solverMLE(...,ConcentrationMatrix=>...) -- output MLE for concentration matrix instead of MLE for covariance matrix

Synopsis

Usage:

solverMLE(G,U,ConcentrationMatrix=>b)
Inputs:
- b, a Boolean value, false by default

Description

By default, solverMLE outputs the MLE for the covariance matrix. By providing true as the value for the option solverMLE(...,ConcentrationMatrix=>...), solverMLE provides the MLE for the concentration matrix.

Note that both the maximum value attained in the log-likelihood function and the ML-degree remain the same.

i1 : G= mixedGraph(graph{{a,b},{b,c}},digraph {{a,d},{c,e},{f,g}},bigraph {{d,e}})

o1 = MixedGraph{Bigraph => Bigraph{d => {e}}}
                                   e => {d}
                Digraph => Digraph{a => {d}}
                                   c => {e}
                                   d => {}
                                   e => {}
                                   f => {g}
                                   g => {}
                Graph => Graph{a => {b}   }
                               b => {a, c}
                               c => {b}

o1 : MixedGraph

i2 : solverMLE (G, random(QQ^7,QQ^7))

o2 = (-8.88546, | 1.76276   -.132596  .0588765 1.19122   -.0121464 0       
                | -.132596  .406406   -.180456 -.0896046 .0372285  0       
                | .0588765  -.180456  4.53915  .0397869  -.93644   0       
                | 1.19122   -.0896046 .0397869 4.6897    5.61757   0       
                | -.0121464 .0372285  -.93644  5.61757   9.69158   0       
                | 0         0         0        0         0         2.42434 
                | 0         0         0        0         0         -.115437
     ------------------------------------------------------------------------
     0        |, 5)
     0        |
     0        |
     0        |
     0        |
     -.115437 |
     .171669  |

o2 : Sequence

i3 : solverMLE (G, random(QQ^7,QQ^7), ConcentrationMatrix=>true)

o3 = (-6.95349, | 2.63818  .250925  -.421645 1.01192  .164301  0       
                | .250925  .493839  .0300089 0        0        0       
                | -.421645 .0300089 6.42505  -.309127 -.386315 0       
                | 1.01192  0        -.309127 .741884  .120456  0       
                | .164301  0        -.386315 .120456  .150534  0       
                | 0        0        0        0        0        2.54322 
                | 0        0        0        0        0        -2.42347
     ------------------------------------------------------------------------
     0        |, 5)
     0        |
     0        |
     0        |
     0        |
     -2.42347 |
     3.70744  |

o3 : Sequence

Further information

Default value: false
Function: solverMLE -- Maximum likelihood estimate of a loopless mixed graph
Option key: ConcentrationMatrix -- optional input to output MLE for concentration matrix instead of MLE for covariance matrix

Functions with optional argument named ConcentrationMatrix: