# isqrtfa: Inverse square-root of a matrix based on its factor... In ERP: Significance Analysis of Event-Related Potentials Data

## Description

This function is not supposed to be called directly by users. It is needed in functions `erpfatest` and `erpFtest` implementing factor-adjusted testing methods.

## Usage

 `1` ```isqrtfa(Psi, B) ```

## Arguments

 `Psi` m-vector of specific variances, where m is the number of rows and columns of the matrix. `B` mxq matrix of loadings, where q is the number of factors

## Details

If Sigma has the q-factor decomposition Sigma=diag(Psi)+BB', then the function returns a matrix Omega such that Sigma^-1 = Omega Omega'. Equivalently, Omega' Sigma Omega = I.

## Value

The mxm matrix Omega (see the details Section).

## Author(s)

David Causeur, IRMAR, UMR 6625 CNRS, Agrocampus Ouest, Rennes, France.

## References

Woodbury, M.A. (1949) The Stability of Out-Input Matrices. Chicago, Ill., 5 pp

## See Also

`emfa`, `ifa`

## Examples

 ```1 2 3 4 5 6 7``` ```data(impulsivity) erpdta = as.matrix(impulsivity[,5:505]) # erpdta contains the whole set of ERP curves fa = emfa(erpdta,nbf=20) # 20-factor modelling of the ERP curves in erpdta Sfa = diag(fa\$Psi)+tcrossprod(fa\$B) # Factorial estimation of the variance iSfa = ifa(fa\$Psi,fa\$B)\$iS # Matrix inversion isqrtSfa = isqrtfa(fa\$Psi,fa\$B) # Inverse square-root of Sfa max(abs(tcrossprod(isqrtSfa)-iSfa)) # Checks that isqrtSfa x t(isqrtSfa) = iSfa ```

ERP documentation built on Dec. 16, 2019, 1:35 a.m.