Description Usage Arguments Details Value Author(s) References See Also Examples

This function is not supposed to be called directly by users. It is needed in functions `erpfatest`

and `erpFtest`

implementing factor-adjusted testing methods.

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

`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 |

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.

The mxm matrix Omega (see the details Section).

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

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

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
``` |

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