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Add tolerance to is_posdef.#130

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darnstrom wants to merge 1 commit intoqpsolvers:mainfrom
darnstrom:strict-posdef
Open

Add tolerance to is_posdef.#130
darnstrom wants to merge 1 commit intoqpsolvers:mainfrom
darnstrom:strict-posdef

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This PR adds a tolerance to the positive-definite check in is_posdef to filter out QPs which have Hessians that are numerically singular.
For example, the problem "TAME" in the MM testset is classified as positive definite, but it has the Hessian

$$ P = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}, $$

which is clearly singular. Numerically the singular eigenvalue evaluates to ~1e-16, and since is_posdef currently simply compares >0, the problem is classified as posef.

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