# eigenvalues.manymatrices: Computation of Eigenvalues of Many Symmetric Matrices In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

 eigenvalues.manymatrices R Documentation

## Computation of Eigenvalues of Many Symmetric Matrices

### Description

This function computes the eigenvalue decomposition of N symmetric positive definite matrices. The eigenvalues are computed by the Rayleigh quotient method (Lange, 2010, p. 120). In addition, the inverse matrix can be calculated.

### Usage

eigenvalues.manymatrices(Sigma.all, itermax=10, maxconv=0.001,
inverse=FALSE )


### Arguments

 Sigma.all An N \times D^2 matrix containing the D^2 entries of N symmetric matrices of dimension D \times D itermax Maximum number of iterations maxconv Convergence criterion for convergence of eigenvectors inverse A logical which indicates if the inverse matrix shall be calculated

### Value

A list with following entries

 lambda Matrix with eigenvalues U An N \times D^2 Matrix of orthonormal eigenvectors logdet Vector of logarithm of determinants det Vector of determinants Sigma.inv Inverse matrix if inverse=TRUE.

### References

Lange, K. (2010). Numerical Analysis for Statisticians. New York: Springer.

### Examples

# define matrices
Sigma <- diag(1,3)
Sigma[ lower.tri(Sigma) ] <- Sigma[ upper.tri(Sigma) ] <- c(.4,.6,.8 )
Sigma1 <- Sigma

Sigma <- diag(1,3)
Sigma[ lower.tri(Sigma) ] <- Sigma[ upper.tri(Sigma) ] <- c(.2,.1,.99 )
Sigma2 <- Sigma

# collect matrices in a "super-matrix"
Sigma.all <- rbind( matrix( Sigma1, nrow=1, byrow=TRUE),
matrix( Sigma2, nrow=1, byrow=TRUE) )
Sigma.all <- Sigma.all[ c(1,1,2,2,1 ), ]

# eigenvalue decomposition
m1 <- sirt::eigenvalues.manymatrices( Sigma.all )
m1

# eigenvalue decomposition for Sigma1
s1 <- svd(Sigma1)
s1


alexanderrobitzsch/sirt documentation built on Feb. 16, 2024, 10:06 a.m.