Add PInv Moore-Penrose pseudoinverse #292
Description
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.