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Sparse Generalized Singular Value Decomposition

sparseGSVD.Rd

Constrained SVD of a matrix (wrapper of PMA:::PMD).

Usage

GPMD(
  X,
  LW,
  RW,
  k = 0,
  rdsLeft = rep(1, k),
  rdsRight = rep(1, k),
  tol.si = .Machine$double.eps
)

Arguments

X

a (data) matrix;

LW

PARAM_DESCRIPTION

RW

PARAM_DESCRIPTION

k

the desired rank of the singular decomposition, Default: 0

rdsLeft

The radius (>0) of the $L_1$ ball for each left vector, Default: rep(1, k)

rdsRight

The radius (>0) of the $L_1$ balls for each right vector, Default: rep(1, k)

tol.si

Tolerance for the computation of the Sparse Index, set by default to .Machine$double.eps

Value

Pseudo-singular vectors and values

Details

DETAILS

Author

Vincent Guillemot, Ju-Chi Yu

Examples

X <- matrix(rnorm(20), 5, 4)
GPMD(X, LW = diag(5), RW = diag(4))
#> $d
#> [1] 1.5566990 1.4846339 1.2773724 0.3208319
#> 
#> $u
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    0    0    0    0
#> [3,]    0    0    0    1
#> [4,]    1    0    0    0
#> [5,]    0    0    1    0
#> 
#> $v
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0   -1    0
#> [3,]    0    1    0    0
#> [4,]    1    0    0    0
#> 
#> $rdsLeft
#> [1] 1 1 1 1
#> 
#> $rdsRight
#> [1] 1 1 1 1
#> 
#> $d_full
#> [1] 1.5566990 1.4846339 1.2773724 0.3208319
#> 
#> $l_full
#> [1] 2.4233119 2.2041377 1.6316804 0.1029331
#> 
#> $l
#> [1] 2.4233119 2.2041377 1.6316804 0.1029331
#> 
#> $p
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    0    0    0    0
#> [3,]    0    0    0    1
#> [4,]    1    0    0    0
#> [5,]    0    0    1    0
#> 
#> $fi
#>          [,1]     [,2]     [,3]      [,4]
#> [1,] 0.000000 1.484634 0.000000 0.0000000
#> [2,] 0.000000 0.000000 0.000000 0.0000000
#> [3,] 0.000000 0.000000 0.000000 0.3208319
#> [4,] 1.556699 0.000000 0.000000 0.0000000
#> [5,] 0.000000 0.000000 1.277372 0.0000000
#> 
#> $q
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0   -1    0
#> [3,]    0    1    0    0
#> [4,]    1    0    0    0
#> 
#> $fj
#>          [,1]     [,2]      [,3]      [,4]
#> [1,] 0.000000 0.000000  0.000000 0.3208319
#> [2,] 0.000000 0.000000 -1.277372 0.0000000
#> [3,] 0.000000 1.484634  0.000000 0.0000000
#> [4,] 1.556699 0.000000  0.000000 0.0000000
#> 
#> $SI
#> $SI$SI
#> [1] 0.3430936 0.3570962 0.4205078 0.3912439
#> 
#> $SI$SIleft
#> [1] 0.3528963 0.3672989 0.4325223 0.4024223
#> 
#> $SI$SIright
#> [1] 0.3308403 0.3443427 0.4054896 0.3772709
#> 
#> $SI$r1
#> [1] 0.4411204 0.4591236 0.5406529 0.5030279
#> 
#> $SI$r2
#> [1] 0.8 0.8 0.8 0.8
#> 
#> $SI$r3
#> [1] 0.75 0.75 0.75 0.75
#> 
#> $SI$r4
#> [1] 0.7777778 0.7777778 0.7777778 0.7777778
#> 
#> $SI$n0inU
#> [1]  4  8 12 16
#> 
#> $SI$n0inV
#> [1]  3  6  9 12
#> 
#> $SI$rdsLeft
#> [1] 1 1 1 1
#> 
#> $SI$rdsRight
#> [1] 1 1 1 1
#> 
#> $SI$radiusIndexLeftG
#> [1] 0.4472136 0.4472136 0.4472136 0.4472136
#> 
#> $SI$radiusIndexRightG
#> [1] 0.5 0.5 0.5 0.5
#> 
#> $SI$radiusIndexLeftA
#> [1] 0.4472136 0.4472136 0.4472136 0.4472136
#> 
#> $SI$radiusIndexRightA
#> [1] 0.5 0.5 0.5 0.5
#> 
#>