:
if (length(xf <- x@factors) && length(yf <- y@factors) &&
!identical(xf, yf))
return(FALSE)
}
for (slt in slts)
if (!identical(slot(x, slt), slot(y, slt)))
return(FALSE)
TRUE
}

##' quasi-identical()  for traditional ('matrix') matrices
mQidentical <- function(x,y, strictClass = TRUE) {
if(!identical(class(x), cy <- class(y))) {
if(strictClass || !is(x, cy))
return(FALSE)
## else try further
}
if(!Qidentical.DN(dimnames(x), dimnames(y)))
return(FALSE)
identical(unname(x), unname(y))
}

Q.C.identical <- function(x,y, sparse = is(x,"sparseMatrix"),
checkClass = TRUE, strictClass = TRUE) {
if(checkClass && class(x) != class(y)) {
if(strictClass || !is(x, class(y)))
return(FALSE) ## else try further
}
if(sparse)
Qidentical(as(x,"CsparseMatrix"), as(y,"CsparseMatrix"),
strictClass=strictClass)
else Qidentical(x,y, strictClass=strictClass)
}

##' <description>
##'
##' <details>
##' @title  Quasi-equal for  'Matrix' matrices
##' @param x  Matrix
##' @param y  Matrix
##' @param superclasses  x and y must coincide in (not) extending these; set to empty,
##'  if no class/inheritance checks should happen.
##' @param dimnames.check  logical indicating if dimnames(.) much match
##' @param tol  NA (--> use "==") or numerical tolerance for all.equal()
##' @return   logical:  Are x and y (quasi) equal ?
Q.eq <- function(x, y,
superclasses =
c("sparseMatrix", "denseMatrix",
"dMatrix", "lMatrix", "nMatrix"),
dimnames.check = TRUE, tol = NA) {
## quasi-equal - for 'Matrix' matrices
if(any(dim(x) != dim(y)))
return(FALSE)
if(dimnames.check &&
!identical(dimnames(x),
dimnames(y))) return(FALSE)
xcl <- getClassDef(class(x))
ycl <- getClassDef(class(y))
for(SC in superclasses) {
if( extends(xcl, SC) &&
!extends(ycl, SC)) return(FALSE)
}
asC <- ## asCommon
if((isDense <- extends(xcl,"denseMatrix")))
function(m) as(m, "matrix")
else function(m)
as(as(as(m,"CsparseMatrix"), "dMatrix"), "generalMatrix") # => "dgC"
if(is.na(tol)) {
if(isDense)
all(x == y | (is.na(x) & is.na(y)))
else ## 'x == y' blows up for large sparse matrices:
isTRUE(all.equal(asC(x), asC(y), tolerance = 0.,
check.attributes = dimnames.check))
}
else if(is.numeric(tol) && tol >= 0) {
isTRUE(all.equal(asC(x), asC(y), tolerance = tol,
check.attributes = dimnames.check))
}
else stop("'tol' must be NA or non-negative number")
}

Q.eq2 <- function(x, y,
superclasses = c("sparseMatrix", "denseMatrix"),
dimnames.check = FALSE, tol = NA)
Q.eq(x,y, superclasses=superclasses,
dimnames.check=dimnames.check, tol=tol)

##' <description>
##'
##' <details>
##' @title  Quasi-equality of  symmpart(m) + skewpart(m) with m
##' @param m  Matrix
##' @param tol  numerical tolerance for all.equal()
##' @return logical
##' @author Martin Maechler
Q.eq.symmpart <- function(m, tol = 8 * .Machine$double.eps) { ss <- symmpart(m) + skewpart(m) if(hasNA <- any(iNA <- is.na(ss))) { ## ss has the NA's symmetrically, but typically m has *not* iiNA <- which(iNA) # <- useful! -- this tests which() methods! ## assign NA's too -- using correct kind of NA: m[iiNA] <- as(NA, Matrix:::.type.kind[Matrix:::.M.kind(m)]) } Q.eq2(m, ss, tol = tol) } ##' sample.int(n, size, replace=FALSE) for really large n: sampleL <- function(n, size) { if(n < .Machine$integer.max)
sample.int(n, size)
else {
i <- unique(round(n * runif(1.8 * size)))
while(length(i) < size) {
i <- unique(c(i, round(n * runif(size))))
}
i[seq_len(size)]
}
}

## Useful Matrix constructors for testing:

##' @title Random Sparse Matrix
##' @param n
##' @param m number of columns; default (=n)  ==> square matrix
##' @param density the desired sparseness density:
##' @param nnz number of non-zero entries; default from \code{density}
##' @param repr character string specifying the sparseness kind of the result.
##' @param giveCsparse *deprecated* logical specifying if result should be CsparseMatrix
##' @return a [CTR]sparseMatrix,  n x m
##' @author Martin Maechler, Mar 2008; July 2020 ('repr' instead og 'giveCsparse')
rspMat <- function(n, m = n, density = 1/4, nnz = round(density * n*m),
repr = c("C","T","R"), giveCsparse)
{
stopifnot(length(n) == 1, n == as.integer(n),
length(m) == 1, m == as.integer(m),
0 <= density, density <= 1,
0 <= nnz,
nnz <= (N <- n*m))
in0 <- sampleL(N, nnz)
x <- sparseVector(i = in0, x = as.numeric(1L + seq_along(in0)), length = N)
dim(x) <- c(n,m)#-> sparseMatrix
## silent, back compatible (not yet warning about 'giveCsparse' deprecation):
repr <- if(missing(repr) && !missing(giveCsparse))
if(giveCsparse) "C" else "T"
else match.arg(repr)
switch(repr,
"C" = as(x, "CsparseMatrix"),
"T" =    x,# TsparseMatrix
"R" = as(x, "RsparseMatrix"))
}

## __DEPRECATED__ !!
rSparseMatrix <- function(nrow, ncol, nnz,
rand.x = function(n) round(rnorm(nnz), 2), ...)
{
stopifnot((nnz <- as.integer(nnz)) >= 0,
nrow >= 0, ncol >= 0, nnz <= nrow * ncol)
.Deprecated("rsparsematrix")
##=========
sparseMatrix(i = sample(nrow, nnz, replace = TRUE),
j = sample(ncol, nnz, replace = TRUE),
x = rand.x(nnz), dims = c(nrow, ncol), ...)
}

rUnitTri <- function(n, upper = TRUE, ...)
{
## Purpose: random unit-triangular sparse Matrix .. built from rspMat()
## ----------------------------------------------------------------------
## Arguments:  n: matrix dimension
##         upper: logical indicating if upper or lower triangular
##         ...  : further arguments passed to rspMat(), eg. 'density'
## ----------------------------------------------------------------------
## Author: Martin Maechler, Date:  5 Mar 2008, 11:35

r <- (if(upper) triu else tril)(rspMat(n, ...))
## make sure the diagonal is empty
diag(r) <- 0
r <- drop0(r)
r@diag <- "U"
r
}

##' Construct a nice (with exact numbers) random artificial  \eqn{A = L D L'}
##' decomposition with a sparse \eqn{n \times n}{n x n} matrix \code{A} of
##' density \code{density} and square root \eqn{D} determined by \code{d0}.
##'
##' If one of \code{rcond} or \code{condest} is true, \code{A} must be
##' non-singular, both use an \eqn{LU} decomposition requiring
##' non-singularity.
##' @title Make Nice Artificial   A = L D L'  (With Exact Numbers) Decomposition
##' @param n matrix dimension \eqn{n \times n}{n x n}
##' @param density ratio of number of non-zero entries to total number
##' @param d0 The sqrt of the diagonal entries of D default \code{10}, to be
##' \dQuote{different} from \code{L} entries.  More generally these can be negative
##' @param rcond logical indicating if \code{\link{rcond}(A, useInv=TRUE)}
##' should be returned which requires non-singular A and D.
##' @param condest logical indicating if \code{\link{condest}(A)$est} ##' should be returned which requires non-singular A and D. ##' @return list with entries A, L, d.half, D, ..., where A inherits from ##' class \code{"\linkS4class{symmetricMatrix}"} and should be equal to ##' \code{as(L \%*\% D \%*\% t(L), "symmetricMatrix")}. ##' @author Martin Maechler, Date: 15 Mar 2008 mkLDL <- function(n, density = 1/3, d0 = 10, d.half = d0 * sample.int(n), # random permutation rcond = (n < 99), condest = (n >= 100)) { stopifnot(n == round(n), density <= 1) n <- as.integer(n) stopifnot(n >= 1, is.numeric(d.half), length(d.half) == n)# no longer (2023-05-24): d.half >= 0 L <- Matrix(0, n,n) nnz <- round(density * n*n) L[sample(n*n, nnz)] <- seq_len(nnz) L <- tril(L, -1L) diag(L) <- 1 ### FIXME: allow *negative* d.half[] entries! dh2 <- d.half^2 non.sing <- sum(dh2 > 0) == n D <- Diagonal(x = dh2) A <- tcrossprod(L * rep(d.half, each=n)) ## = as(L %*% D %*% t(L), "symmetricMatrix") list(A = A, L = L, d.half = d.half, D = D, rcond.A = if (rcond && non.sing) rcond(A, useInv=TRUE), cond.A = if(condest && non.sing) condest(A)$est)
}

eqDeterminant <- function(m1, m2, NA.Inf.ok=FALSE, tol=.Machine$double.eps^0.5, ...) { d1 <- determinant(m1) ## logarithm = TRUE d2 <- determinant(m2) d1m <- as.vector(d1$modulus)# dropping attribute
d2m <- as.vector(d2$modulus) if((identical(d1m, -Inf) && identical(d2m, -Inf)) || ## <==> det(m1) == det(m2) == 0, then 'sign' may even differ ! (is.na(d1m) && is.na(d2m))) ## if both are NaN or NA, we "declare" that's fine here return(TRUE) else if(NA.Inf.ok && ## first can be NA, second infinite: ## wanted: base::determinant.matrix() sometimes gives -Inf instead ## of NA,e.g. for matrix(c(0,NA,0,0,NA,NA,0,NA,0,0,1,0,0,NA,0,1), 4,4)) is.na(d1m) && is.infinite(d2m)) return(TRUE) ## else if(is.infinite(d1m)) d1$modulus <- sign(d1m)* .Machine$double.xmax if(is.infinite(d2m)) d2$modulus <- sign(d2m)* .Machine$double.xmax ## now they are finite or *one* of them is NA/NaN, and all.equal() will tell so: all.equal(d1, d2, tolerance=tol, ...) } ##' @param A a non-negative definite sparseMatrix, typically "dsCMatrix" ##' ##' @return a list with components resulting from calling ##' Cholesky(., perm = .P., LDL = .L., super = .S.) ##' ##' for all 2*2*3 combinations of (.P., .L., .S.) allCholesky <- function(A, verbose = FALSE, silentTry = FALSE) { ## Author: Martin Maechler, Date: 16 Jul 2009 ##' @param r list of CHMfactor objects, typically with names() as '. | .' ##' ##' @return an is(perm,LDL,super) matrix with interesting and *named* rownames CHM_to_pLs <- function(r) { is.perm <- function(.) if(inherits(., "try-error")) NA else .@type[1L] != 0L is.LDL <- function(.)if(inherits(., "try-error")) NA else isLDL(.) r.st <- cbind(perm = sapply(r, is.perm), LDL = sapply(r, is.LDL), super = sapply(r, class) == "dCHMsuper") names(dimnames(r.st)) <- list(" p L s", "") r.st } my.Cholesky <- { if(verbose) function (A, perm = TRUE, LDL = !super, super = FALSE, Imult = 0, ...) { cat(sprintf("Chol..(*, perm= %1d, LDL= %1d, super=%1d):", perm, LDL, super)) r <- Cholesky(A, perm=perm, LDL=LDL, super=super, Imult=Imult, ...) cat(" [Ok]\n") r } else Cholesky } logi <- c(FALSE, TRUE) d12 <- expand.grid(perm = logi, LDL = logi, super = c(logi,NA), KEEP.OUT.ATTRS = FALSE) r1 <- lapply(seq_len(nrow(d12)), function(i) try(do.call(my.Cholesky, c(list(A = A), as.list(d12[i,]))), silent=silentTry)) names(r1) <- apply(d12, 1, function(.) paste(symnum(.), collapse=" ")) dup.r1 <- duplicated(r1) r.all <- CHM_to_pLs(r1) if(!identical(dup.r1, duplicated(r.all))) warning("duplicated( <pLs-matrix> ) differs from duplicated( <CHM-list> )", immediate. = TRUE) list(Chol.A = r1, dup.r.all = dup.r1, r.all = r.all, r.uniq = CHM_to_pLs(r1[ ! dup.r1])) } ##' Cheap Boolean Arithmetic Matrix product ##' Should be equivalent to %&% which is faster [not for large dense!]. ##' Consequently mainly used in checkMatrix() ## The first version (up to Aug.2022) -- possibly what we should use for dense case (!?) boolProd0 <- function(x,y) as((abs(x) %*% abs(y)) > 0, "nMatrix") ## New since Aug.13, 2022, ensuring that zeros are dropped isCRT <- function(x, cl = getClass(class(x))) extends(cl, "CsparseMatrix") || extends(cl, "TsparseMatrix") || extends(cl, "RsparseMatrix") boolProd <- function(x,y) { ## treat x & y, drop0() & coercing to "n" -- this treats NA <==> 1 (!) x <- if(isCRT(x)) .sparse2kind(x, kind="n", drop0=TRUE) else as(drop0(x), "nMatrix") y <- if(isCRT(y)) .sparse2kind(y, kind="n", drop0=TRUE) else as(drop0(y), "nMatrix") r <- (abs(x) %*% abs(y)) > 0 if(isCRT(r)) .sparse2kind(r, kind="n", drop0=TRUE) else # also for "sparseMatrix" cases "indMatrix" (incl "pMatrix") or "diagonalMatrix" ## NB: "diagonalMatrix already *does* drop0(.) when coerced to "nMatrix" as(r, "nMatrix") } .sparse2kind <- Matrix:::.sparse2kind # (FIXME -- a version of this should be exported!) ###----- Checking a "Matrix" ----------------------------------------- ##' Check the compatibility of \pkg{Matrix} package Matrix with a ##' \dQuote{traditional} \R matrix and perform a host of internal consistency ##' checks. ##' ##' @title Check Compatibility of Matrix Package Matrix with Traditional R Matrices ##' ##' @param m a "Matrix" ##' @param m.m as(m, "matrix") {if 'do.matrix' } ##' @param do.matrix logical indicating if as(m, "matrix") should be applied; ##' typically false for large sparse matrices ##' @param do.t logical: is t(m) "feasible" ? ##' @param doNorm ##' @param doOps ##' @param doSummary ##' @param doCoerce ##' @param doCoerce2 ##' @param do.prod ##' @param verbose logical indicating if "progress output" is produced. ##' @param catFUN (when 'verbose' is TRUE): function to be used as generalized cat() ##' @return TRUE (invisibly), unless an error is signalled ##' @author Martin Maechler, since 11 Apr 2008 checkMatrix <- function(m, m.m = if(do.matrix) as(m, "matrix"), do.matrix = !isSparse || prod(dim(m)) < 1e6, do.t = TRUE, doNorm = TRUE, doOps = TRUE, doSummary = TRUE, doCoerce = TRUE, doCoerce2 = doCoerce && !isRsp, doDet = do.matrix, do.prod = do.t && do.matrix && !isRsp, verbose = TRUE, catFUN = cat, MSG = if(interactive() || capabilities("long.double") || isTRUE(get0("doExtras"))) message else function(...) {} ) { ## is also called from dotestMat() in ../tests/Class+Meth.R stopifnot(is(m, "Matrix")) validObject(m) # or error(....) clNam <- class(m) cld <- getClassDef(clNam) ## extends(cld, FOO) is faster than is(m, FOO) isGen <- extends(cld, "generalMatrix") isSym <- extends(cld, "symmetricMatrix") isTri <- extends(cld, "triangularMatrix") isCor <- isSym && (extends(cld, "corMatrix") || extends(cld, "pcorMatrix")) if(isSparse <- extends(cld, "sparseMatrix")) { # also true for these isCsp <- extends(cld, "CsparseMatrix") isRsp <- extends(cld, "RsparseMatrix") isTsp <- extends(cld, "TsparseMatrix") isDiag <- extends(cld, "diagonalMatrix") isInd <- extends(cld, "indMatrix") isPerm <- extends(cld, "pMatrix") } else isCsp <- isRsp <- isTsp <- isDiag <- isInd <- isPerm <- FALSE is.n <- extends(cld, "nMatrix") nonMatr <- clNam != (Mcl <- MatrixClass(clNam, cld)) Cat <- function(...) if(verbose) cat(...) CatF <- function(...) if(verbose) catFUN(...) ## warnNow <- function(...) warning(..., call. = FALSE, immediate. = TRUE) DO.m <- function(expr) if(do.matrix) eval(expr) else TRUE vec <- function(x) { dim(x) <- c(length(x), 1L) dimnames(x) <- list(NULL,NULL) x } eps16 <- 16 * .Machine$double.eps

ina <- is.na(m)
if(do.matrix) {
stopifnot(all(ina == is.na(m.m)),
all(is.nan(m) == is.nan(m.m)),
all(is.finite(m) == is.finite(m.m)),
all(is.infinite(m) == is.infinite(m.m)),
all(m == m | ina), ## check all() , "==" [Compare], "|" [Logic]
if(ncol(m) > 0) identical3(unname(m[,1]), unname(m.m[,1]),
as(m[,1,drop=FALSE], "vector"))
else identical(as(m, "vector"), as.vector(m.m)))
if(any(m != m & !ina)) stop(" any (m != m) should not be true")
} else {
if(any(m != m)) stop(" any (m != m) should not be true")
if(ncol(m) > 0)
stopifnot(identical(unname(m[,1]), as(m[,1,drop=FALSE], "vector")))
else stopifnot(identical(as(m, "vector"), as.vector(as(m, "matrix"))))
}
if(do.t) {
tm <- t(m)
if(isSym) ## check that t() swaps 'uplo'  L <--> U :
stopifnot(c("L","U") == sort(c(m@uplo, tm@uplo)))
ttm <- t(tm)
## notInd: "pMatrix" ok, but others inheriting from "indMatrix" are not
notInd <- (!isInd || isPerm)
if(notInd && (isCsp || isGen || isDiag))
stopifnot(Qidentical(m, ttm, strictClass = !nonMatr))
else if(do.matrix) {
if(notInd) stopifnot(nonMatr || class(ttm) == clNam)
stopifnot(all(m == ttm | ina))
## else : not testing
}

## crossprod()	%*%  etc
if(do.prod) {
c.m <-  crossprod(m, boolArith = FALSE)
tcm <- tcrossprod(m, boolArith = FALSE)
tolQ <- if(isSparse) NA else eps16
stopifnot(dim(c.m) == rep.int(ncol(m), 2),
dim(tcm) == rep.int(nrow(m), 2),
## FIXME: %*% drops dimnames
Q.eq2(c.m, tm %*% m, tol = tolQ),
Q.eq2(tcm, m %*% tm, tol = tolQ),
## should work with dimnames:
Q.eq(m %&% tm, boolProd(m, tm), superclasses=NULL, tol = 0)
,
Q.eq(tm %&% m, boolProd(tm, m), superclasses=NULL, tol = 0)
)
}
}
if(!do.matrix) {
CatF(" will *not* coerce to 'matrix' since do.matrix is FALSE\n")
} else if(doNorm) {
CatF(sprintf(" norm(m [%d x %d]) :", nrow(m), ncol(m)))
for(typ in c("1","I","F","M")) {
Cat('', typ, '')
stopifnot(all.equal(norm(m,typ), norm(m.m,typ)))
}
Cat(" ok\n")
}
if(do.matrix && doSummary) {
summList <- lapply(getGroupMembers("Summary"), get,
envir = asNamespace("Matrix"))
CatF(" Summary: ")
for(f in summList) {
## suppressWarnings():  e.g. any(<double>)	would warn here:
r <- suppressWarnings(identical(f(m), f(m.m)))
if(!isTRUE(r)) { ## typically for prod()
f.nam <- sub("..$", '', sub("^\\.Primitive..", '', format(f))) ## sum() and prod() are sensitive to order of f. p. operations ## particularly on systems where sizeof(long double) == sizeof(double) (if(any(f.nam == c("sum", "prod"))) MSG else stop)( sprintf("%s(m) [= %g] differs from %s(m.m) [= %g]", f.nam, f(m), f.nam, f(m.m))) } } if(verbose) cat(" ok\n") } ## and test 'dim()' as well: d <- dim(m) isSqr <- d[1] == d[2] if(do.t) stopifnot(identical(diag(m), diag(t(m)))) ## TODO: also === diag(band(m,0,0)) if(prod(d) < .Machine$integer.max && !extends(cld, "modelMatrix")) {
vm <- vec(m)
stopifnot(is(vm, "Matrix"), validObject(vm), dim(vm) == c(d[1]*d[2], 1))
}

if(!isInd)
m.d <- local({ m. <- m
diag(m.) <- diag(m) ## << *assigning* to 'm.' now typically annihilates @factor
if(.hasSlot(m, "factors") && length(f <- m@factors))
m.@factors <- f
m. })
if(do.matrix)
stopifnot(identical(dim(m.m), dim(m)),

## now that "pMatrix" subsetting gives *LOGICAL*
## 	      if(isPerm) {
## 		  identical(as.integer(unname(diag(m))), unname(diag(m.m)))
## 	      } else
identical(diag(m), # base:: *and* Matrix diag()  now keep names
diag(m.m)),## not for NA: diag(m) == diag(m.m),
identical(nnzero(m), sum(m.m != 0)),
identical(nnzero(m, na.counted = FALSE),
sum(m.m != 0, na.rm = TRUE)),
identical(nnzero(m, na.counted = TRUE),
sum(m.m != 0 | is.na(m.m)))
)

if(isSparse) {
n0m <- drop0(m) #==> n0m is Csparse
has0 <- !Qidentical(n0m, as(m,"CsparseMatrix"))
}

if(isDiag)
stopifnot(exprs = {
.MJ.Qidentical(m, m.d, strictClass = FALSE,
skipSlots = if(m@diag != "N") c("diag", "x"))
m@diag == "N" || (m.d@diag == "N" &&
identical(m.d@x, diag(m, names = FALSE)))
})
else if(isTri && m@diag != "N")
stopifnot(exprs = {
is(m.d, "triangularMatrix") && m.d@diag == "N"
.MJ.Qidentical(m, m.d, strictClass = FALSE,
skipSlots = c("diag", "p", "i", "j", "x"))
isSparse || all(m == m.d)
})
else if(!isInd)
stopifnot(.MJ.Qidentical(m, m.d, strictClass = FALSE,
skipSlots =
if(((isCsp || isRsp) && has0) || isTsp)
c("p", "i", "j", "x")))

## use non-square matrix when "allowed":

## m12: sparse and may have 0s even if this is not: if(isSparse && has0)
m12 <- as(as(  m, "lMatrix"),"CsparseMatrix")
m12 <- drop0(m12)
if(do.matrix) {
## "!" should work (via as(*, "l...")) :
m11 <- as(as(!!m,"CsparseMatrix"), "lMatrix")
if(!Qidentical(m11, m12))
stopifnot(Qidentical(as(m11, "generalMatrix"),
as(m12, "generalMatrix")))
}
if(isSparse && !isDiag && !is.n) {
## ensure that as(., "nMatrix") gives nz-pattern
CatF("as(., \"nMatrix\") giving full nonzero-pattern: ")
n1 <- as(m, "nMatrix")
ns <- as(m, "nsparseMatrix")
stopifnot(identical(n1,ns),
## only testing [CR]sparseMatrix and indMatrix here ...
## sum(<n.T>) excludes duplicated (i,j) pairs whereas
## length(diagU2N(<[^n].T>)) includes them ...
isTsp ||
(if(isSym) length(if(.hasSlot(n1, "i")) n1@i else n1@j)
else sum(n1)) == length(if(isInd) m@perm else diagU2N(m)@x))
Cat("ok\n")
}

if(doOps) {
## makes sense with non-trivial m (!)
CatF("2*m =?= m+m: ")
if(identical(2*m, m+m)) Cat("identical\n")
else if(do.matrix) {
eq <- as(2*m,"matrix") == as(m+m, "matrix") # but work for NA's:
stopifnot(all(eq | (is.na(m) & is.na(eq))))
Cat("ok\n")
} else {# !do.matrix
stopifnot(identical(as(2*m, "CsparseMatrix"),
as(m+m, "CsparseMatrix")))
Cat("ok\n")
}
if(do.matrix) {
## m == m etc, now for all, see above
CatF("m >= m for all: "); stopifnot(all(m >= m | ina)); Cat("ok\n")
}
if(prod(d) > 0) {
CatF("m < m for none: ")
mlm <- m < m
if(!any(ina)) stopifnot(!any(mlm))
else if(do.matrix) stopifnot(!any(mlm & !ina))
else { ## !do.matrix & any(ina) :  !ina can *not* be used
mlm[ina] <- FALSE
stopifnot(!any(mlm))
}
Cat("ok\n")
}

if(isSqr) {
if(do.matrix) {
## determinant(<dense>) "fails" for triangular with NA such as
## (m <- matrix(c(1:0,NA,1), 2))
CatF("symmpart(m) + skewpart(m) == m: ")
Q.eq.symmpart(m)
CatF("ok;  determinant(): ")
if(!doDet)
Cat(" skipped (!doDet): ")
else if(any(is.na(m.m)) && isTri)
Cat(" skipped: is triang. and has NA: ")
else
stopifnot(eqDeterminant(m, m.m, NA.Inf.ok=TRUE))
Cat("ok\n")
}
} else assertError(determinant(m))
}# end{doOps}

if(doCoerce && do.matrix && canCoerce("matrix", clNam)) {
CatF("as(<matrix>, ",clNam,"): ", sep='')
m3 <- as(m.m, clNam)
Cat("valid:", validObject(m3), "\n")
## m3 should ideally'' be identical to 'm'
}

if(doCoerce2 && do.matrix) { ## not for large m:  !m will be dense
if(is.n) {
mM <- if(nonMatr) as(m, Mcl) else m
stopifnot(identical(mM, as(as(m, "dMatrix"),"nMatrix")),
identical(mM, as(as(m, "lMatrix"),"nMatrix")),
identical(which(m), which(m.m)))
}
else if(extends(cld, "lMatrix")) { ## should fulfill even with NA:
stopifnot(all(m | !m | ina), !any(!m & m & !ina))
if(isTsp) # allow modify, since at end here
m <- asUniqueT(m, isT = TRUE)
stopifnot(identical(m, m & TRUE),
identical(m, FALSE | m))
## also check the  coercions to [dln]Matrix
m. <- if(isSparse && has0) n0m else m
m1. <- m. # replace NA by 1 in m1. , carefully not changing class:
if(any(ina)) m1.@x[is.na(m1.@x)] <- TRUE
stopifnot(identical(m. , as(as(m. , "dMatrix"),"lMatrix")),
clNam == "ldiMatrix" || # <- there's no "ndiMatrix"
## coercion to n* and back: only identical when no extra 0s:
identical(m1., as(as(m1., "nMatrix"),"lMatrix")),
identical(which(m), which(m.m)))
}
else if(extends(cld, "dMatrix")) {
m. <- if(isSparse && has0) n0m else m
m1 <- m1. <- (m. != 0)*1
## replace NA by 1 in m1. , carefully not changing class:
if(any(ina)) m1.@x[is.na(m1.@x)] <- 1
## coercion to n* (nz-pattern!) and back: only identical when no extra 0s and no NAs:
stopifnot(Q.C.identical(m1., as(as(m., "nMatrix"),"dMatrix"),
isSparse, checkClass = FALSE),
Q.C.identical(m1 , as(as(m., "lMatrix"),"dMatrix"),
isSparse, checkClass = FALSE))
}

maybeDense <- if(isSparse) identity else function(.) as(., "denseMatrix")
if(isTri) {
mm. <- m
i0 <- if(m@uplo == "L")
upper.tri(mm.) else lower.tri(mm.)
n.catchWarn <- if(is.n) suppressWarnings else identity
n.catchWarn( mm.[i0] <- 0 ) # ideally, mm. remained triangular, but can be dge*
## Aug.2022 - Coercion deprecations: No longer do as(*, clNam):
CatF("as(mm., \"triangularMatrix\"): ")
tm <- as(mm., "triangularMatrix")
Cat("valid:", validObject(tm), "\n")
if(m@uplo == tm@uplo) { ## otherwise, the matrix effectively was *diagonal*
if(!isSparse && Matrix:::.isPacked(m)) m <- unpack(m) # to match tm
## note that diagU2N(<dtr>) |-> dtC, now dtT:
stopifnot(Qidentical(tm, maybeDense(diagU2N(m))))
}
}
else if(isDiag) {

## TODO

} else {

## TODO
}
}# end {doCoerce2 && ..}

if(doCoerce && isSparse) { ## coerce to sparseVector and back :
v <- as(m, "sparseVector")
stopifnot(length(v) == prod(d))
dim(v) <- d
stopifnot(Q.eq2(m, v))
}

invisible(TRUE)
} ## {checkMatrix}

### --- These use

##' Check QR-consistency of dense and sparse
chk.qr.D.S <- function(d., s., y, Y = Matrix(y), force = FALSE, tol = 1e-10) {
stopifnot(is.qr(d.), is(s., "sparseQR"))
cc <- qr.coef(d.,y)
rank.def <- any(is.na(cc)) && d.$rank < length(d.$pivot)
if(rank.def && force) cc <- mkNA.0(cc) ## set NA's to 0 .. ok, in some case

## when system is rank deficient, have differing cases, not always just NA <-> 0 coef
## FIXME though:  resid & fitted should be well determined
if(force || !rank.def) stopifnot(
is.all.equal3(	    cc	     , qr.coef  (s.,y), drop(qr.coef  (s.,Y)), tol=tol),
is.all.equal3(qr.resid (d.,y), qr.resid (s.,y), drop(qr.resid (s.,Y)), tol=tol),
is.all.equal3(qr.fitted(d.,y), qr.fitted(s.,y), drop(qr.fitted(s.,Y)), tol=tol)
)
}

##' "Combi" calling chkQR() on both "(sparse)Matrix" and 'traditional' version
##' ------  and combine the two qr decompositions using chk.qr.D.S()
##'         [ chkQR() def. in >>>>> ./test-tools-1.R <<<<< ]
##'
##' @title check QR-decomposition, and compare sparse and dense one
##' @param A a 'Matrix' , typically 'sparseMatrix'
##' @param Qinv.chk
##' @param QtQ.chk
##' @param quiet
##' @return list with 'qA' (sparse QR) and 'qa' (traditional (dense) QR)
##' @author Martin Maechler
checkQR.DS.both <- function(A, Qinv.chk, QtQ.chk=NA,
quiet=FALSE, giveRE=TRUE, tol = 1e-13)
{
stopifnot(is(A,"Matrix"))
if(!quiet) cat("classical: ")
qa <- chkQR(as(A, "matrix"), Qinv.chk=TRUE, QtQ.chk=TRUE, tol=tol, giveRE=giveRE)# works always
if(!quiet) cat("[Ok] ---  sparse: ")
qA <- chkQR(A, Qinv.chk=Qinv.chk, QtQ.chk=QtQ.chk, tol=tol, giveRE=giveRE)
validObject(qA)
if(!quiet) cat("[Ok]\n")
chk.qr.D.S(qa, qA, y = 10 + 1:nrow(A), tol = 256*tol)# ok [not done in rank deficient case!]
invisible(list(qA=qA, qa=qa))
}


## Try the Matrix package in your browser

Any scripts or data that you put into this service are public.

Matrix documentation built on Nov. 14, 2023, 5:06 p.m.