gsvdaux: Extract the R, D1, D2 matrices from a gsvd object

In geigen: Calculate Generalized Eigenvalues, the Generalized Schur Decomposition and the Generalized Singular Value Decomposition of a Matrix Pair with Lapack

Description

Returns a component of the object as a matrix

Usage

gsvd.R(z)
gsvd.oR(z)
gsvd.D1(z)
gsvd.D2(z)

Arguments

z	an object created with gsvd

Value

gsvd.R returns the R matrix implied by the GSVD.

gsvd.oR returns the matrix [0 R] implied by the GSVD.

gsvd.D1 returns the matrix D1 implied by the GSVD.

gsvd.D2 returns the matrix D2 implied by the GSVD.

See Also

gsvd

Examples

A <- matrix(c(1,2,3,3,2,1,4,5,6,7,8,8), nrow=2, byrow=TRUE)
B <- matrix(1:18,byrow=TRUE, ncol=6)
A
B

z <- gsvd(A,B)
z

R <- gsvd.R(z)
oR <- gsvd.oR(z)
D1 <- gsvd.D1(z); D2 <- gsvd.D2(z)
R;oR
D1;D2

Example output

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    2    3    3    2    1
[2,]    4    5    6    7    8    8
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    2    3    4    5    6
[2,]    7    8    9   10   11   12
[3,]   13   14   15   16   17   18
$A
     [,1] [,2]     [,3]       [,4]      [,5]      [,6]
[1,]    0    0 1.205375 -1.5493693  8.746719  9.309297
[2,]    0    0 0.000000 -0.7891233 -8.263864 -6.787066

$B
     [,1] [,2] [,3] [,4]     [,5]      [,6]
[1,]    0    0    0    0 31.01906 33.514874
[2,]    0    0    0    0  0.00000  4.855042
[3,]    0    0    0    0  0.00000  0.000000

$m
[1] 2

$k
[1] 2

$l
[1] 2

$alpha
[1] 1 1 0 0 0 0

$beta
[1] 0 0 1 1 0 0

$U
           [,1]       [,2]
[1,] -0.8353324 -0.5497453
[2,] -0.5497453  0.8353324

$V
           [,1]       [,2]       [,3]
[1,] -0.2672612  0.8728716  0.4082483
[2,] -0.5345225  0.2182179 -0.8164966
[3,] -0.8017837 -0.4364358  0.4082483

$Q
              [,1]          [,2]        [,3]       [,4]        [,5]
[1,]  3.283390e-01  3.204993e-01  0.14358353 -0.4950232  0.26318068
[2,] -4.184012e-01 -7.208865e-01  0.08651096  0.0504075  0.06579517
[3,] -3.864914e-01  5.601627e-01  0.02943840  0.5958382 -0.13159034
[4,]  7.148304e-01 -2.396634e-01 -0.23009449  0.4446157 -0.32897585
[5,] -2.382768e-01  7.988780e-02 -0.69208772 -0.4032600 -0.52636136
[6,]  3.774758e-15  1.679212e-15  0.66264932 -0.1925782 -0.72374686
              [,6]
[1,] -6.741999e-01
[2,] -5.393599e-01
[3,] -4.045199e-01
[4,] -2.696799e-01
[5,] -1.348400e-01
[6,] -5.551115e-17

attr(,"class")
[1] "xdgsvd"
         [,1]       [,2]      [,3]      [,4]
[1,] 1.205375 -1.5493693  8.746719  9.309297
[2,] 0.000000 -0.7891233 -8.263864 -6.787066
[3,] 0.000000  0.0000000 31.019056 33.514874
[4,] 0.000000  0.0000000  0.000000  4.855042
     [,1] [,2]     [,3]       [,4]      [,5]      [,6]
[1,]    0    0 1.205375 -1.5493693  8.746719  9.309297
[2,]    0    0 0.000000 -0.7891233 -8.263864 -6.787066
[3,]    0    0 0.000000  0.0000000 31.019056 33.514874
[4,]    0    0 0.000000  0.0000000  0.000000  4.855042
     [,1] [,2] [,3] [,4]
[1,]    1    0    0    0
[2,]    0    1    0    0
     [,1] [,2] [,3] [,4]
[1,]    0    0    1    0
[2,]    0    0    0    1
[3,]    0    0    0    0

geigen documentation built on May 30, 2019, 5:03 p.m.