# Calculates the Maximum likelihood Factor analysis with a covariance Matrix.

### Description

Calculates the Maximum likelihood Factor analysis with a covariance Matrix.

### Usage

1 2 | ```
Factmle_cov(S, rnk, Psi_init = c(), lb = 0.01, index = c(), lb2 = 0.01,
tol = 10^-7, Max_iter = 1000)
``` |

### Arguments

`S` |
The Covariance Matrix. It is a p*p numeric matrix, where p is the number of variables. |

`rnk` |
Rank constraint for the Factor analysis problem. It must a positive integer less than the number of variables p |

`Psi_init` |
The initial value of Psi. It is a p*1 numeric vetor, where p is the number of variables.Default value is a vector of uniform random numbers. |

`lb` |
The lower bound on the Psi values. The default value is set to 0.05 |

`index` |
This option is for modified version of factmle.The default value is a null vector. If assigned a zero vector, it will perform MLFA keeping some of the Psi values specified by the index at a specifed level *lb2* |

`lb2` |
This option of modified version of factmle algorithm. The default value is 0.001. The Psi values specified by the *index* is kept constant at *lb2* while doing MLFA. |

`tol` |
Precision parameter. Default is 10^-7 |

`Max_iter` |
Maximum number of iterations. Default is 1000. |

### Value

A list with the following components

- Psi
A vector containing the unique variances.

- Lambda
A p*rnk matrix containing the factor loadings in the columns.

- Nll
A vector containing the negative Log-likelihood values at every iteration.

- Nllopt
The value of the negative log-likelihood upon convergence.

### See Also

`eigs_sym`

### Examples

1 2 3 4 5 6 7 |