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News forR PackageMatrix

Changes in version 1.7-4 (2025-08-27, svn r5172)

Installation

• Warnings surfaced by-Wtautological-overlap-compareare squashed. These revealed two typos in ‘src/matmult.c’causing optimizations forcrossprod(.sRMatrix, y) andtcrossprod(x,.sRMatrix) to be skipped. Thanks toBrian Ripley and Michael Chirico for the reports.

Bug Fixes

• Methods forband,triu, andtril withsignaturex="matrix" returned a formally invalid.geMatrix (withx slot of class"matrix") insome no-op cases, where no bands are set to zero.

Changes in version 1.7-3 (2025-03-05, svn r5126)

Bug Fixes

• <matrix>o<sparseVector> binary"Ops" work again, returning a matrix (of"Matrix").

• - new("lgeMatrix") and more - <Matrix> now work.

• Useint instead ofRboolean in 2x2 cases in ‘utils-R.c’.

Changes in version 1.7-2 (2025-01-20, svn r5115)

Installation

• Matrix can be installed with parallelbmake.Thanks to Sebastian Meyer for the report and patch inMatrixPR#6861.

Misc

• Test in ‘tests/matprod.R’ comparingt(x) %*% x andcrossprod(x) is amended to toleratesmall numerical differences seen under ‘⁠aarch64⁠’ Linux.

Changes in version 1.7-1 (2024-10-17, svn r4948)

Installation

• Installation under architecture-specific builds ofRworks again. It was broken inMatrix version 1.7-0,where changes to ‘src/Makevars’ resulted inCPPFLAGSnot including-I"${R_INCLUDE_DIR}${R_ARCH}".

SuiteSparse

• Internal SuiteSparse and METIS library sources are patchedto avoid possible use of illegal entry points.

C-Level API

• Registered routinesexp_as_cholmod_factor no longercallscholmod_check_factor before returning, leaving thedecision to check to the caller. Accordingly, mostcholmod_check_* are registered; packages wanting to usethem needLinkingTo: Matrix (>= 1.7-1).

Misc

• Non-API entry pointsOBJECT,IS_S4_OBJECT,SET_OBJECT,ATTRIB, andSET_ATTRIB are nolonger used.

Changes in version 1.7-0 (2024-03-16, svn r4662)

Installation

• Matrix\ge 1.7-0 depends onR\ge 4.4.

Linking

• TheMatrix ABI version is incremented from 1 to 2.

• ReverseLinkingTo built under earlier versions ofMatrix should be rebuilt from sources by users andmaintainers of binary repositories.

SuiteSparse

• The internal SuiteSparse library sources are updated fromversion 5.10.1 to version 7.6.0. We have so far identified onebackwards incompatible change: since SuiteSparse version 7.3.0,cholmod_sort(A) sorts butdoes not pack the matrixA. It seems that nowcholmod_sort andcholmod_copy must be used in conjuction if a sortedand packed result is desired. This change affects onlyreverseLinkingTo relying on the old behaviour. It seemsthat currently there are no such packages on CRAN or Bioconductor.

• CHOLMOD component Partition is compiled along with itsdependencies (METIS, CAMD, CCOLAMD).

• CXSparse is compiled instead of CSparse, which did notsupport complex matrices.

• The internal SuiteSparse and METIS library sources arepatched to squash a significant number of warnings surfaced by-Wall.

Significant User-Visible Changes

• The diagonal elements of theR factor computed byqr(<sparseMatrix>) are no longer constrained to benon-negative, due to differences in the implementation of functioncs_house between SuiteSparse libraries CSparse andCXSparse.

Classes

• indMatrix no longer extends virtual classcompMatrix and so no longer inherits a (never used)factors slot. Objects serialized underMatrix< 1.7-0 and unserialized underMatrix\ge1.7-0 remain valid, retaining a harmlessfactorsattribute.

• Unexported class unionreplValueSp is effectivelyremoved, now having zero members. Actual removal is delayed untilpackage binaries caching the old definition are rebuilt underMatrix version 1.7-0.

• The validity method for classsparseQR no longerrequires non-negativediag(R).

Bug Fixes

• The unary subscriptx[i] is correct again forx of class.s[CT]Matrix and logicaliindexing entries outside of the stored triangle.

Changes in version 1.6-5 (2024-01-06, svn r4560)

C-Level API

• Registered routinecholmod_triplet_as_sexp transposesentries “opposite” thestype when that is nonzero,following CHOLMOD.

• cholmod_defaults is registered so that calls toAPI functionM_cholmod_defaults actually work.

Bug Fixes

• x[] works forx inheriting from virtual classsparseVector.

• length(x) is always an integer forxinheriting from virtual classsparseVector. Truncation didnot occur forx@length of type"double" equal to orgreater than.Machine[["integer.max"]] + 1.

• tril(<n-by-n>, -n) now works again.

• tri[ul](<indMatrix>, k) now works correctly fork != 0.

Misc

• %||% is defined in theMatrix namespace onlyforR< 4.4.0.

Changes in version 1.6-4 (2023-11-29, svn r4523)

Installation

• Warnings surfaced by-Wformat are squashed.

C-Level API

• API functionM_chm_triplet_to_SEXP, removed inMatrix version 1.6-2, is restored (as a macro). It was“covertly” used by packageRmosek.

Bug Fixes

• better deprecation message for..2dge().

Changes in version 1.6-3 (2023-11-13, svn r4513)

Misc

• With anR built withconfigure option--disable-long-double,prod(M) now very slightlydiffers for two differently classed versions ofM.

• checkMatrix() from ‘test-tools-Matrix.R’ getsoptionalMSG argument for suppressingprod()differences.

Changes in version 1.6-2 (2023-11-05, svn r4503)

Compatibility

• Matrix did not pass its checks underR version3.5.0, implicitly violatingDepends: R (>= 3.5). Thisrelease restores compatibility.

Linking

• Support is added for an ABI version relevant to packagesthat link againstMatrix. The ABI version is 1 in thisrelease and will be incremented by 1 in each future release thatchanges the ABI. It is implicitly 0 in previous releases.Versions and their components are defined in a header for use bypackages withLinkingTo: Matrix (>= 1.6-2) in their‘DESCRIPTION’. See ‘inst/include/Matrix/version.h’ and(below)Matrix.Version.

• ReverseLinkingTo built under earlier versions ofMatrix should be rebuilt from sources by users andmaintainers of binary repositories.

C-Level API

• API headers are organized under ‘inst/include/Matrix/’for easier namespacing. Packages should start usingLinkingTo: Matrix (>= 1.6-2) and include the API headerswith, e.g.,#include <Matrix/Matrix.h>.

• Packages including API headers can define macroR_MATRIX_INLINE, typically with#define R_MATRIX_INLINE inline, in order to allow thecompiler to inline stubs for registered routines.

• Some API function prototypes and macros not used by anyreverseLinkingTo are removed or remapped.

• Several API function prototypes usedconst qualifierswhere the registered routines do not.

• The prototype of API functionM_cholmod_band_inplacedid not match that of registered routinecholmod_band_inplace. The prototype ofcholmod_bandwas copied by mistake.

Significant User-Visible Changes

• Methods for generic functionsrbind2,cbind2,%*%,%&%,crossprod, andtcrossprod determine the class of the result using morestrict rules, designed to avoid “surprising” coercionswhere possible. Notably, operations involvingRsparseMatrix now return anRsparseMatrix in morecases.TsparseMatrix anddiagonalMatrix may behandled asCsparseMatrix or asRsparseMatrix,depending on context.

Classes

• New nonvirtual classndiMatrix representing diagonalnonzero pattern matrices. It extends virtual classesdiagonalMatrix andnMatrix.ndiMatrix aretypically obtained as the result ofis.na,is.nan,oris.infinite applied to adiagonalMatrix or as theresult of coercing adiagonalMatrix tonMatrix.(The result of that coercion used to be anntCMatrix. Itis still possible to obtain anntCMatrix by coercion tonsparseMatrix.)

• The validity method for classsparseVector requireslength not exceeding2^53, which on most platformsis the minimum positive integerk such thatk + 1 isnot exactly representable in double precision.

• AdsparseVector withx slot of type"integer" is formally invalid, as always intended.

• Certain never or seldom used class unions are removed.

New Features

• mean(<sparseVector>, trim=) now works efficiently fornonzero values oftrim.

• rep(<sparseVector>, each=) now works efficiently,avoidingrep(., times = rep(each, times = length(.))).

• .m2dense and.m2sparse gain an argumenttrans indicating if vectors that are not matrices should becoerced to 1-row matrices rather than 1-column matrices.

• .m2dense and.m2sparse can be called with oneargument. Theirclass arguments admit new default values".ge" and".gC".

• .diag2dense and.diag2sparse gain an argumentkind indicating the “kind” of the result.

• New exports.M2V and.m2V, for coercingMatrix andmatrix (and in factvector) tosparseVector.

• New exportsisUniqueT andasUniqueT, withoptional argumentbyrow allowing for row-major ordering ofentries.asUniqueT supercedesuniqTsparse, which isno longer documented.

• New exportaggregateT, for aggregatingTsparseMatrixwithout sorting.

• Methods forall.equal now report the packages whereS4 classes are defined.

• sum(x) andprod(x) no longer require acoercion fromsymmetricMatrix togeneralMatrix.Results where coercions are now avoided may differ numerically dueto reordering of adds and multiplies, most commonly on systemswheresizeof(long double) == sizeof(double).

Bug Fixes

• Methods forcbind2 andrbind2 did not in allcases handle vectors as 1-column and 1-row matrices, respectively.

• Methods forcbind2 andrbind2 did not handle0-length vectors (includingNULL) correctly where theresult would have 0 rows and columns, respectively.

• Methods forcbind2 andrbind2 did not handleNA in thex slot ofndenseMatrix correctly(i.e., asTRUE).

• cbind2(<ndenseMatrix>, <ldenseMatrix>) gavengeMatrix instead oflgeMatrix.cbind2(<lsparseMatrix>, <lsparseMatrix>) gavedgCMatrix instead oflgCMatrix. Methods forrbind2 had similar problems.

• rcond(<0-by-0>) now returnsInf; seePR#18543.

• round(<dp[op]Matrix>) andsignif(<dp[op]Matrix>) now returnds[yp]Matrixrather thandp[op]Matrix and now discardfactors.

• Methods forlength now returninteger ratherthandouble if the result does not exceedINT_MAX.

• Methods for subscriptingsparseVector did not behavecompatibly withbase when supplied with fractional,NA, or out-of-bounds subscripts.

• symmpart(x),skewpart(x),band(x, k1, k2),triu(x, k), andtril(x, k) now always return a.diMatrix forx inheriting fromdiagonalMatrix.

• colSums(<(n|l|ind)Matrix>) androwSums(<(n|l|ind)Matrix>) now always give a result of type"integer". Methods differed previously, some giving"double" (asbase does, suboptimally, traditionalmatrices of type"logical").

• Some methods for generic functionlu did not transmitDimnames to the result.

• Some methods for group generic functionSummaryignored arguments matching.... Other methods did notignore the “garbage” elements of thex slot ofdense, triangular matrices.

• kronecker(<n.TMatrix>, <diagonalMatrix>) threw anerror for attempting to access the nonexistentx slot ofits first argument.

• Matrix products now behave exactly asbase whentesting for conformable arguments.

• Numeric products (%*%) did not always return adMatrix.

• Methods forall.equal now “see” attributes ofS4 objects that are not slots. This can be disabled by settingargumentcheck.attributes toNA, which is otherwiseequivalent toTRUE.

• prod(x) is computed more diligently forxinheriting fromsparseMatrix,sparseVector, or.t[rp]Matrix, i.e., thosex that can be understoodto have “structural” zeros. Now, multiplication by zerooccurs at the position of the first structural zero in the matrixor vector (when traversed by row in the case ofRsparseMatrix). An exception isTsparseMatrix, forwhich multiplication by zero occurs before multiplication by anystored entry, regardless of the position of the first structuralzero in the corresponding sorted matrix (to avoid the cost ofsorting).

• tri[ul](<.t[rp]Matrix>, k) was often wrong fornonzerok, setting too many bands to zero.

• C-leveltCsparse_diag (formerlydiag_tC) nowhandles structural zeros andNaN on the main diagonalcorrectly. Option"diagBack" now works correctly.

• expm(x) failed forx of classdtpMatrixordspMatrix, sinceMatrix version 1.6-1.

• .m2dense(x, ".ge") allocated unnecessarily forx without attributes.

Misc

• C code now refers to the symbolfactors asMatrix_factorsSym, rather thanMatrix_factorSym.

• The content of ‘src/Mutils.[ch]’ has been migrated tomore transparently named files: ‘src/attrib.[ch]’,‘src/objects.[ch]’, etc. Similarly, much of‘src/factorizations.[ch]’ have been migrated to‘src/solve.[ch]’ and ‘src/determinant.[ch]’.

• All matrix product code has been migrated to‘products.[Rch]’.

• Files in ‘po/’ and ‘inst/po/’ have been updateddue to more frequent use ofgettextf in ‘R/*.R’.

• C code is prepared to handle complex matrices andtheir factorizations. Notably, new machinery in‘src/cs-etc.[ch]’ will enable linking the CXSparse libraryinstead of the CSparse library, the latter supporting numerictypes but not complex ones.

Changes in version 1.6-1.1 (2023-09-08, hotfix)

Misc

• Export the genericscrossprod() andtcrossprod() explicitly, needed for R-devel when theybecome primitive internal generics.

Changes in version 1.6-1 (2023-08-11, svn r4228)

C-Level API

• Registered routinechm_sparse_to_SEXP sorts and packsits first argumentbefore assigning any struct members tovariables, preventing use-after-free.

Memory

• Four Valgrind-detected memory bugs are fixed.

Classes

• Validity methods for classesCholesky andpCholesky test for a validperm slot.

New Features

• Several new coercion utilities, exported and documented inhelp("fastMisc"). Some of these supercede ones madeavailable (experimentally) inMatrix 1.5-4; for example,.M2m makes both.dense2m and.sparse2mredundant. The superceded ones are not yet formally deprecated,but are no longer documented.

• drop0 is now implemented independently ofCHOLMOD, becoming more efficient notably for logicalarguments, no longer requiring a coercion to double.

• drop0 gains an argumentgive.Csparse tocomplementis.Csparse.FALSE indicates thatRsparseMatrix,TsparseMatrix, andindMatrixarguments should be handled directly, without a coercion toCsparseMatrix. The default value isTRUE, forbackwards compatibility.

Bug Fixes

• <diagonalMatrix> %*% <RsparseMatrix> works again.

• diag(<non-square RsparseMatrix>) <- value worksagain, no longer giving ap slot of lengthDim[2]rather thanDim[1].

• as(<diagonalMatrix>, "symmetricMatrix") now checksfor symmetricDimnames, for consistency.

• as(<indMatrix>, "[nld](sparse)?Matrix") now returns a.gRMatrix or a.gCMatrix depending on themargin slot.

• as(<[CR]sparseMatrix>, "generalMatrix") now checks ifthe number of nonzero entries in the result would exceedINT_MAX and throws an error in that case.

Misc

• Run speed-measuring tests onlyif(doExtras): thesewere too slow when run under Valgrind.

• Most coercion code has been migrated to ‘coerce.[Rch]’from elsewhere.

• The number of methods for generic functionscoerceandas.* has been reduced substantially, from 306 to 194(not counting deprecated ones), partly as a result of efforts todo more fine-grained dispatch in C code.

• Files in ‘po/’ and ‘inst/po/’ have been updated(again), as many more C level messages now use formatstrings as a result ofvsnprintf usage in‘src/validity.c’.

Changes in version 1.6-0 (2023-06-30, svn r4125)

Dependencies

• The following “weak” dependencies, needed only for asmall number of Rd cross references, are removed:MatrixModels,expm,igraph,maptools,sp,spdep. Links to CRAN or Bioconductor in Rd filesare preserved.

• sfsmisc is moved fromEnhances toSuggests, asMatrix does not formally enhance it withmethods or links to documentation.

• grDevices anddatasets are added toImports andSuggests, respectively, asMatrixdoes import fromgrDevices and (in vignettes) does load datafromdatasets.

• Example, test, and vignette code no longer fails whenR_DEFAULT_PACKAGES is set toNULL.

• Example code usesrequireNamespace instead ofrequire to preserve the user's search path.

Significant User-Visible Changes

• Methods for generic functionchol that previouslyreturned an object of classp?Cholesky now return anequivalent object of classdtrMatrix ordtpMatrix.Existing code that relied (correctly) onchol to return theupper triangular Cholesky factor as aMatrix can beexpected to work as before.

Classes

• ClassindMatrix gains amargin slot with value1L or2L (1L being the prototype andpreviously implicit value), indicating that the object representsa row or column index matrix, with ones at[i, perm[i]] or[perm[j], j], respectively.
  
  Methods withindMatrix or its subclasspMatrix inthe signature have been adjusted to account for the new slot.Notably, multiplication on the right by anindMatrix withmargin = 2 is now implemented as a column subscript, andthe transpose of anindMatrix is now the same object butwith “opposite”margin.

• Virtual classMatrixFactorization gains aDimnames slot. Now all factorizations preserve theDimnames of the original, factorizedMatrix, whereaspreviously classesSchur,sparseLU,sparseQR,dCHMsimpl, anddCHMsuper didnot. Users canget the value of the newDimnames slot withdimnames(.) and set it withdimnames(.) <- value.

• Classesp?BunchKaufman andp?Cholesky nolonger extenddtrMatrix ordtpMatrix and in turn nolonger extendMatrix. They retain slotsDim,Dimnames,uplo, andx, but notdiag.This change implies that virtual classesMatrix andMatrixFactorization no longer intersect.

• Classesp?Cholesky gain aperm slot withprototypeinteger(0L) to support representation of pivotedfactorizations, as typically computed by LAPACK routinedpstrf.perm of length 0 is valid and equivalent tothe identity permutation.

• New nonvirtual classpcorMatrix extendingdppMatrix. It is the counterpart ofcorMatrix usingpacked storage, supporting more efficient storage of densecorrelation matrices. Nowpack(<corMatrix>) gives apcorMatrix preserving thesd slot, rather than adppMatrix without ansd slot.

• New virtual classesBunchKaufmanFactorization,SchurFactorization, andQR, extended by existingnonvirtual classesp?BunchKaufman,Schur, andsparseQR, respectively. These are parallel to the existingvirtual classesCholeskyFactorization andLU.Packages defining new factorization classes may extend these.

• Virtual classCHMfactor and its subclasses gainformal validity methods.

• The validity method for classsparseQR now tests thattheV slot is lower trapezoidal and that theR slothas non-negative diagonal elements.

• The validity method for classcorMatrix now toleratesnonfinite elements in thesd slot. It no longer toleratesnonunit diagonal elements in thex slot.

• The prototype of theDim slot of virtual classMatrixFactorization is nowinteger(2L). It waspreviouslyinteger(0L), with the result thatvalidObject(new(<nonvirtual>)) was always an error.

• The prototype of theL slot of classsparseLUis now formally lower triangular, so thatvalidObject(new("sparseLU")) is not an error.

• The prototypes of theQ andT slots of classSchur are now 0-by-0dgeMatrix, so thatvalidObject(new("Schur")) is not an error.

Generic Functions

• New generic functionsexpand1 andexpand2,intended to replaceexpand and coercions from (subclassesof)MatrixFactorization to (subclasses of)Matrix.expand1 is used asexpand1(<MatrixFactorization>, <character string>) andconstructs by name factors appearing in the factorization.expand2 is used asexpand2(<MatrixFactorization>)and returns a named list ofall factors appearing in thefactorization, in order and with row names on the first factorand column names on the last factor. The result can be used toreconstruct the factorizedMatrix as the product of theelements of the list, namelyReduce(`%*%`, expand2(.)).
  
  expand and its methods are retained for backwardscompatibility. They may be formally deprecated in the future,hence new code should useexpand1 andexpand2.Notably,expand1 andexpand2 have methods for allfactorizations inMatrix, whereasexpand continues tohave methods only fordenseLU,sparseLU, andCHMfactor. Seehelp("expand-methods") for a list ofmethods, including useful optional arguments.

New Features

• Methods for subscriptingMatrix now use the moresystematic code in ‘R/subscript.R’ and‘src/subscript.c’, becoming more efficient for alllsparseMatrix(no longer coercing todsparseMatrix and back),sparsesymmetricMatrix(no longer coercing togeneralMatrix and back wheniinx[i, i] is monotone),unpackedMatrix(no longer coercing tomatrix and back), andRsparseMatrix(no longer coercing toTsparseMatrix, then toCsparseMatrix, then back toTsparseMatrix [!]).
  
  x[i, j, drop = FALSE] preserves the class ofx inmore cases wherex is atriangularMatrix,diagonalMatrix, orpMatrix, doing more completechecks oni andj.
  
  Notably, forx inheriting fromRsparseMatrix, theresult is now always anRsparseMatrix, rather than always aTsparseMatrix.

• NULL subscripts, as inx[NULL],x[NULL, j], andx[i, NULL], are now supported forxinheriting fromMatrix. They are handled asinteger(0), consistent withbase.

• Generic functionCholesky gains methods fordenseMatrix returning an object of classp?Cholesky.The method for subclassdsyMatrix admits an argumentperm indicating if the pivoted factorization should becomputed. The correspondingchol method gains an argumentpivot indicating the same. By default,Choleskypivots andchol does not.

• Many subclasses ofMatrixFactorization can now becoerced to “nearby” subclasses ofMatrix. TheresultingMatrix reflects the internal representation ofthe factorization and not necessarily a particular matrix factor.The new coercions are:as(<denseLU>, "dgeMatrix"),as(<BunchKaufman>, "dtrMatrix"),as(<pBunchKaufman>, "dtpMatrix"),as(<Cholesky>, "dtrMatrix"),as(<pCholesky>, "dtpMatrix"),as(<CHMsimpl>, "dtCMatrix"), andas(<CHMsuper>, "dgCMatrix").Seehelp("denseLU-class") (and similar) for details.

• determinant(x, ...) andsolve(a, b, ...)now work forx anda inheriting fromMatrixFactorization, behaving as ifx andawere replaced by the factorizedMatrix. The exception isx inheriting fromCHMfactor, where for backwardscompatibility the default behaviour is still to compute thedeterminant of the Cholesky factor. This exception should beconsideredtemporary, hence defensive code will calldeterminant with (new) optional argumentsqrt set toTRUE orFALSE explicitly, to not rely on the currentdefault value. Seehelp("CHMfactor-class") for details.

• Generic functiondiag gains methods forp?Cholesky andCHMfactor. The result is a numericvector containing the diagonal entries of the diagonal matrixD, as defined inhelp("Cholesky-class") andhelp("CHMfactor-class").

• Thelu andqr methods for classdgCMatrix now admit anorder argument with value in0:3, allowing the expert user to choose among all orderingmethods made available by the CSparse library.

• solve(<dgCMatrix>, b, sparse = TRUE) is now handledentirely in C code viacs_spsolve from theCSparse library.

• New utilitiesinvertPerm,signPerm,isPerm, andasPerm for computing the inverse andsign of a permutation vector, testing if an integer vector is apermutation vector, and coercing a transposition vector to apermutation vector.invertPerm is a more general versionof the already exported functioninvPerm, which is retainedas a wrapper aroundinvertPerm for backwards compatibility.

• Theqr.R method for classsparseQR gains abackPermute argument with defaultFALSE, forcompatibility withbase. FunctionqrR, which existedprimarily to provide a back-permuting option, is retained forbackwards compatibility.

Bug Fixes

• x[integer(0), ] andx[, integer(0)] now give ageneralMatrix result whenx is a 0-by-0diagonalMatrix, for consistency with all other cases ofx[seq_len(n), ] andx[, seq_len(n)], wherexis ann-by-n triangular, symmetric, or diagonalmatrix.

• Forx inheriting fromRsparseMatrix,subassignment of the formx[i, ] <- value is now correctlydistinguished fromx[i] <- value.

• rownames(x[integer(0), , drop = FALSE]) andcolnames(x[, integer(0), drop = FALSE]) are now alwaysNULL and nevercharacter(0), consistent with theimplementation inbase.

• Subscript operations onMatrix now correctly errorwhenever the formal argument ... is matched, as inx[i, j, drop], wherex[i, j, drop = drop] is almost alwaysintended.

• x[i, ] now correctly drops dimensions whenxis a 1-by-nMatrix andi isTRUE.

• Methods forsolve now obey the following rules muchmore strictly:

  • solve(a=<Matrix>, b=<vector>)must return a vector.

  • solve(a=<denseMatrix>, b=<Matrix>)must return adenseMatrix.

  • solve(a=<sparseMatrix>, b=<Matrix>, sparse=FALSE)must return adenseMatrix.

  • solve(a=<sparseMatrix>, b=<Matrix>, sparse=TRUE)must return asparseMatrix.

  resolving some longstanding incompatibilities withbase.
  
  Note that methods for sparsea and missing or sparseb have defaultsparse = TRUE, while methods forsparsea and denseb have defaultsparse = FALSE.

• solve(<symmetricMatrix>) now always gives asymmetricMatrix result.solve(<dpoMatrix>) andsolve(<dppMatrix>) preserve formal positive definiteness,giving adpoMatrix anddppMatrix, respectively.

• BunchKaufman(<matrix>) now works when argumentuplo (documented to be optional) is missing.

• Coercions tocorMatrix now set the diagonal elementsof the result to 1, consistent withcov2cor.

• dimnames(x) <- value now validatesx@Dimbeforevalue to avoid undefined behaviour in C-level check.

• chol2inv(x) now ignores the lower triangular part ofx not inheriting fromtriangularMatrix.

• chol2inv(x) now computescrossprod(solve(x))instead oftcrossprod(solve(x)) for all formally lowertriangularx. Previously,crossprod was used onlyfor densex.

• rcond(x, norm) throws a nicer error forx oflength 0.

• Error messages due to invalidnorm inrcond(x, norm) now refer to the argument asnorm rather thantype.

• rcond(x, norm) now validatesnorm also forx of classd(sy|sp|po|pp)Matrix, even if for suchx all validnorm give the same result.

• which(<[RT]sparseMatrix>, ...) now gives indices incolumn-major order in all cases, to be consistent withhelp("which").

• Factorizations inheriting from virtual classLU arenow cached under the namedenseLU orsparseLU,depending on the nonvirtual class, rather than always under thenameLU. Note that user code shouldnot rely on thedetails of the cache and should instead rely on functions such aslu to retrieve cached factorizations.

• Errors signaled byas(<dsyMatrix>, "dpoMatrix") andas(<dspMatrix>, "dppMatrix") now clarify that the coercionsdo not attempt to test for positive semidefiniteness when thematrix is not positive definite.

Memory

• invPerm(p) no longer segfaults forp that arenot valid permutation vectors.invPerm(NA) was enough totrigger a segfault.

• C code interfacing the CSparse library tests inmore places for failed allocations inside ofcs_*.

Misc

• Help pages for matrix factorization classes and methods havebeen broadly expanded and updated to use consistent notation.

• The length of theMatrix namespace has been reduced by~15%. More than 100 unused symbols have been removed.

• Updates to ‘po/*.{po,pot}’ and ‘inst/po/*’ fortranslators.

Changes in version 1.5-4.1 (2023-05-16, hotfix)

Installation

• ‘src/Lapack-etc.h’ uses#ifdef PR18534fixed,adapting toPR#18534 without breaking installation underR< 4.3.1.

Changes in version 1.5-4 (2023-04-02, svn r3837)

Compatibility

• sequence.default is defined forR< 4.0.0.

C-Level API

• ‘Rinternals.h’ is included in‘inst/include/Matrix.h’ instead of deprecated‘Rdefines.h’. The inclusion is done outside ofextern "C".

Deprecated and Defunct

• The following low level coercion utilities, which werepreviously exported but always “hidden” and undocumented,are now deprecated:..2dge,.C2nC,.T2Cmat,.asmatrix,.dense2sy,.diag2mat,.diag2sT,.diag2tT,.dsy2dsp,.dsy2mat,.dxC2mat,.m2dgC,.m2lgC,.m2ngC,.m2ngCn,.m2ngTn,.n2dgT,.nC2d,.nC2l.
  
  The deprecations follow efforts to define more general and moresystematic (but still fast) coercion utilities, to allow expertusers to bypass S4 dispatch in more cases. The subset of thesecurrently exported is documented underhelp("fastMisc").Deprecation warnings will suggest an appropriate replacement,mostly from that list.
  
  It is not always the case that the replacement can be“dropped in”, hence users should consult the relevantdocumentation when changing their code.

• Warnings signaled by coercion methods deprecated inMatrix 1.5-0 now correctly inherit from classdeprecatedWarning.

Memory

• Calls tosprintf are replaced by equivalent callssnprintf to avoid potential buffer overflow.

Misc

• C-level utilitiesMatrix_memset() andMatrix_memcpy(), both new, are now used in many placesinstead of API macrosMemzero() andMemcpy() whichnever check for overflow. C-level macroAZERO() is nolonger defined.

• C-level macroCalloc_or_Alloca_TO() nowzero-initializes also in thealloca-using case.

Changes in version 1.5-3 (2022-11-10, svn r3772)

Dependencies

• methods is moved fromImports toDependsas suggested in the WRE manual. Nowas and other basic S4machinery are available wheneverMatrix is attached. Thischange affectsR processes started with environment variableR_DEFAULT_PACKAGES set toNULL (or any list notcontainingmethods).

Compatibility

• Test involving sparsePOSIXlt in‘tests/Simple.R’ is adapted to possible (unconditional sinceR version 4.3.0) existence of character componentzone.

Bug Fixes

• dimScale(x) with argumentd1 missing is nolonger an error. (The default value haddiag(x, FALSE)instead ofdiag(x, names = FALSE).)

• (dim|row|col)Scale(x) is no longer an error fortraditional matricesx without adimnames attribute.

• Ourcov2cor() methods now again preserve(symmetrized!)dimnames, fixingMatrixPR#6783 reported byBen Bolker.

• colSums() and friends now always give anamedresult when the marginalDimnames are non-NULL.(Names were “forgotten” fordiagonalMatrix andindMatrix arguments.)

• colSums() and friends now respectna.rm whenhandlingdiagonalMatrix withNA diagonal entries.

• expand(<denseLU>) now “copies-on-modify”, nolonger duplicating them*n-lengthx slot in them == n case, when it can be used directly.

• lu(<m-by-0>),lu(<0-by-n>), andBunchKaufman(<0-by-0>) now give sensible (0-extent)results, rather than a LAPACK error, fordenseMatrix.

New Features

• Diagonal() gets a new optionalnames argument.

• diag(x) <- value is now done in C also for[CRT]sparseMatrix.

• .diagU2N() gets fast counterpart.diagN2U().

• colSums() and friends are now implemented moreefficiently fordenseMatrix and[CRT]sparseMatrix.Notably, methods for triangular and symmetric matrices no longergo viageneralMatrix, and methods for[CRT]sparseMatrix now handle nonzero pattern and logicalmatrices directly (no longer coercing to double, a constraint ofthe earlier implementation using CHOLMOD).

• determinant(<ds[yp]Matrix>) is now computed via theBunch-Kaufman factorization. Factorizations are cached in thefactors slot for future reuse.

Misc

• C-level wrappers for LAPACKd..trf routines gain anargumentwarn indicating how to handleinfo > 0:warn <= 0 is silent,warn = 1 is a warning, andwarn > 1 is an error. In the case ofdp[op]trf, forwhichinfo > 0 implies an incomplete factorization,info is now returned as a length-1 integer.

Changes in version 1.5-2 (2022-10-21, svn r3702)

Classes

• The validity methods for classesl[st]CMatrix nowcorrectly test for structurally nonzero entries on the wrong sideof the main diagonal, and fail in that case. Previously, thistest was performed only ford[st]Matrix.

• The validity method for virtual classsparseVector ismore diligent, catching more edge cases such asNA in thelength ori slot.

• New validity methods forn[st][CRT]Matrix,Schur,denseLU,p?BunchKaufman,p?Cholesky,sparseLU, andsparseQR. Notably,the following properties of factorizations are now checked: thedimensions of each factor, the orientation of each triangular (ortrapezoidal) factor, and the validity of each permutation vector.

Bug Fixes

• lu(x)@L@uplo is now"L", not"U", for0-by-0 and 1-by-1dgCMatrixx.

• The validity method forcorMatrix now throws a bettererror when thesd slot is of type"integer" ratherthan"double".

• .sparseDiagonal() now agrees withDiagonal()when called with no arguments, returning a 0-by-0 (rather than1-by-1) diagonalMatrix.

• sparseMatrix(i, j) with 0-lengthi andj now returns a 0-by-0 matrix rather than throwing aperplexing error.

• sparseMatrix(dims = <list>) andsparseMatrix(x = <dMatrix>) now produce errors.

• diag(x) <- value now coercesdiagonalMatrixx iftypeof(value) is “higher” thantypeof(x@x) in the usual hierarchy, for consistency withmethods fordenseMatrix and withbase::`diag<-`.

• Methods forkronecker() no longer ignore themake.dimnames argument.

• Printing asparseMatrix withNA row or columnnames is no longer an error.

• Products of twopMatrix objectsx andyare now computed correctly. Previously,y %*% x wasreturned instead ofx %*% y!

• Productsx %*% y withx adiagonalMatrix orindMatrix andy atraditional matrix or vector, or withx a traditionalmatrix or vector andy adiagonalMatrix orpMatrix, now treat the unclassed argument as a.geMatrix and return a.geMatrix, for greaterconsistency with other products involving oneMatrix andone non-Matrix.

• Similarly,kronecker(x, y) with one ofx andy aMatrix and the other a traditional matrix orvector now treats the unclassed argument as a.geMatrix.

• dimnames(solve(x)) is nowrev(dimnames(x)) fordenseMatrixx, consistent with the handling ofdimnames bysolve.default. Methods forsparseMatrixx have not been addressed (yet).

Memory

• In many more (but not yet all) places, Cfunctions protect the values ofR_do_slot,Rf_getAttrib,Rf_mkString, etc. from garbagecollections, squashing many new and some oldrchkwarnings.

New Features

• is.nan(x) is now implemented for allxinheriting from virtual classMatrix orsparseVector.

• Diagonal(n=, x=) now recyclesx of anypositive length to lengthn. Previously, recycling wassupported only forx of length 1.

• Products involvingdiagonalMatrix orindMatrixhave been broadly improved as follows:

  • dimnames(A %*% B) is now alwaysc(dimnames(A)[1], dimnames(B)[2]).

  • t?crossprod() methods involvingindMatrix orits subclasspMatrix gain aboolArith argument.

  • Numeric and boolean products are always returned asdMatrix andnMatrix, respectively, except in a fewspecial cases where the product can be represented as anindMatrix. (Previously, coercions were skipped when oneof the operands was unit diagonal.)

  • Products ofdiagonalMatrix with densetriangularMatrix now correctly give atriangularMatrix result (and without unpacking).

  • Products ofdiagonalMatrix with[RT]sparseMatrix now preserve storage, no longer coercingtoCsparseMatrix.

  • crossprod(x, y) no longer requires the product ofncol(x) andncol(y) to be less than2^31when bothx andy areindMatrix. (The newimplementation now always gives adgTMatrix result,whereas previously the result would typically but not always beadgCMatrix.)

• kronecker(<Matrix>, <Matrix>) now gives the correct“shape” (general, [unit] triangular, symmetric, diagonal)in all cases where it can be known without checking.

• kronecker(<[CR]sparseMatrix>, <Matrix>) now retainsthe storage of the first argument, no longer coercing toTsparseMatrix.

• New exported functionsdimScale,rowScale, andcolScale, for scaling rows and columns of a[mM]atrix without losingdimnames and whereappropriate without losing symmetry.

Changes in version 1.5-1 (2022-09-12, svn r3642)

Memory

• ASan-detected memory bugs are fixed in CfunctionsTsparse_as_CRsparse andpMatrix_validate.The former was triggered by.T2C(<0-by-0>) and the latterwas triggered byas(<length-10000 integer>, "pMatrix").

Changes in version 1.5-0 (2022-09-09, svn r3636)

Deprecated and Defunct

• With a few exceptions, direct coercions to non-virtualsubclasses ofMatrix (e.g.,dsCMatrix) have beenformally deprecated. For now, these will continue to work asbefore, but with a warning indicating how to accomplish thedesired coercion via virtual classes (e.g.,symmetricMatrix) alone. How such warnings are signaled iscontrolled by the global optionMatrix.warnDeprecatedCoerce.

  0 or less

  is to be silent.

  1

  is to signal a warning with each deprecatedcoercion.

  2 or greater

  is to signal an error with eachdeprecated coercion.

  NA

  is to signal a message or warning (see below)with the next deprecated coercion and be silent after that.

  If unset or invalid, then the value of the environment variableR_MATRIX_WARN_DEPRECATED_COERCE (NA if unset) isused. This is cached when theMatrix namespace isloaded.
  
  Option values are coerced to integer before use.
  
  To reduce disruption to existing code, theNA case signalsmessages rather than warnings with coercions to the most-usednon-virtual subclasses ofMatrix, namelydg.Matrixandd.CMatrix. This may change in the future.

Classes

• New virtual classunpackedMatrix representing densematrices in unpacked format. It extendsdenseMatrix and isextended by[nld](ge|sy|tr)Matrix, i.e., the subclasses ofdenseMatrix not extendingpackedMatrix.

• The validity method fordppMatrix requiresnon-negative diagonal elements, matching the validity method fordpoMatrix.

• The validity method forMatrix tolerates vector typesother than"character" forDimnames[[i]].

Bug Fixes

• Symmetrization of<Matrix>@Dimnames anddimnames(<matrix>) now goes through C utilitysymmDN() in most places, resolving some earlierinconsistencies.

• Many more validity methods now correctly operate under theassumption that methods for superclasses have already been called,eliminating many redundant checks.

• Validation of<Matrix>@Dim now looks at typebefore length, avoiding a misleading error message.

• Validation of<Matrix>@Dimnames now avoidsisNewList, which had allowed an error message suggestingthatNULL is a list.

• Setting a factor on acompMatrix is now to installthe factor itself, not a copy, for efficiency and consistency withthe semantics of<compMatrix>@factors[[name]] <- value.

• Long vector support in methods for packing and unpackingdenseMatrix, and others.

• diag<- incorrectly preserved the class of densematrices, so that, e.g.,`diag<-`(x=<dpoMatrix>, value=-1)was still adpoMatrix. Now the result is always one of themore general.(ge|tr|sy|tp|sp)Matrix.

• t(<corMatrix>) no longer clears thesd slot.t(<p?BunchKaufman>) now returns one of the more generaldt[rp]Matrix, rather than preserving class and clearing theperm slot.

• t(<symmetricMatrix>) no longer reverses theDimnames slot. Symmetrization ofdn <- x@Dimnamesandt(x)@Dimnames had given different results whendn[[1]] anddn[[2]] were non-NULL andasymmetric.

• isTriangular(x, upper) had incorrectly returnedFALSE forx of classtriangularMatrix whenupper = TRUE andx@uplo = "L" or whenupper = FALSE andx@uplo = "U".isTriangular is nowequivalent toisDiagonal in those cases.

• isSymmetric() was equivalent toisDiagonal()for triangular matrices,not allowing numerical fuzz via anargumenttol. Atol argument is now implemented forall subclasses ofdMatrix except for those inheriting fromsymmetricMatrix ordiagonalMatrix.

• Methods forisSymmetric now also look atDimnames andnames(Dimnames), followingisSymmetric.matrix frombase. See also New Features.

• band(x, -k, k) for sparsex usedisSymmetric(x) (which tolerates numerical fuzz) to test forsymmetry, resulting in loss of information in some cases. Now ittests thatx inherits fromsymmetricMatrix, and soreturnssymmetricMatrix in fewer cases.

• triu(x, k) andtril(x, k) incorrectly requiredk <= m (instead ofk <= n), form-by-nsparsex. They now accept allk from-m ton, with fewer errors in them < n case.

• crossprod(<Rsparse>, <Tsparse>) and similar now workagain (optionalboolArith was not passed on), fixingMatrixPR#6766 by David Cortes. Ditto fortcrossprod(), wherethe old result was even wrong when it had “worked”, beforeMatrix 1.2-0.

• as(<matrix>, "nMatrix") can now be sparseordense, going viaMatrix(), for greater consistency withcoercions todMatrix andlMatrix. (Previously, theresult was always anngTMatrix.)

• forceSymmetric(<[RT]sparseMatrix>) are now moreefficient, returning symmetric[RT]sparseMatrix withoutintermediate coercions toCsparseMatrix.

• tcrossprod(a, b) for unit triangular sparse matricesnow works correctly.

• !<ltrMatrix> is no longer an error in the 0-by-0 unitdiagonal case.

• Coercions among[CRT]sparseMatrix preserve thefactors slot in more cases.

• Coercions of overallocatedl.TMatrix todenseMatrix orCsparseMatrix now giveTRUEinstead ofNA in theNA || TRUE case, followingconventional logic.

• Methods for unpacking and indexingpackedMatrix andfor coercing from[CRT]sparseMatrix todenseMatrixnow check more consistently for overflow ofR_XLEN_T_MAX.

• solve(<ddenseMatrix>, <ANY>) is removed from themethod list. It had allowed infinite recursion, e.g., withsolve(new("dgeMatrix"), NULL).

• is.na(<ndenseMatrix>) gaveTRUE where thex slot hadNA. Now the result is always a zeromatrix.

• is.na(<.t[rp]Matrix>) andis.infinite(<.t[rp]Matrix>) ignored thediag slot,behaving always as thoughdiag == "N". They now giveFALSE on the diagonal in thediag != "N" case.

• Now only “nontrivial” matrix elements determinewhetheris.na(<denseMatrix>) is anndenseMatrix orannsparseMatrix.

• is.na(<ddenseMatrix>) coerced tolMatrix.This unnecessary step is avoided now, saving a potentiallynontrivial allocation.

• solve(<ddenseMatrix>, b) coerced the first argumenttodgeMatrix whenb was not addenseMatrix ortraditionalmatrix. This unnecessary step is avoided now,so that specialized methods ford(tr|sy|po|tp|sp|pp)Matrixare used where possible (including forb inheriting from[ln]denseMatrix,sparseMatrix, ornumLike).

• `dim<-`(x, -x@Dim) is now an error, no longeryielding an invalidMatrix object.

• `dim<-`(x, x@Dim) is now faster, returningxwithout allocation in all cases.

• `dim<-`(x, value) gives a better error whenvalue containsNA or elements exceedingINT_MAX.

• `dim<-`(<RsparseMatrix>, value) is now anRsparseMatrix, rather than aTsparseMatrix.

• For consistency with other methods,symmpart(<diagonalMatrix>) now always inherits from bothdMatrix andsymmetricMatrix, andskewpart(<diagonalMatrix>) now always has symmetricDimnames.

• Zeros on the diagonal ofskewpart(<[CRT]sparseMatrix>) are nowstructural.

• as(<ndenseMatrix>, "(vector|matrix|[dl]Matrix)") andnnzero(<ndenseMatrix>) now correctly treatNA in thex slot asTRUE.

• as(<[nl].TMatrix>, "dMatrix") now correctly handlesthe overallocated case: data for each unique[i,j] pair areaggregated logically (x1 || ... || xn) rather thanarithmetically (x1 + ... + xn), so that elements of theresult are restricted to the setc(0, 1, NA). This bug hadalso affected the result ofsum(<[nl].TMatrix>).

• dimnames(as(x, "matrix")) is nowNULL forallx inheriting fromMatrix, whenx@Dimnames is the triviallist(NULL, NULL).

• .bdiag(<named list>) no longer propagates names totheDim slot of the result.

• as(<named vector>, "denseMatrix") now correctlypropagatesnames to the result.

• as(<d.[CR]Matrix>, "lMatrix") no longer dropsnon-structural zeros, for greater consistency with analogouscoercions.

• Matrix(x, doDiag) now behaves as documented fordiagonal matricesx with asymmetricdimnames,returning adiagonalMatrix whendoDiag = TRUE,rather than atriangularMatrix.

• Matrix(<n-dimensional table>) now works forn != 2.

• Matrix(<sparseVector>) now works for vector lengthsother than 1, no longer giving an error about length mismatch whenneither ofnrow andncol are supplied.

• Matrix(<diagonalMatrix>, doDiag = FALSE) is now asymmetricMatrix, not adiagonalMatrix, matching thedocumentation ofdoDiag.

• Matrix(<.geMatrix>, sparse = TRUE, forceCheck) andMatrix(<.g[CRT]Matrix>, sparse = FALSE, forceCheck) nowrespectforceCheck = FALSE by always returninggeneralMatrix, i.e.,not testing for symmetric ortriangular structure.

• Matrix(0, nrow, ),Matrix(0, , ncol) now throw(correct) errors fornrow,ncol in the interval[0,1), consistent withbase::matrix().

• sparseDefault(<sparseMatrix>) now counts zeroswithout coercing tomatrix, makingMatrix(<sparseMatrix>, sparse = NULL) much more efficient.

• Methods for group genericMath no longer preservex@diag == "U" or losex@Dimnames whenf(0) == 0 andf(1) != 1. (The former happened fortriangularMatrixx and the latter fordiagonalMatrixx.)

• image(Z) for a completely “empty” (all 0)sparseMatrix works again (?!).

• x[i, ] <- value andy[, j] <- value is now anerror in more cases form-by-0CsparseMatrixx and 0-by-nCsparseMatrixy. Inthese cases, subassignment gave a (formally) invalid result.

• chol(<ds[yp]Matrix>) now calls the underlying C-levelroutine exactly once. Previously, it was called an extra time inorder to test for positive definiteness, with the result thrownaway (!). Hence these methods should become approximately twotimes faster.

• dimnames(chol(x)) is identical todimnames(x)in all cases, now even whenchol(x) is constructed from acachedMatrixFactorization, for greater consistency withbase::chol.default().

• chol(<generalMatrix>) no longer looks atDimnames when testing for symmetry.

• lu(<dtCMatrix>) no longer returns an invalidsparseLU object in the lower triangular case.

• lu(x) had sometimes incorrectly cached its returnvalue as element"lu" (rather than"LU") ofx@factors. Now it is always"LU".

• Compare operators, e.g.,a > b,x != y, now work correctly in more dense unitriangular and sparse0-extent cases.

• !<nMatrix> is now always annMatrix, never anlMatrix.

• !<ndenseMatrix> andwhich(<ndenseMatrix>) nowcorrectly handleNA asTRUE.

• anyNA(<denseMatrix>) had incorrectly returnedanyNA(.@x) in many cases, giving false positives for some.(tr|sy)Matrix andndenseMatrix. Now methodsrespect the “rules” of these classes.

• The boolean arithmetic productA %&% B and e.g.,crossprod(A, B, boolArith=TRUE) now should behave as ifdrop0(A) anddrop0(B) were used, i.e., for formallysparse matrices, the boolean product results should be stable withrespect to non-structural vs structural zeros.

• t(<symmetricMatrix>) now retains thefactorsslot, avoiding recomputation.

• Fixed the (quitelong standing)MatrixPR#6777, reportedby Manuel Koller:tcrossprod(<matrix>, <[dln]sCMatrix>) hasbeen wrong in some cases.

Memory

• qr(<big sparse>) could segfault due to integeroverflow inside ofcs_multiply. Now an error is signaledindicating “out of memory”. Reported by Benjamin TynerasMatrixPR#6610.

• Valgrind warning originating incholmod_sdmultis squashed. Reported by David Cortes asMatrixPR#6726.

New Features

• KhatriRao() gets newsparseY = TRUE option andalso works for moreMatrix classes.

• Virtual classpackedMatrix gains methods forpack,unpack,isSymmetric,isTriangular, andisDiagonal implemented in C,replacing those defined for many subclasses individually.

• Virtual classunpackedMatrix gains methods forpack,unpack,isSymmetric,isTriangular,isDiagonal,t,diag, anddiag<- implemented in C, replacing those defined for manysubclasses individually.

• isTriangular andisDiagonal are nowimplemented in C also for[CRT]sparseMatrix andstandardmatrix.isSymmetric is now implemented inC for alldenseMatrix and all[CRT]sparseMatrix, though these C routines arecurrently only called when testing forexact symmetry(always for[ln]Matrix, only whentol = 0 fordMatrix).

• Methods forisSymmetric gain an argumentcheckDN = TRUE indicating whether symmetry ofDimnames should be checked. For backwards compatibilityand consistency withisSymmetric.matrix frombase,the actual condition ischeckDN && check.attributes.

• isTriangular(x, upper) now has akindattributeif and only ifx is triangular andupper isNA.

• diag(<unpackedMatrix>) <- value now behaves likediag(<packedMatrix>) <- value, supporting coercionsdepending ontypeof(value), consistent withdiag<-frombase.

• pack andunpack are now identity functions forpackedMatrix andunpackedMatrix arguments,respectively (previously an error).pack(<.geMatrix>)(previously an error) now behaves aspack(<matrix>), i.e.,by checking for symmetry or triangularity before packing.unpack(<matrix>) now works and is equivalent toas(<matrix>, "unpackedMatrix"), with result inheriting from.(ge|tr|sy)Matrix, as appropriate.

• Many more validity methods implemented in C, for efficiency,including methods forMatrix,compMatrix,diagonalMatrix,indMatrix,pMatrix,corMatrix,[liz]Matrix, andndenseMatrix.

• band(x, k1, k2) is optimized further for both denseand sparsex, returningtriangularMatrix,symmetricMatrix, andpackedMatrix in more cases.

• band() is now implemented also fordiagonalMatrix (onlytri[ul]() worked before).

• Coercions.ge<->.g[CRT],.t[rp]<->.t[CRT],.s[yp]<->.s[CRT], and..[CRT]<->matrix are now fullyimplemented and optimized, with minimal intermediate allocations.These (and others) no longer rely on CHOLMOD, which had handledinteger types as double and required preprocessing in many cases(withdiagU2N(), etc.).

• Fixes in group methods (e.g.,>,&,|),notably for matrices inheriting from classsymmetricMatrix,triangularMatrix,lMatrix, ornMatrix.

• as.vector,as.numeric, andas.logicalare now implemented for allMatrix.

• Subassignment toindMatrix is no longer prohibited,now going viaTsparseMatrix.

• indMatrix gains methods forisTriangular,isDiagonal,diag,diag<-,band,tri[ul], andforceSymmetric. It also gainscoercions to more virtual classes (notablydenseMatrix) anda coercion topMatrix.

• solve(<ddenseMatrix>, <numLike>) now works in allcases.

• determinant(<ds[yp]Matrix>) is now much faster in thepositive definite case, no longer going viadgeMatrix.

• diag(<[CRT]sparseMatrix>) is now done in Cand is highly optimized in the.[ts][CR]Matrix case.

• symmpart andskewpart are now done inC for alldenseMatrix and all[CRT]sparseMatrix. Both now more faithfully preserve the“storage” of their argument. (Previously,symmpart(<packedMatrix>) was anunpackedMatrix, and(symm|skew)part(<[RT]sparseMatrix>) was aCsparseMatrix.)

• as(<vector|matrix>, "([dln]?dense|[dlnCRT]?sparse)Matrix") are now fully and moreconsistently implemented. In the vector case, the result is nowalways alength-by-1generalMatrix. In the matrixcase, structure is now always examined, hence the result is asymmetricMatrix ortriangularMatrix in more cases.

• Matrix(<classed matrix>) now works for classesother thantable.

• lu(<dt[rpCRT]Matrix>) andlu(<ddiMatrix>) nowbehave more consistently. In the diagonal, upper triangular, andunit lower triangular cases, the result is obtained“directly”, i.e., without pivoting. In the non-unit lowertriangular case, it is obtained with pivoting. (Previously,pivoting was never done fordtCMatrix and always done fordt[rpRT]Matrix andddiMatrix.)

• lu(x) now caches its return value also for allds.Matrixx (by default).

• readMM() now warns if the number of entries found isless than number reported in the header.

• x[i] now works fornMatrixi, just asforlMatrixi. This supports constructions such asx[is.na(x)], where the logical operation produces annMatrix because it is neverNA.

Misc

• AZERO() and friends gain an argument specifying azero constant (0 forint arrays, 0.0 fordoublearrays).

• C-level utilities(R_)?[gs]et_factors() have beenrenamed(R_)?[gs]et_factor(), as they only ever get and setone factor.

• The signature ofset_factor() has been changed tomatch otherset*() functions: to(object,name,value)from(object,value,name).

• For clarity,set_factor() now returnsvoid andis used like otherset*() functions (i.e., for its sideeffect). TheR interface is unchanged:R_set_factor()continues to return the value being set.

• C-level utilitiesmake_[di]_matrix_(triangular|symmetric)(),packed_to_full_(double|int)(),full_to_packed_(double|int)(), andinstall_diagonal(_int)?() are replaced by safer, moreconsistently named ones. Previous versions allowed integeroverflow.

• C-level utilitiesdup_mMatrix_as_d?geMatrix() arereplaced by the more generaldense_as_general(), whichtakes arguments controlling memory allocation and the“kind” of the.geMatrix result.

• New C-level utilityDimNames_is_symmetric() withRinterfaceisSymmetricDN(), which should be usedconsistently to test for symmetry of[dD]imnames. Notethat these are intended to behave consistently withsymmetricMatrix_validate(), by allowing, e.g.,list(NULL, nms), but not, e.g.,list(A = NULL, B = nms).

• Coercions totriangularMatrix andsymmetricMatrix are now almost all inherited fromMatrix, whose methods simply calltri[ul]() andforceSymmetric() ifisTriangular() andisSymmetric(), respectively, returnTRUE.

• Many of the exported.*2* utilities have beenredefined as aliases or wrappers of new, more general functions(see below). These not-yet-deprecated functions have beencentralized in ‘R/denseMatrix.R’ and ‘R/sparseMatrix.R’.

• New C-level utilitiesR_(dense|sparse)_as_kind()for coercion from one “kind” to another;R_(dense|sparse)_as_general()for coercion from triangular and symmetric to general;R_(dense|sparse)_band()for coercion to triangular (and other banded);R_(unpacked*|packed*|sparse)_force_symmetric()for coercion to symmetric;R_(dense|sparse)_as_(sparse|dense)()for coercion between dense and sparse of the same “kind”and “structure”;R_diagonal_as_sparse()for coercion fromdiagonalMatrix to any[CRT]sparseMatrix;R_(dense|sparse|geMatrix)_as_(matrix|vector)()for coercion to base matrix and vector; andtCRsparse_as_RCsparse() for the idiomsas(t(<[CR]sparseMatrix>), "[RC]sparseMatrix").These all have not-yet-exportedR wrappers.

• indTri() andindDiag() now in C, with a newargumentpacked for efficiently indexingpackedMatrix.indDiag() now behaves sensibly in then = 0 case.

• .M.kind(),.M.shape(), and (new).M.repr() are now done in C viaR_check_class_etc(), requiring a class definition only in“rare” cases.

Changes in version 1.4-1 (2022-03-21, svn r3446)

Installation

• Some warnings surfaced by-Wconversion aresquashed.

Compatibility

• tryInvokeRestart is defined forR< 4.0.0.Thanks to Michael Chirico for the report.

SuiteSparse

• The patch for header‘SuiteSparse_config/SuiteSparse_config.h’is improved for Windows.

Classes

• New virtual classpackedMatrix representing densematrices in packed format. It extendsdenseMatrix and isextended by[nld](sp|tp)Matrix.

Memory

• Protection stack imbalances detected byrchk arefixed.

Bug Fixes

• diag(x) methods now mostly also keepnamesfromdimnames(x) by default and obeynames=* moregenerally.

New Features

• Methods for subscriptingpackedMatrix, includingdiag(), notably keeping names by default and fort()which are memory efficient, i.e., do not work via unpacking,thanks to Mikael Jagan.

• Newdmperm() implementing a Dulmage-Mendelsohndecomposition, thanks to the persistency of Mauricio Vargas(@uc.cl).

• Export more low-level conversion utilities:.n2dgT,.m2ngCn,.m2ngTn.

• Provide some matrix multiplication methods forRsparseMatrix.

Misc

• Our C sources now useR_Calloc(),R_Free() etc, instead of the shorter versions without'R_'. Consequently, we get closer toSTRICT_R_HEADERS.Also, include<float.h> forDBL_EPSILON.

• ModifiedAZERO() to work withR_xlen_t and newAZEROs() forsize_t.

Changes in version 1.4-0 (2021-12-08, svn r3419)

Compatibility

• ‘inst/test-tools-1.R’:Sys.memGB returnsNA.value = 2.10201 on Windows, no longer callingmemory.limit which is a stub sinceR version 4.2.0.

Memory

• Several low level functions are adjusted to avoid integeroverflow ini+j*m or similar. Reported by Dario Strbenacon the R-devel mailing list (“dgTMatrix SegmentationFault”, June 10, 2021).

• Leak inas(<dtCMatrix>, "denseMatrix") when theargument is unit triangular is fixed. Thanks to Bill Dunlap forthe report and patch inPR#18204.

• Leak incrossprod(<dsCMatrix>) is fixed. Thanks toBill Dunlap for the report and patch inPR#18205.

• Leaks insolve(<dgCMatrix>, <ddenseMatrix>) andlu(<dgCMatrix>) and when the argument is near-singular (orwhen memory is exhausted) are fixed. Thanks to Bill Dunlap forthe report and patch inPR#18206.

• Leaks in[cr]bind2(x, y) when both arguments aresparse and exactly one is nonzero pattern are fixed. Thanks toBill Dunlap for the report and patch inPR#18210.

• solve(<dsCMatrix>, ...) restarts after catchingwarnings signaled fromdsCMatrix_*_solve so that memory isfreed rather than leaked. Thanks to Bill Dunlap for the reportand patch inPR#18214.

Bug Fixes

• sparse.model.matrix(.., contrasts.arg = <.. ddiMatrix ..>) now works correctly, fixingMatrixPR#6673 by Davor Josipovic.

• sparse.model.matrix(..) now also works in cases thecontrast matrix has become adenseMatrix; e.g., in a caseusingpoly(.) in the formula; now works correctly, fixingMatrixPR#6657 and useful suggestions by Nick Hanewinckel.

• Fixed the internalattr.all_Mat() auxiliary forall.equal(), notably for the case when exactly one of thematrices is a basematrix.

• Fixed long-standing bug in therbind2() method forlogical dense matrices, specificallylgeMatrix, thanks tothe notice by Aaron Lun.

• band(M, k1, k2) now also works whenk1 * k2 islarger than 2^31-1, the maximal integer, fixingMatrixPR#6743 byAriel Paulson. Further, it works whenM is a sparsesymmetricMatrix but the band is not symmetric,k1 != -k2.

• sparseVector(i=integer(), length=2^33) now doesshow/print, after fixing a bug in thehead() method forempty sparseVectors. Reported by David Cortes asMatrixPR#6745.

• ss <- <sparseVector>[i] gave an invalid sparseVectorss asss@i was not necessarily sorted; thanks to areport by Quran Wu.

• as(<dsyMatrix>, "generalMatrix") and similar,sometimes didnot use (C-level)symmetric_Dimnames()etc; report (toR'sPR#18250 by Mikael Jagan); fixed all on Clevel. As a consequence, you will now seemore preserveddimnames after matrix transformations or operations which involvedsymmetric matrices.

• as(<ddiMatrix>, "matrix") no longer loses dimnames,thanks to Mikael Jagan's report asMatrixPR#6751.

Misc

• No longer include ‘Rdefines.h’ as it is somewhatdeprecated.

Changes in version 1.3-4 (2021-05-24, svn r3392)

Compatibility

• Tests are further revised for length mismatch warning inmatrix(data, nrow, ncol) underR\ge 4.2.0.

Changes in version 1.3-3 (2021-05-01, svn r3390)

Installation

• Matrix\ge 1.3-3 depends onR\ge 3.5, relaxing the dependency onR\ge3.6 introduced inMatrix version 1.3-0.

Compatibility

• Tests are revised for length mismatch warning inmatrix(data, nrow, ncol) underR\ge 4.2.0.

C-Level API

• ‘inst/include/cholmod.h’ and‘inst/include/Matrix_stubs.c’ needed adjustment after theSparseSuite update inMatrix version 1.3-0.MatrixPR#6714reported by Kasper Kristensen, who maintainsTMB.

Deprecated and Defunct

• cBind() andrBind() are now defunct: simplyusecbind() andrbind() instead.

Classes

• Class unionsMnumeric andnumericVectors areremoved. These were unexported and unused but nonethelessvisible to users, appearing as superclasses of many basic classes.Notably, a proposed change to the validity method forMnumeric would have broken classfactor, whichextendedMnumeric but would not have been valid under theproposal.

Bug Fixes

• Fixed a thinko (in 1.3-2): Now direct coercion fromddiMatrix todgCMatrix, and hence, e.g.,as(Matrix(1, sparse=TRUE), "dgCMatrix") now works.

• Fixed error message in <dtrMatrix> multiplication.

• Fixed long-standing bug inR[,j] <- v whenRis anRsparseMatrix,MatrixPR#6709 by David Cortes.

• as.matrix() andas.array() now work forsparseVector as expected; seeMatrixPR#6708.

• M[,] (and similar) now work as in baseR;MatrixPR#6720 by David Cortes.

• -S now works also whenS has nofactorsslot. It signalled an error, e.g., for sparse triangular matricesS;MatrixPR#6656, reported by Chun Fung (Jackson) Kwok.

• M*2 and similar no longer keep cached factorizations(in 'factors' slot), but drop them via internal new.empty.factors().MatrixPR#6606, reported by Thomas Lumley.

• removed a few duplicated.alias{.} from‘man/*.Rd’.

Misc

• translation updates (of outlines only); finally addedItalian (by Daniele Medri) to svn; updated French (by PhilippeGrosjean), forgotten (R part of) Korean. New Lithuaniantranslations by Gabriele Stupuriene & Rimantas Zakauskas.

• In internaldiagOdiag() method, no longer usematrix(x, n,n) whenx is longer than n*n.

• Eliminating the need for ‘ftp://*’, add the very smalljgl009 MatrixMarket example to our ‘external/’ files.

Changes in version 1.3-2 (2021-01-05, svn r3362)

Installation

• USE_FC_LEN_T is defined before ‘Rconfig.h’ isincluded. UnderR\ge 3.6.2, the effect is thatFC_LEN_T is defined when ‘R_ext/BLAS.h’ is included,and the result is that ‘R_ext/BLAS.h’ definesFCONEas a nonempty value suitable for passing character lengths fromC to Fortran.

Memory

• matrix_trf protects two more objects from garbagecollection, squashing tworchk warnings.

Bug Fixes

• rankMatrix() tweaks for the singular values basedmethods, notablymethod = "maybeGrad".

• as(new("dtCMatrix", diag="U"), "matrix") now works,as C-leveldiagU2N() now also works for 0-dimensionaltriangular matrices; this also fixes a subsetting(“indexing”) bug of such 0-dimensional matrices, thanks toa report by Aaron Lun.

• logical subsetting of 0-dim. (diagonal/triangular) matricesfixes.

• chol(<diagonal dt[CRT]Matrix>) now works.

Changes in version 1.3-1 (2020-12-23, svn r3352)

Bug Fixes

• rankMatrix(<dense>, method="qr.R") no longer assumesnon-negative diagonal entries of theR matrix.

Changes in version 1.3-0 (2020-12-15, svn r3351)

Installation

• Matrix\ge 1.3-0 depends onR\ge 3.6.

• MacroFCONE is defined and used to pass characterlengths from C to Fortran underR\ge3.6.2 (without breaking installation under olderR). Thanksto Brian Ripley.

SuiteSparse

• The internal SuiteSparse library sources are updated fromversion 4.2.1 to version 5.7.1. The change is visible in.SuiteSparse_version().

Significant User-Visible Changes

• Matrix(*, doDiag=TRUE) wheredoDiag=TRUE hasalways been the default is now obeyed also in the sparse case, asalldiagonalMatrix are alsosparseMatrix.
  
  Matrix(0, 3,3) returns addiMatrix instead of adsCMatrix previously. The latter is still returned fromMatrix(0, 3,3, doDiag=FALSE), and e.g.,.symDiagonal(3,pi).
  
  Also a triangular matrix, e.g.,dtrMatrix is detected nowin cases withNAs.
  
  This is both a bug fixand an API change which breaks codethat assumesMatrix(.) to return aCsparseMatrixin cases where it now returns adiagonalMatrix (whichdoes extendsparseMatrix).

New Features

• Subassignment todiagonalMatrix now returns sparsetriangularMatrix more often; also (sparse)symmetricMatrix.

• nearPD() gets new option: Ifbase.matrix = TRUE, the resultingmat component is abasematrix, as often used desired whennearPD() is usedoutside theMatrix package context.

• Factored out newqr2rankMatrix() utility fromrankMatrix().

• NewBunchKaufman(<matrix>) method.

• Addedwrld_1deg sparse matrix example todistributed version ofMatrix (no longer excluding itvia ‘.Rbuildignore’).

• New (simple)mat2triplet() function to be usedinstead ofsummary(<sparseMatrix>) in code.

• Internal.diag2tT() gains new optiondrop0 = TRUE and hence now by default drops zero diagonal entries.Consequently, e.g.,as(<diagonalMatrix>, "CsparseMatrix")now drops such zeros, too.

• sparseMatrix() gets new argumentrepr = "C",superseding the (now deprecated)giveCsparse = TRUE.Allows to returnRsparseMatrix.

  Similarly,rsparsematrix(),fac2sparse() andfac2Sparse() get the newrepr argument and theirgiveCsparse is deprecated, sometimes only informally fornow.

• sparse.model.matrix() gets optionsep = "",with, e.g.,sep = ":" allowing to get easier column names;fromMatrixPR#6581, by Vitalie Spinu.

Memory

• The second argument in calls tocholmod_factorize_pfrominternal_chm_factor was a pointer to 1doubleinstead of adouble array of length 2, resulting in bufferoverflow there.

Bug Fixes

• rankMatrix(<sparse>, method="qr") now returnsNA (orNaN) instead of signalling an error in thecase the sparseQ R decomposition gaveNAs indiag(R).

• Coercion (as(., .)) from e.g.,lsyMatrix toCsparseMatrix silently made asymmetric dimnamessymmetric, as did theinternalforceCspSymmetric(*, dimNames) which may be called fromforceSymmetric().

• MatrixPR#6659, reported by Georg Kindermann:<sparseVector>[i] <- val bug is fixed.

• MatrixPR#6666, reported by Ezra Tucker:which(<ldiMatrix>, array.ind=TRUE) thinko is fixed.

• For R-devel Dec 4, 2020: adapt all.equal() check of sparsematrix images (which contain panel functions with environments).

Changes in version 1.2-18 (2019-11-26, svn r3300)

Compatibility

• ‘inst/test-tools-1.R’: a bug-fixedcanCoerceis used underR< 3.6.2.

Memory

• ddense_skewpart protects another object from garbagecollection, squashing a remainingrchk warning.

Bug Fixes

• as(m, "dgTMatrix") does not losedimnamesanymore whenm is a (traditional)matrix.

• M[logical(0), ] now has dimension0 x k forsparseM as for base matrices.

• log(M, base) (the 2-argument version oflog())wrongly gave the result forbase = exp(1), i.e., the1-argument default.

• ‘test-tools-Matrix.R’:Qidentical() no longerassumesclass(<matrix>) to be of length 1.

Changes in version 1.2-17 (2019-03-20, svn r3294)

Compatibility

• isFALSE is defined forR< 3.5.0.

Memory

• C functions protect more objects from garbagecollection, squashing severalrchk warnings.

Changes in version 1.2-16 (2019-03-04, svn r3291)

New Features

• regression tests depending onsample() now are futureproof reproducible, viaRNGversion(.).

• give information about #{rows} and #{columns} that aresuppressed in print()ing if the matrix is larger thanmax.print.

Bug Fixes

• data(<Matrix-data>) no longer attachesMatrixto the search path.

• Ops group methods, i.e.,Arith,Compare,Logic, now should all work with 0-extentmatrices as well, thanks to bug reports by Aaron Lun, Universityof Cambridge.

• when printing and formatting sparse matrices, seeformatSpMatrix(), themaxp option, e.g., fromgetOption("max.print"), is “rounded up” to 100, asvery small values are very rarely appropriate.

Changes in version 1.2-15 (2018-08-20, svn r3283)

New Features

• image() gets new optional argumentborder.color.

Bug Fixes

• image(Matrix(0, n,m)) now works.

Changes in version 1.2-14 (2018-04-08, svn r3278)

New Features

• German translation updates.

Memory

• dgCMatrix_cholsol protects one more object fromgarbage collection, squashing anrchk warning.

Changes in version 1.2-13 (2018-03-25, svn r3275)

New Features

• Fasteras(<matrix>, "sparseMatrix") and coercion todgCMatrix,ngCMatrix, etc, via new directCmatrix_to_Csparse() which doesnot goviadgeMatrix. This also works for large matricesm, i.e., whenlength(m) >= .Machine$integer.max.

  Also provide low-levelR functions.m2dgC(),.m2lgC(), and.m2ngC() for these.

Memory

• C functions protect more objects from garbagecollection, to be “rather safe than sorry”. Thanks toTomas Kalibera'srchk tools.

Bug Fixes

• cbind(NULL,<Matrix>) no longer returnNULL;analogously forrbind(),rbind2(),cbind2(),fixing very long standing typo in the corresponsingcbind2() andrbind2() methods.

• The deprecation warning (once per session) forcBind() andrBind() finally works (fixing a simplethinko).

• cbind() andrbind() for largish sparsematrices no longer gives an error because of integer overflow (inthe default case wheresparse is not been specified henceis chosen by annzero() based heuristic).

• .symDiagonal(5, 5:1) and.trDiagonal(x = 4:1)now work as expected.

• Sp[i] now is much more efficient for large sparsematricesSp, notably when the result is short.

• <sparseVector>[ <negative integer> ] now also givesthe correct answer when the result is “empty”, i.e., allzero or false.

• largedspMatrix anddtpMatrix objects cannow be constructed vianew(*, Dim = *, x = *) also whenlength(x) is larger than 2^31 (as the C internalvalidation method no longer suffers from integer overflow).

Changes in version 1.2-12 (2017-11-10, svn r3239)

New Features

• crossprod(x,y) andkronecker(x,y) have becomeconsiderably more efficient for largeindMatrix objectsx, y, thanks to private nudging by Boris Vaillant.

Bug Fixes

• MatrixPR#6185:c < 0 now also works for derived sparseMatrices (which onlycontain Matrix classes); via improvinghiddenMatrixClass(). Part of such derived matrices onlywork inR\ge 3.5.0.

• usingAuthors@R in ‘../DESCRIPTION’ to list allcontributors.

• solve(-m) no longer should use a cached Choleskyfactorization (ofm).

Changes in version 1.2-11 (2017-08-10, svn r3225)

Compatibility

• length(<NULL>) <- value is avoided as it isdeprecated inR\ge 3.5.0.

New Features

• S4 method dispatch no longer emits ambiguity notes (bydefault) for everybody, apart from the package maintainer. Youcan reactivate them byoptions(Matrix.ambiguityNotes = TRUE)

Bug Fixes

• rankMatrix(<matrix of all 0>) now gives zero for allmethods, as it should be.

• qr.coef(<sparseQR>, y) now finally has correct (row)names (from pivot back permutation).

• .trDiagonal() utility is now exported.

Changes in version 1.2-10 (2017-04-19, svn r3216)

Memory

• C functions protect more objects from garbagecollection. Thanks to Tomas Kalibera'srchk tools.

Changes in version 1.2-9 (2017-03-08, svn r3211)

New Features

• Ops betweentable,xtabs, and ourmatrices now work.

• as(matrix(diag(3), 3, dimnames=rep(list(c("A","b","c")),2)), "diagonalMatrix")@xis no longer named.

• norm(x, "2") now works as well (and equivalently tobase::norm).

• sparseVector() now also works withoutxargument.

• c.sparseVector() method forc() ofsparseVectors (and available as regular function on purpose).

Bug Fixes

• as(Diagonal(3), "denseMatrix") no longer returns anon-denseddiMatrix.

• S[sel,] <- value and similar no longer segfault, butgive a"not (yet?) supported" error for sparse matricesS and logicalsel whensel containsNAs.

  The same error (instead of a low-level one) is signalled forindexing (with NA-containing logicalsel), i.e.,S[sel,].

• which(x, arr.ind=TRUE, *) (whenx is alMatrix ornMatrix) now works the same asbase::which, obeying an optionaluseNames argumentwhich defaults toTRUE. Previously, the resultingtwo-column matrix typically had emptydimnames.

Changes in version 1.2-8 (2017-01-16, svn r3201)

Compatibility

• Methods forOps handle 0-length operands moreconsistently, matching changes planned forR version 3.4.0.

SuiteSparse

• SuiteSparse_long is defined asint64_t on allplatforms. Hence we now include C99 header ‘inttypes.h’.

• The internal CSparse library sources are patched to avoidbuffer overflow incs_usolve andcs_utsolve whenU is singular.

Bug Fixes

• x[.] <- value now also works forsparseVector, both asx and asvalue.

• x[FALSE] <- value now also works forsparseVector.

• rep(x, *) now works forsparseVector andsparse and denseMatrix-classed matricesx.

Changes in version 1.2-7.1 (2016-08-29, svn r3187)

Installation

• _POSIX_C_SOURCE is definedconditionally with#ifdef __GLIBC__.

Changes in version 1.2-7 (2016-08-27, svn r3185)

New Features

• cBind() andrBind() have been almost silentlydeprecated inR\ge 3.2.0 and now give a warning,“once per session” only.

• bandSparse(*, k=k, *) now returns matrices inheritingfromtriangularMatrix when obvious from the diagonalindicesk.

Bug Fixes

• KhatriRao(X,Y) now also works whenX orY is completely zero.

Changes in version 1.2-6 (2016-04-27, svn r3175)

Bug Fixes

• The 0-dim. Matrix multiplication fix in 1.2-5 did triggerwrong warnings in other diagonal matrix multiplications.

Changes in version 1.2-5 (2016-04-14, svn r3170)

New Features

• isSymmetric(m) now also works forindMatrixm.

• isSymmetric(m) is faster for large dense asymmetricmatrices.

Bug Fixes

• Matrix multiplications (A %*% B) now work correctlywhen one of the matrices is diagonal and the other has a zerodimension.

Changes in version 1.2-4 (2016-02-29, svn r3162)

New Features

• sparseMatrix() gets new argumenttriangularand a smarter default fordims whensymmetric ortriangular is true.

• as(<sparse>, "denseMatrix") now works in more caseswhenprod(dim(.)) is larger than2^{31} - 1. Hence,e.g.,!S now works for much larger sparse matricesS.

Bug Fixes

• creating very large dense matrices, e.g., byas(<sparseM.>, "matrix") would segfault (in case it couldallocate enough storage).

Changes in version 1.2-3 (2015-11-19, svn r3155)

C-Level API

• ‘inst/include/Matrix.h’ tries harder to define‘⁠alloca⁠’ correctly for compilers that do not define__GNUC__.

New Features

• MatrixClass() is exported now.

• More exports of semi-internal functions (for speed, named.<foo>, i.e., inofficial API), such as.solve.dgC.lu().

• more Korean translations

Bug Fixes

• extendedn?CMatrix classes (e.g., fromsetClass(., contains="ngCMatrix")) now can be coerced viaas(.) tod.CMatrix.

• The printing of largish sparse matrices is improved, notablyin the case where columns are suppressed, via newfitWidth = TRUE option inprintSpMatrix2().

• cbind2() andrbind2() no longer fail todeterminesparse when it is unspecified and henceNA, fixingMatrixPR#6259.

Changes in version 1.2-2 (2015-07-03, svn r3131)

Dependencies

• Objects are more systematically imported from “base”packages likestats. It is no longer assumed that thosepackages are attached.

Bug Fixes

• OurcolSums(x),rowMeans(y), ..., methodsnow “keep names”, i.e., if the result is a numeric vector,and the matrixx has column or row names, these become thenames(.) of the result, fixingMatrixPR#6018.

Changes in version 1.2-1 (2015-05-30, svn r3127)

New Features

• Matrix now has aninitialization() methodcoercing 0-length dimnames components toNULL and othernon-NULL dimnames tocharacter. Before, e.g.,numeric dimnames components partially worked, even though it hasalways been documented that non-NULL dimnames should becharacter.

• as.vector(<sparseVector>) etc, now work, too.

• lu(<sparseMatrix>) now keepsdimnames.

• better ‘NEWS.Rd’ (which pleases Kurt andtidy;-)

Memory

• Usingalloca to perform large allocations couldoverflow the stack, leading in some cases to a segfault. Nowalloca is used only for small allocations. Thanks to areport on the R-help mailing list (“does segfault mean(always) a bug?”, May 5, 2015).

Bug Fixes

• S[] <- T andS[] <- spV now work (in morecases) for sparse matrices S, T and sparseVectorspV.

• Optional arguments inimage(), e.g.,main=<..>) now also work forlgCMatrix,nMatrix etc; thanks to a 4.5 years old report by MstislavElagin.

• dimnames(A) <- val now resets thefactors slotto empty, as the factorizations now keep dimnames more often.

• crossprod(<matrix>, Diagonal(<n>)) works again (andthese are tested more systematically).

• Matrix products (%*%,crossprod, andtcrossprod) fordtrMatrix are correct in allcases, including keeping dimnames.

• Matrix(d) (and other coercions toMatrix)now correctly keepsdimnames also whend is atraditionaldiagonal matrix.

Changes in version 1.2-0 (2015-04-03, svn r3096)

Generic Functions

• New generic function%&% for boolean matrixmultiplication: that is, matrix multiplication using booleanarithmetic.

New Features

• New argumentboolArith = NA incrossprod() andtcrossprod().boolArith = TRUE now forces booleanarithmetic, whereboolArith = FALSE forces numeric one.Several of these products are more efficient thanks to new Cfunctionality based on our newchm_transpose_dense(), andothers based ongeMatrix_crossprod,geMatrix_matrix_mm, etc.

• Most dense matrix products, also for non-dgeMatrix,includingl..Matrix andn..Matrix ones are nowdirectly handled by new.Call()s.

• dMatrix (numeric) andlMatrix (logical)matrices can now be coerced tonMatrix (non-zero patternor “boolean”) even when they containNAs, which thenbecomeTRUEs.

• More thorough checking ofcbind2() andrbind2() methods, notably as they are called fromcbind() andrbind() fromR\ge 3.2.0.

  rbind2(<dense>, <dense>) is faster, being based on new Ccode.

• symmetric Matrices (i.e., inheriting fromsymmetricMatrix) are allowed to havedimnames ofthe formlist(NULL, <names>)and now print correctlyand get correctly coerced to general matrices.

• indMatrix object (“index matrices”) no longerneed to be “skinny”.

• rsparseMatrix() now acceptsrand.x = NULL andthen creates a randompattern matrix(nsparseMatrix).

• anyDuplicatedT() anduniqTsparse() low levelutilities are exported now.

• Partial Korean translations of messages.

Deprecated and Defunct

• ForR\ge 3.2.0,cBind() andrBind() are deprecated, as they are no longer needed sincecbind() andrbind() do work automatically.

Bug Fixes

• Fix somerbind2() methods.

• t() now transposes the dimnames even for symmetricmatrices.

• diag(M) <- val did not always recycleval tofull length, e.g., whenM was adtrMatrix.

• crossprod(<indMatrix>) was wrong in cases where thematrix had all-zero columns.

• Matrix products (%*%,crossprod, andtcrossprod) with one sparse and one dense argument nowreturnnumeric (adMatrix) when they should, i.e.,unless the new settingboolArith = TRUE is applied.

Changes in version 1.1-5 (2015-01-18, svn r3037)

Compatibility

• Methods for matrix multiplication (%*%,crossprod,tcrossprod) are revised to match thebehaviour ofR\ge 3.2.0, which better toleratesmatrix-vector products.

New Features

• More use ofanyNA() (for speedup).

• isTriangular() gets new optional argumentupper = NA.

Bug Fixes

• crossprod() andtcrossprod() fixes for several<diagonal> o <sparse> combinations.

• rowMeans(<dgeMatrix>, na.rm=TRUE) was wrongsometimes.

• fix and speedup of coercions (as(., .)) from and tosymmetric or triangular matrices.

• invPerm() coercion to integer

• dimnames( solve(.,.) ) fix [r3036]

• tril() andtriu() now return correctuplo.

• names(dimnames(.)) now preserved, e.g. insymmpart() or subsetting (A[i,j]).

Changes in version 1.1-4 (2014-06-14, svn r2994)

New Features

• newrsparsematrix() for random sparse Matrices.

• improved warnings, notably for unused arguments previouslyswallowed into....

Bug Fixes

• crossprod(<vec>, <dsyMatrix>) fixed.

• crossprod() andkronecker() fixes for some<indMatrix> cases.

Changes in version 1.1-3 (2014-03-30, svn r2982)

New Features

• %*% andcrossprod() now also work withsparseVectors.

• speedup ofcrossprod(v, <sparseM>), thanks to nudgeby Niels Richard Hansen.

• new help page for all such matrix products(‘../man/matrix-products.Rd’).

Bug Fixes

• image() now gets correctylim again.

• More consistent matrix products.

Changes in version 1.1-2-2 (2014-03-04, svn r2966)

Bug Fixes

• correct adaption toR 3.1.0

• usingtolerance (and not ‘tol’) inall.equal()

Changes in version 1.1-2 (2014-01-28, svn r2962)

New Features

• export fast power-user coercion utilities.dsy2mat(),.dxC2mat(),.T2Cmat(),..2dge().

Bug Fixes

• matrix products now (mostly) work withsparseVectors;and correctly in some more cases.

Changes in version 1.1-1.1 (2013-12-30, svn r2957)

Installation

• Matrix\ge 1.1-1.1 depends onR\ge 2.15.2 to ease checking.

Compatibility

• ‘inst/test-tools-1.R’:assertCondition isdefined forR< 3.0.2 and used byassertWarningthere.

Changes in version 1.1-1 (2013-12-28, svn r2933)

New Features

• image(.., xlim, ylim): nicer defaults for the axislimits, andylim is sorted decreasingly; not strictlyback-compatible but should never harm.

• rankMatrix(*, method="qr") now usingtol

• T2graph() andgraph2T() export oldfunctionality explicitly. Tweaks in conversions betweengraph andsparseMatrix objects. Notably,as(<graph>, <Matrix>) now more often returns a (0/1pattern) n..Matrix.

• sparseMatrix(): newuse.last.ij argument.

Bug Fixes

• KhatriRao(): fix rownames (X <-> Y)

• qr.coef(),qr.fitted, andqr.resid nowalso work withsparse RHSy.

• sparse matrix “sub assignments”, e.g.,M[ii] <- v, speedup and fixes.

• bug fixes also inM[negative indices] <- value and<sparseMatrix>[cbind(i,j)].

Changes in version 1.1-0 (2013-10-21, svn r2930)

Dependencies

• methods,stats,utils, andlatticeare moved fromDepends toImports.

SuiteSparse

• The internal SuiteSparse library sources are updated to thelatest version. Use new function.SuiteSparse_version toget the version in use.

C-Level API

• ‘inst/include/cholmod.h’ is updated to reflect changesin SuiteSparse. Notably, there were changes in the layout of thevariouscholmod_*_struct.

New Features

• fac2sparse andfac2Sparse now exported, with anewgiveCsparse option.

Bug Fixes

• fixed long lasting undetectedsolve(<dsCMatrix>, *)bug.

• Ourall.equal() methods no longer sometimes returnc("TRUE", "....difference..").

• rankMatrix(<matrix>): fix the internalx.densedefinition.

Changes in version 1.0-14 (2013-09-12, svn r2907)

Bug Fixes

• Revert some wrong changes tosolve(<sparse>, *) from1.0-13 (“stop gap fix” forR 3.0.2).

Changes in version 1.0-13 (2013-09-10, svn r2904)

Classes

• New nonvirtual classindMatrix representing row indexmatrices, i.e., matrices whose rows are standard unit vectors. ItextendssparseMatrix and is extended bypMatrix, theclass of permutation matrices.

Generic Functions

• New generic functionsisTriangular andisDiagonal for testing if the argument is (upper or lower)triangular or diagonal. These were defined previously but neverexported or documented.

New Features

• Many methods forpMatrix are generalized to supportindMatrix. All (initial) functionality was contributed byFabian Scheibl, Univ. Munich.

• New (efficient)KhatriRao() function by MichaelCysouw

• rankMatrix(M, method="qr") no longer needssval which makes it considerably more useful for largesparseM.

• Start providinganyNA methods forR\ge3.1.0.

• solve(<sparse> a, <sparse> b): ifa issymmetric, now computesparse result.

• nearPD() gets new optionconv.norm.type = "I".

• determinant(<dpoMatrix>) now useschol(), andhence also an existing (‘cached’) Cholesky factor.

• 3 newC -> R utilities (including hiddenRfunction.set.factors() for caching also fromR, notjust in C).

Bug Fixes

• M[] <- v for unitriangularM now correct.

• lu(.) no longer sometimes returns unsorted columns.

Changes in version 1.0-12 (2013-03-26, svn r2872)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-11 (2013-02-02)

New Features

• .

Bug Fixes

• as(<csr>, "dgCMatrix") (from packageSparseM) now works again.

• .

Changes in version 1.0-10 (2012-10-22)

New Features

• .sparseDiagonal(): newunitri argument, andmore flexibility;

• newsolve(<dsCMatrix>, <missing>) via efficient Ccode.

Bug Fixes

• .

Changes in version 1.0-9 (2012-09-05)

New Features

• newsparseVector() constructor function.

• is.finite()is.infinite() now work for ourmatrices andsparseVector objects.

• diag(.) <- V now preserves symmetricity,triangularity and even uni-triangularity sometimes.

Bug Fixes

• Quite a few fixes forOps (arithmetic, logic, etc)group methods.

• Ditto fordiagonalMatrix methods.

Changes in version 1.0-6 (2012-03-16)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-5 (2012-03-15)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-4 (2012-02-21)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-3 (2012-01-13)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-2 (2011-11-19)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-1 (2011-10-18)

New Features

• .

Bug Fixes

• .

Changes in version 1.0-0 (2011-10-04)

New Features

• .

Bug Fixes

• .

Changes in version 0.9996875-3 (2011-08-13)

New Features

• .

Bug Fixes

• .

Changes in version 0.9996875-2 (2011-08-09)

New Features

• .

Bug Fixes

• .

Changes in version 0.9996875-1 (2011-08-08)

New Features

• .

Bug Fixes

• .

Changes in version 0.999375-50 (2011-04-08)

New Features

• .

Bug Fixes

• .

Changes in version 0.95-1 (2005-02-18, svn r561)

Authorship

• During Douglas Bates' sabbatical in Zurich, Martin Maechlerbecomes co-author ofMatrix.

New Features

• Beginning of class reorganization with a more systematicnaming scheme.

Bug Fixes

• More (correct) coercionsas(<from>, <to>).

Changes in version 0.9-1 (2005-01-24, svn r451)

New Features

• lme4 / lmer specificR code moved out tolme4package.

Bug Fixes

• .

Changes in version 0.8-2 (2004-04-05, svn r51)

Description

• Matrix version 0.8-2 is a full refactor. Classes,generic functions, and methods are newly implemented in S4.S3 machinery is removed. The remaining items in this sectiondescribe the state of things in version 0.8-2 rather than changessince version 0.3-26.

• Matrix\ge 0.8-2 depends onR\ge 1.9.0.

• Depends: methods is added to ‘DESCRIPTION’.

• Douglas Bates becomes the sole author ofMatrix.

• The package is retitled “Classes and Methods forNumerical Linear Algebra using LAPACK, LDL, TAUCS, METIS, andUMFPACK”.

• The package sources are now maintained in a Subversionrepository.

Changes in version 0.3-26 (2003-11-03)

Bug Fixes

• The default expressions of formal argumentstransposeandleft of generic functionfacmul are changed fromF andT toFALSE andTRUE, as only thelatter are reserved words.

Changes in version 0.3-25 (2003-10-30)

Deprecated and Defunct

• S3 generic functiondeterminant is removed as it wasported toR\ge 1.8.0.

Significant User-Visible Changes

• A namespace forMatrix is defined using directives in‘NAMESPACE’.

• S3 generic functionseigen,expand,facmul,lu,norm,rcond,schur,andunpack are exported.

• S3 methods are registered and not exported, hence theycontinue to be available but only through calls to exported S3generic functions.

• FunctionsMatrix,SVD,as.Matrix,diagDet, andhilbert are exported.

• FunctionsMatrix.class,*.test, andis.* are exported but intended only for internal use.

• FunctionsasObject andprependClass are notexported.

• Load hook.First.lib is removed and replaced by auseDynLib directive in ‘NAMESPACE’.

Changes in version 0.3-24 (2003-04-20)

Significant User-Visible Changes

• S3 generic functiondet is renameddeterminant.

Methods

• determinant.Matrix (formerlydet.Matrix)computes theLU factorization of its argument instead of theQR factorization.

Changes in version 0.3-23 (2003-03-30)

Description

• Matrix\ge 0.3-23 depends onR\ge 1.7.0.

Installation

• ‘configure’, ‘configure.in’, ‘configure.win’,‘cleanup’, ‘src/Makevars.in’, and‘src/Makevars.win’ are removed and replaced by a simple‘src/Makevars’ arranging forMatrix to useR'sLAPACK_LIBS andBLAS_LIBS. The simplification ismade possible byR version 1.7-0, which is configured bydefault to build, link against, and install a shared LAPACK.

Changes in version 0.3-22 (2003-02-03)

Bug Fixes

• Empty directory ‘data’ is removed.

Changes in version 0.3-21 (2002-10-25)

Description

• The package is retitled “Classes and Methods forNumerical Linear Algebra using LAPACK”.

Installation

• ‘configure.win’ and ‘src/Makevars.win’ are addedto support installation under Windows, thanks to Brian Ripley.

• More#undef in the C++ sources to supportinstallation under Windows, thanks to Brian Ripley.

Changes in version 0.3-20 (2002-10-08)

Installation

• ‘configure.ac’ setsCFLAGS before expandingAC_PROG_CC and setsFLIBS before expandingACX_BLAS andACX_LAPACK.

• Autoconf macroOCTAVE_BLAS_LIBS, which is no longerused, is removed from ‘aclocal.m4’.

Bug Fixes

• Unwanted Autoconf output is removed from ‘aclocal.m4’.

Changes in version 0.3-19 (2002-07-22)

Bug Fixes

• PACKAGE = "Matrix" is passed to.Call torestrict name lookup toMatrix.

• The C++ sources use qualified name lookup (as instd::<name>) in more places.

• The C++ sources get pointers to matrix datawithout taking the address of the first element, which is wrong fora matrix of length 0.

Changes in version 0.3-18 (2002-05-03)

Compatibility

• *_ELT macros are no longer defined forR<1.2.0 asMatrix depends onR\ge 1.5.0.

Changes in version 0.3-17 (2002-04-30)

Description

• Matrix\ge 0.3-17 depends onR\ge 1.5.0.

Installation

• ‘configure.in’ is replaced by ‘configure.ac’contributed by Kurt Hornik. ‘configure.ac’ makes use ofR CMD config, a utility added inR version 1.5-0.

• Autoconf macrosACX_BLAS andACX_LAPACK,written by Steven G. Johnson, are added to ‘aclocal.m4’ andexpanded in ‘configure.ac’.

• The configured value ofLAPACK_LIBS is prepended toPKG_LIBS in ‘src/Makevars.in’.

Changes in version 0.3-16 (2001-12-10)

Documentation

• A preliminary ‘ChangeLog’.

Compatibility

• Rd files are adapted to use\method{}{} markupintroduced inR version 1.2.2.

• One usage of.Alias, deprecated inR version1.4.1, is removed.

Bug Fixes

• S3 methods gain formal argument... where needed tomatch the generic function.

• The name of a class member function in ‘src/tgmd.h’ waswas spuriously qualified.

Changes in version 0.3-15 (2001-05-15)

Installation

• The configured value ofBLAS_LIBS is prepended toPKG_LIBS in ‘src/Makevars.in’.

Changes in version 0.3-13 (2001-05-10)

Installation

• The C++ sources undefine macroslength andappend in many places to allow for class member functionswith those names.

Changes in version 0.3-10 (2001-05-04)

Bug Fixes

• The C++ sources use qualified name lookup (as instd::<name>) in more places.

Changes in version 0.3-9 (2001-03-09)

Bug Fixes

• The C++ sources no longer write tostderrand (in most places)stdout, no longer use theassert macro, and no longer callexit.

Changes in version 0.3-8 (2001-01-10)

Description

• ‘DESCRIPTION’ gets aMaintainer field andDouglas Bates is named there.

Bug Fixes

• Removes around 100 non-source files wrongly bundled inMatrix version 0.3-7.

Changes in version 0.3-7 (2000-12-03)

Installation

• FLIBS is appended toPKG_LIBS in‘src/Makevars.in’.

Documentation

• A basic ‘README’.

Changes in version 0.3-6 (2000-10-30)

Description

• Matrix\ge 0.3-6 depends onR\ge 1.1.1.

Installation

• ‘configure’ makes use ofHAVE_F77_UNDERSCORE in‘Rconfig.h’.

• PKG_LIBS andPKG_LDFLAGS to the configuredvalues ofLIBS andLDFLAGS in ‘src/Makevars.in’.

Changes in version 0.3-5 (2000-08-20)

Deprecated and Defunct

• eigen.Matrix argumentschur, which was unused,is removed.

Methods

• An S3 methodschur.Matrix interfacing LAPACK routinedgeesx. It returnslist(values, schur, vectors).

• For arguments not inheriting fromMatrix subclassHermitian,eigen.Matrix is now an interface toLAPACK routinedgeevx, and its optional argumentsbalance andrcond, which were unused, can now beused to request balancing and the reciprocal condition numbers ofthe eigenvalues and right eigenvectors. The return value is nowlist(values, vectors, rcond) withvectors = list(left, right) andrcond = list(values, vectors).

Changes in version 0.3-3 (2000-08-11)

Installation

• ‘configure’ skips the check for BLAS in the SunPerformance Library if the C compiler isgcc.

Compatibility

• STRING_ELT,SET_STRING_ELT,VECTOR_ELT,andSET_VECTOR_ELT are used in place ofSTRING andVECTOR.*_ELT macros are defined forR<1.2.0 to not break compatibility.

Significant User-Visible Changes

• SVD(x, nu = 0, nv)$u andSVD(x, nu, nv = 0)$vtareNULL rather than empty matrices.

Methods

• An S3 methodlu.Matrix interfacing LAPACK routinedgetrf. It returnslist(l, u, permutation), withattributenorms = list(one, infinity) containing the oneand infinity norms. An optional argument is provided to disablecomputation ofone andinfinity.

Bug Fixes

• SVD(x, nu, nv) allocated for the right singularvalues a matrix with dimensionsc(ncol(x), nv) instead ofc(nv, ncol(x)). Buffer overflow could occur in LAPACKroutinedgesvd ifnv < ncol(x).

Changes in version 0.3-1 (2000-07-24)

Generic Functions

• S3 generic functioneigen.

Methods

• An S3 methodeigen.Matrix interfacing LAPACK routinesdgeev anddsyev, the latter only for argumentsinheriting fromMatrix subclassHermitian. Itreturnslist(values, vectors), wherevectors islist(left, right) for non-Hermitian arguments and anumeric matrix forHermitian arguments. An optionalargument is provided to disable computation ofvectors.

• S3 methodsdet.Matrix,det.UpperTriangular,det.UnitUpperTriangular,det.LowerTriangular, anddet.UnitLowerTriangular computing the modulus of thedeterminant or its logarithm. These returnlist(modulus, sign). Componentmodulus has alogical attributelogarithm indicating if the determinantissign * exp(modulus) orsign * modulus.det.Matrix computes theQR factorization of itsargument using LAPACK routinedgeqrf.

Bug Fixes

• Matrix.class(x) could be incomplete or contain badelements for orthogonalx.

New Features

• A functionas.Matrix for coercing an object toclassMatrix, parallel toas.matrix. The returnvalue inherits from subclasses ofMatrix if tests forstructure are satisfied.

• FunctionsasObject andprependClass forsetting and prepending to theclass attribute of theargument.

• A functiondiagDet for computing the determinant of atriangular matrix given the diagonal entries.

Changes in version 0.2-4 (2000-07-18)

Installation

• A ‘configure’ script detecting options for linking BLASand LAPACK. It is generated from ‘configure.in’ which makesuse of an Autoconf macroOCTAVE_BLAS_LIBS defined in‘aclocal.m4’.

• ‘src/Makevars’ is now generated from‘src/Makevars.in’.

• A ‘cleanup’ script removing generated files.

Documentation

• A Texinfo manual ‘R-Matrix.texi’ containingimplementation details and describing how LAPACK++ was modifiedforMatrix.

Methods

• An S3 methodrcond.Matrix interfacing LAPACK routinesd*con.

Bug Fixes

• Exceptions thrown by LAPACK++ are caught and handled asRerrors.

• UpperTriangular.test andLowerTriangular.testreturned a maximum rather than a maximum modulus for realarguments.

Changes in version 0.2-1 (2000-07-15)

Description

• Matrix version 0.2-1 is the first one to bedistributed by CRAN.

• The package is titled “A Matrix Library forR”.

• Douglas Bates is the maintainer and principal author.Saikat DebRoy is a co-author.

• Matrix\ge 0.2-1 depends onR\ge 1.1.0.

Installation

• A modified LAPACK++ (Linear Algebra PACKage in C++, version1.1a) is compiled alongside theMatrix sources. LAPACK++ isa C++ interface to LAPACK originally developed byRoldan Pozo.

Classes

• S3 classMatrix with subclassesHermitian,UpperTriangular (recursively,UnitUpperTriangular),andLowerTriangular (recursively,UnitLowerTriangular). Objects are traditional numericmatrices with aclass attribute indicating theirstructural properties. Objects are interfaced in C++using the parallel class hierarchy defined by LAPACK++.

Generic Functions

• S3 generic functionsdet,expand,facmul,lu,norm,rcond,schur,andunpack.

Methods

• An S3 methodnorm.Matrix interfacing LAPACK routinesdlan*.

• An S3 methodsolve.Matrix interfacing LAPACK routinesd*trf andd*trs.

• An S3 methodas.matrix.Matrix just dropping the classattribute.

• An S3 methodprint.Matrix just printing theas.matrix result.

New Features

• A functionMatrix constructing objects of classMatrix from numeric vectors and matrices, parallel tobase functionmatrix.

• A functionMatrix.class returning a character vectorcontaining the subclasses ofMatrix that would be valid forthe argument.

• FunctionsHermitian.test,UpperTriangular.test,LowerTriangular.test,Orthogonal.test, andOrthonormal.test returning amaximum modulus distance useful for testing the respectiveproperty.

• Functionsis.Hermitian,is.UpperTriangular,is.LowerTriangular, andis.Orthonormal testing ifthe*.test value does not exceed a tolerance.

• FunctionSVD interfacing LAPACK routinedgesvd.SVD(x, nu, nv) returnslist(d, u, vt) containing the singular values (sortednon-increasingly), firstnu left singular vectors (storedcolumn-wise), and firstnv right singular vectors (storedrow-wise).

• Functionhilbert constructing then-by-nHilbert matrix.