Sparse logical matrices

Description

The lsparseMatrix class is a virtual class of sparse matrices with TRUE/FALSE or NA entries. Only the positions of the elements that are TRUE are stored.

These can be stored in the “triplet” form (class TsparseMatrix, subclasses lgTMatrix, lsTMatrix, and ltTMatrix) or in compressed column-oriented form (class CsparseMatrix, subclasses lgCMatrix, lsCMatrix, and ltCMatrix) or–rarely–in compressed row-oriented form (class RsparseMatrix, subclasses lgRMatrix, lsRMatrix, and ltRMatrix). The second letter in the name of these non-virtual classes indicates general, symmetric, or triangular.

Details

Note that triplet stored (TsparseMatrix) matrices such as lgTMatrix may contain duplicated pairs of indices (i,j) as for the corresponding numeric class dgTMatrix where for such pairs, the corresponding x slot entries are added. For logical matrices, the x entries corresponding to duplicated index pairs (i,j) are “added” as well if the addition is defined as logical or, i.e., “TRUE + TRUE |-> TRUE” and “TRUE + FALSE |-> TRUE”. Note the use of uniqTsparse() for getting an internally unique representation without duplicated (i,j) entries.

Objects from the Class

Objects can be created by calls of the form new("lgCMatrix", ...) and so on. More frequently objects are created by coercion of a numeric sparse matrix to the logical form, e.g. in an expression x != 0.

The logical form is also used in the symbolic analysis phase of an algorithm involving sparse matrices. Such algorithms often involve two phases: a symbolic phase wherein the positions of the non-zeros in the result are determined and a numeric phase wherein the actual results are calculated. During the symbolic phase only the positions of the non-zero elements in any operands are of interest, hence any numeric sparse matrices can be treated as logical sparse matrices.

Slots

x:

Object of class "logical", i.e., either TRUE, NA, or FALSE.

uplo:

Object of class "character". Must be either "U", for upper triangular, and "L", for lower triangular. Present in the triangular and symmetric classes but not in the general class.

diag:

Object of class "character". Must be either "U", for unit triangular (diagonal is all ones), or "N" for non-unit. The implicit diagonal elements are not explicitly stored when diag is "U". Present in the triangular classes only.

p:

Object of class "integer" of pointers, one for each column (row), to the initial (zero-based) index of elements in the column. Present in compressed column-oriented and compressed row-oriented forms only.

i:

Object of class "integer" of length nnzero (number of non-zero elements). These are the row numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.

j:

Object of class "integer" of length nnzero (number of non-zero elements). These are the column numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed row-oriented forms only.

Dim:

Object of class "integer" - the dimensions of the matrix.

Methods

coerce

signature(from = "dgCMatrix", to = "lgCMatrix")

t

signature(x = "lgCMatrix"): returns the transpose of x

which

signature(x = "lsparseMatrix"), semantically equivalent to base function which(x, arr.ind); for details, see the lMatrix class documentation.

See Also

the class dgCMatrix and dgTMatrix

Examples

(m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL)))
(lm <- (m > 1)) # lgC
!lm     # no longer sparse
stopifnot(is(lm,"lsparseMatrix"),
          identical(!lm, m <= 1))

data(KNex)
str(mmG.1 <- (KNex $ mm) > 0.1)# "lgC..."
table(mmG.1@x)# however with many ``non-structural zeros''
## from logical to nz_pattern -- okay when there are no NA's :
nmG.1 <- as(mmG.1, "nMatrix") # <<< has "TRUE" also where mmG.1 had FALSE
## from logical to "double"
dmG.1 <- as(mmG.1, "dMatrix") # has '0' and back:
lmG.1 <- as(dmG.1, "lMatrix") # has no extra FALSE, i.e. drop0() included
stopifnot(identical(nmG.1, as((KNex $ mm) != 0,"nMatrix")),
          validObject(lmG.1), all(lmG.1@x),
          # same "logical" but lmG.1 has no 'FALSE' in x slot:
          all(lmG.1 == mmG.1))

class(xnx <- crossprod(nmG.1))# "nsC.."
class(xlx <- crossprod(mmG.1))# "dsC.." : numeric
is0 <- (xlx == 0)
mean(as.vector(is0))# 99.3% zeros: quite sparse, but
table(xlx@x == 0)# more than half of the entries are (non-structural!) 0
stopifnot(isSymmetric(xlx), isSymmetric(xnx),
          ## compare xnx and xlx : have the *same* non-structural 0s :
          sapply(slotNames(xnx),
                 function(n) identical(slot(xnx, n), slot(xlx, n))))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Matrix)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Matrix/lsparseMatrix-classes.Rd_%03d_medium.png", width=480, height=480)
> ### Name: lsparseMatrix-classes
> ### Title: Sparse logical matrices
> ### Aliases: lsparseMatrix-class lgCMatrix-class ltCMatrix-class
> ###   lsCMatrix-class lgRMatrix-class ltRMatrix-class lsRMatrix-class
> ###   lgTMatrix-class ltTMatrix-class lsTMatrix-class
> ###   Ops,lsparseMatrix,lsparseMatrix-method
> ###   Arith,lsparseMatrix,Matrix-method Arith,Matrix,lsparseMatrix-method
> ###   Arith,lgCMatrix,lgCMatrix-method Arith,lgTMatrix,lgTMatrix-method
> ###   Compare,lsparseMatrix,lsparseMatrix-method
> ###   Logic,lsparseMatrix,lsparseMatrix-method
> ###   Logic,lgCMatrix,lgCMatrix-method Logic,lgTMatrix,lgTMatrix-method
> ###   Logic,lsCMatrix,lsCMatrix-method Logic,ltCMatrix,ltCMatrix-method
> ###   -,lsparseMatrix,missing-method !,lsparseMatrix-method
> ###   coerce,lsparseMatrix,matrix-method
> ###   coerce,lsparseMatrix,dsparseMatrix-method
> ###   coerce,lgCMatrix,dgCMatrix-method coerce,lgCMatrix,lgTMatrix-method
> ###   coerce,lgCMatrix,lgeMatrix-method coerce,lgCMatrix,lsCMatrix-method
> ###   coerce,lgCMatrix,ltCMatrix-method coerce,lgCMatrix,matrix-method
> ###   coerce,lgTMatrix,dgTMatrix-method coerce,lgTMatrix,lgCMatrix-method
> ###   coerce,lgTMatrix,lgeMatrix-method coerce,lgTMatrix,lsCMatrix-method
> ###   coerce,lgTMatrix,triangularMatrix-method
> ###   coerce,lgTMatrix,symmetricMatrix-method
> ###   coerce,lgTMatrix,ltTMatrix-method coerce,lgTMatrix,matrix-method
> ###   coerce,lsCMatrix,dgTMatrix-method coerce,lsCMatrix,dsCMatrix-method
> ###   coerce,lsCMatrix,generalMatrix-method
> ###   coerce,lsCMatrix,lgCMatrix-method coerce,lsCMatrix,lgTMatrix-method
> ###   coerce,lsCMatrix,lsTMatrix-method coerce,lsCMatrix,matrix-method
> ###   coerce,lsTMatrix,dsTMatrix-method coerce,lsTMatrix,lgCMatrix-method
> ###   coerce,lsTMatrix,lgTMatrix-method coerce,lsTMatrix,lsCMatrix-method
> ###   coerce,lsTMatrix,lsyMatrix-method coerce,lsTMatrix,matrix-method
> ###   coerce,ltCMatrix,dMatrix-method coerce,ltCMatrix,dtCMatrix-method
> ###   coerce,ltCMatrix,lgCMatrix-method coerce,ltCMatrix,ltTMatrix-method
> ###   coerce,ltCMatrix,matrix-method coerce,ltTMatrix,dtTMatrix-method
> ###   coerce,ltTMatrix,generalMatrix-method
> ###   coerce,ltTMatrix,lgCMatrix-method coerce,ltTMatrix,lgTMatrix-method
> ###   coerce,ltTMatrix,ltCMatrix-method coerce,ltTMatrix,ltrMatrix-method
> ###   coerce,ltTMatrix,matrix-method coerce,matrix,lgCMatrix-method
> ###   coerce,matrix,lgTMatrix-method coerce,matrix,lsCMatrix-method
> ###   coerce,matrix,ltCMatrix-method coerce,matrix,ltTMatrix-method
> ###   t,lgCMatrix-method t,lgTMatrix-method t,lsCMatrix-method
> ###   t,ltCMatrix-method t,lsTMatrix-method t,ltTMatrix-method
> ###   which,lgTMatrix-method which,lsparseMatrix-method
> ###   which,lsparseVector-method which,lsTMatrix-method
> ###   which,ltTMatrix-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> (m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL)))
3 x 5 sparse Matrix of class "dgCMatrix"
           
A . 1 . . 2
B . . 2 . 1
C 2 . 1 . .
> (lm <- (m > 1)) # lgC
3 x 5 sparse Matrix of class "lgCMatrix"
           
A . : . . |
B . . | . :
C | . : . .
> !lm     # no longer sparse
3 x 5 Matrix of class "lgeMatrix"
   [,1] [,2]  [,3] [,4]  [,5]
A  TRUE TRUE  TRUE TRUE FALSE
B  TRUE TRUE FALSE TRUE  TRUE
C FALSE TRUE  TRUE TRUE  TRUE
> stopifnot(is(lm,"lsparseMatrix"),
+           identical(!lm, m <= 1))
> 
> data(KNex)
> str(mmG.1 <- (KNex $ mm) > 0.1)# "lgC..."
Formal class 'lgCMatrix' [package "Matrix"] with 6 slots
  ..@ i       : int [1:8755] 0 2 25 27 163 165 1258 1261 1276 1278 ...
  ..@ p       : int [1:713] 0 13 17 26 38 43 52 56 61 67 ...
  ..@ Dim     : int [1:2] 1850 712
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
  ..@ x       : logi [1:8755] TRUE TRUE TRUE TRUE TRUE TRUE ...
  ..@ factors : list()
> table(mmG.1@x)# however with many ``non-structural zeros''

FALSE  TRUE 
 4320  4435 
> ## from logical to nz_pattern -- okay when there are no NA's :
> nmG.1 <- as(mmG.1, "nMatrix") # <<< has "TRUE" also where mmG.1 had FALSE
> ## from logical to "double"
> dmG.1 <- as(mmG.1, "dMatrix") # has '0' and back:
> lmG.1 <- as(dmG.1, "lMatrix") # has no extra FALSE, i.e. drop0() included
> stopifnot(identical(nmG.1, as((KNex $ mm) != 0,"nMatrix")),
+           validObject(lmG.1), all(lmG.1@x),
+           # same "logical" but lmG.1 has no 'FALSE' in x slot:
+           all(lmG.1 == mmG.1))
> 
> class(xnx <- crossprod(nmG.1))# "nsC.."
[1] "nsCMatrix"
attr(,"package")
[1] "Matrix"
> class(xlx <- crossprod(mmG.1))# "dsC.." : numeric
[1] "dsCMatrix"
attr(,"package")
[1] "Matrix"
> is0 <- (xlx == 0)
> mean(as.vector(is0))# 99.3% zeros: quite sparse, but
[1] 0.9928769
> table(xlx@x == 0)# more than half of the entries are (non-structural!) 0

FALSE  TRUE 
 2158  2760 
> stopifnot(isSymmetric(xlx), isSymmetric(xnx),
+           ## compare xnx and xlx : have the *same* non-structural 0s :
+           sapply(slotNames(xnx),
+                  function(n) identical(slot(xnx, n), slot(xlx, n))))
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>