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Correct typos, move doc portion to comment and fix borrow to clone

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metric-space 2022-03-05 13:52:42 -05:00
parent c8a920ff2c
commit 3413ab7da8
1 changed files with 26 additions and 27 deletions
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53
nalgebra-lapack/src/generalized_eigenvalues.rs
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@ -181,7 +181,7 @@ where
/// Calculates the generalized eigenvectors (left and right) associated with the generalized eigenvalues /// Calculates the generalized eigenvectors (left and right) associated with the generalized eigenvalues
/// Outputs two matrices. /// Outputs two matrices.
/// The first output matix contains the left eigenvectors of the generalized eigenvalues /// The first output matrix contains the left eigenvectors of the generalized eigenvalues
/// as columns. /// as columns.
/// The second matrix contains the right eigenvectors of the generalized eigenvalues /// The second matrix contains the right eigenvectors of the generalized eigenvalues
/// as columns. /// as columns.
@ -196,46 +196,45 @@ where
/// ///
/// u(j)**H * A = lambda(j) * u(j)**H * B /// u(j)**H * A = lambda(j) * u(j)**H * B
/// where u(j)**H is the conjugate-transpose of u(j). /// where u(j)**H is the conjugate-transpose of u(j).
/// pub fn eigenvectors(&self) -> (OMatrix<Complex<T>, D, D>, OMatrix<Complex<T>, D, D>)
/// How the eigenvectors are build up:
///
/// Since the input entries are all real, the generalized eigenvalues if complex come in pairs
/// as a consequence of <https://en.wikipedia.org/wiki/Complex_conjugate_root_theorem>
/// The Lapack routine output reflects this by expecting the user to unpack the complex eigenvalues associated
/// eigenvectors from the real matrix output via the following procedure
///
/// (Note: VL stands for the lapack real matrix output containing the left eigenvectors as columns,
/// VR stands for the lapack real matrix output containing the right eigenvectors as columns)
///
/// If the j-th and (j+1)-th eigenvalues form a complex conjugate pair,
/// then
///
/// u(j) = VL(:,j)+i*VL(:,j+1)
/// u(j+1) = VL(:,j)-i*VL(:,j+1)
///
/// and
///
/// u(j) = VR(:,j)+i*VR(:,j+1)
/// v(j+1) = VR(:,j)-i*VR(:,j+1).
///
pub fn eigenvectors(self) -> (OMatrix<Complex<T>, D, D>, OMatrix<Complex<T>, D, D>)
where where
DefaultAllocator: DefaultAllocator:
Allocator<Complex<T>, D, D> + Allocator<Complex<T>, D> + Allocator<(Complex<T>, T), D>, Allocator<Complex<T>, D, D> + Allocator<Complex<T>, D> + Allocator<(Complex<T>, T), D>,
{ {
/*
How the eigenvectors are built up:
Since the input entries are all real, the generalized eigenvalues if complex come in pairs
as a consequence of the [complex conjugate root thorem](https://en.wikipedia.org/wiki/Complex_conjugate_root_theorem)
The Lapack routine output reflects this by expecting the user to unpack the complex eigenvalues associated
eigenvectors from the real matrix output via the following procedure
(Note: VL stands for the lapack real matrix output containing the left eigenvectors as columns,
VR stands for the lapack real matrix output containing the right eigenvectors as columns)
If the j-th and (j+1)-th eigenvalues form a complex conjugate pair,
then
u(j) = VL(:,j)+i*VL(:,j+1)
u(j+1) = VL(:,j)-i*VL(:,j+1)
and
u(j) = VR(:,j)+i*VR(:,j+1)
v(j+1) = VR(:,j)-i*VR(:,j+1).
*/
let n = self.vsl.shape().0; let n = self.vsl.shape().0;
let mut l = self let mut l = self
.vsl .vsl
.clone()
.map(|x| Complex::new(x, T::RealField::zero())); .map(|x| Complex::new(x, T::RealField::zero()));
let mut r = self let mut r = self
.vsr .vsr
.clone()
.map(|x| Complex::new(x, T::RealField::zero())); .map(|x| Complex::new(x, T::RealField::zero()));
let eigenvalues = &self.raw_eigenvalues(); let eigenvalues = self.raw_eigenvalues();
let mut c = 0; let mut c = 0;