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 added method `Vector::axcpy` generalises `Vector::gemv` to
noncommutative cases since it allows us to write for `gemv`
`self.axcpy(alpha, &col2, val, beta)`, instead the usual
`self.axpy(alpha * val, &col2, beta)`. Hence, `axcpy` preserves the
order of scalar multiplication which is important for applications where
commutativity is not guaranteed (e.g., matrices of quaternions, etc.).
This commmit also removes helpers `array_axpy` and `array_ax`, and
replaces them with `array_axcpy` and `array_axc` respectively, which
like above preserve the order of scalar multiplication.
Finally, `Vector::axpy` is preserved, however, now expressed in terms of
`Vector::axcpy` like so:
```
self.axcpy(alpha * val, &col2, beta)
```
Avi Weinstock
Jakub Konka
sebcrozet
Jake Shadle
Greizgh
Jack Wrenn
Bruce Mitchener
Bernardo Meurer