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# solverMLE(...,ZeroTolerance=>...) -- optional input to set the largest absolute value that should be treated as zero

- Usage:
    `solverMLE(G,U,ZeroTolerance=>n)`
- Inputs:
  - n, a real number, default is 1e-10

## Description

After computing the variety of the zero-dimensional ideal of the score equations, solverMLE needs to determine which points lie in the PD cone. A matrix is assumed to be positive definite if for all eigenvalues e:

- realPart e > ZeroTolerance

- abs imaginaryPart e <= ZeroTolerance

If an MLE matrix contains an imaginary part below the tolerance level, then only the real part is reported in the output. (See checkPD(...,ZeroTolerance=>...))

## See also

- checkPD -- returns positive definite matrices from a list of symmetric matrices

## Functions with optional argument named ZeroTolerance:

- checkPD(...,ZeroTolerance=>...) -- optional input to set the largest absolute value that should be treated as zero
- checkPSD(...,ZeroTolerance=>...) -- optional input to set the largest absolute value that should be treated as zero
- solverMLE(...,ZeroTolerance=>...) -- optional input to set the largest absolute value that should be treated as zero

## Further information

- Default value: 1e-10
- Function: solverMLE -- Maximum likelihood estimate of a loopless mixed graph
- Option key: ZeroTolerance -- optional input to set the largest absolute value that should be treated as zero

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GraphicalModelsMLE.m2:1690:0.