Add PInv Moore-Penrose pseudoinverse

Start in numrs/src/linalg.rs at the proposed Pinv traits and the existing self.svd(true, true) call. Check how ndarray-linalg represents real and complex Scalar values and how matrix multiplication is supported across those types. Done means a generic Moore-Penrose pseudoinverse with optional rcond that avoids the reported multiplication error and matches the NumPy and MATLAB references.

I was porting some code from NumPy, and needed the pinv[1][2] function (Moore-Penrose pseudoinverse). I have started implementing it but have run into some issues making it generic over real and complex numbers.

pub trait Pinv {
    type B;
    type E;
    type C;
    fn pinv(&self, rcond: Option<Self::E>) -> Result<Self::B, Error>;
}

pub trait PInvVInto {
    type B;
    type E;
    fn pinv(self, rcond: Option<Self::E>) -> Result<Self::B, Error>;
}

pub trait PInvInplace {
    type B;
    type E;
    fn pinv(&mut self, rcond: Option<Self::E>) -> Result<Self::B, Error>;
}

impl<A, S> Pinv for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack + PartialOrd + Zero,
    S: Data<Elem = A>,
{
    type E = A::Real;
    type B = Array2<A>;
    type C = Array1<A::Real>;

    fn pinv(&self, rconf: Option<Self::E>) -> Result<Self::B, Error> {
        let result: (Option<Self::B>, Self::C, Option<Self::B>) =
            self.svd(true, true).map_err(|_| Error::SvdFailed)?;
        if let (Some(u), s, Some(vt)) = result {
            // discard small singular values
            let s: Self::C = if let Some(rconf) = rconf {
                s.mapv(|v| if v > rconf { v } else { Zero::zero() })
            } else {
                s
            };

            let u = u.reversed_axes();
            let s = s.insert_axis(Axis(1));
            let x1 = s * u;
            Ok(&vt.reversed_axes() * x1)
        } else {
            Err(Error::SvdFailed)
        }
    }
}

At the moment I am getting this error

error[E0277]: cannot multiply `ndarray::ArrayBase<OwnedRepr<<A as ndarray_linalg::Scalar>::Real>, Dim<[usize; 2]>>` by `ndarray::ArrayBase<OwnedRepr<A>, Dim<[usize; 2]>>`
  --> numrs/src/linalg.rs:58:24
   |
58 |             let x1 = s * u;
   |                        ^ no implementation for `ndarray::ArrayBase<OwnedRepr<<A as ndarray_linalg::Scalar>::Real>, Dim<[usize; 2]>> * ndarray::ArrayBase<OwnedRepr<A>, Dim<[usize; 2]>>`
   |
   = help: the trait `Mul<ndarray::ArrayBase<OwnedRepr<A>, Dim<[usize; 2]>>>` is not implemented for `ndarray::ArrayBase<OwnedRepr<<A as ndarray_linalg::Scalar>::Real>, Dim<[usize; 2]>>`
help: consider extending the `where` bound, but there might be an alternative better way to express this requirement
   |
38 |     S: Data<Elem = A>, ndarray::ArrayBase<OwnedRepr<<A as ndarray_linalg::Scalar>::Real>, Dim<[usize; 2]>>: Mul<ndarray::ArrayBase<OwnedRepr<A>, Dim<[usize; 2]>>>

My understanding this is because I am trying to multiple Scalar::Real with a Scalar, but I am not sure how this should be fixed.

1. https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html
2. https://www.mathworks.com/help/matlab/ref/pinv.html