R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("Matrix-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('Matrix')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "Cholesky-class"
> 
> ### * Cholesky-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Cholesky-class
> ### Title: Cholesky and Bunch-Kaufman Decompositions
> ### Aliases: Cholesky-class pCholesky-class BunchKaufman-class
> ###   pBunchKaufman-class
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> (pm <- crossprod(Matrix(rnorm(18), nrow = 6, ncol = 3)))
3 x 3 Matrix of class "dpoMatrix"
           [,1]       [,2]       [,3]
[1,]  4.4511090 -0.9597934 -1.8089651
[2,] -0.9597934  3.6449567 -0.9330699
[3,] -1.8089651 -0.9330699  7.4494130
> (ch <- chol(pm))
3 x 3 Matrix of class "Cholesky"
         [,1]      [,2]       [,3]
[1,] 2.109765 -0.454929 -0.8574249
[2,] 0.000000  1.854183 -0.7135957
[3,] 0.000000  0.000000  2.4909871
> if (toupper(ch@uplo) == "U") # which is TRUE
+    crossprod(ch)
3 x 3 Matrix of class "dpoMatrix"
           [,1]       [,2]       [,3]
[1,]  4.4511090 -0.9597934 -1.8089651
[2,] -0.9597934  3.6449567 -0.9330699
[3,] -1.8089651 -0.9330699  7.4494130
> stopifnot(all.equal(as(crossprod(ch), "matrix"),
+                     as(pm, "matrix"), tol=1e-14))
> 
> 
> 
> cleanEx(); ..nameEx <- "Hilbert"
> 
> ### * Hilbert
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Hilbert
> ### Title: Generate a Hilbert matrix
> ### Aliases: Hilbert
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> Hilbert(6)
6 x 6 Matrix of class "dpoMatrix"
          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
[1,] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667
[2,] 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667 0.1428571
[3,] 0.3333333 0.2500000 0.2000000 0.1666667 0.1428571 0.1250000
[4,] 0.2500000 0.2000000 0.1666667 0.1428571 0.1250000 0.1111111
[5,] 0.2000000 0.1666667 0.1428571 0.1250000 0.1111111 0.1000000
[6,] 0.1666667 0.1428571 0.1250000 0.1111111 0.1000000 0.0909091
> 
> 
> 
> cleanEx(); ..nameEx <- "LU-class"
> 
> ### * LU-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: LU-class
> ### Title: LU Matrix Decompositions
> ### Aliases: LU-class expand,LU-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> mm <- Matrix(round(rnorm(9),2), nrow = 3, ncol = 3)
> mm
3 x 3 Matrix of class "dgeMatrix"
      [,1]  [,2] [,3]
[1,] -0.63  1.60 0.49
[2,]  0.18  0.33 0.74
[3,] -0.84 -0.82 0.58
> str(lum <- lu(mm))
Formal class 'LU' [package "Matrix"] with 2 slots
  ..@ x   : num [1:9] -0.840  0.750 -0.214 -0.820  2.215 ...
  ..@ perm: int [1:3] 3 3 3
> elu <- expand(lum)
> elu
$L
3 x 3 Matrix of class "dgeMatrix"
           [,1]       [,2] [,3]
[1,]  1.0000000 0.00000000    0
[2,]  0.7500000 1.00000000    0
[3,] -0.2142857 0.06965495    1

$U
3 x 3 Matrix of class "dgeMatrix"
      [,1]   [,2]      [,3]
[1,] -0.84 -0.820 0.5800000
[2,]  0.00  2.215 0.0550000
[3,]  0.00  0.000 0.8604547

$P
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    0    0    1
[3,]    1    0    0

> elu$L %*% elu$U
3 x 3 Matrix of class "dgeMatrix"
      [,1]  [,2] [,3]
[1,] -0.84 -0.82 0.58
[2,] -0.63  1.60 0.49
[3,]  0.18  0.33 0.74
> 
> 
> 
> cleanEx(); ..nameEx <- "Matrix"
> 
> ### * Matrix
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Matrix
> ### Title: Construct a Classed Matrix
> ### Aliases: Matrix
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> Matrix(0, 3, 2)             # a 3 by 2 matrix of zeros
3 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]    0    0
[2,]    0    0
[3,]    0    0
> Matrix(1:6, 3, 2)           # a 3 by 2 matrix
3 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6
> Matrix(1:6, nrow=3)
3 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6
> Matrix(1:6, ncol=2)
3 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6
> Matrix(1:9, nrow=3,
+        dimnames = list(c("a", "b", "c"), c("A", "B", "C")))
3 x 3 Matrix of class "dgeMatrix"
  A B C
a 1 4 7
b 2 5 8
c 3 6 9
> 
> 
> 
> cleanEx(); ..nameEx <- "Schur"
> 
> ### * Schur
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Schur
> ### Title: Schur Decomposition of a Matrix
> ### Aliases: Schur Schur,dgeMatrix,logical-method
> ###   Schur,dgeMatrix,missing-method Schur,ddenseMatrix,logical-method
> ###   Schur,ddenseMatrix,missing-method
> ### Keywords: algebra
> 
> ### ** Examples
> 
> Schur(Hilbert(9))              # Schur factorization (real eigenvalues)
$WR
[1] 1.725883e+00 3.216331e-01 3.103893e-02 1.978934e-03 8.758085e-05
[6] 2.673013e-06 5.385613e-08 6.460905e-10 3.499686e-12

$WI
[1] 0 0 0 0 0 0 0 0 0

$T
          [,1]          [,2]          [,3]          [,4]          [,5]
 [1,] 1.725883 -8.838711e-17 -9.209102e-17 -3.691953e-17  8.715622e-18
 [2,] 0.000000  3.216331e-01  6.201553e-17  4.849090e-17  1.140026e-17
 [3,] 0.000000  0.000000e+00  3.103893e-02  3.623390e-18 -1.203632e-17
 [4,] 0.000000  0.000000e+00  0.000000e+00  1.978934e-03 -4.821162e-18
 [5,] 0.000000  0.000000e+00  0.000000e+00  0.000000e+00  8.758085e-05
 [6,] 0.000000  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 [7,] 0.000000  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 [8,] 0.000000  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 [9,] 0.000000  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
               [,6]          [,7]          [,8]          [,9]
 [1,] -1.215402e-17  1.625908e-18  2.445276e-17  8.671224e-18
 [2,]  7.053257e-18 -4.456591e-18 -1.780442e-17 -1.220396e-18
 [3,] -1.849371e-17 -4.746535e-18 -6.077071e-18  4.933090e-18
 [4,] -1.849532e-17 -2.227903e-18  7.826424e-19  3.723369e-18
 [5,] -5.450015e-18 -6.872636e-19 -2.453266e-18 -5.719701e-20
 [6,]  2.673013e-06  1.121956e-18  2.834097e-18  3.948825e-18
 [7,]  0.000000e+00  5.385613e-08 -1.805502e-18  1.279404e-19
 [8,]  0.000000e+00  0.000000e+00  6.460905e-10 -1.491291e-18
 [9,]  0.000000e+00  0.000000e+00  0.000000e+00  3.499686e-12

$Z
           [,1]        [,2]        [,3]        [,4]        [,5]         [,6]
 [1,] 0.7091817  0.63411890  0.29150563  0.09654587  0.02509744  0.005224405
 [2,] 0.4290994 -0.09547484 -0.62126159 -0.56574091 -0.29718372 -0.107648322
 [3,] 0.3179060 -0.25768723 -0.36113842  0.26290950  0.60646687  0.465721999
 [4,] 0.2554416 -0.30295702 -0.10458213  0.43898728  0.08575865 -0.495332526
 [5,] 0.2146560 -0.31134174  0.07804869  0.32718380 -0.32141465 -0.282373552
 [6,] 0.1856468 -0.30599625  0.20198227  0.12522530 -0.39722099  0.216365380
 [7,] 0.1638323 -0.29532381  0.28533408 -0.08708961 -0.22555349  0.424545808
 [8,] 0.1467699 -0.28278221  0.34115205 -0.28063056  0.08749818  0.194400829
 [9,] 0.1330265 -0.26989403  0.37816853 -0.44689612  0.46505176 -0.426091101
               [,7]          [,8]          [,9]
 [1,]  0.0008620699  0.0001078102 -8.936307e-06
 [2,] -0.0281988594 -0.0052559005  6.197802e-04
 [3,]  0.2107961543  0.0612017719 -1.053480e-02
 [4,] -0.5489968847 -0.2819875020  7.547180e-02
 [5,]  0.3885427422  0.5768471862 -2.776472e-01
 [6,]  0.3476433685 -0.4086211268  5.683289e-01
 [7,] -0.2535560341 -0.2714694097 -6.540970e-01
 [8,] -0.4521777108  0.5447688462  3.958146e-01
 [9,]  0.3358493180 -0.2156782744 -9.795376e-02

> A <- Matrix(rnorm( 9*9, sd = 100), nrow = 9)
> schur.A <- Schur(A)
> #mod.eig <- Mod(schur.A$values) # eigenvalue modulus
> #schur.A
> 
> 
> 
> cleanEx(); ..nameEx <- "VarCorr"
> 
> ### * VarCorr
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: VarCorr
> ### Title: Extract variance and correlation components
> ### Aliases: VarCorr
> ### Keywords: models
> 
> ### ** Examples
> 
> (fm1 <- lmer(decrease ~ treatment + (1|rowpos) + (1|colpos),
+              OrchardSprays))
Linear mixed-effects model fit by REML
Formula: decrease ~ treatment + (1 | rowpos) + (1 | colpos) 
   Data: OrchardSprays 
      AIC      BIC    logLik MLdeviance REMLdeviance
 534.7596 558.5073 -256.3798   558.4304     512.7596
Random effects:
 Groups   Name        Variance Std.Dev.
 rowpos   (Intercept)  37.5295  6.1261 
 colpos   (Intercept)   2.5252  1.5891 
 Residual             380.8313 19.5149 
# of obs: 64, groups: rowpos, 8; colpos, 8

Fixed effects:
            Estimate Std. Error DF t value  Pr(>|t|)    
(Intercept)   4.6250     7.2533 56  0.6376  0.526308    
treatmentB    3.0000     9.7574 56  0.3075  0.759636    
treatmentC   20.6250     9.7574 56  2.1138  0.039002 *  
treatmentD   30.3750     9.7574 56  3.1130  0.002915 ** 
treatmentE   58.5000     9.7574 56  5.9954 1.546e-07 ***
treatmentF   64.3750     9.7574 56  6.5975 1.597e-08 ***
treatmentG   63.8750     9.7574 56  6.5463 1.939e-08 ***
treatmentH   85.6250     9.7574 56  8.7753 4.170e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> VarCorr(fm1)
 Groups   Name        Variance Std.Dev.
 rowpos   (Intercept)  37.5295  6.1261 
 colpos   (Intercept)   2.5252  1.5891 
 Residual             380.8313 19.5149 
> 
> 
> 
> cleanEx(); ..nameEx <- "Xtrct-methods"
> 
> ### * Xtrct-methods
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: [-methods
> ### Title: Methods for "[": Extraction or Subsetting in Package 'Matrix'.
> ### Aliases: [-methods [,dgTMatrix,missing,missing,ANY-method
> ###   [,dgTMatrix,missing,numeric,logical-method
> ###   [,dgTMatrix,missing,numeric,missing-method
> ###   [,dgTMatrix,numeric,missing,logical-method
> ###   [,dgTMatrix,numeric,missing,missing-method
> ###   [,dgTMatrix,numeric,numeric,logical-method
> ###   [,dgTMatrix,numeric,numeric,missing-method
> ###   [,dsparseMatrix,missing,missing,ANY-method
> ###   [,dsparseMatrix,missing,numeric,logical-method
> ###   [,dsparseMatrix,missing,numeric,missing-method
> ###   [,dsparseMatrix,numeric,missing,logical-method
> ###   [,dsparseMatrix,numeric,missing,missing-method
> ###   [,dsparseMatrix,numeric,numeric,logical-method
> ###   [,dsparseMatrix,numeric,numeric,missing-method
> ### Keywords: methods array
> 
> ### ** Examples
> 
> str(m <- Matrix(round(rnorm(7*4),2), nrow = 7))
Formal class 'dgeMatrix' [package "Matrix"] with 5 slots
  ..@ rcond   : num(0) 
  ..@ factors : list()
  ..@ x       : num [1:28] -0.63 0.18 -0.84 1.6 0.33 -0.82 0.49 0.74 0.58 -0.31 ...
  ..@ Dim     : int [1:2] 7 4
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> ## wrongly looses class: m[]; error: m[1,1]
> 
> ## Don't show: 
>  if(FALSE) {## still all fail
+    ch[2,3]
+    ch[1,]
+    ch[,2]
+    pm[2,3]
+    pm[1,]
+    pm[,2]
+  }
> ## End Don't show
> 
> 
> 
> cleanEx(); ..nameEx <- "bCrosstab"
> 
> ### * bCrosstab
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bCrosstab
> ### Title: Create pairwise crosstabulation
> ### Aliases: bCrosstab
> ### Keywords: manip algebra
> 
> ### ** Examples
> 
> str(esoph)
`data.frame':	88 obs. of  5 variables:
 $ agegp    : Ord.factor w/ 6 levels "25-34"<"35-44"<..: 1 1 1 1 1 1 1 1 1 1 ...
 $ alcgp    : Ord.factor w/ 4 levels "0-39g/day"<"40-79"<..: 1 1 1 1 2 2 2 2 3 3 ...
 $ tobgp    : Ord.factor w/ 4 levels "0-9g/day"<"10-19"<..: 1 2 3 4 1 2 3 4 1 2 ...
 $ ncases   : num  0 0 0 0 0 0 0 0 0 0 ...
 $ ncontrols: num  40 10 6 5 27 7 4 7 2 1 ...
> bCrosstab(with(esoph,list(agegp, alcgp))) $ ctab
$"V1:V1"
6 x 6 sparse Matrix of class "dsCMatrix"
                      
[1,] 15 .  .  .  .  . 
[2,] .  15 .  .  .  . 
[3,] .  .  16 .  .  . 
[4,] .  .  .  16 .  . 
[5,] .  .  .  .  15 . 
[6,] .  .  .  .  .  11

$"V2:V1"
4 x 6 sparse Matrix of class "dgCMatrix"
                
[1,] 4 4 4 4 4 3
[2,] 4 4 4 4 3 4
[3,] 3 4 4 4 4 2
[4,] 4 3 4 4 4 2

$"V2:V2"
4 x 4 sparse Matrix of class "dsCMatrix"
                
[1,] 23 .  .  . 
[2,] .  23 .  . 
[3,] .  .  21 . 
[4,] .  .  .  21

> 
> grps <- with(esoph, list(age = agegp, alc = alcgp, tob = tobgp))
> bCn <- bCrosstab( grps, reorder = FALSE)
> stopifnot(all.equal(bCn$flist, grps))
> str(bC <- bCrosstab(grps))
List of 2
 $ flist:List of 3
  ..$ age: Ord.factor w/ 6 levels "25-34"<"35-44"<..: 1 1 1 1 1 1 1 1 1 1 ...
  ..$ tob: Ord.factor w/ 4 levels "0-9g/day"<"10-19"<..: 1 2 3 4 1 2 3 4 1 2 ...
  ..$ alc: Ord.factor w/ 4 levels "0-39g/day"<"40-79"<..: 1 1 1 1 2 2 2 2 3 3 ...
 $ ctab :List of 6
  ..$ age:age:Formal class 'dsCMatrix' [package "Matrix"] with 7 slots
  .. .. ..@ uplo    : chr "U"
  .. .. ..@ i       : int [1:6] 0 1 2 3 4 5
  .. .. ..@ p       : int [1:7] 0 1 2 3 4 5 6
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:6] 15 15 16 16 15 11
  .. .. ..@ Dim     : Named int [1:2] 6 6
  .. .. .. ..- attr(*, "names")= chr [1:2] "age" "age"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
  ..$ tob:age:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  .. .. ..@ i       : int [1:24] 0 1 2 3 0 1 2 3 0 1 ...
  .. .. ..@ p       : int [1:7] 0 4 8 12 16 20 24
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:24] 4 4 3 4 4 4 4 3 4 4 ...
  .. .. ..@ Dim     : Named int [1:2] 4 6
  .. .. .. ..- attr(*, "names")= chr [1:2] "tob" "age"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
  ..$ tob:tob:Formal class 'dsCMatrix' [package "Matrix"] with 7 slots
  .. .. ..@ uplo    : chr "U"
  .. .. ..@ i       : int [1:4] 0 1 2 3
  .. .. ..@ p       : int [1:5] 0 1 2 3 4
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:4] 24 24 20 20
  .. .. ..@ Dim     : Named int [1:2] 4 4
  .. .. .. ..- attr(*, "names")= chr [1:2] "tob" "tob"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
  ..$ alc:age:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  .. .. ..@ i       : int [1:24] 0 1 2 3 0 1 2 3 0 1 ...
  .. .. ..@ p       : int [1:7] 0 4 8 12 16 20 24
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:24] 4 4 3 4 4 4 4 3 4 4 ...
  .. .. ..@ Dim     : Named int [1:2] 4 6
  .. .. .. ..- attr(*, "names")= chr [1:2] "alc" "age"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
  ..$ alc:tob:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  .. .. ..@ i       : int [1:16] 0 1 2 3 0 1 2 3 0 1 ...
  .. .. ..@ p       : int [1:5] 0 4 8 12 16
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:16] 6 6 6 6 6 6 6 6 5 6 ...
  .. .. ..@ Dim     : Named int [1:2] 4 4
  .. .. .. ..- attr(*, "names")= chr [1:2] "alc" "tob"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
  ..$ alc:alc:Formal class 'dsCMatrix' [package "Matrix"] with 7 slots
  .. .. ..@ uplo    : chr "U"
  .. .. ..@ i       : int [1:4] 0 1 2 3
  .. .. ..@ p       : int [1:5] 0 1 2 3 4
  .. .. ..@ factors : list()
  .. .. ..@ x       : num [1:4] 23 23 21 21
  .. .. ..@ Dim     : Named int [1:2] 4 4
  .. .. .. ..- attr(*, "names")= chr [1:2] "alc" "alc"
  .. .. ..@ Dimnames:List of 2
  .. .. .. ..$ : NULL
  .. .. .. ..$ : NULL
> bC$ctab$"alc:age" # generally 4 obs. per cell, but not always:
4 x 6 sparse Matrix of class "dgCMatrix"
                
[1,] 4 4 4 4 4 3
[2,] 4 4 4 4 3 4
[3,] 3 4 4 4 4 2
[4,] 4 3 4 4 4 2
> aa.m <- as(bC$ctab$"alc:age", "matrix")
> table(aa.m) # #(2,3,4) = (2, 4, 18)
aa.m
 2  3  4 
 2  4 18 
> stopifnot(all.equal(as.vector(t(aa.m)),
+                     as.vector(table(with(esoph, alcgp:agegp))), tol=0))
> 
> 
> 
> cleanEx(); ..nameEx <- "corrmatrix-class"
> 
> ### * corrmatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: corrmatrix-class
> ### Title: Class "corrmatrix"
> ### Aliases: corrmatrix-class coerce,pdIdent,corrmatrix-method
> ###   coerce,pdMat,corrmatrix-method coerce,pdNatural,corrmatrix-method
> ###   coerce<-,pdNatural,corrmatrix-method
> ###   coerce,pdmatrix,corrmatrix-method
> ### Keywords: classes
> 
> ### ** Examples
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "dCholCMatrix-class"
> 
> ### * dCholCMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dCholCMatrix-class
> ### Title: Cholesky Decompositions of dsCMatrix Objects
> ### Aliases: dCholCMatrix-class lCholCMatrix-class
> ###   solve,lCholCMatrix,missing-method solve,lCholCMatrix,lgCMatrix-method
> ###   t,lCholCMatrix-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> data(mm)
> xpx <- crossprod(mm)
> str(xpx)
Formal class 'dsCMatrix' [package "Matrix"] with 7 slots
  ..@ uplo    : chr "L"
  ..@ i       : int [1:4902] 0 257 261 280 419 421 426 427 431 449 ...
  ..@ p       : int [1:713] 0 16 22 36 55 63 76 82 90 101 ...
  ..@ factors : list()
  ..@ x       : num [1:4902] 1.0000 0.2774 0.1961 0.2774 0.0958 ...
  ..@ Dim     : int [1:2] 712 712
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> str(ch <- chol(xpx))
Formal class 'dCholCMatrix' [package "Matrix"] with 11 slots
  ..@ perm    : int [1:712] 579 39 38 578 583 46 80 599 48 585 ...
  ..@ Parent  : int [1:712] 1 62 3 62 5 24 7 118 9 76 ...
  ..@ D       : num [1:712] 1 1 1 1 1 ...
  ..@ uplo    : chr "L"
  ..@ diag    : chr "U"
  ..@ i       : int [1:7809] 1 62 63 355 356 357 694 695 699 700 ...
  ..@ p       : int [1:713] 0 16 31 42 52 61 69 76 82 89 ...
  ..@ factors : list()
  ..@ x       : num [1:7809] -5.55e-11 -2.93e-01 -3.22e-01 -4.14e-01  1.92e-01 ...
  ..@ Dim     : int [1:2] 712 712
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> 
> ## Visualize the sparseness:
> image(xpx, main=paste("crossprod(mm) : Sparse",dQuote(class(xpx))))
> image(ch, main=paste("chol (crossprod(mm)) : Sparse", dQuote(class(ch))))
> 
> 
> 
> cleanEx(); ..nameEx <- "ddenseMatrix-class"
> 
> ### * ddenseMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ddenseMatrix-class
> ### Title: Virtual Class "ddenseMatrix" of Numeric Dense Matrices
> ### Aliases: ddenseMatrix-class show,ddenseMatrix-method
> ###   coerce,ddenseMatrix,matrix-method
> ###   crossprod,ddenseMatrix,missing-method diag,ddenseMatrix-method
> ###   lu,ddenseMatrix-method norm,ddenseMatrix,missing-method
> ###   norm,ddenseMatrix,character-method rcond,ddenseMatrix,missing-method
> ###   rcond,ddenseMatrix,character-method solve,ddenseMatrix,missing-method
> ###   solve,ddenseMatrix,ANY-method t,ddenseMatrix-method
> ###   tcrossprod,ddenseMatrix-method
> ### Keywords: classes
> 
> ### ** Examples
> 
> showClass("ddenseMatrix")
Virtual Class

Slots:
                                                   
Name:     rcond  factors        x      Dim Dimnames
Class:  numeric     list  numeric  integer     list

Extends: 
Class "dMatrix", directly
Class "Matrix", by class "dMatrix"

Known Subclasses: 
Class "dgeMatrix", directly
Class "dtpMatrix", directly
Class "dspMatrix", directly
Class "dtrMatrix", by class "dgeMatrix"
Class "dsyMatrix", by class "dgeMatrix"
> 
> 
> 
> cleanEx(); ..nameEx <- "dgCMatrix-class"
> 
> ### * dgCMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dgCMatrix-class
> ### Title: Compressed, sparse, column-oriented numeric matrices
> ### Aliases: dgCMatrix-class \%*\%,dgCMatrix,dgeMatrix-method
> ###   \%*\%,dgCMatrix,matrix-method \%*\%,dgeMatrix,dgCMatrix-method
> ###   \%*\%,matrix,dgCMatrix-method coerce,matrix,dgCMatrix-method
> ###   coerce,dgeMatrix,dgCMatrix-method coerce,dgCMatrix,dgTMatrix-method
> ###   coerce,dgCMatrix,dgBCMatrix-method coerce,dgCMatrix,matrix-method
> ###   coerce,dgCMatrix,dgeMatrix-method crossprod,dgCMatrix,missing-method
> ###   crossprod,dgCMatrix,matrix-method
> ###   crossprod,dgCMatrix,dgeMatrix-method diag,dgCMatrix-method
> ###   dim,dgCMatrix-method image,dgCMatrix-method t,dgCMatrix-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> m <- Matrix(1:12, nrow = 3)
> (mC <- as(m, "dgCMatrix"))
3 x 4 sparse Matrix of class "dgCMatrix"
             
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> str(mC)
Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  ..@ i       : int [1:12] 0 1 2 0 1 2 0 1 2 0 ...
  ..@ p       : int [1:5] 0 3 6 9 12
  ..@ factors : list()
  ..@ x       : num [1:12] 1 2 3 4 5 6 7 8 9 10 ...
  ..@ Dim     : int [1:2] 3 4
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> mC[,1]
[1] 1 2 3
> 
> 
> 
> cleanEx(); ..nameEx <- "dgTMatrix-class"
> 
> ### * dgTMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dgTMatrix-class
> ### Title: Sparse matrices in triplet form
> ### Aliases: dgTMatrix-class +,dgTMatrix,dgTMatrix-method
> ###   coerce,dgTMatrix,dgCMatrix-method coerce,dgTMatrix,dgeMatrix-method
> ###   coerce,dgTMatrix,dsCMatrix-method coerce,dgTMatrix,matrix-method
> ###   coerce,dgeMatrix,dgTMatrix-method coerce,matrix,dgTMatrix-method
> ###   crossprod,dgTMatrix,missing-method crossprod,dgTMatrix,matrix-method
> ###   crossprod,dgTMatrix,numeric-method image,dgTMatrix-method
> ###   kronecker,dgTMatrix,dgTMatrix-method t,dgTMatrix-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> m <- Matrix(1:28, nrow = 4)
> (mT <- as(m, "dgTMatrix"))
4 x 7 sparse Matrix of class "dgTMatrix"
                       
[1,] 1 5  9 13 17 21 25
[2,] 2 6 10 14 18 22 26
[3,] 3 7 11 15 19 23 27
[4,] 4 8 12 16 20 24 28
> 
> mT[1,]
[1]  1  5  9 13 17 21 25
> mT[4, drop = FALSE]
1 x 7 sparse Matrix of class "dgTMatrix"
                       
[1,] 4 8 12 16 20 24 28
> 
> 
> 
> cleanEx(); ..nameEx <- "dpoMatrix-class"
> 
> ### * dpoMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dpoMatrix-class
> ### Title: Positive semi-definite, dense, numeric matrices
> ### Aliases: dpoMatrix-class dppMatrix-class
> ###   coerce,dpoMatrix,dppMatrix-method coerce,dppMatrix,dpoMatrix-method
> ###   rcond,dpoMatrix,character-method rcond,dppMatrix,character-method
> ###   rcond,dpoMatrix,missing-method rcond,dppMatrix,missing-method
> ###   chol,dpoMatrix-method chol,dppMatrix-method chol,dpoMatrix,ANY-method
> ###   chol,dppMatrix,ANY-method determinant,dpoMatrix,logical-method
> ###   determinant,dppMatrix,logical-method solve,dpoMatrix,dgeMatrix-method
> ###   solve,dppMatrix,dgeMatrix-method solve,dpoMatrix,matrix-method
> ###   solve,dppMatrix,matrix-method solve,dpoMatrix,missing-method
> ###   solve,dppMatrix,missing-method solve,dpoMatrix,numeric-method
> ###   solve,dppMatrix,numeric-method solve,dppMatrix,integer-method
> ### Keywords: classes algebra
> 
> ### ** Examples
> 
> h6 <- Hilbert(6)
> rcond(h6)
[1] 3.439939e-08
> str(h6)
Formal class 'dpoMatrix' [package "Matrix"] with 6 slots
  ..@ uplo    : chr "U"
  ..@ rcond   : Named num 3.44e-08
  .. ..- attr(*, "names")= chr "O"
  ..@ factors :List of 1
  .. ..$ Cholesky:Formal class 'Cholesky' [package "Matrix"] with 7 slots
  .. .. .. ..@ uplo    : chr "U"
  .. .. .. ..@ diag    : chr "N"
  .. .. .. ..@ rcond   : num(0) 
  .. .. .. ..@ factors : list()
  .. .. .. ..@ x       : num [1:36] 1 0 0 0 0 ...
  .. .. .. ..@ Dim     : int [1:2] 6 6
  .. .. .. ..@ Dimnames:List of 2
  .. .. .. .. ..$ : NULL
  .. .. .. .. ..$ : NULL
  ..@ x       : num [1:36] 1.000 0.500 0.333 0.250 0.200 ...
  ..@ Dim     : int [1:2] 6 6
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> solve(h6)
6 x 6 Matrix of class "dpoMatrix"
      [,1]    [,2]     [,3]     [,4]     [,5]     [,6]
[1,]    36    -630     3360    -7560     7560    -2772
[2,]  -630   14700   -88200   211680  -220500    83160
[3,]  3360  -88200   564480 -1411200  1512000  -582120
[4,] -7560  211680 -1411200  3628800 -3969000  1552320
[5,]  7560 -220500  1512000 -3969000  4410000 -1746360
[6,] -2772   83160  -582120  1552320 -1746360   698544
> str(hp6 <- as(h6, "dppMatrix"))
Formal class 'dppMatrix' [package "Matrix"] with 6 slots
  ..@ uplo    : chr "U"
  ..@ rcond   : Named num 3.44e-08
  .. ..- attr(*, "names")= chr "O"
  ..@ factors :List of 1
  .. ..$ pCholesky:Formal class 'pCholesky' [package "Matrix"] with 7 slots
  .. .. .. ..@ uplo    : chr "U"
  .. .. .. ..@ diag    : chr "N"
  .. .. .. ..@ rcond   : num(0) 
  .. .. .. ..@ factors : list()
  .. .. .. ..@ x       : num [1:21] 1.000 0.500 0.289 0.333 0.289 ...
  .. .. .. ..@ Dim     : int [1:2] 6 6
  .. .. .. ..@ Dimnames:List of 2
  .. .. .. .. ..$ : NULL
  .. .. .. .. ..$ : NULL
  ..@ x       : num [1:21] 1.000 0.500 0.333 0.333 0.250 ...
  ..@ Dim     : int [1:2] 6 6
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> 
> 
> 
> cleanEx(); ..nameEx <- "dsparseMatrix-class"
> 
> ### * dsparseMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dsparseMatrix-class
> ### Title: Virtual Class "dsparseMatrix" of Numeric Sparse Matrices
> ### Aliases: dsparseMatrix-class
> ### Keywords: classes
> 
> ### ** Examples
> 
> showClass("dsparseMatrix")

Slots:
                                 
Name:         x      Dim Dimnames
Class:  numeric  integer     list

Extends: 
Class "dMatrix", directly
Class "sparseMatrix", directly
Class "Matrix", by class "dMatrix"
Class "Matrix", by class "sparseMatrix"

Known Subclasses: 
Class "dgTMatrix", directly
Class "dgCMatrix", directly
Class "dgRMatrix", directly
Class "dtTMatrix", by class "dgTMatrix"
Class "dsTMatrix", by class "dgTMatrix"
Class "dtCMatrix", by class "dgCMatrix"
Class "dsCMatrix", by class "dgCMatrix"
> 
> 
> 
> cleanEx(); ..nameEx <- "dsyMatrix-class"
> 
> ### * dsyMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dsyMatrix-class
> ### Title: Symmetric, dense matrices
> ### Aliases: \%*\%,dgeMatrix,dsyMatrix-method
> ###   \%*\%,dspMatrix,dgeMatrix-method \%*\%,dspMatrix,integer-method
> ###   \%*\%,dspMatrix,matrix-method \%*\%,dspMatrix,numeric-method
> ###   \%*\%,dsyMatrix,dgeMatrix-method coerce,dspMatrix,dgeMatrix-method
> ###   coerce,dspMatrix,dsyMatrix-method coerce,dspMatrix,matrix-method
> ###   coerce,dsyMatrix,dgeMatrix-method coerce,dsyMatrix,dspMatrix-method
> ###   coerce,dsyMatrix,matrix-method dspMatrix-class dsyMatrix-class
> ###   norm,dspMatrix,character-method norm,dspMatrix,missing-method
> ###   norm,dsyMatrix,character-method norm,dsyMatrix,missing-method
> ###   rcond,dspMatrix,character-method rcond,dspMatrix,missing-method
> ###   rcond,dsyMatrix,character-method rcond,dsyMatrix,missing-method
> ###   solve,dspMatrix,dgeMatrix-method solve,dspMatrix,integer-method
> ###   solve,dspMatrix,matrix-method solve,dspMatrix,missing-method
> ###   solve,dspMatrix,numeric-method solve,dsyMatrix,dgeMatrix-method
> ###   solve,dsyMatrix,matrix-method solve,dsyMatrix,missing-method
> ###   t,dspMatrix-method t,dsyMatrix-method unpack,dspMatrix-method
> ### Keywords: classes
> 
> ### ** Examples
> 
> ## Only upper triangular part matters (when uplo == "U" as per default)
> (sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77)))
2 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]   14   32
[2,]   32   77
> (c2 <- chol(sy2))
2 x 2 Matrix of class "Cholesky"
         [,1]     [,2]
[1,] 3.741657 8.552360
[2,] 0.000000 1.963961
> all.equal(c2, c2. <- chol(as(sy2, "dpoMatrix")))# equal, but not same class
[1] TRUE
> str(c2)
Formal class 'Cholesky' [package "Matrix"] with 7 slots
  ..@ uplo    : chr "U"
  ..@ diag    : chr "N"
  ..@ rcond   : num(0) 
  ..@ factors : list()
  ..@ x       : num [1:4] 3.74 0.00 8.55 1.96
  ..@ Dim     : int [1:2] 2 2
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> 
> ## An example where chol() can't work
> (sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7)))
2 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]   14    2
[2,]    2   -7
> 
> validObject(as(sy3, "dpoMatrix"), test=TRUE) # >> is not pos.def.
[1] "dpoMatrix is not positive definite"
> try(chol(sy3)) ## Error: not pos.def
Error in chol(sy3) : Lapack routine dpotrf returned error code 2
> 
> 
> 
> cleanEx(); ..nameEx <- "expand"
> 
> ### * expand
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: expand
> ### Title: Expand a Decomposition into Factors
> ### Aliases: expand
> ### Keywords: algebra
> 
> ### ** Examples
> 
> (x <- Matrix(round(rnorm(9),2), 3, 3))
3 x 3 Matrix of class "dgeMatrix"
      [,1]  [,2] [,3]
[1,] -0.63  1.60 0.49
[2,]  0.18  0.33 0.74
[3,] -0.84 -0.82 0.58
> (ex <- expand(lux <- lu(x)))
$L
3 x 3 Matrix of class "dgeMatrix"
           [,1]       [,2] [,3]
[1,]  1.0000000 0.00000000    0
[2,]  0.7500000 1.00000000    0
[3,] -0.2142857 0.06965495    1

$U
3 x 3 Matrix of class "dgeMatrix"
      [,1]   [,2]      [,3]
[1,] -0.84 -0.820 0.5800000
[2,]  0.00  2.215 0.0550000
[3,]  0.00  0.000 0.8604547

$P
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    0    0    1
[3,]    1    0    0

> 
> 
> 
> cleanEx(); ..nameEx <- "expm"
> 
> ### * expm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: expm
> ### Title: Matrix exponential
> ### Aliases: expm expm,ddenseMatrix-method expm,dgeMatrix-method
> ### Keywords: algebra math
> 
> ### ** Examples
> 
> (m1 <- Matrix(c(1,0,1,1), nc = 2))
2 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]    1    1
[2,]    0    1
> (e1 <- expm(m1)) ; e <- exp(1)
2 x 2 Matrix of class "dgeMatrix"
         [,1]     [,2]
[1,] 2.718282 2.718282
[2,] 0.000000 2.718282
> stopifnot(all.equal(e1@x, c(e,0,e,e), tol = 1e-15))
> (m2 <- Matrix(c(-49, -64, 24, 31), nc = 2))
2 x 2 Matrix of class "dgeMatrix"
     [,1] [,2]
[1,]  -49   24
[2,]  -64   31
> (e2 <- expm(m2))
2 x 2 Matrix of class "dgeMatrix"
           [,1]      [,2]
[1,] -0.7357588 0.5518191
[2,] -1.4715176 1.1036382
> (m3 <- Matrix(cbind(0,rbind(6*diag(3),0)), nc = 4))
4 x 4 Matrix of class "dgeMatrix"
     [,1] [,2] [,3] [,4]
[1,]    0    6    0    0
[2,]    0    0    6    0
[3,]    0    0    0    6
[4,]    0    0    0    0
> (e3 <- expm(m3))
4 x 4 Matrix of class "dgeMatrix"
     [,1] [,2] [,3] [,4]
[1,]    1    6   18   36
[2,]    0    1    6   18
[3,]    0    0    1    6
[4,]    0    0    0    1
> 
> 
> 
> cleanEx(); ..nameEx <- "facmul"
> 
> ### * facmul
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: facmul
> ### Title: Multiplication by Decomposition Factors
> ### Aliases: facmul facmul.default
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> library(Matrix)
> x <- Matrix(rnorm(9), 3, 3)
> ## Not run: 
> ##D qrx <- qr(x)                      # QR factorization of x
> ##D y <- rnorm(3)
> ##D facmul( qr(x), factor = "Q", y)   # form Q y
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "fixef"
> 
> ### * fixef
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fixef
> ### Title: Extract Fixed Effects
> ### Aliases: fixef fixed.effects fixef,ANY-method fixef,mer-method
> ###   fixef,glmer-method
> ### Keywords: models
> 
> ### ** Examples
> 
> fixef(lmer(decrease ~ treatment + (1|rowpos) + (1|colpos),
+              OrchardSprays))
(Intercept)  treatmentB  treatmentC  treatmentD  treatmentE  treatmentF 
      4.625       3.000      20.625      30.375      58.500      64.375 
 treatmentG  treatmentH 
     63.875      85.625 
> 
> 
> 
> cleanEx(); ..nameEx <- "lmer"
> 
> ### * lmer
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lmer
> ### Title: Fit (Generalized) Linear Mixed-Effects Models
> ### Aliases: lmer lmer,formula-method
> ### Keywords: models methods
> 
> ### ** Examples
> 
> (fm1 <- lmer(decrease ~ treatment + (1|rowpos) + (1|colpos),
+              OrchardSprays))
Linear mixed-effects model fit by REML
Formula: decrease ~ treatment + (1 | rowpos) + (1 | colpos) 
   Data: OrchardSprays 
      AIC      BIC    logLik MLdeviance REMLdeviance
 534.7596 558.5073 -256.3798   558.4304     512.7596
Random effects:
 Groups   Name        Variance Std.Dev.
 rowpos   (Intercept)  37.5295  6.1261 
 colpos   (Intercept)   2.5252  1.5891 
 Residual             380.8313 19.5149 
# of obs: 64, groups: rowpos, 8; colpos, 8

Fixed effects:
            Estimate Std. Error DF t value  Pr(>|t|)    
(Intercept)   4.6250     7.2533 56  0.6376  0.526308    
treatmentB    3.0000     9.7574 56  0.3075  0.759636    
treatmentC   20.6250     9.7574 56  2.1138  0.039002 *  
treatmentD   30.3750     9.7574 56  3.1130  0.002915 ** 
treatmentE   58.5000     9.7574 56  5.9954 1.546e-07 ***
treatmentF   64.3750     9.7574 56  6.5975 1.597e-08 ***
treatmentG   63.8750     9.7574 56  6.5463 1.939e-08 ***
treatmentH   85.6250     9.7574 56  8.7753 4.170e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> 
> 
> cleanEx(); ..nameEx <- "lu"
> 
> ### * lu
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lu
> ### Title: Triangular Decomposition of a Square Matrix
> ### Aliases: lu
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> x <- Matrix(rnorm(9), 3, 3)
> lu(x)
An object of class "LU"
Slot "x":
[1] -0.83562861  0.74967970 -0.21976668 -0.82046838  2.21036930  0.06749830
[7]  0.57578135  0.05577746  0.86109738

Slot "perm":
[1] 3 3 3

> 
> 
> 
> cleanEx(); ..nameEx <- "mm"
> 
> ### * mm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mm
> ### Title: A sample sparse model matrix
> ### Aliases: mm
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(mm)
> data(y)
> class(mm)
[1] "dgCMatrix"
attr(,"package")
[1] "Matrix"
> dim(mm)
[1] 1850  712
> str(mm)
Formal class 'dgCMatrix' [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 ...
  ..@ factors : list()
  ..@ x       : num [1:8755] 0.277 0.277 0.277 0.277 0.277 ...
  ..@ Dim     : int [1:2] 1850 712
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> str(y)
 num [1:1850] 64.07  5.88 64.03  5.96 76.41 ...
> sparse.sol <- solve(crossprod(mm), crossprod(mm, y))
> str(sparse.sol)
Formal class 'dgeMatrix' [package "Matrix"] with 5 slots
  ..@ rcond   : num(0) 
  ..@ factors : list()
  ..@ x       : num [1:712] 823 340 473 349 188 ...
  ..@ Dim     : int [1:2] 712 1
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> 
> 
> 
> cleanEx(); ..nameEx <- "norm"
> 
> ### * norm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: norm
> ### Title: Norm of a Matrix
> ### Aliases: norm
> ### Keywords: algebra
> 
> ### ** Examples
> 
> x <- Hilbert(9)
> norm(x, "1")
[1] 2.828968
> norm(x, "I")
[1] 2.828968
> norm(x, "F")
[1] 1.755872
> norm(x, "M")
[1] 1
> 
> 
> 
> cleanEx(); ..nameEx <- "pMatrix-class"
> 
> ### * pMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pMatrix-class
> ### Title: Permutation matrices
> ### Aliases: pMatrix-class \%*\%,matrix,pMatrix-method
> ###   \%*\%,pMatrix,matrix-method \%*\%,pMatrix,pMatrix-method
> ###   \%*\%,dgeMatrix,pMatrix-method \%*\%,pMatrix,dgeMatrix-method
> ###   coerce,integer,pMatrix-method coerce,pMatrix,matrix-method
> ###   solve,pMatrix,missing-method t,pMatrix-method
> ### Keywords: classes
> 
> ### ** Examples
> 
> (pm1 <- as(as.integer(c(2,3,1)), "pMatrix"))
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    0    1    0
[2,]    0    0    1
[3,]    1    0    0
> t(pm1) # is the same as
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    0    0    1
[2,]    1    0    0
[3,]    0    1    0
> solve(pm1)
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    0    0    1
[2,]    1    0    0
[3,]    0    1    0
> pm1 %*% t(pm1) # check that the transpose is the inverse
3 x 3 Matrix of class "pMatrix"
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1
> stopifnot(identical(diag(3), as(pm1 %*% t(pm1), "matrix")))
> (mm <- round(array(rnorm(3 * 3), c(3, 3)), 2))
      [,1]  [,2] [,3]
[1,] -0.63  1.60 0.49
[2,]  0.18  0.33 0.74
[3,] -0.84 -0.82 0.58
> mm %*% pm1
      [,1] [,2]  [,3]
[1,]  1.60 0.49 -0.63
[2,]  0.33 0.74  0.18
[3,] -0.82 0.58 -0.84
> pm1 %*% mm
      [,1]  [,2] [,3]
[1,]  0.18  0.33 0.74
[2,] -0.84 -0.82 0.58
[3,] -0.63  1.60 0.49
> try(as(as.integer(c(3,3,1)), "pMatrix"))# Error: not a permutation
Error in validObject(.Object) : invalid class "pMatrix" object: 'perm' slot is not a valid permutation
> 
> 
> 
> cleanEx(); ..nameEx <- "ranef"
> 
> ### * ranef
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ranef
> ### Title: Extract Random Effects
> ### Aliases: ranef random.effects ranef-methods ranef,ANY-method
> ###   ranef,lmer-method
> ### Keywords: models methods
> 
> ### ** Examples
> 
> ranef(lmer(decrease ~ treatment + (1|rowpos) + (1|colpos),
+              OrchardSprays))
$rowpos
  (Intercept)
1   7.5836801
2   3.1202607
3   2.5692213
4  -3.1615887
5  -3.7126281
6  -3.3820045
7  -2.5554453
8  -0.4614955

$colpos
   (Intercept)
1  0.406933949
2  0.520277254
3 -0.292016432
4 -0.008658169
5 -0.323500683
6 -0.298313282
7 -0.298313282
8  0.293590644

attr(,"varFac")
attr(,"varFac")$rowpos
, , 1

           [,1]
[1,] 0.05526038

, , 2

           [,1]
[1,] 0.05526038

, , 3

           [,1]
[1,] 0.05526038

, , 4

           [,1]
[1,] 0.05526038

, , 5

           [,1]
[1,] 0.05526038

, , 6

           [,1]
[1,] 0.05526038

, , 7

           [,1]
[1,] 0.05526038

, , 8

           [,1]
[1,] 0.05526038


attr(,"varFac")$colpos
, , 1

            [,1]
[1,] 0.006314726

, , 2

            [,1]
[1,] 0.006314726

, , 3

            [,1]
[1,] 0.006314726

, , 4

            [,1]
[1,] 0.006314726

, , 5

            [,1]
[1,] 0.006314726

, , 6

            [,1]
[1,] 0.006314726

, , 7

            [,1]
[1,] 0.006314726

, , 8

            [,1]
[1,] 0.006314726


attr(,"stdErr")
[1] 19.5149
attr(,"class")
[1] "lmer.ranef"
attr(,"class")attr(,"package")
[1] "Matrix"
> 
> 
> 
> cleanEx(); ..nameEx <- "rcond"
> 
> ### * rcond
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rcond
> ### Title: Estimate the Reciprocal Condition Number
> ### Aliases: rcond
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> x <- Matrix(rnorm(9), 3, 3)
> rcond(x)
[1] 0.1803670
> rcond(Hilbert(9))  # should be about 9.1e-13
[1] 9.093775e-13
> 
> 
> 
> cleanEx(); ..nameEx <- "sparseMatrix-class"
> 
> ### * sparseMatrix-class
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sparseMatrix-class
> ### Title: Virtual Class "sparseMatrix" - Mother of Sparse Matrices
> ### Aliases: sparseMatrix-class show,sparseMatrix-method
> ###   \%*\%,sparseMatrix,ddenseMatrix-method
> ###   \%*\%,ddenseMatrix,sparseMatrix-method
> ###   crossprod,sparseMatrix,ddenseMatrix-method
> ###   crossprod,ddenseMatrix,sparseMatrix-method
> ### Keywords: classes
> 
> ### ** Examples
> 
> showClass("sparseMatrix") ## and look at the help() of its subclasses

Slots:
                        
Name:       Dim Dimnames
Class:  integer     list

Extends: "Matrix"

Known Subclasses: "dsparseMatrix", "lsparseMatrix"
> 
> 
> 
> cleanEx(); ..nameEx <- "tcrossprod"
> 
> ### * tcrossprod
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: tcrossprod
> ### Title: Cross-product of transpose
> ### Aliases: tcrossprod-methods tcrossprod,dgCMatrix-method
> ###   tcrossprod,dgTMatrix-method tcrossprod
> ### Keywords: methods algebra
> 
> ### ** Examples
> 
>  ## A random sparce "incidence" matrix :
>  m <- matrix(0, 400, 500)
>  set.seed(12)
>  m[runif(314, 0, length(m))] <- 1
>  mm <- as(m, "dgCMatrix")
>  object.size(m) / object.size(mm) # smaller by a factor of 242.88
[1] 242.8840
> 
>  ## tcrossprod() is very fast:
>  system.time(tCmm <- tcrossprod(mm))# "0" practically
[1] 0 0 0 0 0
>  system.time(cm <- crossprod(t(m))) #
[1] 0.17 0.01 0.19 0.00 0.00
> 
>  stopifnot(identical(cm, as(tCmm, "matrix")))
> 
>  ## show "sparse" (sub) matrix
>  tc <- cm[1:16, 1:30]
>  storage.mode(tc) <- "character" ; tc[tc == "0"] <- "."
>  dimnames(tc)[[2]] <- rep("", ncol(tc))
>  noquote(tc)
                                                                 
 [1,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 [2,] . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 [3,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 [4,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 [5,] . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . .
 [6,] . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
 [7,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 [8,] . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . .
 [9,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[10,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[11,] . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . .
[12,] . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . .
[13,] . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . .
[14,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[15,] . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . .
[16,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 
> 
> 
> cleanEx(); ..nameEx <- "unpack"
> 
> ### * unpack
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: unpack
> ### Title: Full Storage Representation of Packed Matrices
> ### Aliases: unpack
> ### Keywords: array algebra
> 
> ### ** Examples
> 
> showMethods("unpack")

Function "unpack":
x = "dspMatrix"
x = "dtpMatrix"
> (cp4 <- chol(Hilbert(4))) # is triangular
4 x 4 Matrix of class "Cholesky"
     [,1]      [,2]      [,3]       [,4]
[1,]    1 0.5000000 0.3333333 0.25000000
[2,]    0 0.2886751 0.2886751 0.25980762
[3,]    0 0.0000000 0.0745356 0.11180340
[4,]    0 0.0000000 0.0000000 0.01889822
> tp4 <- as(cp4,"dtpMatrix")# [t]riangular [p]acked
> str(tp4)
Formal class 'dtpMatrix' [package "Matrix"] with 7 slots
  ..@ uplo    : chr "U"
  ..@ diag    : chr "N"
  ..@ rcond   : num(0) 
  ..@ factors : list()
  ..@ x       : num [1:10] 1.000 0.500 0.289 0.333 0.289 ...
  ..@ Dim     : int [1:2] 4 4
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
> (unpack(tp4))
4 x 4 Matrix of class "dgeMatrix"
     [,1]      [,2]      [,3]       [,4]
[1,]    1 0.5000000 0.3333333 0.25000000
[2,]    0 0.2886751 0.2886751 0.25980762
[3,]    0 0.0000000 0.0745356 0.11180340
[4,]    0 0.0000000 0.0000000 0.01889822
> 
> ## Not run: 
> ##D ## once we have Diagonal() :
> ##D unpack(Diagonal( 1:3))
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "y"
> 
> ### * y
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: y
> ### Title: A sample response vector
> ### Aliases: y
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(y)
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  11.68 0.32 12.06 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')