The previous implementation was correct only for real elements. The
Cholesky decomposition is `L L^H`, so the determinant is `det(L) *
det(L^H)`. Since `L` is a triangular matrix, `det(L)` is the product
of the diagonal elements of `L`. Since `L^H` is triangular and its
diagonal elements are the conjugates of the diagonal elements of `L`,
`det(L^H)` is the conjugate of `det(L)`. So, the overall determinant
is the product of the diagonal elements of `L` times its conjugate.
Most call sites still invoke UB through `assume_init`. Said call sites instead invoke `unimplemented!()` if the `no_unsound_assume_init` feature is enabled, to make it easier to gradually fix them.
Progress towards #556.
The various nalgebra-lapack FooScalars are still Copy because they make use of uninitialized memory.
nalgebgra-glm Number still uses Copy because upstream `approx` requires it.
This should semantically be a no-op, but enables refactorings to use non-Copy scalars on a case-by-case basis.
Also, the only instance of a `One + Zero` trait bound was changed into a `Zero + One` bound to match the others.
The following sed scripts were used in the refactoring (with each clause added to reduce the error count of `cargo check`):
```bash
export RELEVANT_SOURCEFILES="$(find src -name '*.rs') $(find examples -name '*.rs')"
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar,/N: Scalar+Copy,/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Field/N: Scalar + Copy + Field/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Zero/N: Scalar + Copy + Zero/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Closed/N: Scalar + Copy + Closed/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Eq/N: Scalar + Copy + Eq/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialOrd/N: Scalar + Copy + PartialOrd/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + Zero/N: Scalar + Copy + Zero/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialEq/N: Scalar + Copy + PartialEq/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar>/N: Scalar+Copy>/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + $bound/N: Scalar + Copy + $bound/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $bound/N: Scalar + Copy + $bound/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar,/N\1: Scalar+Copy,/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $trait/N: Scalar + Copy + $trait/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + Superset/N\1: Scalar + Copy + Superset/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(hash::\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar {/N\1: Scalar + Copy {/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Bounded\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Lattice\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Meet\|Join\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(fmt::\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Ring\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Hash\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Send\|Sync\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/One + Zero/Zero + One/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \($marker\)/N\1: Scalar + Copy + \2/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar>/N\1: Scalar + Copy>/' $f; done
for f in $RELEVANT_SOURCEFILES; do sed -i 's/Scalar+Copy/Scalar + Copy/' $f; done
```
The eigenvalue problem is solved in two different method that use different methods
to calculate the discriminant of the solution to the quadratic equation.
Use the method whose computation is considered more stable.
