[R] Generate positive definite matrix with constraints

[mary]

Hi, I have a question for my simulation problem:

I would like to generate a positive (or semi def positive) covariance
matrix, non singular, in wich the spectral decomposition returns me the same
values for all dimensions but differs only in eigenvectors.

Ex.
sigma
[,1] [,2]
[1,] 5.05 4.95
[2,] 4.95 5.05

> eigen(sigma)
$values
[1] 10.0 0.1

$vectors
[,1] [,2]
[1,] 0.7071068 -0.7071068
[2,] 0.7071068 0.7071068

(In theory: Using the spectral decomposition, the matrix Σ can be re-written
as
Σ = 5 ( 1, 1) 1 + 0.05 (1, -1) 1
1 -1 )
This because I would generate another covariance matrix in wich variables
are more than 2.
Thank you

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[mary]

Sorry in the previuos message I've inverted: I would like generate ...
"same eigenvectors and different eigenvalues"





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[Gabor Grothendieck]

On Sun, May 19, 2013 at 10:33 AM, mary <mary...@libero.it> wrote:
>
> Sorry in the previuos message I've inverted: I would like generate ...
> "same eigenvectors and different eigenvalues"

Try this:

m0 <- 5 + matrix(c(.05, -.05, -.05, .05), 2)
m0.values <- eigen(m0)$values
with(eigen(matrix(rnorm(4), 2)), vectors %*% diag(m0.values) %*% solve(vectors))

[Gabor Grothendieck]

On Sun, May 19, 2013 at 4:57 PM, Gabor Grothendieck
<ggroth...@gmail.com> wrote:
> On Sun, May 19, 2013 at 10:33 AM, mary <mary...@libero.it> wrote:
>>
>> Sorry in the previuos message I've inverted: I would like generate ...
>> "same eigenvectors and different eigenvalues"
>
> Try this:
>
> m0 <- 5 + matrix(c(.05, -.05, -.05, .05), 2)
> m0.values <- eigen(m0)$values
> with(eigen(matrix(rnorm(4), 2)), vectors %*% diag(m0.values) %*% solve(vectors))

I think I reversed it too. If that's not it try this:

m0.vectors <- eigen(m0)$vectors
with(eigen(matrix(rnorm(4), 2)), m0.vectors %*% diag(values) %*%
solve(m0.vectors.0))


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[Gabor Grothendieck]

On Sun, May 19, 2013 at 5:04 PM, Gabor Grothendieck

<ggroth...@gmail.com> wrote:
> On Sun, May 19, 2013 at 4:57 PM, Gabor Grothendieck
> <ggroth...@gmail.com> wrote:
>> On Sun, May 19, 2013 at 10:33 AM, mary <mary...@libero.it> wrote:
>>>
>>> Sorry in the previuos message I've inverted: I would like generate ...
>>> "same eigenvectors and different eigenvalues"
>>
>> Try this:
>>
>> m0 <- 5 + matrix(c(.05, -.05, -.05, .05), 2)
>> m0.values <- eigen(m0)$values
>> with(eigen(matrix(rnorm(4), 2)), vectors %*% diag(m0.values) %*% solve(vectors))
>
> I think I reversed it too. If that's not it try this:
>
> m0.vectors <- eigen(m0)$vectors
> with(eigen(matrix(rnorm(4), 2)), m0.vectors %*% diag(values) %*%
> solve(m0.vectors.0))
>

That did not take into account the positive definite requirement. Try this:

m0.vectors <- eigen(m0)$vectors
t.m0.vectors <- t(m0.vectors)
n <- 3 # no of samples
tmp <- apply(rWishart(n, 2, diag(2)), 3, function(w) list(m0.vectors
%*% diag(eigen(w)$values) %*% t.m0.vectors))
simplify2array(tmp)

The result is a list of matrices.

[mary]

Thank you but I want to create a matrix (4,4) or (8,8) not just only a (2,2)
matrix...



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[Gabor Grothendieck]

On Mon, May 20, 2013 at 10:01 AM, mary <mary...@libero.it> wrote:
>
> Thank you but I want to create a matrix (4,4) or (8,8) not just only a (2,2)
> matrix...
>

provide an m0 matrix of the appropriate dimensions and change 2 to the
new dimension in the relevant lines.

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